Author name code: mackay ADS astronomy entries on 2022-09-14 author:"Mackay, Duncan H." ------------------------------------------------------------------------ Title: Mini-filament eruption, QSL reconnection, and reconnection-driven outflows: IRIS and AIA/HMI/SDO observations and modelling Authors: Madjarska, Maria S.; Mackay, Duncan H.; Galsgaard, Klaus; Xie, Haixia; Wiegelmann, Thomas Bibcode: 2022cosp...44.2533M Altcode: We will present unique observations of a mini-filament eruption associated with cancelling magnetic fluxes of a small-scale loop system known as a coronal bright point. The event is uniquely recorded in both the imaging and spectroscopic data taken with the Interface Region Imaging Spectrograph (IRIS). The study aims at providing a better understanding of the physical processes driving these ubiquitous small-scale eruptions. We also analysed images taken in the extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) and line-of-sight magnetic-field data from the Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. As the observations can only give an inkling about the possible physical processes at play, we also employed a non-linear force-free field (NLFFF) relaxation approach based on the HMI magnetogram time series. Furthermore, we computed the squashing factor, Q, in different horizontal planes of the NLFFF model. This allowed us to further investigate the evolution of the magnetic-field structures involved in the eruption process. Title: Eruptions from coronal bright points: A spectroscopic view by IRIS of a mini-filament eruption, QSL reconnection, and reconnection-driven outflows Authors: Madjarska, Maria S.; Mackay, Duncan H.; Galsgaard, Klaus; Wiegelmann, Thomas; Xie, Haixia Bibcode: 2022A&A...660A..45M Altcode: 2022arXiv220200370M Context. Our study investigates a mini-filament eruption associated with cancelling magnetic fluxes. The eruption originates from a small-scale loop complex commonly known as a coronal bright point (CBP). The event is uniquely recorded in both the imaging and spectroscopic data taken with the Interface Region Imaging Spectrograph (IRIS).
Aims: The investigation aims to gain a better understanding of the physical processes driving these ubiquitous small-scale eruptions.
Methods: We analysed IRIS spectroscopic and slit-jaw imaging observations as well as images taken in the extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) and line-of-sight magnetic-field data from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory. As the observations can only indicate the possible physical processes at play, we also employed a non-linear force-free field (NLFFF) relaxation approach based on the HMI magnetogram time series. This allowed us to further investigate the evolution of the magnetic-field structures involved in the eruption process.
Results: We identified a strong small-scale brightening as a micro-flare in a CBP, recorded in emission from chromospheric to flaring plasmas. The mini-eruption is manifested via the ejection of hot (CBP loops) and cool (mini-filament) plasma recorded in both the imaging and spectroscopic data. The micro-flare is preceded by the appearance of an elongated bright feature in the IRIS slit-jaw 1400 Å images, located above the polarity inversion line. The micro-flare starts with an IRIS pixel size brightening and propagates bi-directionally along the elongated feature. We detected, in both the spectral and imaging IRIS data and AIA data, strong flows along and at the edges of the elongated feature; we believe that these represent reconnection outflows. Both edges of the elongated feature that wrap around the edges of the erupting MF evolve into a J-type shape, creating a sigmoid appearance. A quasi-separatrix layer (QSL) is identified in the vicinity of the polarity inversion line by computing the squashing factor, Q, in different horizontal planes of the NLFFF model.
Conclusions: This CBP spectro-imaging study provides further evidence that CBPs represent downscaled active regions and, as such, they may make a significant contribution to the mass and energy balance of the solar atmosphere. They are the sources of all range of typical active-region features, including magnetic reconnection along QSLs, (mini-)filament eruptions, (micro-)flaring, reconnection outflows, etc. The QSL reconnection site has the same spectral appearance as the so-called explosive events identified by strong blue- and red-shifted emission, thus providing an answer to an outstanding question regarding the true nature of this spectral phenomenon.

Movies associated to Figs. A.1 and A.2 are available at https://www.aanda.org Title: A Comparison of Sparse and Non-sparse Techniques for Electric-Field Inversion from Normal-Component Magnetograms Authors: Mackay, Duncan H.; Yeates, Anthony R. Bibcode: 2021SoPh..296..178M Altcode: An important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm's law. Yeates (Astrophys. J.836(1), 131, 2017) put forward a new "sparse" technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm's law compared to previously used "non-sparse" techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen (Astrophys. J.729(2), 97, 2011). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen (2011) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates (2017) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates (2017) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen (2011) method produces consistent results using either approach. The sparse technique of Yeates (2017) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise. Title: Determining the source and eruption dynamics of a stealth CME using NLFFF modelling and MHD simulations Authors: Yardley, S. L.; Pagano, P.; Mackay, D. H.; Upton, L. A. Bibcode: 2021A&A...652A.160Y Altcode: 2021arXiv210614800Y Context. Coronal mass ejections (CMEs) that exhibit weak or no eruption signatures in the low corona, known as stealth CMEs, are problematic as upon arrival at Earth they can lead to geomagnetic disturbances that were not predicted by space weather forecasters.
Aims: We investigate the origin and eruption of a stealth event that occurred on 2015 January 3 that was responsible for a strong geomagnetic storm upon its arrival at Earth.
Methods: To simulate the coronal magnetic field and plasma parameters of the eruption we use a coupled approach. This approach combines an evolutionary nonlinear force-free field model of the global corona with a MHD simulation.
Results: The combined simulation approach accurately reproduces the stealth event and suggests that sympathetic eruptions occur. In the combined simulation we found that three flux ropes form and then erupt. The first two flux ropes, which are connected to a large AR complex behind the east limb, erupt first producing two near-simultaneous CMEs. These CMEs are closely followed by a third, weaker flux rope eruption in the simulation that originated between the periphery of AR 12252 and the southern polar coronal hole. The third eruption coincides with a faint coronal dimming, which appears in the SDO/AIA 211 Å observations, that is attributed as the source responsible for the stealth event and later the geomagnetic disturbance at 1 AU. The incorrect interpretation of the stealth event being linked to the occurrence of a single partial halo CME observed by LASCO/C2 is mainly due to the lack of STEREO observations being available at the time of the CMEs. The simulation also shows that the LASCO CME is not a single event but rather two near-simultaneous CMEs.
Conclusions: These results show the significance of the coupled data-driven simulation approach in interpreting the eruption and that an operational L5 mission is crucial for space weather forecasting.

Movie associated with Fig. 4 is available at https://www.aanda.org Title: Identifying Non-potential Energy Hot Spots In A Global Coronal Simulation Authors: Corchado Albelo, M. F.; Gibson, S. E.; Linker, J.; Mackay, D. H.; Dalmasse, K.; Malanushenko, A. Bibcode: 2021AAS...23832803C Altcode: Observing the global coronal magnetic field remains a difficult task; limiting our understanding of the evolution of global phenomena in these external layers of the solar atmosphere. Therefore, we rely on models to get the solar exterior global field. While models can extrapolate the magnetic field from surface flux and vector magnetogram observations, e.g. by assuming a current-free corona, other techniques are used to simulate the current-carrying field via magnetohydrodynamic (MHD) evolution or surface flux transport of large scale field, and inserting current-carrying small scale field structures like twisted flux ropes into the corona. These current-carrying fields are of interest for studying solar energetic eruptions like coronal mass ejections and flares because they provide the energy reservoir needed to drive these events. Previous studies suggest that ground-based infrared polarimetric measurements of Fe XIII (1074.7 nm) line correlate with the energy of the current-carrying field. In this study we generated synthetic polarimetric observations from a fully-resolved magnetohydrodynamics model of the August 21, 2017 eclipse. The synthetic observations were used as input to a diagnostic we developed to identify regions where the modeling team inserted twisted flux ropes. The diagnostic evaluated linearly and circularly polarized synthetic observations of the corona as a means to identify the current-carrying magnetic energy density. We found that the diagnostic does identify the distribution of flux ropes in the corona. Thus, our findings motivate the implementation of polarimetric measurements to identify "hot spots" in which we can insert flux ropes and a degree of the twist/shear in the current-carrying field. Title: Finding a second Sun - How can we detect solar-like magnetic cycles with Zeeman-Doppler-Imaging (ZDI)? Authors: Lehmann, Lisa Theres; Hussain, Gaitee A. J.; Vidotto, Aline A.; Jardine, Moira M.; Mackay, Duncan H. Bibcode: 2021csss.confE..68L Altcode: Spectropolarimetric surveys have now been running for long enough to reveal solar-like magnetic activity cycles, e.g., for 61 Cyg A (Boko Saikia et al. 2018). Our work examines if a solar-like cycle can be observed with ZDI, given that this technique only detects the large-scale field for very slowly-rotating and low-activity stars like our Sun. We aim to determine the best strategy to detect stellar cycles, and which parameters are most sensitive to cycle changes.This poster presents our paper: Lehmann, L. T., et al., 2021, MNRAS, 500, 1243 (https://ui.adsabs.harvard.edu/abs/2021MNRAS.500.1243L) Title: Identifying solar-like magnetic cycles with Zeeman-Doppler-Imaging Authors: Lehmann, L. T.; Hussain, G. A. J.; Vidotto, A. A.; Jardine, M. M.; Mackay, D. H. Bibcode: 2021MNRAS.500.1243L Altcode: 2020MNRAS.500.1243L; 2020arXiv201010214L; 2020MNRAS.tmp.3102L We are reaching the point where spectropolarimetric surveys have run for long enough to reveal solar-like magnetic activity cycles. In this paper, we investigate what would be the best strategy to identify solar-like magnetic cycles and ask which large-scale magnetic field parameters best follow a solar-type magnetic cycle and are observable with the Zeeman-Doppler-Imaging (ZDI) technique. We approach these questions using the 3D non-potential flux transport simulations of Yeates & Mackay (2012) modelling the solar vector magnetic field over 15 yr (centred on solar cycle 23). The flux emergence profile was extracted from solar synoptic maps and used as input for a photospheric flux transport model in combination with a non-potential coronal evolution model. We synthesize spectropolarimetric data from the simulated maps and reconstruct them using ZDI. The ZDI observed solar cycle is set into the context of other cool star observations and we present observable trends of the magnetic field topology with time, sunspot number, and S-index. We find that the axisymmetric energy fraction is the best parameter of the ZDI detectable large-scale field to trace solar-like cycles. Neither the surface averaged large-scale field or the total magnetic energy is appropriate. ZDI seems also to be able to recover the increase of the toroidal energy with S-index. We see further that ZDI might unveil hints of the dynamo modes that are operating and of the global properties of the small-scale flux emergence like active latitudes. Title: Simulating the Coronal Evolution of Bipolar Active Regions to Investigate the Formation of Flux Ropes Authors: Yardley, S. L.; Mackay, D. H.; Green, L. M. Bibcode: 2021SoPh..296...10Y Altcode: 2020arXiv201207708Y The coronal magnetic field evolution of 20 bipolar active regions (ARs) is simulated from their emergence to decay using the time-dependent nonlinear force-free field method of Mackay, Green, and van Ballegooijen (Astrophys. J. 729, 97, 2011). A time sequence of cleaned photospheric line-of-sight magnetograms, which covers the entire evolution of each AR, is used to drive the simulation. A comparison of the simulated coronal magnetic field with the 171 and 193 Å observations obtained by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA), is made for each AR by manual inspection. The results show that it is possible to reproduce the evolution of the main coronal features such as small- and large-scale coronal loops, filaments and sheared structures for 80% of the ARs. Varying the boundary and initial conditions, along with the addition of physical effects such as Ohmic diffusion, hyperdiffusion and a horizontal magnetic field injection at the photosphere, improves the match between the observations and simulated coronal evolution by 20%. The simulations were able to reproduce the build-up to eruption for 50% of the observed eruptions associated with the ARs. The mean unsigned time difference between the eruptions occurring in the observations compared to the time of eruption onset in the simulations was found to be ≈5 hrs. The simulations were particularly successful in capturing the build-up to eruption for all four eruptions that originated from the internal polarity inversion line of the ARs. The technique was less successful in reproducing the onset of eruptions that originated from the periphery of ARs and large-scale coronal structures. For these cases global, rather than local, nonlinear force-free field models must be used. While the technique has shown some success, eruptions that occur in quick succession are difficult to reproduce by this method and future iterations of the model need to address this. Title: Links between prominence/filament magnetic field and plasma: What can 3D WPFS models teach us? Authors: Gunár, Stanislav; Schmieder, Brigitte; Aulanier, Guillaume; Heinzel, Petr; Mackay, Duncan; Dudik, Jaroslav Bibcode: 2021cosp...43E1769G Altcode: The magnetic field constitutes the skeleton and the driving force of prominences/filaments. It supports the dense prominence plasma against gravity and insulates it from the hot, coronal environment. The magnetic field is also responsible for the prominence stability, evolution and eruptions which affect the heliosphere and ultimately the Earth. However, a strong imbalance exists between the numerous efforts in detailed modelling of prominence magnetic field and its understanding from observations. That is due to the complex nature of the direct (and indirect) observations of solar magnetic fields which are challenging at the best of times and even more so in prominences or filaments. The direct observations of the prominence magnetic field require high-precision spectro-polarimetric measurements and realistic assumptions about the plasma structure which allow us to infer the field configuration from its effect on the polarized light emergent from the observed structures. The indirect observations rely on the perceived location, shape and dynamics of the prominence or filament plasma, often using moving small-scale plasma structures as tracers guided by the field lines. Both methods thus rely on the presence of observable plasma in the magnetic field configuration, and on the radiation which carries the information about the in-situ conditions to the observer. No prominence/filament magnetic field measurements are made without these two additional components, which are sometimes an afterthought in the magnetic field models. We have developed 3D Whole-Prominence Fine Structure (WPFS) models to illuminate the links between the prominence magnetic field, its plasma distributed among numerous fine structures and the radiation which carries the information about the prominence physical conditions to the observer. What can we learn from these 3D models? For example, we can see that a small change of the magnetic field configuration can have a large effect on the perceived structure of prominences and filaments visible in the H-alpha line. Consequently, this means that significant changes observed in prominences or filaments do not need to suggest that equally large changes in the underlying magnetic field configuration had to occur. In another example, we see that seemingly incomparable differences in the morphological look of prominences (long horizontal fine structures versus small blobs of plasma arranged into more-less vertical features) may not need to imply the existence of radically different magnetic field configurations. Rather, they might simply be manifestations of projection effects that can differ greatly depending on the viewing angle under which we observe the naturally three-dimensional prominences/filaments. Title: Eruptions from coronal hole bright points: Observations and non-potential modelling Authors: Madjarska, Maria S.; Galsgaard, Klaus; Mackay, Duncan H.; Koleva, Kostadinka; Dechev, Momchil Bibcode: 2020A&A...643A..19M Altcode: 2020arXiv200904628M Context. We report on the third part of a series of studies on eruptions associated with small-scale loop complexes named coronal bright points (CBPs).
Aims: A single case study of a CBP in an equatorial coronal hole with an exceptionally large size is investigated to expand on our understanding of the formation of mini-filaments, their destabilisation, and the origin of the eruption triggering the formation of jet-like features recorded in extreme ultraviolet (EUV) and X-ray emission. We aim to explore the nature of the so-called micro-flares in CBPs associated with jets in coronal holes and mini coronal mass ejections in the quiet Sun.
Methods: Co-observations from the Atmospheric Imaging Assembly (AIA) and Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory as well as GONG Hα images are used together with a non-linear force free field (NLFFF) relaxation approach, where the latter is based on a time series of HMI line-of-sight magnetograms.
Results: A mini-filament (MF) that formed beneath the CBP arcade about 3-4 h before the eruption is seen in the Hα and EUV AIA images to lift up and erupt triggering the formation of an X-ray jet. No significant photospheric magnetic flux concentration displacement (convergence) is observed and neither is magnetic flux cancellation between the two main magnetic polarities forming the CBP in the time period leading to MF lift-off. The CBP micro-flare is associated with three flare kernels that formed shortly after the MF lift-off. No observational signature is found for magnetic reconnection beneath the erupting MF. The applied NLFFF modelling successfully reproduces both the CBP loop complex as well as the magnetic flux rope that hosts the MF during the build-up to the eruption.
Conclusions: The applied NLFFF modelling is able to clearly show that an initial potential field can be evolved into a non-potential magnetic field configuration that contains free magnetic energy in the region that observationally hosts the eruption. The comparison of the magnetic field structure shows that the magnetic NLFFF model contains many of the features that can explain the different observational signatures found in the evolution and eruption of the CBP. In the future, it may eventually indicate the location of destabilisation that results in the eruptions of flux ropes.

Movies associated to Figs. 9 and B.2 are available at https://www.aanda.org Title: Investigation of the Middle Corona with SWAP and a Data-Driven Non-Potential Coronal Magnetic Field Model Authors: Meyer, Karen A.; Mackay, Duncan H.; Talpeanu, Dana-Camelia; Upton, Lisa A.; West, Matthew J. Bibcode: 2020SoPh..295..101M Altcode: 2020arXiv200702668M The large field-of-view of the Sun Watcher using Active Pixel System detector and Image Processing (SWAP) instrument onboard the PRoject for Onboard Autonomy 2 (PROBA2) spacecraft provides a unique opportunity to study extended coronal structures observed in the EUV in conjunction with global coronal magnetic field simulations. A global non-potential magnetic field model is used to simulate the evolution of the global corona from 1 September 2014 to 31 March 2015, driven by newly emerging bipolar active regions determined from Helioseismic and Magnetic Imager (HMI) magnetograms. We compare the large-scale structure of the simulated magnetic field with structures seen off-limb in SWAP EUV observations. In particular, we investigate how successful the model is in reproducing regions of closed and open structures, the scale of structures, and compare the evolution of a coronal fan observed over several rotations. The model is found to accurately reproduce observed large-scale, off-limb structures. When discrepancies do arise they mainly occur off the east solar limb due to active regions emerging on the far side of the Sun, which cannot be incorporated into the model until they are observed on the Earth-facing side. When such "late" active region emergences are incorporated into the model, we find that the simulated corona self-corrects within a few days, so that simulated structures off the west limb more closely match what is observed. Where the model is less successful, we consider how this may be addressed, through model developments or additional observational products. Title: Hydrogen non-equilibrium ionisation effects in coronal mass ejections Authors: Pagano, P.; Bemporad, A.; Mackay, D. H. Bibcode: 2020A&A...637A..49P Altcode: 2020arXiv200312337P Context. A new generation of coronagraphs used to study solar wind and coronal mass ejections (CMEs) are being developed and launched. These coronagraphs will heavily rely on multi-channel observations where visible light (VL) and UV-EUV (ultraviolet-extreme ultraviolet) observations provide new plasma diagnostics. One of these instruments, Metis on board ESA-Solar Orbiter, will simultaneously observe VL and the UV Lyman-α line. The number of neutral hydrogen atoms (a small fraction of coronal protons) is a key parameter for deriving plasma properties, such as the temperature from the observed Lyman-α line intensity. However, these measurements are significantly affected if non-equilibrium ionisation effects occur, which can be relevant during CMEs.
Aims: The aim of this work is to determine if non-equilibrium ionisation effects are relevant in CMEs and, in particular, when and in which regions of the CME plasma ionisation equilibrium can be assumed for data analysis.
Methods: We used a magneto-hydrodynamic (MHD) simulation of a magnetic flux rope ejection to generate a CME. From this, we then reconstructed the ionisation state of hydrogen atoms in the CME by evaluating both the advection of neutral and ionised hydrogen atoms and the ionisation and recombination rates in the MHD simulation.
Results: We find that the equilibrium ionisation assumption mostly holds in the core of the CME, which is represented by a magnetic flux rope. In contrast, non-equilibrium ionisation effects are significant at the CME front, where we find about 100 times more neutral hydrogen atoms than prescribed by ionisation equilibrium conditions. We find this to be the case even if this neutral hydrogen excess might be difficult to identify due to projection effects.
Conclusions: This work provides key information for the development of a new generation of diagnostic techniques that aim to combine visible light and Lyman-α line emissions. The results show that non-equilibrium ionisation effects need to be considered when we analyse CME fronts. Incorrectly assuming equilibrium ionisation in these regions would lead to a systematic underestimate of plasma temperatures. Title: Modelling and observations: Comparison of the magnetic field properties in a prominence Authors: Mackay, D. H.; Schmieder, B.; López Ariste, A.; Su, Y. Bibcode: 2020A&A...637A...3M Altcode: Context. Direct magnetic field measurements in solar prominences occur infrequently and are difficult to make and interpret. As a consequence, alternative methods are needed to derive the main properties of the magnetic field that supports the prominence mass. This is important for our understanding of solar prominences, but also for understanding how eruptive prominences may affect space weather.
Aims: We present the first direct comparison of the magnetic field strength derived from spectro-polarimetric observations of a solar prominence, with corresponding results from a theoretical flux rope model constructed from on-disc normal component magnetograms.
Methods: We first used spectro-polarimetric observations of a prominence obtained with the magnetograph THEMIS operating in the Canary Islands to derive the magnetic field of the observed prominence by inverting the Stokes parameters measured in the He D3 line. Next, we constructed two data-constrained non-linear force-free field (NLFFF) models of the same prominence. In one model we assumed a strongly twisted flux rope solution, and in the other a weakly twisted flux rope solution.
Results: The physical extent of the prominence at the limb (height and length) is best reproduced with the strongly twisted flux rope solution. The line-of-sight average of the magnetic field for the strongly twisted solution results in a magnetic field that has a magnitude of within a factor of 1-2 of the observed magnetic field strength. For the peak field strength along the line of sight, an agreement to within 20% of the observations is obtained for the strongly twisted solution. The weakly twisted solution produces significantly lower magnetic field strengths and gives a poor agreement with the observations.
Conclusions: The results of this first comparison are promising. We found that the flux rope insertion method of producing a NLFFF is able to deduce the overall properties of the magnetic field in an observed prominence. Title: Measuring stellar magnetic helicity density Authors: Lund, K.; Jardine, M.; Lehmann, L. T.; Mackay, D. H.; See, V.; Vidotto, A. A.; Donati, J. -F.; Fares, R.; Folsom, C. P.; Jeffers, S. V.; Marsden, S. C.; Morin, J.; Petit, P. Bibcode: 2020MNRAS.493.1003L Altcode: 2020arXiv200111749L; 2020MNRAS.tmp..292L Helicity is a fundamental property of a magnetic field but to date it has only been possible to observe its evolution in one star - the Sun. In this paper, we provide a simple technique for mapping the large-scale helicity density across the surface of any star using only observable quantities: the poloidal and toroidal magnetic field components (which can be determined from Zeeman-Doppler imaging) and the stellar radius. We use a sample of 51 stars across a mass range of 0.1-1.34 M⊙ to show how the helicity density relates to stellar mass, Rossby number, magnetic energy, and age. We find that the large-scale helicity density increases with decreasing Rossby number Ro, peaking at Ro ≃ 0.1, with a saturation or decrease below that. For both fully and partially convective stars, we find that the mean absolute helicity density scales with the mean squared toroidal magnetic flux density according to the power law: |< {h }> | ∝ < {{{B}_{tor}}^2_{} > }^{0.86 ± 0.04}. The scatter in this relation is consistent with the variation across a solar cycle, which we compute using simulations and observations across solar cycles 23 and 24, respectively. We find a significant decrease in helicity density with age. Title: A New Space Weather Tool for Identifying Eruptive Active Regions Authors: Pagano, Paolo; Mackay, Duncan H.; Yardley, Stephanie L. Bibcode: 2019ApJ...886...81P Altcode: 2019arXiv191004226P One of the main goals of solar physics is the timely identification of eruptive active regions. Space missions such as Solar Orbiter or future space weather forecasting missions would largely benefit from this achievement. Our aim is to produce a relatively simple technique that can provide real-time indications or predictions that an active region will produce an eruption. We expand on the theoretical work of Pagano et al. that was able to distinguish eruptive from non-eruptive active regions. From this, we introduce a new operational metric that uses a combination of observed line-of-sight magnetograms, 3D data-driven simulations, and the projection of the 3D simulations forward in time. Results show that the new metric correctly distinguishes active regions as eruptive when observable signatures of eruption have been identified and as non-eruptive when there are no observable signatures of eruption. After successfully distinguishing eruptive from non-eruptive active regions we illustrate how this metric may be used in a “real-time” operational sense were three levels of warning are categorized. These categories are: high risk (red), medium risk (amber), and low risk (green) of eruption. Through considering individual cases, we find that the separation into eruptive and non-eruptive active regions is more robust the longer the time series of observed magnetograms used to simulate the build up of magnetic stress and free magnetic energy within the active region. Finally, we conclude that this proof of concept study delivers promising results where the ability to categorize the risk of an eruption is a major achievement. Title: Understanding the Plasma and Magnetic Field Evolution of a Filament Using Observations and Nonlinear Force-free Field Modeling Authors: Yardley, Stephanie L.; Savcheva, Antonia; Green, Lucie M.; van Driel-Gesztelyi, Lidia; Long, David; Williams, David R.; Mackay, Duncan H. Bibcode: 2019ApJ...887..240Y Altcode: 2019arXiv191101314Y We present observations and magnetic field models of an intermediate filament present on the Sun in 2012 August, associated with a polarity inversion line that extends from AR 11541 in the east into the quiet Sun at its western end. A combination of Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly, SDO/Helioseismic and Magnetic Imager (HMI), and Global Oscillation Network Group Hα data allow us to analyze the structure and evolution of the filament from 2012 August 4 23:00 UT to 2012 August 6 08:00 UT when the filament was in equilibrium. By applying the flux rope insertion method, nonlinear force-free field models of the filament are constructed using SDO/HMI line-of-sight magnetograms as the boundary condition at the two times given above. Guided by observed filament barbs, both modeled flux ropes are split into three sections each with a different value of axial flux to represent the nonuniform photospheric field distribution. The flux in the eastern section of the rope increases by 4 × 1020 Mx between the two models, which is in good agreement with the amount of flux canceled along the internal PIL of AR 11541, calculated to be 3.2 × 1020 Mx. This suggests that flux cancellation builds flux into the filament’s magnetic structure. Additionally, the number of field line dips increases between the two models in the locations where flux cancellation, the formation of new filament threads, and growth of the filament is observed. This suggests that flux cancellation associated with magnetic reconnection forms concave-up magnetic field that lifts plasma into the filament. During this time, the free magnetic energy in the models increases by 0.2 × 1031 ergs. Title: A Prospective New Diagnostic Technique for Distinguishing Eruptive and Noneruptive Active Regions Authors: Pagano, Paolo; Mackay, Duncan H.; Yardley, Stephanie L. Bibcode: 2019ApJ...883..112P Altcode: 2019arXiv190809223P Active regions are the source of the majority of magnetic flux rope ejections that become coronal mass ejections (CMEs). To identify in advance which active regions will produce an ejection is key for both space weather prediction tools and future science missions such as Solar Orbiter. The aim of this study is to develop a new technique to identify which active regions are more likely to generate magnetic flux rope ejections. The new technique will aim to (i) produce timely space weather warnings and (ii) open the way to a qualified selection of observational targets for space-borne instruments. We use a data-driven nonlinear force-free field (NLFFF) model to describe the 3D evolution of the magnetic field of a set of active regions. We determine a metric to distinguish eruptive from noneruptive active regions based on the Lorentz force. Furthermore, using a subset of the observed magnetograms, we run a series of simulations to test whether the time evolution of the metric can be predicted. The identified metric successfully differentiates active regions observed to produce eruptions from the noneruptive ones in our data sample. A meaningful prediction of the metric can be made between 6 and 16 hr in advance. This initial study presents an interesting first step in the prediction of CME onset using only line-of-sight magnetogram observations combined with NLFFF modeling. Future studies will address how to generalize the model such that it can be used in a more operational sense and for a variety of simulation approaches. Title: Nonlinear Force-free Field Modeling of Solar Coronal Jets in Theoretical Configurations Authors: Meyer, K. A.; Savcheva, A. S.; Mackay, D. H.; DeLuca, E. E. Bibcode: 2019ApJ...880...62M Altcode: Coronal jets occur frequently on the Sun, and may contribute significantly to the solar wind. With the suite of instruments available now, we can observe these phenomena in greater detail than ever before. Modeling and simulations can assist further with understanding the dynamic processes involved, but previous studies tended to consider only one mechanism (e.g., emergence or rotation) for the origin of the jet. In this study we model a series of idealized archetypal jet configurations and follow the evolution of the coronal magnetic field. This is a step toward understanding these idealized situations before considering their observational counterparts. Several simple situations are set up for the evolution of the photospheric magnetic field: a single parasitic polarity rotating or moving in a circular path; as well as opposite polarity pairs involved in flyby (shearing), cancellation or emergence; all in the presence of a uniform, open background magnetic field. The coronal magnetic field is evolved in time using a magnetofrictional relaxation method. While magnetofriction cannot accurately reproduce the dynamics of an eruptive phase, the structure of the coronal magnetic field, as well as the buildup of electric currents and free magnetic energy are instructive. Certain configurations and motions produce a flux rope and allow the significant buildup of free energy, reminiscent of the progenitors of so-called blowout jets, whereas other, simpler configurations are more comparable to the standard jet model. The next stage is a comparison with observed coronal jet structures and their corresponding photospheric evolution. Title: 3D Whole-Prominence Fine Structure Model as a Test Case for Verification and Development of Magnetic Field Inversion Techniques Authors: Gunár, S.; Mackay, D. H.; Štěpán, J.; Heinzel, P.; Trujillo Bueno, J. Bibcode: 2019ASPC..526..159G Altcode: We show the potential of a new 3D whole-prominence fine structure model to serve as a well-controlled yet complex environment for testing inversion techniques for the magnetic field inference. The realistic 3D magnetic field and plasma environment provided by the model can be used for the direct synthesis of spectro-polarimetric data. Such synthetic data can be analyzed by advanced inversion tools and their results compared with the known properties provided by the model. Title: Observing the simulations: applying ZDI to 3D non-potential magnetic field simulations Authors: Lehmann, L. T.; Hussain, G. A. J.; Jardine, M. M.; Mackay, D. H.; Vidotto, A. A. Bibcode: 2019MNRAS.483.5246L Altcode: 2018arXiv181103703L; 2018MNRAS.tmp.3287L The large-scale magnetic fields of stars can be obtained with the Zeeman Doppler Imaging (ZDI) technique, but their interpretation is still challenging as the contribution of the small-scale field or the reliability of the reconstructed field properties is still not fully understood. To quantify this, we use 3D non-potential magnetic field simulations for slowly rotating solar-like stars as inputs to test the capabilities of ZDI. These simulations are based on a flux transport model connected to a non-potential coronal evolution model using the observed solar flux emergence pattern. We first compare four field prescriptions regarding their reconstruction capabilities and investigate the influence of the spatial resolution of the input maps on the corresponding circularly polarized profiles. We then generate circularly polarized spectra based on our high-resolution simulations of three stellar models with different activity levels, and reconstruct their large-scale magnetic fields using a non-potential ZDI code assuming two different stellar inclination angles. Our results show that the ZDI technique reconstructs the main features of slowly rotating solar-like stars but with ∼ one order of magnitude less magnetic energy. The large-scale field morphologies are recovered up to harmonic modes ℓ ∼ 5, especially after averaging over several maps for each stellar model. While ZDI is not able to reproduce the input magnetic energy distributions across individual harmonic modes, the fractional energies across the modes are generally within 20 per cent agreement. The fraction of axisymmetric and toroidal field tends to be overestimated for stars with solar flux emergence patterns for more pole-on inclination angles. Title: Eruptions from quiet Sun coronal bright points. II. Non-potential modelling Authors: Galsgaard, Klaus; Madjarska, Maria S.; Mackay, Duncan H.; Mou, Chaozhou Bibcode: 2019A&A...623A..78G Altcode: 2019arXiv190109875G Context. Our recent observational study shows that the majority of coronal bright points (CBPs) in the quiet Sun are sources of one or more eruptions during their lifetime.
Aims: Here, we investigate the non-potential time-dependent structure of the magnetic field of the CBP regions with special emphasis on the time-evolving magnetic structure at the spatial locations where the eruptions are initiated.
Methods: The magnetic structure is evolved in time using a non-linear force-free field (NLFFF) relaxation approach based on a time series of helioseismic and magnetic imager (HMI) longitudinal magnetograms. This results in a continuous time series of NLFFFs. The time series is initiated with a potential field extrapolation based on a magnetogram taken well before the time of the eruptions. This initial field is then evolved in time in response to the observed changes in the magnetic field distribution at the photosphere. The local and global magnetic field structures from the time series of NLFFF field solutions are analysed in the vicinity of the eruption sites at the approximate times of the eruptions.
Results: The analysis shows that many of the CBP eruptions reported in a recent publication contain a twisted flux tube located at the sites of eruptions. The presence of flux ropes at these locations provides in many cases a direct link between the magnetic field structure, their eruption, and the observation of mini coronal mass ejections (mini-CMEs). It is found that all repetitive eruptions are homologous.
Conclusions: The NLFFF simulations show that twisted magnetic field structures are created at the locations hosting eruptions in CBPs. These twisted structures are produced by footpoint motions imposed by changes in the photospheric magnetic field observations. The true nature of the micro-flares remains unknown. Further 3D data-driven magnetohydrodynamic modelling is required to show how these twisted regions become unstable and erupt.

Movies associated to Figs. 1-5 are available at https://www.aanda.org Title: Active Region evolution prior to magnetic flux rope ejections Authors: Pagano, P.; Mackay, D. H. Bibcode: 2019NCimC..42...34P Altcode: Magnetic flux rope ejections from the Sun are the main progenitors of Coronal Mass Ejections and thus driver of the Space Weather. To study and understand these phenomena is key to tackle the challenges of Space Weather and to do so we need tools to identify where and when magnetic flux ropes are ejected. We run a non-linear force-free field magnetofrictional simulation of the active region AR11261 over the two days prior to an observed magnetic flux rope ejection. We analyse the distribution of three quantities from the numerical model at the time of the flux rope ejections and we verify that in this application they highlight the location where the flux rope ejection originates. Title: Magnetic Helicity Condensation and the Solar Cycle Authors: Mackay, Duncan H.; DeVore, C. Richard; Antiochos, Spiro K.; Yeates, Anthony R. Bibcode: 2018ApJ...869...62M Altcode: Solar filaments exhibit a global chirality pattern where dextral/sinistral filaments, corresponding to negative/positive magnetic helicity, are dominant in the northern/southern hemisphere. This pattern is opposite to the sign of magnetic helicity injected by differential rotation along east-west oriented polarity inversion lines, posing a major conundrum for solar physics. A resolution of this problem is offered by the magnetic helicity-condensation model of Antiochos. To investigate the global consequences of helicity condensation for the hemispheric chirality pattern, we apply a temporally and spatially averaged statistical approximation of helicity condensation. Realistic magnetic field configurations in both the rising and declining phases of the solar cycle are simulated. For the helicity-condensation process, we assume convective cells consisting of positive/negative vorticities in the northern/southern hemisphere that inject negative/positive helicity. The magnitude of the vorticity is varied as a free parameter, corresponding to different rates of helicity injection. To reproduce the observed percentages of dominant and minority filament chiralities, we find that a vorticity of magnitude 2.5 × 10-6 s-1 is required. This rate, however, is insufficient to produce the observed unimodal profile of chirality with latitude. To achieve this, a vorticity of at least 5 × 10-6 s-1 is needed. Our results place a lower limit on the small-scale helicity injection required to dominate differential rotation and reproduce the observed hemispheric pattern. Future studies should aim to establish whether the helicity injection rate due to convective flows and/or flux emergence across all latitudes of the Sun is consistent with our results. Title: The Role of Flux Cancellation in Eruptions from Bipolar ARs Authors: Yardley, S. L.; Green, L. M.; van Driel-Gesztelyi, L.; Williams, D. R.; Mackay, D. H. Bibcode: 2018ApJ...866....8Y Altcode: 2018arXiv180810635Y The physical processes or trigger mechanisms that lead to the eruption of coronal mass ejections (CMEs), the largest eruptive phenomenon in the heliosphere, are still undetermined. Low-altitude magnetic reconnection associated with flux cancellation appears to play an important role in CME occurrence as it can form an eruptive configuration and reduce the magnetic flux that contributes to the overlying, stabilizing field. We conduct the first comprehensive study of 20 small bipolar ARs (ARs) in order to probe the role of flux cancellation as an eruption trigger mechanism. We categorize eruptions from the bipolar regions into three types related to location, and find that the type of eruption produced depends on the evolutionary stage of the AR. In addition, we find that ARs that form eruptive structures by flux cancellation (low-altitude reconnection) had, on average, lower flux cancellation rates than the AR sample as a whole. Therefore, while flux cancellation plays a key role, by itself it is insufficient for the production of an eruption. The results provide supporting evidence that although flux cancellation in a sheared arcade may be able to build an eruptive configuration, a successful eruption depends upon the removal of sufficient overlying and stabilizing field. Convergence of the bipole polarities also appears to be present in regions that produce an eruption. These findings have important implications for understanding the physical processes that occur on our Sun in relation to CMEs and for space weather forecasting. Title: Global Non-Potential Magnetic Models of the Solar Corona During the March 2015 Eclipse Authors: Yeates, Anthony R.; Amari, Tahar; Contopoulos, Ioannis; Feng, Xueshang; Mackay, Duncan H.; Mikić, Zoran; Wiegelmann, Thomas; Hutton, Joseph; Lowder, Christopher A.; Morgan, Huw; Petrie, Gordon; Rachmeler, Laurel A.; Upton, Lisa A.; Canou, Aurelien; Chopin, Pierre; Downs, Cooper; Druckmüller, Miloslav; Linker, Jon A.; Seaton, Daniel B.; Török, Tibor Bibcode: 2018SSRv..214...99Y Altcode: 2018arXiv180800785Y Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models. Title: Predicting the corona for the 21 August 2017 total solar eclipse Authors: Mikić; , Zoran; Downs, Cooper; Linker, Jon A.; Caplan, Ronald M.; Mackay, Duncan H.; Upton, Lisa A.; Riley, Pete; Lionello, Roberto; Török, Tibor; Titov, Viacheslav S.; Wijaya, Janvier; Druckmüller, Miloslav; Pasachoff, Jay M.; Carlos, Wendy Bibcode: 2018NatAs...2..913M Altcode: 2018NatAs.tmp..120M The total solar eclipse that occurred on 21 August 2017 across the United States provided an opportunity to test a magnetohydrodynamic model of the solar corona driven by measured magnetic fields. We used a new heating model based on the dissipation of Alfvén waves, and a new energization mechanism to twist the magnetic field in filament channels. We predicted what the corona would look like one week before the eclipse. Here, we describe how this prediction was accomplished, and show that it compared favourably with observations of the eclipse in white light and extreme ultraviolet. The model allows us to understand the relationship of observed features, including streamers, coronal holes, prominences, polar plumes and thin rays, to the magnetic field. We show that the discrepancies between the model and observations arise from limitations in our ability to observe the Sun's magnetic field. Predictions of this kind provide opportunities to improve the models, forging the path to improved space weather prediction. Title: Connecting the large- and the small-scale magnetic fields of solar-like stars Authors: Lehmann, L. T.; Jardine, M. M.; Mackay, D. H.; Vidotto, A. A. Bibcode: 2018MNRAS.478.4390L Altcode: 2018MNRAS.tmp.1193L; 2018arXiv180504420L A key question in understanding the observed magnetic field topologies of cool stars is the link between the small- and the large-scale magnetic field and the influence of the stellar parameters on the magnetic field topology. We examine various simulated stars to connect the small scale with the observable large-scale field. The highly resolved 3D simulations we used couple a flux transport model with a non-potential coronal model using a magnetofrictional technique. The surface magnetic field of these simulations is decomposed into spherical harmonics which enables us to analyse the magnetic field topologies on a wide range of length scales and to filter the large-scale magnetic field for a direct comparison with the observations. We show that the large-scale field of the self-consistent simulations fits the observed solar-like stars and is mainly set up by the global dipolar field and the large-scale properties of the flux pattern, e.g. the averaged latitudinal position of the emerging small-scale field and its global polarity pattern. The stellar parameter flux emergence rate, differential rotation, and meridional flow affect the large-scale magnetic field topology. An increased flux emergence rate increases the magnetic flux in all field components and an increased differential rotation increases the toroidal field fraction by decreasing the poloidal field. The meridional flow affects the distribution of the magnetic energy across the spherical harmonic modes. Title: Large-Scale Patterns of Filament Channels and Filaments Authors: Mackay, Duncan Bibcode: 2018cosp...42E2112M Altcode: In this review the properties and large-scale patterns of filament channels and filaments will be considered. Initially, the global formation locations of filament channels and filaments arediscussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long time-scales are described, along with the origin of the hemispheric pattern of filaments. Title: 3D modelling of magnetic field and plasma structure of entire prominences Authors: Gunár, Stanislav; Anzer, Ulrich; Heinzel, Petr; Mackay, Duncan Bibcode: 2018cosp...42E1315G Altcode: The 3D Whole-Prominence Fine Structure (WPFS) model allows us for the first time to simulate entire prominences/filaments including their numerous fine structures. This model combines a 3D magnetic field configuration of an entire prominence obtained from non-linear force-free field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along hundreds of fine structures within the 3D magnetic model. The prominence plasma has realistic density and temperature distributions including the prominence-corona transition region. This allows us to produce synthetic H-alpha images of simulated prominences both in emission on the solar limb and in absorption against the solar disk (viewed as filaments) using a single model.Such 3D WPFS model provides us with consistent information about the prominence magnetic field configuration, prominence fine structure plasma and its radiative output. Moreover, we are able to follow the evolution of modeled prominences caused by changes of the underlying photospheric magnetic flux distribution. Thanks to these capabilities we can study links between the photospheric flux distribution, prominence magnetic field configuration, distribution and composition of the prominence plasma and its observable signatures. These relationships are important for interpretation of the observed imaging and spectral/spectropolarimetric data and for inference of the properties of the prominence magnetic field. Title: Can 3D whole-prominence fine structure models be used for assessment of the prominence plasma mass and distribution prior to the onset of CMEs? Authors: Gunár, Stanislav; Schmieder, Brigitte; Aulanier, Guillaume; Anzer, Ulrich; Heinzel, Petr; Mackay, Duncan; Dudik, Jaroslav Bibcode: 2018cosp...42E1316G Altcode: Two complex 3D models of entire prominences including their numerous fine structures were recently developed. The first 3D Whole-Prominence Fine Structure (WPFS) model was developed by Gunár and Mackay. The second 3D WPFS model was put forward by Gunár, Aulanier, Dudík, Heinzel, and Schmieder. These 3D prominence models combine simulations of the 3D magnetic field configuration of an entire prominence with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along hundreds of fine structures. The assumed prominence plasma has realistic density and temperature distributions including the prominence-corona transition region.These 3D WPFS models allow us to study the distribution and the mass of the prominence plasma contained in prominence magnetic field configurations. These can be crucial during the onset and early evolution of CMEs. Moreover, prominence plasma represents a bulk of the material ejected by CMEs into the interplanetary space. Here, we investigate the potential of using the 3D WPFS models for assessment of the role the prominence plasma plays in the initiation and evolution of CMEs. Title: A new technique for observationally derived boundary conditions for space weather Authors: Pagano, Paolo; Mackay, Duncan Hendry; Yeates, Anthony Robinson Bibcode: 2018JSWSC...8A..26P Altcode: 2018arXiv180207516P Context. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona.
Methods: To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results.The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4 R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4 R⊙ that in future may be applied to interplanetary space weather prediction models.
Conclusions: In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a number of technical and scientific challenges that still need to be addressed. Nevertheless, we illustrate that coupling quasi-static and MHD simulations in this way can significantly reduce the computational time required to produce realistic space weather boundary conditions. Title: Photospheric Observations of Surface and Body Modes in Solar Magnetic Pores Authors: Keys, Peter H.; Morton, Richard J.; Jess, David B.; Verth, Gary; Grant, Samuel D. T.; Mathioudakis, Mihalis; Mackay, Duncan H.; Doyle, John G.; Christian, Damian J.; Keenan, Francis P.; Erdélyi, Robertus Bibcode: 2018ApJ...857...28K Altcode: 2018arXiv180301859K Over the past number of years, great strides have been made in identifying the various low-order magnetohydrodynamic wave modes observable in a number of magnetic structures found within the solar atmosphere. However, one aspect of these modes that has remained elusive, until now, is their designation as either surface or body modes. This property has significant implications for how these modes transfer energy from the waveguide to the surrounding plasma. Here, for the first time to our knowledge, we present conclusive, direct evidence of these wave characteristics in numerous pores that were observed to support sausage modes. As well as outlining methods to detect these modes in observations, we make estimates of the energies associated with each mode. We find surface modes more frequently in the data, as well as that surface modes appear to carry more energy than those displaying signatures of body modes. We find frequencies in the range of ∼2-12 mHz, with body modes as high as 11 mHz, but we do not find surface modes above 10 mHz. It is expected that the techniques we have applied will help researchers search for surface and body signatures in other modes and in differing structures from those presented here. Title: Simulating the Coronal Evolution of AR 11437 Using SDO/HMI Magnetograms Authors: Yardley, Stephanie L.; Mackay, Duncan H.; Green, Lucie M. Bibcode: 2018ApJ...852...82Y Altcode: 2017arXiv171200396Y The coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. A sequence of photospheric line-of-sight magnetograms produced by the Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager (HMI) is used to drive the simulation and continuously evolve the coronal magnetic field of the active region through a series of nonlinear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/Atmospheric Imaging Assembly (AIA) observations show that many aspects of the active region’s observed coronal evolution are reproduced. In particular, it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occurred on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at 14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and 10 hr before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion, and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field. Title: Quiescent Prominences in the Era of ALMA. II. Kinetic Temperature Diagnostics Authors: Gunár, Stanislav; Heinzel, Petr; Anzer, Ulrich; Mackay, Duncan H. Bibcode: 2018ApJ...853...21G Altcode: We provide the theoretical background for diagnostics of the thermal properties of solar prominences observed by the Atacama Large Millimeter/submillimeter Array (ALMA). To do this, we employ the 3D Whole-Prominence Fine Structure (WPFS) model that produces synthetic ALMA-like observations of a complex simulated prominence. We use synthetic observations derived at two different submillimeter/millimeter (SMM) wavelengths—one at a wavelength at which the simulated prominence is completely optically thin and another at a wavelength at which a significant portion of the simulated prominence is optically thick—as if these were the actual ALMA observations. This allows us to develop a technique for an analysis of the prominence plasma thermal properties from such a pair of simultaneous high-resolution ALMA observations. The 3D WPFS model also provides detailed information about the distribution of the kinetic temperature and the optical thickness along any line of sight. We can thus assess whether the measure of the kinetic temperature derived from observations accurately represents the actual kinetic temperature properties of the observed plasma. We demonstrate here that in a given pixel the optical thickness at the wavelength at which the prominence plasma is optically thick needs to be above unity or even larger to achieve a sufficient accuracy of the derived information about the kinetic temperature of the analyzed plasma. Information about the optical thickness cannot be directly discerned from observations at the SMM wavelengths alone. However, we show that a criterion that can identify those pixels in which the derived kinetic temperature values correspond well to the actual thermal properties in which the observed prominence can be established. Title: Modeling the 21 August 2017 Total Solar Eclipse: Prediction Results and New Techniques Authors: Downs, C.; Mikic, Z.; Caplan, R. M.; Linker, J.; Lionello, R.; Torok, T.; Titov, V. S.; Riley, P.; MacKay, D.; Upton, L. Bibcode: 2017AGUFMSH13B2475D Altcode: As has been our tradition for past solar eclipses, we conducted a high resolution magnetohydrodynamic (MHD) simulation of the corona to predict the appearance of the 21 August 2017 solar eclipse. In this presentation, we discuss our model setup and our forward modeled predictions for the corona's appearance, including images of polarized brightness and EUV/soft X-Ray emission. We show how the combination of forward modeled observables and knowledge of the underlying magnetic field from the model can be used to interpret the structures seen during the eclipse. We also discuss two new features added to this year's prediction. First, in an attempt to improve the morphological shape of streamers in the low corona, we energize the large-scale magnetic field by emerging shear and canceling flux within filament channels. The handedness of the shear is deduced from a magnetofrictional model, which is driven by the evolving photospheric field produced by the Advective Flux Transport model. Second, we apply our new wave-turbulence-driven (WTD) model for coronal heating. This model has substantially fewer free parameters than previous empirical heating models, but is inherently sensitive to the 3D geometry and connectivity of the magnetic field--a key property for modeling the thermal-magnetic structure of the corona. We examine the effect of these considerations on forward modeled observables, and present them in the context of our final 2017 eclipse prediction (www.predsci.com/corona/aug2017eclipse). Research supported by NASA's Heliophysics Supporting Research and Living With a Star Programs. Title: The Role of Small-Scale Processes in Solar Active Region Decay Authors: Meyer, Karen; Mackay, Duncan Bibcode: 2017SPD....4810106M Altcode: Active regions are locations of intense magnetic activity on the Sun, whose evolution can result in highly energetic eruptive phenomena such as solar flares and coronal mass ejections (CMEs). Therefore, fast and accurate simulation of their evolution and decay is essential in the prediction of Space Weather events. In this talk we present initial results from our new model for the photospheric evolution of active region magnetic fields. Observations show that small-scale processes appear to play a role in the dispersal and decay of solar active regions, for example through cancellation at the boundary of sunspot outflows and erosion of flux by surrounding convective cells. Our active region model is coupled to our existing model for the evolution of small-scale photospheric magnetic features. Focusing first on the active region decay phase, we consider the evolution of its magnetic field due to both large-scale (e.g. differential rotation) and small-scale processes, such as its interaction with surrounding small-scale magnetic features and convective flows.This project is funded by The Carnegie Trust for the Universities of Scotland, through their Research Incentives Grant scheme. Title: New Techniques Used in Modeling the 2017 Total Solar Eclipse: Energizing and Heating the Large-Scale Corona Authors: Downs, Cooper; Mikic, Zoran; Linker, Jon A.; Caplan, Ronald M.; Lionello, Roberto; Torok, Tibor; Titov, Viacheslav; Riley, Pete; Mackay, Duncan; Upton, Lisa Bibcode: 2017SPD....4820802D Altcode: Over the past two decades, our group has used a magnetohydrodynamic (MHD) model of the corona to predict the appearance of total solar eclipses. In this presentation we detail recent innovations and new techniques applied to our prediction model for the August 21, 2017 total solar eclipse. First, we have developed a method for capturing the large-scale energized fields typical of the corona, namely the sheared/twisted fields built up through long-term processes of differential rotation and flux-emergence/cancellation. Using inferences of the location and chirality of filament channels (deduced from a magnetofrictional model driven by the evolving photospheric field produced by the Advective Flux Transport model), we tailor a customized boundary electric field profile that will emerge shear along the desired portions of polarity inversion lines (PILs) and cancel flux to create long twisted flux systems low in the corona. This method has the potential to improve the morphological shape of streamers in the low solar corona. Second, we apply, for the first time in our eclipse prediction simulations, a new wave-turbulence-dissipation (WTD) based model for coronal heating. This model has substantially fewer free parameters than previous empirical heating models, but is inherently sensitive to the 3D geometry and connectivity of the coronal field---a key property for modeling/predicting the thermal-magnetic structure of the solar corona. Overall, we will examine the effect of these considerations on white-light and EUV observables from the simulations, and present them in the context of our final 2017 eclipse prediction model.Research supported by NASA's Heliophysics Supporting Research and Living With a Star Programs. Title: Prediction of the Solar Corona for the 2017 August 21 Total Solar Eclipse Authors: Mikic, Zoran; Downs, Cooper; Linker, Jon A.; Caplan, Ronald M.; Lionello, Roberto; Torok, Tibor; Titov, Viacheslav; Riley, Pete; Mackay, Duncan; Upton, Lisa Bibcode: 2017SPD....4820801M Altcode: It has become our tradition to predict the structure of the corona prior to eclipses, using a magnetohydrodynamic (MHD) model based on measurements of photospheric magnetic fields on the Sun. We plan to continue this tradition for the August 21, 2017 total solar eclipse that will sweep across the United States. We will predict the structure of the corona using SDO/HMI photospheric magnetic field data, including images of polarization brightness, magnetic field line traces, and images of simulated emission in EUV and X-rays. These images can be compared directly with observations of the total eclipse, as well as observations from SDO/AIA, Hinode/XRT, and STEREO/EUVI. This year we will attempt to energize the magnetic field within filament channels for a more realistic prediction, by constructing flux ropes at the locations where filament channels are observed. The handedness of the flux ropes will be deduced from a magnetofrictional model driven by the evolving photospheric field produced by the Advective Flux Transport model.Research supported by NASA's Heliophysics Supporting Research and Living With a Star Programs. Title: Origin and Ion Charge State Evolution of Solar Wind Transients during 4 - 7 August 2011 Authors: Rodkin, D.; Goryaev, F.; Pagano, P.; Gibb, G.; Slemzin, V.; Shugay, Y.; Veselovsky, I.; Mackay, D. H. Bibcode: 2017SoPh..292...90R Altcode: 2016arXiv161005048R We present a study of the complex event consisting of several solar wind transients detected by the Advanced Composition Explorer (ACE) on 4 - 7 August 2011, which caused a geomagnetic storm with Dst =−110 nT. The supposed coronal sources, three flares and coronal mass ejections (CMEs), occurred on 2 - 4 August 2011 in active region (AR) 11261. To investigate the solar origin and formation of these transients, we study the kinematic and thermodynamic properties of the expanding coronal structures using the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) EUV images and differential emission measure (DEM) diagnostics. The Helioseismic and Magnetic Imager (HMI) magnetic field maps were used as the input data for the 3D magnetohydrodynamic (MHD) model to describe the flux rope ejection (Pagano, Mackay, and Poedts, 2013b). We characterize the early phase of the flux rope ejection in the corona, where the usual three-component CME structure formed. The flux rope was ejected with a speed of about 200 kms−1 to the height of 0.25 R⊙. The kinematics of the modeled CME front agrees well with the Solar Terrestrial Relations Observatory (STEREO) EUV measurements. Using the results of the plasma diagnostics and MHD modeling, we calculate the ion charge ratios of carbon and oxygen as well as the mean charge state of iron ions of the 2 August 2011 CME, taking into account the processes of heating, cooling, expansion, ionization, and recombination of the moving plasma in the corona up to the frozen-in region. We estimate a probable heating rate of the CME plasma in the low corona by matching the calculated ion composition parameters of the CME with those measured in situ for the solar wind transients. We also consider the similarities and discrepancies between the results of the MHD simulation and the observations. Title: Origin and Ion Charge State Evolution of Solar Wind Transients 4 - 7 August 2011 Authors: Rodkin, Denis; Goryaev, Farid; Pagano, Paolo; Gibb, Gordon; Slemzin, Vladimir; Shugay, Yulia; Veselovsky, Igor; Mackay, Duncan Bibcode: 2017EGUGA..19.6920R Altcode: Identification of transients and their origins on the Sun is one of the most important problems of the space weather forecasting. In our work, we present a case study of the complex event consisting of several solar wind transients detected by ACE on 4 - 7 August 2011, that caused a geomagnetic storm with Dst= - 110 nT. The supposed coronal sources - three flares and coronal mass ejections (CMEs) occurred on 2 - 4 August 2011 in the active region AR 11261. To investigate the solar origins and formation of these transients, we studied kinematic and thermodynamic properties of expanding coronal structures using the SDO/AIA EUV images and the differential emission measure (DEM) diagnostics. The Helioseismic and Magnetic Imager (HMI) magnetic field maps were used as the input data for the 3D numerical model to describe the flux rope ejection. We characterize the early phase of the flux rope ejection in the corona, where the usual three-component CME structure formed. The flux rope ejected with the speed about 200 km/s to the height of 0.25 Rsun. The kinematics of the modeled CME front well agrees with the STEREO EUV measurements. Using the results of the plasma diagnostics and MHD modeling, we calculated the ion charge ratios of carbon and oxygen as well as the mean charge state of iron ions of the 2 August 2011 CME taking into account the processes of heating, cooling, expansion, ionization and recombination of the moving plasma in the corona up to the freeze-in region. We estimated a probable heating rate of the CME plasma in the low corona by matching the calculated ion composition parameters of the CME with that measured in-situ parameters of the solar wind transients. We also consider the similarities and discrepancies between the results of the MHD simulation and the observation of the event. Our results show that analysis of the ion composition of CMEs enables to disclose a relationship between parameters of the solar wind transients and properties of their solar origins, which opens new possibilities to validate and improve the solar wind forecasting models. Title: The energy budget of stellar magnetic fields: comparing non-potential simulations and observations Authors: Lehmann, L. T.; Jardine, M. M.; Vidotto, A. A.; Mackay, D. H.; See, V.; Donati, J. -F.; Folsom, C. P.; Jeffers, S. V.; Marsden, S. C.; Morin, J.; Petit, P. Bibcode: 2017MNRAS.466L..24L Altcode: 2016arXiv161008314L The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic field topology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the high-resolution non-potential magnetofrictional simulations and the relatively low-resolution observations, we filter out the small-scale field in the simulations using a spherical harmonics decomposition. We show that the large-scale field topologies of the solar-based simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes which are similar to the observations. These global non-potential evolution model simulations capture key magnetic features of the observed solar-like stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of M-dwarfs or stars with dominantly toroidal field. Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies. Title: Observations and Modelling of the Pre-flare Period of the 29 March 2014 X1 Flare Authors: Woods, M. M.; Harra, L. K.; Matthews, S. A.; Mackay, D. H.; Dacie, S.; Long, D. M. Bibcode: 2017SoPh..292...38W Altcode: 2017arXiv170106457W On 29 March 2014, NOAA Active Region (AR) 12017 produced an X1 flare that was simultaneously observed by an unprecedented number of observatories. We have investigated the pre-flare period of this flare from 14:00 UT until 19:00 UT using joint observations made by the Interface Region Imaging Spectrometer (IRIS) and the Hinode Extreme Ultraviolet Imaging Spectrometer (EIS). Spectral lines providing coverage of the solar atmosphere from the chromosphere to the corona were analysed to investigate pre-flare activity within the AR. The results of the investigation have revealed evidence of strongly blue-shifted plasma flows, with velocities up to 200 kms−1, being observed 40 minutes prior to flaring. These flows are located along the filament present in the active region and are both spatially discrete and transient. In order to constrain the possible explanations for this activity, we undertake non-potential magnetic field modelling of the active region. This modelling indicates the existence of a weakly twisted flux rope along the polarity inversion line in the region where a filament and the strong pre-flare flows are observed. We then discuss how these observations relate to the current models of flare triggering. We conclude that the most likely drivers of the observed activity are internal reconnection in the flux rope, early onset of the flare reconnection, or tether-cutting reconnection along the filament. Title: Combined Global NLFFF simulations and MHD simulations of flux rope ejections Authors: Pagano, P.; Mackay, D.; Yeates, A. Bibcode: 2017psio.confE.117P Altcode: No abstract at ADS Title: Quiescent Prominences in the Era of ALMA: Simulated Observations Using the 3D Whole-prominence Fine Structure Model Authors: Gunár, Stanislav; Heinzel, Petr; Mackay, Duncan H.; Anzer, Ulrich Bibcode: 2016ApJ...833..141G Altcode: We use the detailed 3D whole-prominence fine structure model to produce the first simulated high-resolution ALMA observations of a modeled quiescent solar prominence. The maps of synthetic brightness temperature and optical thickness shown in the present paper are produced using a visualization method for synthesis of the submillimeter/millimeter radio continua. We have obtained the simulated observations of both the prominence at the limb and the filament on the disk at wavelengths covering a broad range that encompasses the full potential of ALMA. We demonstrate here extent to which the small-scale and large-scale prominence and filament structures will be visible in the ALMA observations spanning both the optically thin and thick regimes. We analyze the relationship between the brightness and kinetic temperature of the prominence plasma. We also illustrate the opportunities ALMA will provide for studying the thermal structure of the prominence plasma from the cores of the cool prominence fine structure to the prominence-corona transition region. In addition, we show that detailed 3D modeling of entire prominences with their numerous fine structures will be important for the correct interpretation of future ALMA observations of prominences. Title: Modeling the Sun’s Small-scale Global Photospheric Magnetic Field Authors: Meyer, K. A.; Mackay, D. H. Bibcode: 2016ApJ...830..160M Altcode: We present a new model for the Sun’s global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of small-scale magnetic features across the full solar surface is simulated, subject to the influence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between small-scale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2.5 R ⊙, around 10-100 times less than that determined for typical Helioseismic and Magnetic Imager synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is currently observed, and hence a much higher cosmic ray flux at Earth. Title: The Possible Impact of L5 Magnetograms on Non-potential Solar Coronal Magnetic Field Simulations Authors: Weinzierl, Marion; Mackay, Duncan H.; Yeates, Anthony R.; Pevtsov, Alexei A. Bibcode: 2016ApJ...828..102W Altcode: The proposed Carrington-L5 mission would bring instruments to the L5 Lagrange point to provide us with crucial data for space weather prediction. To assess the importance of including a magnetograph, we consider the possible differences in non-potential solar coronal magnetic field simulations when magnetograph observations are available from the L5 point, compared with an L1-based field of view (FOV). A timeseries of synoptic radial magnetic field maps is constructed to capture the emergence of two active regions from the L5 FOV. These regions are initially absent in the L1 magnetic field maps, but are included once they rotate into the L1 FOV. Non-potential simulations for these two sets of input data are compared in detail. Within the bipolar active regions themselves, differences in the magnetic field structure can exist between the two simulations once the active regions are included in both. These differences tend to reduce within 5 days of the active region being included in L1. The delayed emergence in L1 can, however, lead to significant persistent differences in long-range connectivity between the active regions and the surrounding fields, and also in the global magnetic energy. In particular, the open magnetic flux and the location of open magnetic footpoints, are sensitive to capturing the real-time of emergence. These results suggest that a magnetograph at L5 could significantly improve predictions of the non-potential corona, the interplanetary magnetic field, and of solar wind source regions on the Sun. Title: Magnetic reconnection between a solar filament and nearby coronal loops Authors: Li, Leping; Zhang, Jun; Peter, Hardi; Priest, Eric; Chen, Huadong; Guo, Lijia; Chen, Feng; Mackay, Duncan Bibcode: 2016NatPh..12..847L Altcode: 2016arXiv160503320L Magnetic reconnection is difficult to observe directly but coronal structures on the Sun often betray the magnetic field geometry and its evolution. Here we report the observation of magnetic reconnection between an erupting filament and its nearby coronal loops, resulting in changes in the filament connection. X-type structures form when the erupting filament encounters the loops. The filament becomes straight, and bright current sheets form at the interfaces. Plasmoids appear in these current sheets and propagate bi-directionally. The filament disconnects from the current sheets, which gradually disperse and disappear, then reconnects to the loops. This evolution suggests successive magnetic reconnection events predicted by theory but rarely detected with such clarity in observations. Our results confirm the three-dimensional magnetic reconnection theory and have implications for the evolution of dissipation regions and the release of magnetic energy for reconnection in many magnetized plasma systems. Title: Properties of the prominence magnetic field and plasma distributions as obtained from 3D whole-prominence fine structure modeling Authors: Gunár, S.; Mackay, D. H. Bibcode: 2016A&A...592A..60G Altcode:
Aims: We analyze distributions of the magnetic field strength and prominence plasma (temperature, pressure, plasma β, and mass) using the 3D whole-prominence fine structure model.
Methods: The model combines a 3D magnetic field configuration of an entire prominence, obtained from non-linear force-free field simulations, with a detailed semi-empirically derived description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model.
Results: We show that in the modeled prominence, the variations of the magnetic field strength and its orientation are insignificant on scales comparable to the smallest dimensions of the observed prominence fine structures. We also show the ability of the 3D whole-prominence fine structure model to reveal the distribution of the prominence plasma with respect to its temperature within the prominence volume. This provides new insights into the composition of the prominence-corona transition region. We further demonstrate that the values of the plasma β are small throughout the majority of the modeled prominences when realistic photospheric magnetic flux distributions and prominence plasma parameters are assumed. While this is generally true, we also find that in the region with the deepest magnetic dips, the plasma β may increase towards unity. Finally, we show that the mass of the modeled prominence plasma is in good agreement with the mass of observed non-eruptive prominences. Title: Impact of an L5 Magnetograph on Nonpotential Solar Global Magnetic Field Modeling Authors: Mackay, Duncan H.; Yeates, Anthony R.; Bocquet, Francois-Xavier Bibcode: 2016ApJ...825..131M Altcode: We present the first theoretical study to consider what improvement could be obtained in global nonpotential modeling of the solar corona if magnetograph data were available from the L5 Lagrange point, in addition to from the direction of Earth. To consider this, we first carry out a “reference Sun” simulation over two solar cycles. An important property of this simulation is that random bipole emergences are allowed across the entire solar surface at any given time (such as can occur on the Sun). Next, we construct two “limited data” simulations, where bipoles are only included when they could be seen from (I) an Earth-based magnetograph and (II) either Earth- or L5-based magnetographs. The improvement in reproducing the reference Sun simulation when an L5 view is available is quantified through considering global quantities in the limited data simulations. These include surface and polar flux, total magnetic energy, volume electric current, open flux, and the number of flux ropes. Results show that when an L5 observational viewpoint is included, the accuracy of the global quantities in the limited data simulations can increase by 26%-40%. This clearly shows that a magnetograph at the L5 point could significantly increase the accuracy of global nonpotential modeling and with this the accuracy of future space weather forecasts. Title: Large-Scale Patterns of Filament Channels and Filaments Authors: Mackay, Duncan Bibcode: 2016cosp...41E1213M Altcode: In this review the properties and large-scale patterns of filament channels and filaments will be considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long time-scales are described, along with the origin of the hemispheric pattern of filaments. Title: A New Technique for the Photospheric Driving of Non-potential Solar Coronal Magnetic Field Simulations Authors: Weinzierl, Marion; Yeates, Anthony R.; Mackay, Duncan H.; Henney, Carl J.; Arge, C. Nick Bibcode: 2016ApJ...823...55W Altcode: In this paper, we develop a new technique for driving global non-potential simulations of the Sun’s coronal magnetic field solely from sequences of radial magnetic maps of the solar photosphere. A primary challenge to driving such global simulations is that the required horizontal electric field cannot be uniquely determined from such maps. We show that an “inductive” electric field solution similar to that used by previous authors successfully reproduces specific features of the coronal field evolution in both single and multiple bipole simulations. For these cases, the true solution is known because the electric field was generated from a surface flux-transport model. The match for these cases is further improved by including the non-inductive electric field contribution from surface differential rotation. Then, using this reconstruction method for the electric field, we show that a coronal non-potential simulation can be successfully driven from a sequence of ADAPT maps of the photospheric radial field, without including additional physical observations which are not routinely available. Title: Stellar coronal response to differential rotation and flux emergence Authors: Gibb, G. P. S.; Mackay, D. H.; Jardine, M. M.; Yeates, A. R. Bibcode: 2016MNRAS.456.3624G Altcode: 2016arXiv160303419G We perform a numerical parameter study to determine what effect varying differential rotation and flux emergence has on a star's non-potential coronal magnetic field. In particular we consider the effects on the star's surface magnetic flux, open magnetic flux, mean azimuthal field strength, coronal free magnetic energy, coronal heating and flux rope eruptions. To do this, we apply a magnetic flux transport model to describe the photospheric evolution, and couple this to the non-potential coronal evolution using a magnetofrictional technique. A flux emergence model is applied to add new magnetic flux on to the photosphere and into the corona. The parameters of this flux emergence model are derived from the solar flux emergence profile, however the rate of emergence can be increased to represent higher flux emergence rates than the Sun's. Overall we find that flux emergence has a greater effect on the non-potential coronal properties compared to differential rotation, with all the aforementioned properties increasing with increasing flux emergence rate. Although differential rotation has a lesser effect on the overall coronal properties compared to flux emergence, varying differential rotation does alter the coronal structure. As the differential rotation rate increases, the corona becomes more open, and more non-potential. Title: Solar coronal magnetic fields derived using seismology techniques applied to omnipresent sunspot waves Authors: Jess, David B.; Reznikova, Veronika E.; Ryans, Robert S. I.; Christian, Damian J.; Keys, Peter H.; Mathioudakis, Mihalis; Mackay, Duncan H.; Krishna Prasad, S.; Banerjee, Dipankar; Grant, Samuel D. T.; Yau, Sean; Diamond, Conor Bibcode: 2016NatPh..12..179J Altcode: 2016arXiv160506112J Sunspots on the surface of the Sun are the observational signatures of intense manifestations of tightly packed magnetic field lines, with near-vertical field strengths exceeding 6,000 G in extreme cases. It is well accepted that both the plasma density and the magnitude of the magnetic field strength decrease rapidly away from the solar surface, making high-cadence coronal measurements through traditional Zeeman and Hanle effects difficult as the observational signatures are fraught with low-amplitude signals that can become swamped with instrumental noise. Magneto-hydrodynamic (MHD) techniques have previously been applied to coronal structures, with single and spatially isolated magnetic field strengths estimated as 9-55 G (refs ,,,). A drawback with previous MHD approaches is that they rely on particular wave modes alongside the detectability of harmonic overtones. Here we show, for the first time, how omnipresent magneto-acoustic waves, originating from within the underlying sunspot and propagating radially outwards, allow the spatial variation of the local coronal magnetic field to be mapped with high precision. We find coronal magnetic field strengths of 32 +/- 5 G above the sunspot, which decrease rapidly to values of approximately 1 G over a lateral distance of 7,000 km, consistent with previous isolated and unresolved estimations. Our results demonstrate a new, powerful technique that harnesses the omnipresent nature of sunspot oscillations to provide magnetic field mapping capabilities close to a magnetic source in the solar corona. Title: Towards a Data-Optimized Coronal Magnetic Field Model (DOC-FM): Synthetic Test Beds and Multiwavelength Forward Modeling Authors: Gibson, S. E.; Dalmasse, K.; Fan, Y.; Fineschi, S.; MacKay, D.; Rempel, M.; White, S. M. Bibcode: 2015AGUFMSH54B..04G Altcode: Understanding the physical state of the solar corona is key to deciphering the origins of space weather as well as to realistically representing the environment to be navigated by missions such as Solar Orbiter and Solar Probe Plus. However, inverting solar coronal observations to reconstruct this physical state -- and in particular the three-dimensional coronal magnetic field - is complicated by limited lines of sight and by projection effects. On the other hand, the sensitivity of multiwavelength observations to different physical mechanisms implies a potential for simultaneous probing of different parts of the coronal plasma. In order to study this complementarity, and to ultimately establish an optimal set of observations for constraining the three-dimensional coronal magnetic field, we are developing a suite of representative simulations to act as diagnostic test beds. We will present three such test beds: a coronal active region, a quiescent prominence, and a global corona. Each fully define the physical state of density, temperature, and vector magnetic field in three dimensions throughout the simulation domain. From these test beds, and using the FORWARD SolarSoft IDL codes, we will create a broad range of synthetic data. Radio observables will include intensity and circular polarization (including gyroresonance effects) and Faraday rotation for a range of frequencies. Infrared and visible forbidden line diagnostics of Zeeman and saturated Hanle effects will yield full Stokes vector (I, Q, U, V) synthetic data, and UV permitted line Hanle diagnostics will yield intensity and linear polarization. In addition, we will synthesize UV and SXR imager data, UV/EUV spectrometric data, and white light brightness and polarized brightness. All of these synthetic data, along with the "ground truth" physical state of the simulations from which they are derived, will be made available to the community for the purpose of testing coronal inversion techniques. Title: 3D Whole-prominence Fine Structure Modeling. II. Prominence Evolution Authors: Gunár, Stanislav; Mackay, Duncan H. Bibcode: 2015ApJ...812...93G Altcode: We use the new three-dimensional (3D) whole-prominence fine structure model to study the evolution of prominences and their fine structures in response to changes in the underlying photospheric magnetic flux distribution. The applied model combines a detailed 3D prominence magnetic field configuration with a realistic description of the prominence plasma distributed along multiple fine structures. In addition, we utilize an approximate Hα visualization technique to study the evolution of the visible cool prominence plasma both in emission (prominence) and absorption (filament). We show that the initial magnetic field configuration of the modeled prominence is significantly disturbed by the changing position of a single polarity of a magnetic bipole as the bipole is advected toward the main body of the filament. This leads to the creation of a barb, which becomes the dominant feature visible in the synthetic Hα images of both the prominence and filament views. The evolution of the bipole also creates conditions that lead to the disappearance and reappearance of large portions of the main body. We also show that an arch-like region containing a dark void (a bubble) can be naturally produced in the synthetic prominence Hα images. While not visible in terms of the magnetic field lines, it is due to a lack of Hα emission from low-pressure, low-density plasma located in shallow magnetic dips lying along the lines of sight intersecting the dark void. In addition, a quasi-vertical small-scale feature consisting of short and deep dips, piled one above the other, is produced. Title: Influence of Non-Potential Coronal Magnetic Topology on Solar-Wind Models Authors: Edwards, S. J.; Yeates, A. R.; Bocquet, F. -X.; Mackay, D. H. Bibcode: 2015SoPh..290.2791E Altcode: 2015arXiv151100427E By comparing a magneto-frictional model of the low-coronal magnetic-field to a potential-field source-surface model, we investigate the possible impact of non-potential magnetic structure on empirical solar-wind models. These empirical models (such as Wang-Sheeley-Arge) estimate the distribution of solar-wind speed solely from the magnetic-field structure in the low corona. Our models are computed in a domain between the solar surface and 2.5 solar radii, and they are extended to 0.1 AU using a Schatten current-sheet model. The non-potential field has a more complex magnetic skeleton and quasi-separatrix structures than the potential field, leading to different sub-structure in the solar-wind speed proxies. It contains twisted magnetic structures that can perturb the separatrix surfaces traced down from the base of the heliospheric current sheet. A significant difference between the models is the greater amount of open magnetic flux in the non-potential model. Using existing empirical formulae this leads to higher predicted wind speeds for two reasons: partly because magnetic-flux tubes expand less rapidly with height, but more importantly because more open-field lines are further from coronal-hole boundaries. Title: Future capabilities of CME polarimetric 3D reconstructions with the METIS instrument: A numerical test Authors: Pagano, P.; Bemporad, A.; Mackay, D. H. Bibcode: 2015A&A...582A..72P Altcode: 2015arXiv150805276P Context. Understanding the 3D structure of coronal mass ejections (CMEs) is crucial for understanding the nature and origin of solar eruptions. However, owing to the optical thinness of the solar corona we can only observe the line of sight integrated emission. As a consequence the resulting projection effects hide the true 3D structure of CMEs. To derive information on the 3D structure of CMEs from white-light (total and polarized brightness) images, the polarization ratio technique is widely used. The soon-to-be-launched METIS coronagraph on board Solar Orbiter will use this technique to produce new polarimetric images.
Aims: This work considers the application of the polarization ratio technique to synthetic CME observations from METIS. In particular we determine the accuracy at which the position of the centre of mass, direction and speed of propagation, and the column density of the CME can be determined along the line of sight.
Methods: We perform a 3D MHD simulation of a flux rope ejection where a CME is produced. From the simulation we (i) synthesize the corresponding METIS white-light (total and polarized brightness) images and (ii) apply the polarization ratio technique to these synthesized images and compare the results with the known density distribution from the MHD simulation. In addition, we use recent results that consider how the position of a single blob of plasma is measured depending on its projected position in the plane of the sky. From this we can interpret the results of the polarization ratio technique and give an estimation of the error associated with derived parameters.
Results: We find that the polarization ratio technique reproduces with high accuracy the position of the centre of mass along the line of sight. However, some errors are inherently associated with this determination. The polarization ratio technique also allows information to be derived on the real 3D direction of propagation of the CME. The determination of this is of fundamental importance for future space weather forecasting. In addition, we find that the column density derived from white-light images is accurate and we propose an improved technique where the combined use of the polarization ratio technique and white-light images minimizes the error in the estimation of column densities. Moreover, by applying the comparison to a set of snapshots of the simulation we can also assess the errors related to the trajectory and the expansion of the CME.
Conclusions: Our method allows us to thoroughly test the performance of the polarization ratio technique and allows a determination of the errors associated with it, which means that it can be used to quantify the results from the analysis of the forthcoming METIS observations in white light (total and polarized brightness). Finally, we describe a satellite observing configuration relative to the Earth that can allow the technique to be efficiently used for space weather predictions.

A movie attached to Fig. 15 is available in electronic form at http://www.aanda.org Title: High-resolution fine-structure synthetic imaging of an entire prominence using 3D whole-prominence fine structure modelling Authors: Gunar, Stanislav; Mackay, Duncan; Heinzel, Petr; Anzer, Ulrich Bibcode: 2015IAUGA..2251323G Altcode: The newly developed 3D whole-prominence fine structure (WPFS) model (Gunár & Mackay 2015) allows us for the first time to simulate entire prominences/filaments including their numerous fine structures. This model combines a 3D magnetic field configuration of an entire prominence obtained from non-linear force-free field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along hundreds of fine structures within the 3D magnetic model. The prominence plasma has realistic density and temperature distributions including the prominence-corona transition region.To produce the high-resolution synthetic H-alpha images of the WPFS model we use a novel fast approximate radiative transfer visualization technique (Heinzel et al. 2015). This allows us for the first time to produce images of the prominences in emission on the solar limb and filaments in absorption against the solar disk using a single model. The prominence plasma and magnetic field are described in the WPFS model on scales that allow us to produce synthetic images with resolution matching that of the state-of-the-art observations, or indeed that of the upcoming solar observatories, such as DKIST or Solar-C. Moreover, to complement the prominence/filament synthetic images we have consistent information about the magnetic field and plasma parameters everywhere in the modeled prominences. This allows us to investigate the apparent puzzling nature of the observed prominence and filament fine structures. We can also study the connections between the local configuration of the magnetic field and the observable structure of the finest prominence/filament features. In addition, we are able to investigate the prominence evolution. We can consistently study the influence of the varying photospheric flux distribution on the prominence magnetic field configuration and its effect on the observable prominence plasma. Title: 3D Whole-Prominence Fine Structure Modeling Authors: Gunár, Stanislav; Mackay, Duncan H. Bibcode: 2015ApJ...803...64G Altcode: We present the first 3D whole-prominence fine structure model. The model combines a 3D magnetic field configuration of an entire prominence obtained from nonlinear force-free field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Through the use of a novel radiative transfer visualization technique for the Hα line such plasma-loaded magnetic field model produces synthetic images of the modeled prominence comparable with high-resolution observations. This allows us for the first time to use a single technique to consistently study, in both emission on the limb and absorption against the solar disk, the fine structures of prominences/filaments produced by a magnetic field model. Title: Numerical Simulations of a Flux Rope Ejection Authors: Pagano, P.; Mackay, D. H.; Poedts, S. Bibcode: 2015JApA...36..123P Altcode: 2015JApA..tmp...19P Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. One of the most successful models to explain CMEs is the flux rope ejection model, where a magnetic flux rope is expelled from the solar corona after a long phase along which the flux rope stays in equilibrium while magnetic energy is being accumulated. However, still many questions are outstanding on the detailed mechanism of the ejection and observations continuously provide new data to interpret and put in the context. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. However, these observations are difficult to interpret in terms of basic physical mechanisms and quantities, thus, we need to compare equivalent quantities to test and improve our models. In our work, we intend to bridge the gap between models and observations with our model of flux rope ejection where we consistently describe the full life span of a flux rope from its formation to ejection. This is done by coupling the global non-linear force-free model (GNLFFF) built to describe the slow low- β formation phase, with a full MHD simulation run with the software MPI-AMRVAC, suitable to describe the fast MHD evolution of the flux rope ejection that happens in a heterogeneous β regime. We also explore the parameter space to identify the conditions upon which the ejection is favoured (gravity stratification and magnetic field intensity) and we produce synthesised AIA observations (171 Å and 211 Å). To carry this out, we run 3D MHD simulation in spherical coordinates where we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. Our model of flux rope ejection is successful in realistically describing the entire life span of a flux rope and we also set some conditions for the backgroud solar corona to favour the escape of the flux rope, so that it turns into a CME. Furthermore, our MHD simulation reproduces many of the features found in the AIA observations. Title: Formation and Large-Scale Patterns of Filament Channels and Filaments Authors: Mackay, Duncan H. Bibcode: 2015ASSL..415..355M Altcode: The properties and large-scale patterns of filament channels and filaments are considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long time-scales are described, along with the origin of the hemispheric pattern of filaments. Title: Stellar differential rotation and coronal time-scales Authors: Gibb, G. P. S.; Jardine, M. M.; Mackay, D. H. Bibcode: 2014MNRAS.443.3251G Altcode: 2014arXiv1407.3388G We investigate the time-scales of evolution of stellar coronae in response to surface differential rotation and diffusion. To quantify this, we study both the formation time and lifetime of a magnetic flux rope in a decaying bipolar active region. We apply a magnetic flux transport model to prescribe the evolution of the stellar photospheric field, and use this to drive the evolution of the coronal magnetic field via a magnetofrictional technique. Increasing the differential rotation (i.e. decreasing the equator-pole lap time) decreases the flux rope formation time. We find that the formation time is dependent upon the lap time and the surface diffusion time-scale through the relation τ_Form ∝ √{τ_Lapτ_Diff}. In contrast, the lifetimes of flux ropes are proportional to the lap time (τLife∝τLap). With this, flux ropes on stars with a differential rotation of more than eight times the solar value have a lifetime of less than 2 d. As a consequence, we propose that features such as solar-like quiescent prominences may not be easily observable on such stars, as the lifetimes of the flux ropes which host the cool plasma are very short. We conclude that such high differential rotation stars may have very dynamical coronae. Title: Simulating AIA observations of a flux rope ejection Authors: Pagano, P.; Mackay, D. H.; Poedts, S. Bibcode: 2014A&A...568A.120P Altcode: 2014arXiv1407.8397P Context. Coronal mass ejections (CMEs) are the most violent phenomena observed on the Sun. Currently, extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. In particular, observations now show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. While this is the case, these observations are difficult to interpret in terms of basic physical mechanisms and quantities. To fully understand CMEs we need to compare equivalent quantities derived from both observations and theoretical models. This will aid in bridging the gap between observations and models.
Aims: To this end, we aim to produce synthesised AIA observations from simulations of a flux rope ejection. To carry this out we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME.
Methods: We perform a simulation where a flux rope is ejected from the solar corona. From the density and temperature of the plasma in the simulation we synthesise AIA observations. The emission is then integrated along the line of sight using the instrumental response function of AIA.
Results: We sythesise observations of AIA in the channels at 304 Å, 171 Å, 335 Å, and 94 Å. The synthesised observations show a number of features similar to actual observations and in particular reproduce the general development of CMEs in the low corona as observed by AIA. In particular we reproduce an erupting and expanding arcade in the 304 Å and 171 Å channels with a high density core.
Conclusions: The ejection of a flux rope reproduces many of the features found in the AIA observations. This work is therefore a step forward in bridging the gap between observations and models, and can lead to more direct interpretations of EUV observations in terms of flux rope ejections. We plan to improve the model in future studies in order to perform a more quantitative comparison.

Movies associated with Figs. 3, 9, and 10 are available in electronic form at http://www.aanda.org Title: The Sun's Magnetic Field During a Grand Minimum of Activity Authors: Meyer, Karen; Mackay, Duncan Bibcode: 2014AAS...22411205M Altcode: During a grand minimum of solar activity, no sunspots are observed on the photosphere, but what might the Sun's magnetic field look like? One possibility is that there would be no active regions or larger scale magnetic activity. We have extended our photospheric model for small-scale magnetic flux evolution to cover the full Sun. As an initial study, we consider how the surface magnetic field of the Sun would look if only smaller-scale magnetic features were allowed to emerge. We also consider the resultant coronal and inner heliospheric magnetic fields, and discuss potential consequences of such fields for Earth. Title: Dynamic properties of bright points in an active region Authors: Keys, P. H.; Mathioudakis, M.; Jess, D. B.; Mackay, D. H.; Keenan, F. P. Bibcode: 2014A&A...566A..99K Altcode: 2014arXiv1405.3923K Context. Bright points (BPs) are small-scale, magnetic features ubiquitous across the solar surface. Previously, we have observed and noted their properties for quiet Sun regions. Here, we determine the dynamic properties of BPs using simultaneous quiet Sun and active region data.
Aims: The aim of this paper is to compare the properties of BPs in both active and quiet Sun regions and to determine any difference in the dynamics and general properties of BPs as a result of the varying magnetic activity within these two regions.
Methods: High spatial and temporal resolution G-band observations of active region AR11372 were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. Three subfields of varying polarity and magnetic flux density were selected with the aid of magnetograms obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Bright points within these subfields were subsequently tracked and analysed.
Results: It is found that BPs within active regions display attenuated velocity distributions with an average horizontal velocity of ~0.6 km s-1, compared to the quiet region which had an average velocity of 0.9 km s-1. Active region BPs are also ~21% larger than quiet region BPs and have longer average lifetimes (~132 s) than their quiet region counterparts (88 s). No preferential flow directions are observed within the active region subfields. The diffusion index (γ) is estimated at ~1.2 for the three regions.
Conclusions: We confirm that the dynamic properties of BPs arise predominately from convective motions. The presence of stronger field strengths within active regions is the likely reason behind the varying properties observed. We believe that larger amounts of magnetic flux will attenuate BP velocities by a combination of restricting motion within the intergranular lanes and by increasing the number of stagnation points produced by inhibited convection. Larger BPs are found in regions of higher magnetic flux density and we believe that lifetimes increase in active regions as the magnetic flux stabilises the BPs. Title: Data-constrained Magnetofrcitional Simulation of a Flux Rope Build-up in a Sigmoidal Active Region Authors: Savcheva, Antonia Stefanova; Mackay, D.; Meyer, K.; Gibb, G.; DeLuca, E. Bibcode: 2014shin.confE...3S Altcode: We present a data-constrained magnetofrictional (MF) simulation of the evolution over two days of the sigmoidal active region from 6-7 Dec 2007. The lower boundary condition is supplied by a series of line-of-sight (LoS) namgnetograms from MDI, but for the first time the initial condition is taken from a data-constrained non-linear force-free (NLFFF) model of the active region early on Dec 6. The NLFFF model is produced with the flux rope insertion method and is constrained by a LoS magnetogram, filament path from STEREO, and coronal loops from XRT. The initial condition is that of a sheared arcade and as time progresses the photospheric evolution builds a flux rope, which becomes unstable a few hours before the actual observed eruption. We show field lines and current density distributions over time and compare them to XRT images. We present the evolution of the free and potential energy and relative helicity in the region. We compare our results to a previous a simulation starting from a potential field as initial condition. Title: The solar cycle variation of topological structures in the global solar corona Authors: Platten, S. J.; Parnell, C. E.; Haynes, A. L.; Priest, E. R.; Mackay, D. H. Bibcode: 2014A&A...565A..44P Altcode: 2014arXiv1406.5333P Context. The complicated distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the (separatrix) surfaces that divide the field into topologically distinct regions, allowing open-field regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections with other separatrix surfaces (i.e., separators) are important likely energy release sites.
Aims: The aim of this paper is to investigate, throughout the solar cycle, the nature of coronal magnetic-field topologies that arise under the potential-field source-surface approximation. In particular, we characterise the typical global fields at solar maximum and minimum.
Methods: Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potential-field source-surface model. This allows the variations in the coronal skeleton to be studied over three solar cycles.
Results: The main building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes criss-crossing throughout the atmosphere. Many open-field regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar magnetic dipole. A strong dipole results in a simple large-scale structure involving just two large polar open-field regions, but, at short radial distances between ± 60° latitude, the small-scale topology is complex. If the solar magnetic dipole if weak, as in the recent minimum, then the low-latitude quiet-sun magnetic fields may be globally significant enough to create many disconnected open-field regions between ± 60° latitude, in addition to the two polar open-field regions. Title: Global-scale Consequences of Magnetic-helicity Injection and Condensation on the Sun Authors: Mackay, Duncan H.; DeVore, C. Richard; Antiochos, Spiro K. Bibcode: 2014ApJ...784..164M Altcode: In the recent paper of Antiochos, a new concept for the injection of magnetic helicity into the solar corona by small-scale convective motions and its condensation onto polarity inversion lines (PILs) was developed. We investigate this concept through global simulations of the Sun's photospheric and coronal magnetic fields, and compare the results with the hemispheric pattern of solar filaments. Assuming that the vorticity of the cells is predominantly counterclockwise/clockwise in the northern/southern hemisphere, the convective motions inject negative/positive helicity into each hemisphere. The simulations show that: (1) on a north-south oriented PIL, both differential rotation and convective motions inject the same sign of helicity, which matches that required to reproduce the hemispheric pattern of filaments. (2) On a high-latitude east-west oriented polar crown or subpolar crown PIL, the vorticity of the cells has to be approximately 2-3 times greater than the local differential-rotation gradient in order to overcome the incorrect sign of helicity injection from differential rotation. (3) In the declining phase of the cycle, as a bipole interacts with the polar field, in some cases, helicity condensation can reverse the effect of differential rotation along the east-west lead arm but not in all cases. The results show that this newly developed concept of magnetic helicity injection and condensation, in conjunction with the mechanisms used in Yeates et al., is a viable explanation for the hemispheric pattern of filaments. Future observational studies should focus on examining the vorticity component within convective motions to determine both its magnitude and latitudinal variation relative to the differential-rotation gradient on the Sun. Title: Simulating the Formation of a Sigmoidal Flux Rope in AR10977 from SOHO/MDI Magnetograms Authors: Gibb, G. P. S.; Mackay, D. H.; Green, L. M.; Meyer, K. A. Bibcode: 2014ApJ...782...71G Altcode: The modeling technique of Mackay et al. is applied to simulate the coronal magnetic field of NOAA active region AR10977 over a seven day period (2007 December 2-10). The simulation is driven with a sequence of line-of-sight component magnetograms from SOHO/MDI and evolves the coronal magnetic field though a continuous series of non-linear force-free states. Upon comparison with Hinode/XRT observations, results show that the simulation reproduces many features of the active region's evolution. In particular, it describes the formation of a flux rope across the polarity inversion line during flux cancellation. The flux rope forms at the same location as an observed X-ray sigmoid. After five days of evolution, the free magnetic energy contained within the flux rope was found to be 3.9 × 1030 erg. This value is more than sufficient to account for the B1.4 GOES flare observed from the active region on 2007 December 7. At the time of the observed eruption, the flux rope was found to contain 20% of the active region flux. We conclude that the modeling technique proposed in Mackay et al.—which directly uses observed magnetograms to energize the coronal field—is a viable method to simulate the evolution of the coronal magnetic field. Title: Where Do Solar Filaments Form? Authors: Mackay, Duncan H.; Gaizauskas, Victor; Yeates, Anthony R. Bibcode: 2014IAUS..300..445M Altcode: In the present study, we consider where large, stable solar filaments form relative to underlying magnetic polarities. We find that 92% of all large stable filaments form in magnetic configurations involving the interaction of two or more bipoles. Only 7% form above the Polarity Inversion Line (PIL) of a single bipole. This indicates that a key element in the formation of large-scale stable filaments is the convergence of magnetic flux, resulting in either flux cancellation or coronal reconnection. Title: Magnetohydrodynamic study on the effect of the gravity stratification on flux rope ejections Authors: Pagano, Paolo; Mackay, Duncan H.; Poedts, Stefaan Bibcode: 2014IAUS..300..197P Altcode: Coronal Mass Ejections (CMEs) are one of the most violent phenomena found on the Sun. One model to explain their occurrence is the flux rope ejection model where these magnetic structures firt form in the solar corona then are ejected to produce a CME. We run simulations coupling two models. The Global Non-Linear Force-Free Field (GNLFFF) evolution model to follow the quasi-static formation of a flux rope and MHD simulations for the production of a CME through the loss of equilibrium and ejection of this flux rope in presence of solar gravity and density stratification. Our realistic multi-beta simulations describe the CME following the flux rope ejection and highlight the decisive role played by the gravity stratification on the CME propagation speed. Title: Local and global coronal magnetic-field extrapolation Authors: Yeates, Anthony; Mackay, Duncan Bibcode: 2014cosp...40E3714Y Altcode: Extrapolation relies on assumptions, and coronal magnetic field modelling based on photospheric magnetogram data is no exception. A current research problem is how best to go beyond the current-free assumption of traditional potential-field extrapolations. I will argue that realistic modelling requires not just the input of a photospheric magnetogram at a single time, but rather a time history of such data. As evidence for this viewpoint, I will present results from a global model that takes into account this time-dependence to approximate a continuously evolving sequence of nonlinear force-free fields. Not only does magnetic helicity accumulate in magnetic flux ropes, which can eventually lose equilibrium and "erupt", but we find that the local magnetic direction in these ropes can be sensitive to the time history over multiple years. This allows for an observational test of the model using observations of Halpha filaments. Title: Explaining the Hemispheric Pattern of Filament Chirality Authors: Mackay, Duncan H.; Yeates, Anthony R. Bibcode: 2014IAUS..300..172M Altcode: Solar filaments are known to exhibit a hemispheric pattern in their chirality, where dextral/sinistral filaments dominate in the northern/southern hemisphere. We show that this pattern may be explained through data driven 3D global magnetic field simulations of the Sun's large-scale magnetic field. Through a detailed comparison with 109 filaments over a 6 month period, the model correctly reproduces the filament chirality and helicity with a 96% agreement. The data driven simulation is extended to run over a full solar cycle, where predictions are made for the spatial and temporal dependence of the hemispheric pattern over the solar cycle. Title: The Influence of the Magnetic Field on Running Penumbral Waves in the Solar Chromosphere Authors: Jess, D. B.; Reznikova, V. E.; Van Doorsselaere, T.; Keys, P. H.; Mackay, D. H. Bibcode: 2013ApJ...779..168J Altcode: 2013arXiv1310.7939J We use images of high spatial and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a near-circular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the period-distance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and force-free field extrapolations, we attribute this behavior to the cut-off frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cut-off frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magneto-acoustic waves generated in the photosphere. Title: Effect of gravitational stratification on the propagation of a CME Authors: Pagano, P.; Mackay, D. H.; Poedts, S. Bibcode: 2013A&A...560A..38P Altcode: 2013arXiv1310.6960P Context. Coronal mass ejections (CMEs) are the most violent phenomenon found on the Sun. One model that explains their occurrence is the flux rope ejection model. A magnetic flux rope is ejected from the solar corona and reaches the interplanetary space where it interacts with the pre-existing magnetic fields and plasma. Both gravity and the stratification of the corona affect the early evolution of the flux rope.
Aims: Our aim is to study the role of gravitational stratification on the propagation of CMEs. In particular, we assess how it influences the speed and shape of CMEs and under what conditions the flux rope ejection becomes a CME or when it is quenched.
Methods: We ran a set of MHD simulations that adopt an eruptive initial magnetic configuration that has already been shown to be suitable for a flux rope ejection. We varied the temperature of the backgroud corona and the intensity of the initial magnetic field to tune the gravitational stratification and the amount of ejected magnetic flux. We used an automatic technique to track the expansion and the propagation of the magnetic flux rope in the MHD simulations. From the analysis of the parameter space, we evaluate the role of gravitational stratification on the CME speed and expansion.
Results: Our study shows that gravitational stratification plays a significant role in determining whether the flux rope ejection will turn into a full CME or whether the magnetic flux rope will stop in the corona. The CME speed is affected by the background corona where it travels faster when the corona is colder and when the initial magnetic field is more intense. The fastest CME we reproduce in our parameter space travels at ~850 km s-1. Moreover, the background gravitational stratification plays a role in the side expansion of the CME, and we find that when the background temperature is higher, the resulting shape of the CME is flattened more.
Conclusions: Our study shows that although the initiation mechanisms of the CME are purely magnetic, the background coronal plasma plays a key role in the CME propagation, and full MHD models should be applied when one focuses especially on the production of a CME from a flux rope ejection.

Movies are available in electronic form at http://www.aanda.org Title: Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms Authors: Meyer, K. A.; Mackay, D. H.; van Ballegooijen, A. A.; Parnell, C. E. Bibcode: 2013SoPh..286..357M Altcode: 2013arXiv1303.1342M This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. (Solar Phys.272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5 - 0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release. Title: A Non-Linear Force-Free Field Model for the Solar Magnetic Carpet Authors: Meyer, Karen; Mackay, D.; van Ballegooijen, A.; Parnell, C. Bibcode: 2013SPD....4430201M Altcode: The magnetic carpet is defined to be the small-scale photospheric magnetic field of the quiet-Sun. Recent high resolution, high cadence observations have shown that although small-scale, the magnetic carpet is far from 'quiet', it is continually evolving in a complex and dynamic manner. I will present a two-component model for the dynamic evolution of the Sun's magnetic carpet. The first component is a 2D model for the photospheric evolution of the small-scale solar magnetic field, that reproduces many observed parameters. The basic evolution of magnetic elements within the model is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. The synthetic magnetograms produced by the 2D model are then applied as photospheric boundary data to drive the continuous evolution of a 3D non-linear force-free coronal field. We studied the resultant complex, small-scale coronal magnetic field, in particular the energetics of the field. Title: Filament Chirality over an Entire Cycle Determined with an Automated Detection Module -- a Neat Surprise! Authors: Martens, Petrus C.; Yeates, A. R.; Mackay, D.; Pillai, K. G. Bibcode: 2013SPD....4410104M Altcode: Using metadata produced by automated solar feature detection modules developed for SDO (Martens et al. 2012) we have discovered some trends in filament chirality and filament-sigmoid relations that are new and in part contradict the current consensus. Automated detection of solar features has the advantage over manual detection of having the detection criteria applied consistently, and in being able to deal with enormous amounts of data, like the 1 Terabyte per day that SDO produces. Here we use the filament detection module developed by Bernasconi, which has metadata from 2000 on, and the sigmoid sniffer, which has been producing metadata from AIA 94 A images since October 2011. The most interesting result we find is that the hemispheric chirality preference for filaments (dextral in the north, and v.v.), studied in detail for a three year period by Pevtsov et al. (2003) seems to disappear during parts of the decline of cycle 23 and during the extended solar minimum that followed. Moreover the hemispheric chirality rule seems to be much less pronounced during the onset of cycle 24. For sigmoids we find the expected correlation between chirality and handedness (S or Z) shape but not as strong as expected. Title: Puzzling nature of the fine structure of quiescent prominences and filaments Authors: Gunár, Stanislav; Heinzel, Petr; Anzer, Ulrich; Mackay, Duncan H. Bibcode: 2013JPhCS.440a2035G Altcode: Even after more than 160 years of observations and modelling of solar prominences their true nature contains many open questions. In this work we argue that current 2D prominence fine structure models can help us to understand the puzzling connection between quasi-vertical fine structures often seen in quiescent prominences observed on the solar limb and horizontally aligned dark fibrils representing the fine structures of prominences observed in absorption against the solar disk (filaments). Title: Magnetohydrodynamic simulations of the ejection of a magnetic flux rope Authors: Pagano, P.; Mackay, D. H.; Poedts, S. Bibcode: 2013A&A...554A..77P Altcode: Context. Coronal mass ejections (CME's) are one of the most violent phenomena found on the Sun. One model to explain their occurrence is the flux rope ejection model. In this model, magnetic flux ropes form slowly over time periods of days to weeks. They then lose equilibrium and are ejected from the solar corona over a few hours. The contrasting time scales of formation and ejection pose a serious problem for numerical simulations.
Aims: We simulate the whole life span of a flux rope from slow formation to rapid ejection and investigate whether magnetic flux ropes formed from a continuous magnetic field distribution, during a quasi-static evolution, can erupt to produce a CME.
Methods: To model the full life span of magnetic flux ropes we couple two models. The global non-linear force-free field (GNLFFF) evolution model is used to follow the quasi-static formation of a flux rope. The MHD code ARMVAC is used to simulate the production of a CME through the loss of equilibrium and ejection of this flux rope.
Results: We show that the two distinct models may be successfully coupled and that the flux rope is ejected out of our simulation box, where the outer boundary is placed at 2.5 R⊙. The plasma expelled during the flux rope ejection travels outward at a speed of 100 km s-1, which is consistent with the observed speed of CMEs in the low corona.
Conclusions: Our work shows that flux ropes formed in the GNLFFF can lead to the ejection of a mass loaded magnetic flux rope in full MHD simulations. Coupling the two distinct models opens up a new avenue of research to investigate phenomena where different phases of their evolution occur on drastically different time scales.

Movies are available in electronic form at http://www.aanda.org Title: The Storage and Dissipation of Magnetic Energy in the Quiet Sun Corona Determined from SDO/HMI Magnetograms Authors: Meyer, K. A.; Sabol, J.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2013ApJ...770L..18M Altcode: In recent years, higher cadence, higher resolution observations have revealed the quiet-Sun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the small-scale coronal magnetic field exhibits similar complexity. For the first time, the quiet-Sun coronal magnetic field is continuously evolved through a series of non-potential, quasi-static equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain small-scale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex small-scale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona. Title: Non-linear force-free magnetic dip models of quiescent prominence fine structures Authors: Gunár, S.; Mackay, D. H.; Anzer, U.; Heinzel, P. Bibcode: 2013A&A...551A...3G Altcode:
Aims: We use 3D non-linear force-free magnetic field modeling of prominence/filament magnetic fields to develop the first 2D models of individual prominence fine structures based on the 3D configuration of the magnetic field of the whole prominence.
Methods: We use an iterative technique to fill the magnetic dips produced by the 3D modeling with realistic prominence plasma in hydrostatic equilibrium and with a temperature structure that contains the prominence-corona transition region. With this well-defined plasma structure the radiative transfer can be treated in detail in 2D and the resulting synthetic emission can be compared with prominence/filament observations.
Results: Newly developed non-linear force-free magnetic dip models are able to produce synthetic hydrogen Lyman spectra in a qualitative agreement with a range of quiescent prominence observations. Moreover, the plasma structure of these models agrees with the gravity induced prominence fine structure models which have already been shown to produce synthetic spectra in good qualitative agreement with several observed prominences.
Conclusions: We describe in detail the iterative technique which can be used to produce realistic plasma models of prominence fine structures located in prominence magnetic field configurations containing dips, obtained using any kind of magnetic field modeling. Title: SWIFF: Space weather integrated forecasting framework Authors: Lapenta, Giovanni; Pierrard, Viviane; Keppens, Rony; Markidis, Stefano; Poedts, Stefaan; Šebek, Ondřej; Trávníček, Pavel M.; Henri, Pierre; Califano, Francesco; Pegoraro, Francesco; Faganello, Matteo; Olshevsky, Vyacheslav; Restante, Anna Lisa; Nordlund, Åke; Trier Frederiksen, Jacob; Mackay, Duncan H.; Parnell, Clare E.; Bemporad, Alessandro; Susino, Roberto; Borremans, Kris Bibcode: 2013JSWSC...3A..05L Altcode: SWIFF is a project funded by the Seventh Framework Programme of the European Commission to study the mathematical-physics models that form the basis for space weather forecasting. The phenomena of space weather span a tremendous scale of densities and temperature with scales ranging 10 orders of magnitude in space and time. Additionally even in local regions there are concurrent processes developing at the electron, ion and global scales strongly interacting with each other. The fundamental challenge in modelling space weather is the need to address multiple physics and multiple scales. Here we present our approach to take existing expertise in fluid and kinetic models to produce an integrated mathematical approach and software infrastructure that allows fluid and kinetic processes to be modelled together. SWIFF aims also at using this new infrastructure to model specific coupled processes at the Solar Corona, in the interplanetary space and in the interaction at the Earth magnetosphere. Title: The Sun's Global Photospheric and Coronal Magnetic Fields: Observations and Models Authors: Mackay, Duncan H.; Yeates, Anthony R. Bibcode: 2012LRSP....9....6M Altcode: 2012arXiv1211.6545M In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the large-scale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in non-eruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified. Title: Chirality of High-latitude Filaments over Solar Cycle 23 Authors: Yeates, A. R.; Mackay, D. H. Bibcode: 2012ApJ...753L..34Y Altcode: 2012arXiv1206.2327Y A non-potential quasi-static evolution model coupling the Sun's photospheric and coronal magnetic fields is applied to the problem of filament chirality at high latitudes. For the first time, we run a continuous 15 year simulation, using bipolar active regions determined from US National Solar Observatory, Kitt Peak magnetograms between 1996 and 2011. Using this simulation, we are able to address the outstanding question of whether magnetic helicity transport from active latitudes can overcome the effect of differential rotation at higher latitudes. Acting alone, differential rotation would produce high-latitude filaments with opposite chirality to the majority type in each hemisphere. We find that differential rotation can indeed lead to opposite chirality at high latitudes, but only for around 5 years of the solar cycle following the polar field reversal. At other times, including the rising phase, transport of magnetic helicity from lower latitudes overcomes the effect of in situ differential rotation, producing the majority chirality even on the polar crowns at polar field reversal. These simulation predictions will allow for future testing of the non-potential coronal model. The results indicate the importance of long-term memory and helicity transport from active latitudes when modeling the structure and topology of the coronal magnetic field at higher latitudes. Title: The Sun's global magnetic field Authors: Mackay, D. H. Bibcode: 2012RSPTA.370.3151M Altcode: No abstract at ADS Title: Solar Magnetic Carpet II: Coronal Interactions of Small-Scale Magnetic Fields Authors: Meyer, K. A.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2012SoPh..278..149M Altcode: 2012arXiv1211.3924M This paper is the second in a series of studies working towards constructing a realistic, evolving, non-potential coronal model for the solar magnetic carpet. In the present study, the interaction of two magnetic elements is considered. Our objectives are to study magnetic energy build-up, storage and dissipation as a result of emergence, cancellation, and flyby of these magnetic elements. In the future these interactions will be the basic building blocks of more complicated simulations involving hundreds of elements. Each interaction is simulated in the presence of an overlying uniform magnetic field, which lies at various orientations with respect to the evolving magnetic elements. For these three small-scale interactions, the free energy stored in the field at the end of the simulation ranges from 0.2 - 2.1×1026 ergs, whilst the total energy dissipated ranges from 1.3 - 6.3×1026 ergs. For all cases, a stronger overlying field results in higher energy storage and dissipation. For the cancellation and emergence simulations, motion perpendicular to the overlying field results in the highest values. For the flyby simulations, motion parallel to the overlying field gives the highest values. In all cases, the free energy built up is sufficient to explain small-scale phenomena such as X-ray bright points or nanoflares. In addition, if scaled for the correct number of magnetic elements for the volume considered, the energy continually dissipated provides a significant fraction of the quiet Sun coronal heating budget. Title: Using Kepler transit observations to measure stellar spot belt migration rates Authors: Llama, J.; Jardine, M.; Mackay, D. H.; Fares, R. Bibcode: 2012MNRAS.422L..72L Altcode: 2012arXiv1202.3785L; 2012MNRAS.tmpL.421L Planetary transits provide a unique opportunity to investigate the surface distributions of star spots. Our aim is to determine if, with continuous observation (such as the data that will be provided by the Kepler mission), we can in addition measure the rate of drift of the spot belts. We begin by simulating magnetic cycles suitable for the Sun and more active stars, incorporating both flux emergence and surface transport. This provides the radial magnetic field distribution on the stellar surface as a function of time. We then model the transit of a planet whose orbital axis is misaligned with the stellar rotation axis. Such a planet could occult spots at a range of latitudes. This allows us to complete the forward modelling of the shape of the transit light curve. We then attempt the inverse problem of recovering spot locations from the transit alone. From this we determine if transit light curves can be used to measure spot belt locations as a function of time. We find that for low-activity stars such as the Sun, the 3.5-year Kepler window is insufficient to determine this drift rate. For more active stars, it may be difficult to distinguish subtle differences in the nature of flux emergence, such as the degree of overlap of the 'butterfly wings'. The rate and direction of drift of the spot belts can however be determined for these stars. This would provide a critical test of dynamo theory. Title: The structure and evolution of global solar magnetic fields Authors: Mackay, Duncan H. Bibcode: 2011IAUS..273..290M Altcode: This review will discuss both observational and theoretical aspects of the Sun's global magnetic field. First recent observations will be described, along with the main physical processes leading to the time evolution and structure of the global field. Following this, recent theoretical models of both the global surface and coronal magnetic field will be presented. The application of these models to the structure of the corona, formation of solar filaments, the onset of CMEs and finally the origin and variation of the Sun's open flux will be discussed. Title: Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms Authors: Meyer, K. A.; Mackay, D. H.; van Ballegooijen, A. A.; Parnell, C. E. Bibcode: 2011SoPh..272...29M Altcode: 2011SoPh..tmp..294M; 2011SoPh..tmp..198M; 2011SoPh..tmp..319M; 2011SoPh..tmp..267M; 2011arXiv1108.1080M This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×1016 - 1019 Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×1016 Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling. Title: Magnetic helicity evolution inside a hexagonal convective cell Authors: Smyrli, Aimilia; Mackay, Duncan; Zuccarello, Francesca Bibcode: 2011IAUS..274..192S Altcode: Magnetic helicity has received considerable attention in the area of fluid dynamics. Recently, this quantity is attracting the interest of solar physicists and much research has been carried out related to magnetic helicity generation and transport through different solar layers, starting from the interior and the convection zone, towards the photosphere, the corona and finally into the heliosphere. Taking into account the global importance of supergranular cells in convection theories, we study the motion of magnetic features into such a geometrical element simplified as hexagonal cell and we analyse the results in terms of the accumulated magnetic helicity. We compute the emergence of a bipole inside the hexagonal cell and its motion from the centre of the cell towards its sides and its vertices, where the magnetic elements are considered to be sinking down. Multiple bipoles are also considered and phenomena such as cancellation, coalescence and fragmentation are also investigated. We find that the most important process for the accumulation of magnetic helicity is the shear motion between the polarities. The magnetic helicity accumulation changes its trend when one polarity reaches the side of the hexagon, and later the vertex. It has zero value when there is no shear motion inside the hexagonal cell, and it is constant when there is no shear between the two polarities during their motion along the cell sides. Title: Modeling the Dispersal of an Active Region: Quantifying Energy Input into the Corona Authors: Mackay, Duncan H.; Green, L. M.; van Ballegooijen, Aad Bibcode: 2011ApJ...729...97M Altcode: 2011arXiv1102.5296M In this paper, a new technique for modeling nonlinear force-free fields directly from line-of-sight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the evolution of coronal magnetic fields between successive force-free equilibria over long periods of time. It is illustrated by applying it to SOHO: MDI observations of a decaying active region, NOAA AR 8005. The active region is modeled during a four-day period around its central meridian passage. Over this time, the dispersal of the active region is dominated by random motions due to small-scale convective cells. Through studying the buildup of magnetic energy in the model, it is found that such small-scale motions may inject anywhere from (2.5-3) × 1025 erg s-1 of free magnetic energy into the coronal field. Most of this energy is stored within the center of the active region in the low corona, below 30 Mm. After four days, the buildup of free energy is 10% that of the corresponding potential field. This energy buildup is sufficient to explain the radiative losses at coronal temperatures within the active region. Small-scale convective motions therefore play an integral part in the energy balance of the corona. This new technique has wide ranging applications with the new high-resolution, high-cadence observations from the SDO:HMI and SDO:AIA instruments. Title: Trend of photospheric magnetic helicity flux in active regions generating halo coronal mass ejections Authors: Smyrli, A.; Zuccarello, F.; Romano, P.; Zuccarello, F. P.; Guglielmino, S. L.; Spadaro, D.; Hood, A. W.; Mackay, D. Bibcode: 2010A&A...521A..56S Altcode: Context. Coronal mass ejections (CMEs) are very energetic events (~ 1032 erg) initiated in the solar atmosphere, resulting in the expulsion of magnetized plasma clouds that propagate into interplanetary space. It has been proposed that CMEs can play an important role in shedding magnetic helicity, avoiding its endless accumulation in the corona.
Aims: The aim of this work is to investigate the behavior of magnetic helicity accumulation in sites where the initiation of CMEs occurred to determine whether and how changes in magnetic helicity accumulation are temporally correlated with CME occurrence.
Methods: We used MDI/SOHO line-of-sight magnetograms to calculate magnetic flux evolution and magnetic helicity injection in 10 active regions that gave rise to halo CMEs observed during the period 2000 February to 2003 June.
Results: The magnetic helicity injection does not have a unique trend in the events analyzed: in 40% of the cases it shows a large sudden and abrupt change that is temporally correlated with a CME occurrence, while in the other cases it shows a steady monotonic trend, with a slight change in magnetic helicity at CME occurrence.
Conclusions: The results obtained from the sample of events that we have analyzed indicate that major changes in magnetic helicity flux are observed in active regions characterized by emergence of new magnetic flux and/or generating halo CMEs associated with X-class flares or filament eruptions. In some of the analyzed cases the changes in magnetic helicity flux follow the CME events and can be attributed to a process of restoring a torque balance between the subphotospheric and the coronal domain of the flux tubes.

Appendix is only available in electronic form at http://www.aanda.org Title: A nonpotential model for the Sun's open magnetic flux Authors: Yeates, A. R.; Mackay, D. H.; van Ballegooijen, A. A.; Constable, J. A. Bibcode: 2010JGRA..115.9112Y Altcode: 2010JGRA..11509112Y; 2010arXiv1006.4011Y Measurements of the interplanetary magnetic field (IMF) over several solar cycles do not agree with computed values of open magnetic flux from potential field extrapolations. The discrepancy becomes greater around solar maximum in each cycle when the IMF can be twice as strong as predicted by the potential field model. Here we demonstrate that this discrepancy may be resolved by allowing for electric currents in the low corona (below 2.5R$\odot$). We present a quasi-static numerical model of the large-scale coronal magnetic evolution, which systematically produces these currents through flux emergence and shearing by surface motions. The open flux is increased by 75%-85% at solar maximum, but only 25% at solar minimum, bringing it in line with estimates from IMF measurements. The additional open flux in the nonpotential model arises through inflation of the magnetic field by electric currents, with superimposed fluctuations due to coronal mass ejections. The latter are modeled by the self-consistent ejection of twisted magnetic flux ropes. Title: Modelling stellar coronae from surface magnetograms: the role of missing magnetic flux Authors: Johnstone, C.; Jardine, M.; Mackay, D. H. Bibcode: 2010MNRAS.404..101J Altcode: 2010arXiv1001.2526J; 2010MNRAS.tmp..379J Recent advances in spectropolarimetry have allowed the reconstruction of stellar coronal magnetic fields. This uses Zeeman-Doppler magnetograms (ZDI) of the surface magnetic field as a lower boundary condition. The ZDI maps, however, suffer from the absence of information about the magnetic field over regions of the surface due to the presence of dark starspots and portions of the surface out of view due to a tilt in the rotation axis. They also suffer from finite resolution which leads to small-scale field structures being neglected. This paper explores the effects of this loss of information on the extrapolated coronal fields. For this, we use simulated stellar surface magnetic maps for two hypothetical stars. Using the potential field approximation, the coronal fields and emission measures are calculated. This is repeated for the cases of missing information due to, (i) starspots, (ii) a large area of the stellar surface out of view and (iii) a finite resolution. The largest effect on the magnetic field structure arises when a significant portion of the stellar surface remains out of view. This changes the nature of the field lines that connect to this obscured hemisphere. None the less, the field structure in the visible hemisphere is reliably reproduced. Thus, the calculation of the locations and surface filling factors of accretion funnels is reasonably well reproduced for the observed hemisphere. The decrease with height of the magnetic pressure, which is important in calculating disc truncation radii for accreting stars, is also largely unaffected in the equatorial plane. The fraction of surface flux that is open and therefore able to supply angular momentum loss in a wind, however, is often overestimated in the presence of missing flux. The magnitude and rotational modulation of the calculated emission measures is consistently decreased by the loss of magnetic flux in dark starspots. For very inactive stars, this may make it impossible to recover a magnetic cycle in the coronal emission. Finite resolution has little effect on those quantities, such as the emission measure and the average coronal electron density, that can currently be observed. Title: Physics of Solar Prominences: II—Magnetic Structure and Dynamics Authors: Mackay, D. H.; Karpen, J. T.; Ballester, J. L.; Schmieder, B.; Aulanier, G. Bibcode: 2010SSRv..151..333M Altcode: 2010SSRv..tmp...32M; 2010arXiv1001.1635M Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them. Title: Comparison of a Global Magnetic Evolution Model with Observations of Coronal Mass Ejections Authors: Yeates, A. R.; Attrill, G. D. R.; Nandy, Dibyendu; Mackay, D. H.; Martens, P. C. H.; van Ballegooijen, A. A. Bibcode: 2010ApJ...709.1238Y Altcode: 2009arXiv0912.3347Y The relative importance of different initiation mechanisms for coronal mass ejections (CMEs) on the Sun is uncertain. One possible mechanism is the loss of equilibrium of coronal magnetic flux ropes formed gradually by large-scale surface motions. In this paper, the locations of flux rope ejections in a recently developed quasi-static global evolution model are compared with observed CME source locations over a 4.5 month period in 1999. Using extreme ultraviolet data, the low-coronal source locations are determined unambiguously for 98 out of 330 CMEs. An alternative method of determining the source locations using recorded Hα events was found to be too inaccurate. Despite the incomplete observations, positive correlation (with coefficient up to 0.49) is found between the distributions of observed and simulated ejections, but only when binned into periods of 1 month or longer. This binning timescale corresponds to the time interval at which magnetogram data are assimilated into the coronal simulations, and the correlation arises primarily from the large-scale surface magnetic field distribution; only a weak dependence is found on the magnetic helicity imparted to the emerging active regions. The simulations are limited in two main ways: they produce fewer ejections, and they do not reproduce the strong clustering of observed CME sources into active regions. Due to this clustering, the horizontal gradient of radial photospheric magnetic field is better correlated with the observed CME source distribution (coefficient 0.67). Our results suggest that while the gradual formation of magnetic flux ropes over weeks can account for many observed CMEs, especially at higher latitudes, there exists a second class of CMEs (at least half) for which dynamic active region flux emergence on shorter timescales must be the dominant factor. Improving our understanding of CME initiation in future will require both more comprehensive observations of CME source regions and more detailed magnetic field simulations. Title: Trend of photospheric helicity flux in active regions generating halo CMEs Authors: Smyrli, Aimilia; Zuccarello, Francesco; Zuccarello, Francesca; Romano, Paolo; Guglielmino, Salvatore Luigi; Spadaro, Daniele; Hood, Alan; Mackay, Duncan Bibcode: 2010cosp...38.1860S Altcode: 2010cosp.meet.1860S Coronal Mass Ejections (CMEs) are very energetic events initiated in the solar atmosphere, re-sulting in the expulsion of magnetized plasma clouds that propagate into interplanetary space. It has been proposed that CMEs can play an important role in shedding magnetic helicity, avoiding its endless accumulation in the corona. We therefore investigated the behavior of magnetic helicity accumulation in sites where the initiation of CMEs occurred, in order to de-termine whether and how changes in magnetic helicity accumulation are temporally correlated with CME occurrence. After identifying the active regions (AR) where the CMEs were ini-tiated by means of a double cross-check based on the flaring-eruptive activity and the use of SOHO/EIT difference images, we used MDI magnetograms to calculate magnetic flux evolu-tion, magnetic helicity injection rate and magnetic helicity injection in 10 active regions that gave rise to 12 halo CMEs observed during the period February 2000 -June 2003. No unique behavior in magnetic helicity injection accompanying halo CME occurrence is found. In fact, in some cases there is an abrupt change in helicity injection timely correlated with the CME event, while in some others no significant variation is recorded. However, our analysis show that the most significant changes in magnetic flux and magnetic helicity injection are associated with impulsive CMEs rather than gradual CMEs. Moreover, the most significant changes in mag-netic helicity are observed when X-class flares or eruptive filaments occur, while the occurrence of flares of class C or M seems not to affect significantly the magnetic helicity accumulation. Title: A Non-Linear Force-Free Field Model for the Evolving Magnetic Structure of Solar Filaments Authors: Mackay, Duncan H.; van Ballegooijen, A. A. Bibcode: 2009SoPh..260..321M Altcode: In this paper the effect of a small magnetic element approaching the main body of a solar filament is considered through non-linear force-free field modeling. The filament is represented by a series of magnetic dips. Once the dips are calculated, a simple hydrostatic atmosphere model is applied to determine which structures have sufficient column mass depth to be visible in Hα. Two orientations of the bipole are considered, either parallel or anti-parallel to the overlying arcade. The magnetic polarity that lies closest to the filament is then advected towards the filament. Initially for both the dominant and minority polarity advected elements, right/left bearing barbs are produced for dextral/sinsitral filaments. The production of barbs due to dominant polarity elements is a new feature. In later stages the filament breaks into two dipped sections and takes a highly irregular, non-symmetrical form with multiple pillars. The two sections are connected by field lines with double dips even though the twist of the field is less than one turn. Reconnection is not found to play a key role in the break up of the filament. The non-linear force-free fields produce very different results to extrapolated linear-force free fields. For the cases considered here the linear force-free field does not produce the break up of the filament nor the production of barbs as a result of dominant polarity elements. Title: Solar Cycle Variations of Coronal Null Points: Implications for the Magnetic Breakout Model of Coronal Mass Ejections Authors: Cook, G. R.; Mackay, D. H.; Nandy, Dibyendu Bibcode: 2009ApJ...704.1021C Altcode: In this paper, we investigate the solar cycle variation of coronal null points and magnetic breakout configurations in spherical geometry, using a combination of magnetic flux transport and potential field source surface models. Within the simulations, a total of 2843 coronal null points and breakout configurations are found over two solar cycles. It is found that the number of coronal nulls present at any time varies cyclically throughout the solar cycle, in phase with the flux emergence rate. At cycle maximum, peak values of 15-17 coronal nulls per day are found. No significant variation in the number of nulls is found from the rising to the declining phase. This indicates that the magnetic breakout model is applicable throughout both phases of the solar cycle. In addition, it is shown that when the simulations are used to construct synoptic data sets, such as those produced by Kitt Peak, the number of coronal nulls drops by a factor of 1/6. The vast majority of the coronal nulls are found to lie above the active latitudes and are the result of the complex nature of the underlying active region fields. Only 8% of the coronal nulls are found to be connected to the global dipole. Another interesting feature is that 18% of coronal nulls are found to lie above the equator due to cross-equatorial interactions between bipoles lying in the northern and southern hemispheres. As the majority of coronal nulls form above active latitudes, their average radial extent is found to be in the low corona below 1.25 R sun (175, 000 km above the photosphere). Through considering the underlying photospheric flux, it is found that 71% of coronal nulls are produced though quadrupolar flux distributions resulting from bipoles in the same hemisphere interacting. When the number of coronal nulls present in each rotation is compared to the number of bipoles emerging, a wide scatter is found. The ratio of coronal nulls to emerging bipoles is found to be approximately 1/3. Overall, the spatio-temporal evolution of coronal nulls is found to follow the typical solar butterfly diagram and is in qualitative agreement with the observed time dependence of coronal mass ejection source-region locations. Title: Non-potential Enhancement of the Sun's Open Magnetic Flux Authors: Yeates, Anthony R.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2009shin.confE.182Y Altcode: Measurements of the interplanetary magnetic field (IMF) over several solar cycles do not agree with expected values of open magnetic flux from potential field models. The discrepancy becomes greater around solar maximum in each cycle, when the IMF can be twice as strong as predicted by the models. It has previously been suggested that the increased rate of coronal mass ejections around solar maximum could be responsible for enhancing the open flux. We test this idea by removing the potential field assumption in simulations of the coronal magnetic field evolution over the solar cycle. The simulations use magneto-frictional relaxation in response to flux emergence and surface flux transport, and allow for the development of coronal currents and for the ejection of twisted magnetic flux ropes. Preliminary results show that the non-potential fields have significantly more open flux than potential extrapolations, in agreement with IMF observations. We find that the additional open flux arises from two separate effects: temporary enhancement due to coronal mass ejections, and a background enhancement due to the non-potential nature of the force-free equilibria. (Supported by NASA/LWS grant NNG05GK32G, and NASA contract NNM07AB07C to SAO.) Title: Initiation of Coronal Mass Ejections in a Global Evolution Model Authors: Yeates, A. R.; Mackay, D. H. Bibcode: 2009ApJ...699.1024Y Altcode: 2009arXiv0904.4419Y Loss of equilibrium of magnetic flux ropes is a leading candidate for the origin of solar coronal mass ejections (CMEs). The aim of this paper is to explore to what extent this mechanism can account for the initiation of CMEs in the global context. A simplified MHD model for the global coronal magnetic field evolution in response to flux emergence and shearing by large-scale surface motions is described and motivated. Using automated algorithms for detecting flux ropes and ejections in the global magnetic model, the effects of key simulation parameters on the formation of flux ropes and the number of ejections are considered, over a 177 day period in 1999. These key parameters include the magnitude and sign of magnetic helicity emerging in active regions, and coronal diffusion. The number of flux ropes found in the simulation at any one time fluctuates between about 28 and 48, sustained by the emergence of new bipolar regions, but with no systematic dependence on the helicity of these regions. However, the emerging helicity does affect the rate of flux rope ejections, which doubles from 0.67 per day if the bipoles emerge untwisted to 1.28 per day in the run with greatest emerging twist. The number of ejections in the simulation is also increased by 20%-30% by choosing the majority sign of emerging bipole helicity in each hemisphere, or by halving the turbulent diffusivity in the corona. For reasonable parameter choices, the model produces approximately 50% of the observed CME rate. This indicates that the formation and loss of equilibrium of flux ropes may be a key element in explaining a significant fraction of observed CMEs. Title: A Global Magnetic Field Evolution Model for the Solar Corona Authors: Yeates, Anthony R.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2009SPD....40.3708Y Altcode: We have developed new simulations of the global magnetic field evolution in the solar corona. Using a coupled surface flux transport and magnetofrictional model, we can follow, for the first time, the build-up of magnetic helicity and shear on a global scale over many solar rotations. The evolution is driven by surface motions and by flux emergence, with properties of new active regions determined from synoptic normal-component photospheric magnetograms from NSO/Kitt Peak. As a first application we compare the model to observations of sheared magnetic fields in filaments (aka. prominences), over a 6-month period. We have unprecedented success in reproducing the chirality (axial magnetic field direction) of filaments. Depending on the sign of helicity in newly-emerging regions, the correct chirality is simulated for up to 96% of filaments tested. On the basis of these simulations, an explanation for the observed hemispheric pattern of filament chirality is put forward, including why exceptions occur for filaments in certain locations. When too much axial magnetic flux builds up in filament channels, magnetic flux ropes lose equilibrium and are ejected from the simulation. Using automated techniques for detecting flux ropes and their ejection in the global simulations, we find that the number of ejections depends on both the magnitude and sign of the emerging helicity. For reasonable parameter choices, loss of equilibrium of magnetic flux ropes formed by quasi-static flux cancellation produces about 50% of the observed CME rate. Title: A Prominence Puzzle Explained? Authors: Yeates, A. R.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2009AIPC.1094..216Y Altcode: 2009csss...15..216Y Long-standing observations reveal a global organisation of the magnetic field direction in solar prominences (aka filaments), large clouds of cool dense plasma suspended in the Sun's hot corona. However, theorists have thus far been unable to explain the origin of this hemispheric pattern. In particular, simple shearing by large-scale surface motions would appear to lead to the wrong magnetic field direction. To explain the observations, we have developed a new model of the global magnetic field evolution in the solar corona over six months. For the first time our model can follow the build-up of magnetic helicity and shear on a global scale, driven by flux emergence and surface motions. The model is successful in predicting the correct magnetic field direction in the vast majority of prominences tested, and has enabled us to determine the key physical mechanisms behind the mysterious hemispheric pattern. Title: Evolution of Current Helicity in Full-Sun Simulations Authors: Yeates, A. R.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2009AIPC.1094..772Y Altcode: 2009csss...15..772Y The density of current helicity quantifies the location of twisted and sheared non-potential structures in a magnetic field. We simulate the continuous evolution over many solar rotations of the magnetic field in the Sun's global corona, in response to flux emergence and shearing by photospheric motions. The latitudinal distribution of current helicity in our simulation develops a clear statistical pattern, matching the observed hemispheric sign at active latitudes. Also in agreement with observations there is significant scatter and intermixing of both signs of helicity, and we find local values of current helicity density that are much higher than those predicted by linear force-free extrapolations. Forthcoming full-disk vector magnetograms from Solar Dynamics Observatory will provide an ideal opportunity to test our theoretical results. Title: Modelling the Global Solar Corona: III. Origin of the Hemispheric Pattern of Filaments Authors: Yeates, A. R.; Mackay, D. H. Bibcode: 2009SoPh..254...77Y Altcode: 2008arXiv0810.0517Y; 2008SoPh..tmp..179Y We consider the physical origin of the hemispheric pattern of filament chirality on the Sun. Our 3D simulations of the coronal field evolution over a period of six months, based on photospheric magnetic measurements, were previously shown to be highly successful at reproducing observed filament chiralities. In this paper we identify and describe the physical mechanisms responsible for this success. The key mechanisms are found to be (1) differential rotation of north - south polarity inversion lines, (2) the shape of bipolar active regions, and (3) evolution of skew over a period of many days. As on the real Sun, the hemispheric pattern in our simulations holds in a statistical sense. Exceptions arise naturally for filaments in certain locations relative to bipolar active regions or from interactions among a number of active regions. Title: Evolution and Distribution of Current Helicity in Full-Sun Simulations Authors: Yeates, A. R.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2008ApJ...680L.165Y Altcode: 2008arXiv0805.1883Y Current helicity quantifies the location of twisted and sheared nonpotential structures in a magnetic field. We simulate the evolution of magnetic fields in the solar atmosphere in response to flux emergence and shearing by photospheric motions. In our global-scale simulation over many solar rotations, the latitudinal distribution of current helicity develops a clear statistical pattern, matching the observed hemispheric sign at active latitudes. In agreement with observations, there is significant scatter and intermixing of both signs of helicity, where we find local values of current helicity density that are much higher than those predicted by linear force-free extrapolations. Forthcoming full-disk vector magnetograms from the Solar Dynamics Observatory will provide an ideal opportunity to test our theoretical results on the evolution and distribution of current helicity, both globally and in single active regions. Title: Where Do Solar Filaments Form?: Consequences for Theoretical Models Authors: Mackay, Duncan H.; Gaizauskas, Victor; Yeates, Anthony R. Bibcode: 2008SoPh..248...51M Altcode: 2008SoPh..tmp...25M This paper examines the locations where large, stable solar filaments form relative to magnetic bipoles lying underneath them. The study extends the earlier work of F. Tang to include two additional classification categories for stable filaments and to consider their population during four distinct phases of the solar cycle. With this new classification scheme, results show that over 92% of filaments form in flux distributions that are nonbipolar in nature where the filament lies either fully (79%) or partially (13%) above a polarity inversion line (PIL) external to any single bipole. Filaments that form within a single bipole (traditionally called Type A) are not as common as previously thought. These results are a significant departure from those of F. Tang. Consistency with the earlier work is shown when our data are regrouped to conform to the two-category classification scheme for filaments adopted by F. Tang. We also demonstrate that only filaments that form along the external PIL lying between two bipoles (62% of the full sample, traditionally called Type B) show any form of solar cycle dependence, where their number significantly increases with magnetic activity over the solar cycle. Finally, current observations and theoretical models for the formation of filaments are discussed in the context of the present results. We conclude that key elements in the formation of the majority of filaments considered within this study must be the convergence of magnetic flux resulting in either flux cancellation or coronal reconnection. Title: Twisted solar active region magnetic fields as drivers of space weather: Observational and theoretical investigations Authors: Nandy, Dibyendu; Mackay, Duncan H.; Canfield, Richard C.; Martens, P. C. H. Bibcode: 2008JASTP..70..605N Altcode: The properties and dynamics of magnetic fields on the Sun's photosphere and outer layers--notably those within solar active regions--govern the eruptive activity of the Sun. These photospheric magnetic fields also act as the evolving lower boundary of the Sun-Earth coupled system. Quantifying the physical attributes of these magnetic fields and exploring the mechanisms underlying their influence on the near-Earth space environment are of vital importance for forecasting and mitigating adverse space weather effects. In this context, we discuss here a novel technique for measuring twist in the magnetic field lines of solar active regions that does not invoke the force-free field assumption. Twist in solar active regions can play an important role in flaring activity and the initiation of CMEs via the kink instability mechanism; we outline a procedure for determining this solar active region eruptive potential. We also discuss how twist in active region magnetic fields can be used as inputs in simulations of the coronal and heliospheric fields; specifically, we explore through simulations, the formation, evolution and ejection of magnetic flux ropes that originate in twisted magnetic structures. The results and ideas presented here are relevant for exploring the role of twisted solar active region magnetic fields and flux ropes as drivers of space weather in the Sun-Earth system. Title: Modelling the Global Solar Corona II: Coronal Evolution and Filament Chirality Comparison Authors: Yeates, A. R.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2008SoPh..247..103Y Altcode: 2007arXiv0711.2887Y This paper considers the hemispheric pattern of solar filaments using newly developed simulations of the real photospheric and 3D coronal magnetic fields over a six-month period, on a global scale. The magnetic field direction in the simulation is compared directly with the chirality of observed filaments, at their observed locations. In our model the coronal field evolves through a continuous sequence of nonlinear force-free equilibria, in response to the changing photospheric boundary conditions and the emergence of new magnetic flux. In total 119 magnetic bipoles with properties matching observed active regions are inserted. These bipoles emerge twisted and inject magnetic helicity into the solar atmosphere. When we choose the sign of this active-region helicity to match that observed in each hemisphere, the model produces the correct chirality for up to 96% of filaments, including exceptions to the hemispheric pattern. If the emerging bipoles have zero helicity, or helicity of the opposite sign, then this percentage is much reduced. In addition, the simulation produces a higher proportion of filaments with the correct chirality after longer times. This indicates that a key element in the evolution of the coronal field is its long-term memory, and the build-up and transport of helicity from low to high latitudes over many months. It highlights the importance of continuous evolution of the coronal field, rather than independent extrapolations at different times. This has significant consequences for future modelling such as that related to the origin and development of coronal mass ejections. Title: Exploring the Physical Basis of Solar Cycle Predictions: Flux Transport Dynamics and Persistence of Memory in Advection- versus Diffusion-dominated Solar Convection Zones Authors: Yeates, Anthony R.; Nandy, Dibyendu; Mackay, Duncan H. Bibcode: 2008ApJ...673..544Y Altcode: 2007arXiv0709.1046Y The predictability, or lack thereof, of the solar cycle is governed by numerous separate physical processes that act in unison in the interior of the Sun. Magnetic flux transport and the finite time delay that it introduces, specifically in the so-called Babcock-Leighton models of the solar cycle with spatially segregated source regions for the α- and Ω-effects, play a crucial rule in this predictability. Through dynamo simulations with such a model, we study the physical basis of solar cycle predictions by examining two contrasting regimes, one dominated by diffusive magnetic flux transport in the solar convection zone, the other dominated by advective flux transport by meridional circulation. Our analysis shows that diffusion plays an important role in flux transport, even when the solar cycle period is governed by the meridional flow speed. We further examine the persistence of memory of past cycles in the advection- and diffusion-dominated regimes through stochastically forced dynamo simulations. We find that in the advection-dominated regime this memory persists for up to three cycles, whereas in the diffusion-dominated regime this memory persists for mainly one cycle. This indicates that solar cycle predictions based on these two different regimes would have to rely on fundamentally different inputs, which may be the cause of conflicting predictions. Our simulations also show that the observed solar cycle amplitude-period relationship arises more naturally in the diffusion-dominated regime, thereby supporting those dynamo models in which diffusive flux transport plays a dominant role in the solar convection zone. Title: Yohkoh SXT Full-Resolution Observations of Sigmoids: Structure, Formation, and Eruption Authors: Canfield, Richard C.; Kazachenko, Maria D.; Acton, Loren W.; Mackay, D. H.; Son, Ji; Freeman, Tanya L. Bibcode: 2007ApJ...671L..81C Altcode: We study the structure of 107 bright sigmoids using full-resolution (2.5" pixels) images from the Yohkoh Soft X-Ray Telescope (SXT) obtained between 1991 December and 2001 December. We find that none of these sigmoids are made of single loops of S or inverse-S shape; all comprise a pattern of multiple loops. We also find that all S-shaped sigmoids are made of right-bearing loops and all inverse-S-shaped sigmoids of left-bearing loops, without exception. We co-align the SXT images with Kitt Peak magnetograms to determine the magnetic field directions in each sigmoid. We use a potential-field source surface model to determine the direction of the overlying magnetic field. We find that sigmoids for which the relative orientation of these two fields has a parallel component outnumber antiparallel ones by more than an order of magnitude. We find that the number of sigmoids per active region varies with the solar cycle in a manner that is consistent with this finding. Finally, those few sigmoids that are antiparallel erupt roughly twice as often as those that are parallel. We briefly discuss the implications of these results in terms of formation and eruption mechanisms of flux tubes and sigmoids. Title: Formation of polar starspots through meridional circulation Authors: Holzwarth, V.; Mackay, D. H.; Jardine, M. Bibcode: 2007AN....328.1108H Altcode: To explain the observed intermingling of polarities in the magnetic field distributions of rapidly rotating stars, surface magnetic flux transport models demand the presence of fast meridional flows. We combine simulations of the pre-eruptive and post-eruptive magnetic flux transport in cool stars to investigate the influence of a fast meridional circulation on the latitudinal eruption pattern of magnetic flux tubes and on the polar magnetic field properties. Magnetic flux tubes rising through the convection zone experience an enhanced latitude-dependent poleward deflection through meridional flows, which renders the wings of stellar butterfly diagrams convex. The larger amount of magnetic flux emerging at higher latitudes supports the intermingling of opposite polarities of polar magnetic fields and yields magnetic flux densities in the polar regions about 20% higher than in the case disregarding the pre-eruptive deflection. Taking the pre-eruptive evolution of magnetic flux into account therefore eases the need for the fast meridional flows predicted by previous investigations. Title: Modelling the Global Solar Corona: Filament Chirality Observations and Surface Simulations Authors: Yeates, A. R.; Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2007SoPh..245...87Y Altcode: 2007arXiv0707.3256Y The hemispheric pattern of solar filaments is considered in the context of the global magnetic field of the solar corona. In recent work Mackay and van Ballegooijen have shown how, for a pair of interacting magnetic bipoles, the observed chirality pattern could be explained by the dominant range of bipole tilt angles and helicity in each hemisphere. This study aims to test this earlier result through a direct comparison between theory and observations, using newly developed simulations of the actual surface and 3D coronal magnetic fields over a 6-month period, on a global scale. We consider two key components: (1) observations of filament chirality for the sample of 255 filaments and (2) our new simulations of the large-scale surface magnetic field. Based on a flux-transport model, these will be used as the lower boundary condition for the future 3D coronal simulations. Our technique differs significantly from those of other authors, where the coronal field is either assumed to be purely potential or has to be reset back to potential every 27 days for the photospheric field to remain accurate. In our case we ensure accuracy by the insertion of newly emerging bipolar active regions, based on observed photospheric synoptic magnetograms. The large-scale surface field is shown to remain accurate over the 6-month period, without any resetting. This new technique will enable future simulations to consider the long-term buildup and transport of helicity and shear in the coronal magnetic field over many months or years. Title: Modeling the Hemispheric Pattern of Solar Filaments Authors: Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2007ASPC..368..343M Altcode: New results in modeling the hemispheric pattern of solar filaments are presented. The simulations consider what type of chirality forms along the Polarity Inversion Line (PIL) lying in between two magnetic bipoles as they interact. The results demonstrate not only the origin of the dominant hemispheric pattern, but also why exceptions to it occur. The dominant hemispheric pattern may be attributed to the dominant range of bipole tilt angles and helicities in each hemisphere (\cite{dunc-1989SoPh..124...81W,dunc-1995ApJ...440L.109P}). Exceptions to the hemispheric pattern occur in cases of no initial helicity or for helicity of the minority type in each hemisphere, when large positive bipole tilt angles are used. As the simulations show a clear dependence of the chirality on observational quantities, this may be used to check the validity of the results. Title: Models of the Large-Scale Corona: Formation, Evolution and Lift-Off of Magnetic Flux Ropes Authors: Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2007ASPC..368..251M Altcode: No abstract at ADS Title: Model for the Coupled Evolution of Subsurface and Coronal Magnetic Fields in Solar Active Regions Authors: van Ballegooijen, A. A.; Mackay, D. H. Bibcode: 2007ApJ...659.1713V Altcode: According to Babcock's theory of the solar dynamo, bipolar active regions are Ω-shaped loops emerging from a toroidal field located near the base of the convection zone. In this paper, a mean field model for the evolution of a twisted Ω-loop is developed. The model describes the coupled evolution of the magnetic field in the convection zone and the corona after the loop has fully emerged into the solar atmosphere. Such a coupled evolution is required to fully understand what happens to the coronal and subsurface fields as magnetic flux cancels at polarity inversion lines on the photosphere. The jump conditions for the magnetic field at the photosphere are derived from the magnetic stress balance between the convection zone and corona. The model reproduces the observed spreading of active region magnetic flux over the solar surface. At polarity inversion lines, magnetic flux submerges below the photosphere, but the component of magnetic field along the inversion line cannot submerge, because the field in the upper convection zone is nearly radial. Therefore, magnetic shear builds up in the corona above the inversion line, which eventually leads to a loss of equilibrium of the coronal fields and the ``lift-off'' of a coronal flux rope. Fields that submerge are transported back to the base of the convection zone, leading to the repair of the toroidal flux rope. Following Martens and Zwaan, interactions between bipoles are also considered. Title: Modeling magnetic flux ropes in the solar atmosphere Authors: van Ballegooijen, A. A.; Deluca, E. E.; Squires, K.; Mackay, D. H. Bibcode: 2007JASTP..69...24V Altcode: 2007JATP...69...24V Coronal flux ropes are highly sheared or twisted magnetic fields overlying polarity inversion lines on the solar photosphere. The formation of such flux ropes is briefly discussed. A coronal flux rope can be stable for many days and then suddenly lose equilibrium and erupt, producing a coronal mass ejection (CME). To understand what causes such eruptions, we need to determine the 3D magnetic structure of observed active regions prior to CMEs. This requires constructing nonlinear force free field models of active regions based on observed photospheric vector fields, Hα filaments, or coronal loop structures. We describe a new method for constructing models containing flux ropes. Title: The impact of meridional circulation on stellar butterfly diagrams and polar caps Authors: Holzwarth, V.; Mackay, D. H.; Jardine, M. Bibcode: 2006MNRAS.369.1703H Altcode: 2006astro.ph..4102H; 2006MNRAS.tmp..558H Observations of rapidly rotating solar-like stars show a significant mixture of opposite-polarity magnetic fields within their polar regions. To explain these observations, models describing the surface transport of magnetic flux demand the presence of fast meridional flows. Here, we link subsurface and surface magnetic flux transport simulations to investigate (i) the impact of meridional circulations with peak velocities of <=125ms-1 on the latitudinal eruption pattern of magnetic flux tubes and (ii) the influence of the resulting butterfly diagrams on polar magnetic field properties. Prior to their eruption, magnetic flux tubes with low field strengths and initial cross-sections below ~300km experience an enhanced poleward deflection through meridional flows (assumed to be polewards at the top of the convection zone and equatorwards at the bottom). In particular, flux tubes which originate between low and intermediate latitudes within the convective overshoot region are strongly affected. This latitude-dependent poleward deflection of erupting magnetic flux renders the wings of stellar butterfly diagrams distinctively convex. The subsequent evolution of the surface magnetic field shows that the increased number of newly emerging bipoles at higher latitudes promotes the intermingling of opposite polarities of polar magnetic fields. The associated magnetic flux densities are about 20 per cent higher than in the case disregarding the pre-eruptive deflection, which eases the necessity for fast meridional flows predicted by previous investigations. In order to reproduce the observed polar field properties, the rate of the meridional circulation has to be of the order of 100ms-1, and the latitudinal range from which magnetic flux tubes originate at the base of the convective zone (<~50°) must be larger than in the solar case (<~35°). Title: Models of the Large-Scale Corona. II. Magnetic Connectivity and Open Flux Variation Authors: Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2006ApJ...642.1193M Altcode: In this paper the changing connectivity of the coronal magnetic field during the formation and ejection of magnetic flux ropes is considered. Using recent simulations of the coronal field, it is shown that reconnection may occur both above and below the flux ropes. Those occurring above slowly strip away coronal arcades overlying the flux ropes and allow the flux ropes to be ejected. In contrast, those below help to push the flux ropes out. It is found that the reconnection occurring below each flux rope may result in significant skew being maintained within the coronal field above the PIL after the flux rope is ejected. In addition, after the eruption, as the coronal field closes down, the large-scale transport of open flux across the bipoles takes place through the process of ``interchange reconnection.'' As a result, new photospheric domains of open flux are created within the centers of the bipoles, where field lines were previously closed. The net open flux in the simulation may be split into two distinct contributions. The first contribution is due to the nonpotential equilibrium coronal fields of the bipoles. The second contribution is a temporary enhancement to this during the ejection of the flux ropes, where previously closed field lines become open. It is shown that the nonpotential equilibrium contribution to the open flux is significantly higher than that due to a potential field deduced from the same photospheric boundary conditions. These results suggest that the nonpotential nature of coronal magnetic fields may affect the variation of the Sun's open flux during periods of high solar activity and should be considered in future simulations. Title: Models of the Large-Scale Corona. I. Formation, Evolution, and Liftoff of Magnetic Flux Ropes Authors: Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2006ApJ...641..577M Altcode: The response of the large-scale coronal magnetic field to transport of magnetic flux in the photosphere is investigated. In order to follow the evolution on long timescales, the coronal plasma velocity is assumed to be proportional to the Lorentz force (magnetofriction), causing the coronal field to evolve through a series of nonlinear force-free states. Magnetofrictional simulations are used to study the formation and evolution of coronal flux ropes, highly sheared and/or twisted fields located above polarity inversion lines on the photosphere. As in our earlier studies, the three-dimensional numerical model includes the effects of the solar differential rotation and small-scale convective flows; the latter are described in terms of surface diffusion. The model is extended to include the effects of coronal magnetic diffusion, which limits the degree of twist of coronal flux ropes, and the solar wind, which opens up the field at large height. The interaction of two bipolar magnetic regions is considered. A key element in the formation of flux ropes is the reconnection of magnetic fields associated with photospheric flux cancellation at the polarity inversion lines. Flux ropes are shown to form both above the external inversion line between bipoles (representing type B filaments) and above the internal inversion line of each bipole in a sigmoid shape. It is found that once a flux rope has formed, the coronal field may diverge from equilibrium with the ejection of the flux rope. After the flux rope is ejected, the coronal field once again relaxes down to an equilibrium. This ability to follow the evolution of the coronal fields through eruptions is essential for future full-Sun simulations in which multiple bipoles are evolved for many months or years. Title: Simulated X-ray cycles in rapidly rotating solar-like stars Authors: McIvor, T.; Jardine, M.; Mackay, D.; Holzwarth, V. Bibcode: 2006MNRAS.367..592M Altcode: 2006MNRAS.tmp..259M It is generally accepted that the presence of a hot magnetic corona provides the source of X-ray emission in cool stars. With this connection one could expect to see the variation of magnetic flux in the activity cycle of a star mirrored by a similar variation in the stars X-ray emission. Using magnetic maps produced from flux emergence and transport simulations and assuming a potential field for the corona, we can extrapolate the coronal magnetic field and hence calculate the variation of the X-ray emission. We consider three types of activity cycle that successfully reproduce the pattern of intermingled magnetic flux at high latitudes, a feature observed with Zeeman-Doppler imaging. The three different cycles take the form of (1) an enhanced butterfly pattern where flux emergence is extended to a latitude of 70°, (2) an extended emergence profile as before but with an overlap of 4 yr in the butterfly diagram and (3) where no butterfly diagram is used. The cyclic variation in the X-ray emission is around two orders of magnitude for cases (1) and (3), but less than one order of magnitude for case (2). For all three cases, the rotational modulation of the X-ray emission is greatest at cycle minimum, but the emission measure weighted density varies little over the cycle. For cases (1) and (2) the fraction of the total flux that is open (along which a wind can escape) varies little over the cycle, but for case (3) this is three times larger at cycle minimum than at maximum. Our results clearly show that although magnetic cycles may exist for stars they are not necessarily observable in the X-ray emission. Title: Role of Large-scale Magnetic Fields and Material Flows in the Formation of Filaments and Filament Channels Authors: Mackay, D. H. Bibcode: 2005ASPC..346..177M Altcode: In this review paper we discuss the role of large-scale magnetic fields and material flows in the formation of solar filaments and filament channels. Particular attention is paid to the type of magnetic configurations within which filaments form. Observations of the formation of filaments are described along with the wide variety of theoretical models and mechanisms which have been put forward to explain filament formation. Simulations are presented which consider the origin of the large-scale hemispheric pattern that exists for the axial magnetic fields within filaments. The role that mass motions play in filament formation is introduced from both observational and theoretical viewpoints. A summary concludes with recommendations for future observing programs which would advance our understanding of the formation mechanism of filaments. Title: New Results in Modeling the Hemispheric Pattern of Solar Filaments Authors: Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2005ApJ...621L..77M Altcode: New results in modeling the hemispheric pattern of solar filaments through magnetic flux transport and magnetofrictional simulations are presented. The simulations consider for the first time what type of chirality forms along the polarity inversion line lying in between two magnetic bipoles as they interact. Such interactions are important for filament formation, as observations by F. Tang show that the majority of filaments form in between bipolar regions rather than within a single magnetic bipole. The simulations also include additional physics of coronal diffusion and a radial outflow velocity at the source surface, which was not included in previous studies. The results clearly demonstrate for the first time not only the origin of the dominant hemispheric pattern but also why exceptions to it may occur. The dominant hemispheric pattern may be attributed to the dominant range of bipole tilt angles and helicities in each hemisphere. Exceptions to the hemispheric pattern are found to only occur in cases of no initial helicity or for helicity of the minority type in each hemisphere when large positive bipole tilt angles (α>20deg) are used. As the simulations show a clear dependence of the hemispheric pattern and its exceptions on observational quantities, this may be used to check the validity of the results. Future programs to consider this are put forward. Title: Activity cycles and polar caps on solar-like stars Authors: Jardine, M.; Mackay, D. H.; Hussain, G. A. J.; McIvor, T. Bibcode: 2005ESASP.560..107J Altcode: 2005csss...13..107J No abstract at ADS Title: Polar caps on active stars: magnetic flux emergence and transport Authors: Mackay, D. H.; Jardine, M.; Collier Cameron, A.; Donati, J. -F.; Hussain, G. A. J. Bibcode: 2004MNRAS.354..737M Altcode: In recent years, Zeeman Doppler imaging of rapidly rotating solar-like stars has shown high-latitude magnetic flux patterns of intermingled magnetic polarities. Such high-latitude intermingling of positive and negative flux is inconsistent with our present understanding of how magnetic flux emerges on the Sun and is transported poleward. To determine how these patterns may arise, magnetic flux transport simulations are carried out. These simulations follow the evolution of the radial magnetic field at the surface of the star as new magnetic bipoles emerge and are advected poleward by the surface effects of differential rotation, meridional flow and supergranular diffusion. To produce intermingling of flux at high latitudes, key parameters such as the emergence profiles and transport coefficients are varied from presently used solar values. In doing so, it is found that, in order to explain the high-latitude intermingling, at least two of these parameters must be changed. First, the emergence profile must be extended to higher latitudes (λ= 50°-70°), and secondly the value of the meridional flow must be increased by around a factor of 10 (~100 m s-1). The results show that the observed intermingling of high-latitude flux can only occur through a flux emergence and transport process that is significantly different from that which occurs on the Sun. Observable features produced by both of these changes are considered, and the significance of the simulations to future observing programmes discussed. Finally the emergence profile and transport coefficients that best fit the observations of the young active star AB Dor (period = 0.514 d) are put forward. Title: A Possible Solar Cycle Dependence to the Hemispheric Pattern of Filaments? Authors: Mackay, D. H. Bibcode: 2003csss...12..595M Altcode: The origin of the hemispheric pattern of filaments is considered for both the rising and declining phases of the solar cycle. This is carried out by using a magnetic flux transport model which considers how bipoles interact with surrounding polar fields. For the rising phase of the cycle a range of initial twists and tilt angles of the bipoles consistent with observations can be found which reproduces the observed hemispheric pattern. For the declining phase no such range can be found. To determine whether there is a cycle variation to the hemispheric pattern new detailed observations are required. Title: Helicity as a Component of Filament Formation Authors: Mackay, D. H.; Gaizauskas, V. Bibcode: 2003SoPh..216..121M Altcode: In this paper we seek the origin of the axial component of the magnetic field in filaments by adapting theory to observations. A previous paper (Mackay, Gaizauskas, and van Ballegooijen, 2000) showed that surface flows acting on potential magnetic fields for 27 days - the maximum time between the emergence of magnetic flux and the formation of large filaments between the resulting activity complexes - cannot explain the chirality or inverse polarity nature of the observed filaments. We show that the inclusion of initial helicity, for which there is observational evidence, in the flux transport model results in sufficiently strong dextral fields of inverse polarity to account for the existence and length of an observed filament within the allotted time. The simulations even produce a large length of dextral chirality when just small amounts of helicity are included in the initial configuration. The modeling suggests that the axial field component in filaments can result from a combination of surface (flux transport) and sub-surface (helicity) effects acting together. Here surface effects convert the large-scale helicity emerging in active regions into a smaller-scale magnetic-field component parallel to the polarity inversion line so as to form a magnetic configuration suitable for a filament. Title: Magnetic Flux Transport Simulations of Solar Surface Magnetic Distributions During a Grand Minimum Authors: Mackay, D. H. Bibcode: 2003SoPh..213..173M Altcode: It is well known that magnetic activity on the Sun modulates from one cycle to the next. The most striking occurrence of this is called a grand minimum where magnetic activity all but disappears. The latest grand minimum occurred between the years 1645 and 1715 and is called the Maunder minimum. In this paper magnetic flux transport simulations are used to consider what type of surface magnetic field configurations may be produced both during and after a grand minimum depending on how the grand minimum occurs. It is shown that the surface configurations during and after a grand minimum strongly depend on the phase of the cycle in which the grand minimum starts and whether it lasts for an odd or even number of cycles. If the grand minimum starts around cycle minimum then a significant amount of large-scale magnetic flux may persist on the Sun at high latitudes during the grand minimum. In contrast, if it starts at cycle maximum during the grand minimum it is possible for there to be essentially zero large-scale magnetic flux over the entire surface of the Sun. It is shown that for a single grand minimum event the reversal of the polar fields at the presently observed time in the solar cycle is only reproduced if the event starts at cycle minimum and extends over an even number of cycles. In contrast, if the grand minimum runs for an odd number of cycles it is possible for there to be no reversal of the polar fields or for the reversals to occur at times inconsistent with our present understanding of the solar cycle. Consequences of the assumptions made in the modelling are discussed and the significance of the simulations for direct modelling of events such as the Maunder minimum are considered. Title: Statistical Flux Tube Properties of 3D Magnetic Carpet Fields Authors: Close, R. M.; Parnell, C. E.; Mackay, D. H.; Priest, E. R. Bibcode: 2003SoPh..212..251C Altcode: The quiet-Sun photosphere consists of numerous magnetic flux fragments of both polarities that evolve with granular and supergranular flow fields. These concentrations give rise to a web of intermingled magnetic flux tubes which characterise the coronal magnetic field. Here, the nature of these flux tubes is studied. The photosphere is taken to be the source plane and each photospheric fragment is represented by a series of point sources. By analysing the potential field produced by these sources, it is found that the distribution of flux tube lengths obtained by (i) integrating forward from positive sources and (ii) tracing back from negative sources is highly dependent on the total flux imbalance within the region of interest. It is established that the relation between the footpoint separation of a flux tube and its height cannot be assumed to be linear. Where there is a significant imbalance of flux within a region, it is found that fragments of the dominant polarity will have noticeably more connections, on average, than the minority polarity fragments. Despite this difference, the flux from a single fragment of either polarity is typically divided such that (i) 60-70% connects to one opposite-polarity fragment, (ii) 25-30% goes to a further 1 to 2 opposite-polarity fragments, and (iii) any remaining flux may connect to as many as another 50 or more other opposite-polarity fragments. This is true regardless of any flux imbalance within the region. It is found that fragments connect preferentially to their nearest neighbours, with, on average, around 60-70% of flux closing down within 10 Mm of a typical fragment. Only 50% of the flux in a quiet region extends higher than 2.5 Mm above the solar surface and 5-10% extends higher than 25 Mm. The fragments that contribute to the field above this height cover a range of sizes, with even the smallest of fragments contributing to the field at heights of over 50 Mm. Title: The Skew of High-Latitude X-ray Arcades in the Declining Phase of Cycle 22 Authors: Mc Allister, A. H.; Mackay, D. H.; Martin, S. F. Bibcode: 2002SoPh..211..155M Altcode: The chirality of high-latitude coronal arcades in the declining phase of cycle 22 has been studied. It is found that the observed skew of the high-latitude arcades is opposite to the dominant arcade skew at lower latitudes. This new result which applies only to the declining phase of the solar cycle is consistent with differential rotation and the simulations of Mackay and van Ballegooijen (2001). Limitations of the present study are discussed along with its consequences for the global pattern of filaments in each hemisphere. The results suggest that, for the declining phase, the previously observed global pattern may be more complex with latitudinal variations. Future observing programs required to clarify the issue are discussed. Title: Inferring X-ray coronal structures from Zeeman-Doppler images Authors: Jardine, M.; Wood, K.; Collier Cameron, A.; Donati, J. -F.; Mackay, D. H. Bibcode: 2002MNRAS.336.1364J Altcode: 2002astro.ph..7522J We have modelled the X-ray emission from the young rapid rotator AB Doradus (Prot= 0.514 d) using as a basis Zeeman-Doppler maps of the surface magnetic field. This allows us to reconcile the apparently conflicting observations of a high X-ray emission measure and coronal density with a low rotational modulation in the X-ray band. The technique is to extrapolate the coronal field from the surface maps by assuming the field to be potential. We then determine the coronal density for an isothermal corona by solving hydrostatic equilibrium along each field line and scaling the surface plasma pressure with the surface magnetic pressure. We set the density to zero along those field lines that are open and those where at any point along their length the plasma pressure exceeds the magnetic pressure. We then calculate the optically thin X-ray emission measure and rotational modulation for models with a range of coronal densities. Although the corona can be very extended, much of the emission comes from high-latitude regions close to the stellar surface. Since these are always in view as the star rotates, there is little rotational modulation. We find that emission measures in the observed range 1052.8-1053.3 cm-3 can be reproduced with densities in the range 109-1010.7 cm-3 for coronae at temperatures of 106-107 K. Title: The Evolution of the Sun's Open Magnetic Flux - II. Full Solar Cycle Simulations Authors: Mackay, D. H.; Priest, E. R.; Lockwood, M. Bibcode: 2002SoPh..209..287M Altcode: In this paper the origin and evolution of the Sun's open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1-2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun's open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested. Title: Evolution of a density enhancement in a stratified atmosphere with uniform vertical magnetic field Authors: Mackay, D. H.; Galsgaard, K. Bibcode: 2002ESASP.505..485M Altcode: 2002solm.conf..485M; 2002IAUCo.188..485M The evolution of a density enhancement under the effect of gravity in a stratified atmosphere is considered. The atmosphere is threaded with an initially uniform vertical magnetic field. The magnetic field plays an important role in the evolution of the density enhancement and if strong enough results in the density enhancement rebounding a number of times. Both upward and downward velocities of the enhancement are obtained with speeds much less than the free fall speed. The enhancement can remain in the corona at least 11 times longer than a free-fall particle. The relevance of the simulations to the solar atmosphere is then discussed. Title: Solar cycle variation of the temperature structure within the cores of coronal streamers Authors: Culhane, J. L.; Foley, C. R.; Patsourakos, S.; Mackay, D. Bibcode: 2002ESASP.508..371C Altcode: 2002soho...11..371C We use the Coronal Diagnostic Spectrometer onboard the Solar and Heliospheric Observatory (SOHO) to analyze conditions in coronal streamer structures observed close to solar minimum (1996, July 8) and near maximum (1999, August 5). From emission line intensities (Fe IX-XV ions), the line ratio method gives the radial temperature behaviour. The solar minimum peak values were about 1.4 MK at 1.3 R0, while near solar maximum values were consistent with Yohkoh observations at the last maximum, displaying an asymptotic temperature of around 2.2 MK above 1.2 R0. We discuss the observations in relation to possible mechanisms for energy deposition in large coronal structures. Title: The Evolution of the Sun's Open Magnetic Flux - I. A Single Bipole Authors: Mackay, D. H.; Priest, E. R.; Lockwood, M. Bibcode: 2002SoPh..207..291M Altcode: In this paper the origin and evolution of the Sun's open magnetic flux are considered for single magnetic bipoles as they are transported across the Sun. The effects of magnetic flux transport on the radial field at the surface of the Sun are modeled numerically by developing earlier work by Wang, Sheeley, and Lean (2000). The paper considers how the initial tilt of the bipole axis (α) and its latitude of emergence affect the variation and magnitude of the surface and open magnetic flux. The amount of open magnetic flux is estimated by constructing potential coronal fields. It is found that the open flux may evolve independently from the surface field for certain ranges of the tilt angle. For a given tilt angle, the lower the latitude of emergence, the higher the magnitude of the surface and open flux at the end of the simulation. In addition, three types of behavior are found for the open flux depending on the initial tilt angle of the bipole axis. When the tilt is such that αge2° the open flux is independent of the surface flux and initially increases before decaying away. In contrast, for tilt angles in the range −16°<α<2° the open flux follows the surface flux and continually decays. Finally, for αle−16° the open flux first decays and then increases in magnitude towards a second maximum before decaying away. This behavior of the open flux can be explained in terms of two competing effects produced by differential rotation. Firstly, differential rotation may increase or decrease the open flux by rotating the centers of each polarity of the bipole at different rates when the axis has tilt. Secondly, it decreases the open flux by increasing the length of the polarity inversion line where flux cancellation occurs. The results suggest that, in order to reproduce a realistic model of the Sun's open magnetic flux over a solar cycle, it is important to have accurate input data on the latitude of emergence of bipoles along with the variation of their tilt angles as the cycle progresses. Title: What are the Origins of Quiescent Coronal Soft X-Rays? Authors: Foley, C. R.; Culhane, J. L.; Patsourakos, S.; Yurow, R.; Moroney, C.; Mackay, D. Bibcode: 2002mwoc.conf..341F Altcode: We have examined the evolution and modulation of the Sun's atmosphere from the photosphere up to the outer corona through the decline and rise of solar cycles 22, and 23 respectfully. For this we have used Yohkoh soft X-ray telescope (SXT) images, Kitt peak magnetograms and EUV spectra provided by the Coronal Diagnostic Spectrometer (CDS). We find as Hara (1996, 1997) found, that there is a modulation of the coronal brightness which varies annually in the high latitude activity zones, and that this is linked to the presence and disappearance of active regions on the sun's disk. We interpret our results with regards to the emergence and diffusion of magnetic flux. We find that the appearance of high latitude activity zones may be explained simply by the decay of diffused active region flux, We also find evidence for a positive temperature gradient within the corona from the emission profiles in the different lines. Title: Solar cycle variation of the temperature structure within the cores of coronal streamers Authors: Foley, C. R.; Patsourakos, S.; Culhane, J. L.; MacKay, D. Bibcode: 2002A&A...381.1049F Altcode: We use the Coronal Diagnostic Spectrometer onboard the Solar and Heliospheric Observatory (SOHO) to analyze conditions in coronal streamer structures observed close to solar minimum (1996 July 8) and near maximum (1999 August 5). We measured the intensities of emission lines from Fe IX-XV ions and found the most intense emission to be from Fe XI at solar minimum and from Fe XV at solar maximum. We then used the line ratio method with transitions in selected ions to extract the radial temperature behavior in the structures. The solar minimum peak values were about 1.4 MK at 1.3 Rsun, while values derived close to solar maximum were consistent with the Yohkoh observations at the last maximum, displaying an apparently asymptotic temperature of around 2.2 MK above 1.2 Rsun. We discuss the observations in relation to possible mechanisms for energy deposition in large coronal structures at different phases of the solar cycle. Title: A Possible Solar Cycle Dependence to the Hemispheric Pattern of Filament Magnetic Fields? Authors: Mackay, D. H.; van Ballegooijen, A. A. Bibcode: 2001ApJ...560..445M Altcode: The origin of the observed hemispheric pattern of filament magnetic fields is considered. Using a magnetic flux transport model, we simulate the interactions of magnetic bipoles with each other and with polar magnetic fields in the rising and declining phases of the solar activity cycle. In contrast to previous studies, the nonpotential character of the initial coronal fields is taken into account, and the dependence of the hemispheric pattern on the initial tilt and helicity of the bipoles is considered. For the rising phase of the cycle, a range of initial bipole twists and tilt angles can be found that reproduce the observed hemispheric pattern. However, for the declining phase no such range can be found: the predicted fields on the return arms at the rear of switchbacks are consistent with filament observations, but those on the high-latitude east-west arms are not. It is argued that existing observations of the hemispheric pattern are weighted toward the rising phase of the solar activity cycle and may give us a biased view of the Sun. New observations of filament magnetic fields are needed to determine whether there is a cycle dependence of the observed hemispheric pattern. Title: Evolution of Solar Filament Channels Observed during a Major Poleward Surge of Photospheric Magnetic Flux Authors: Gaizauskas, V.; Mackay, D. H.; Harvey, K. L. Bibcode: 2001ApJ...558..888G Altcode: We describe the evolution of a solar filament channel marked by extremes: a length near one solar radius, and a duration of a year. Its genesis centers on an episode of flux emergence so powerful that it launched a surge of photospheric magnetic flux almost to the northern polar cap. This extraordinary injection of new flux at the solar surface occurred in midterm of the longest lived activity complex of cycle 21 (~20 rotations). The new flux emerged just north of the equator as a pair of adjacent activity complexes-a ``supercluster'' of sunspots-remote from other active regions in a longitude band spanning ~90°. Channels quickly formed along separate polarity inversion lines in this large-scale quadrupolar configuration. None of the initial channels survived more than two solar rotations; none merged to form a greater whole. As individual bipoles within and between the activity complexes expanded, fragmented, and cancelled, only flux at the outermost edges of the adjacent complexes survived, thanks to the remoteness of other strong concentrations of magnetic flux. The result, after three solar rotations, was a simplified bipolar pattern of poleward-streaming flux subject to global processes of flux transport that sustained and extended it for up to a year. The long and long-lived filament channel formed in the shape of a ``switchback'' along the polarity inversion between the converging streams of opposite polarity flux, continuing along the polarity inversion between the migrating flux and the flux in the polar cap. Our observations reveal large-scale swirled patterns of chromospheric fibrils from which we infer that substantial negative helicity was built up across both adjacent activity complexes during their emergence. The patterns were still detectable in the migrating flux after the source regions had disappeared. Convergence of opposite polarity fluxes with negative helicity leads naturally to dextral filaments and filament channels, consistent with the chirality rule for the northern hemisphere found by Martin, Bilimoria, & Tracadas. We measured the chiralities of 10 filament channels associated with the initial massive emergence of magnetic flux and its subsequent surge poleward. Implications of our findings on models for forming filaments and filament channels are discussed. Title: Evolution of a Density Enhancement in a Stratified Atmosphere With Uniform Vertical Magnetic Field Authors: Mackay, D. H.; Galsgaard, K. Bibcode: 2001SoPh..198..289M Altcode: In this paper the evolution of a density enhancement under the effect of gravity in a stratified atmosphere is considered in a 2D simulation. The stratified atmosphere is chosen with a high-density photosphere, transition region and low-density corona where the enhancement is added in non-equilibrium to the corona. The atmosphere is also threaded with an initially uniform vertical magnetic field. If sufficiently strong, the magnetic field plays an important role in the evolution of the density enhancement as it tries to gain equilibrium. It not only enables the density enhancement to maintain its shape as it falls, but if strong enough results in the density enhancement rebounding a number of times. Therefore both upward and downward velocities of the enhancement are obtained. In all cases the density enhancement is found to fall with speeds much less than the free-fall speed and can remain in the corona at least 11 times longer than a free-fall particle. The relevance of the simulations to the solar atmosphere is then discussed. Title: The Temperature of The Extended Solar Corona Authors: Foley, C. R.; Culhane, J. L.; Mackay, D. Bibcode: 2001IAUS..203..505F Altcode: We use the Coronal Diagnostic Spectrometer instrument on board the Solar and Heliospheric Observatory to analyse coronal helmet streamer structures observed close to the solar minimum / maximum on the 1996 July 8 / 1999 July 4-5th. The radial variation of peak electron temperature is extracted out to 2 solar radii. These are found to agree well with Yohkoh observations close to the solar maximum, but are found to be reduced by around half a million close to the solar minimum. Extrapolations of the photospheric field observations of MDI are used to aid interpreted with regard to the energy depostion in the low corona and solar wind. Title: Theory of Solar Chromospheric and Coronal Magnetic Fields Authors: van Ballegooijen, A. A.; Mackay, D. H. Bibcode: 2001ASPC..248..105V Altcode: 2001mfah.conf..105V No abstract at ADS Title: Comparison of Theory and Observations of the Chirality of Filaments within a Dispersing Activity Complex Authors: Mackay, D. H.; Gaizauskas, V.; van Ballegooijen, A. A. Bibcode: 2000ApJ...544.1122M Altcode: We investigate the origin of the hemispheric pattern of filaments and filament channels by comparing theoretical predictions with observations of the chirality of filament channels within a dispersing activity complex. Our aim is to determine how the chirality of each specific channel arises so that general principles underlying the hemispheric pattern can be recognized. We simulate the field lines representing the filaments in the activity complex by applying a model of global flux transport to an initial magnetic configuration. The model combines the surface effects of differential rotation, meridional flows, and supergranular diffusion along with a magnetofrictional relaxation method in the overlying corona. The simulations are run with and without injecting axial magnetic fields at polarity inversion lines in the dispersing activity complex for four successive solar rotations. When the initial magnetic configuration, based on synoptic magnetic maps, is set to a potential field at the beginning of each rotation, the simulations poorly predict the chirality of the filament channels and filaments. The cases that predict the correct chirality correspond to an initial polarity inversion line, which is north-south the wrong chirality arises when the initial polarity inversion lines lie east-west. Results improve when field-line connectivities at low latitudes are retained and allowed to propagate to higher latitudes without resetting the field to a potential configuration between each rotation. When axial flux emergence exceeding 1×1019 Mx day-1 is included at the location of each filament, an excellent agreement is obtained between the theory and observations. In additon to predicting the correct chirality in all cases, axial flux emergence allows more readily the production of inverse-polarity dipped field lines needed to support filamentary mass. An origin for the hemispheric pattern as a result of the combined effects of flux transport, axial flux emergence, and magnetic helicity is then discussed. Title: A Method to Determine the Heating Mechanisms of the Solar Corona Authors: Priest, E. R.; Foley, C. R.; Heyvaerts, J.; Arber, T. D.; Mackay, D.; Culhane, J. L.; Acton, L. W. Bibcode: 2000ApJ...539.1002P Altcode: One of the paradigms about coronal heating has been the belief that the mean or summit temperature of a coronal loop is completely insensitive to the nature of the heating mechanisms. However, we point out that the temperature profile along a coronal loop is highly sensitive to the form of the heating. For example, when a steady state heating is balanced by thermal conduction, a uniform heating function makes the heat flux a linear function of distance along the loop, while T7/2 increases quadratically from the coronal footpoints; when the heating is concentrated near the coronal base, the heat flux is small and the T7/2 profile is flat above the base; when the heat is focused near the summit of a loop, the heat flux is constant and T7/2 is a linear function of distance below the summit. It is therefore important to determine how the heat deposition from particular heating mechanisms varies spatially within coronal structures such as loops or arcades and to compare it to high-quality measurements of the temperature profiles. We propose a new two-part approach to try and solve the coronal heating problem, namely, first of all to use observed temperature profiles to deduce the form of the heating, and second to use that heating form to deduce the likely heating mechanism. In particular, we apply this philosophy to a preliminary analysis of Yohkoh observations of the large-scale solar corona. This gives strong evidence against heating concentrated near the loop base for such loops and suggests that heating uniformly distributed along the loop is slightly more likely than heating concentrated at the summit. The implication is that large-scale loops are heated in situ throughout their length, rather than being a steady response to low-lying heating near their feet or at their summits. Unless waves can be shown to produce a heating close enough to uniform, the evidence is therefore at present for these large loops more in favor of turbulent reconnection at many small randomly distributed current sheets, which is likely to be able to do so. In addition, we suggest that the decline in coronal intensity by a factor of 100 from solar maximum to solar minimum is a natural consequence of the observed ratio of magnetic field strength in active regions and the quiet Sun; the altitude of the maximum temperature in coronal holes may represent the dissipation height of Alfvén waves by turbulent phase mixing; and the difference in maximum temperature in closed and open regimes may be understood in terms of the roles of the conductive flux there. Title: Mean Field Model for the Formation of Filament Channels on the Sun Authors: van Ballegooijen, A. A.; Priest, E. R.; Mackay, D. H. Bibcode: 2000ApJ...539..983V Altcode: The coronal magnetic field is subject to random footpoint motions that cause small-scale twisting and braiding of field lines. We present a mean field theory describing the effects of such small-scale twists on the large-scale coronal field. This theory assumes that the coronal field is force free, with electric currents flowing parallel or antiparallel to magnetic field lines. Random footpoint motions are described in terms of diffusion of the mean magnetic field at the photosphere. The appropriate mean field equations are derived, and a numerical method for solving these equations in three dimensions is presented. Preliminary results obtained with this method are also presented. In particular the formation of filament channels is studied. Filament channels are regions where the coronal magnetic field is strongly aligned with the underlying polarity inversion line in the photosphere. It is found that magnetic flux cancellation plays an important role in the formation of such channels. Various models of the coronal field are presented, including some in which the axial field is assumed to originate from below the photosphere. The models reproduce many of the observed features of filament channels, but the observed hemisphere pattern of dextral and sinistral channels remains a mystery. Title: How Accurately Can We Determine the Coronal Heating Mechanism in the Large-Scale Solar Corona? Authors: Mackay, D. H.; Galsgaard, K.; Priest, E. R.; Foley, C. R. Bibcode: 2000SoPh..193...93M Altcode: In recent papers by Priest et al., the nature of the coronal heating mechanism in the large-scale solar corona was considered. The authors compared observations of the temperature profile along large coronal loops with simple theoretical models and found that uniform heating along the loop gave the best fit to the observed data. This then led them to speculate that turbulent reconnection is a likely method to heat the large-scale solar corona. Here we reconsider their data and their suggestion about the nature of the coronal heating mechanism. Two distinct models are compared with the observations of temperature profiles. This is done to determine the most likely form of heating under different theoretical constraints. From this, more accurate judgments on the nature of the coronal heating mechanism are made. It is found that, due to the size of the error estimates in the observed temperatures, it is extremely difficult to distinguish between some of the different heat forms. In the initial comparison the limited range of observed temperatures (T>1.5 MK) in the data sets suggests that heat deposited in the upper portions of the loop, fits the data more accurately than heat deposited in the lower portions. However if a fuller model temperature range (T<1.0 MK) is used results in contridiction to this are found. In light of this several improvements are required from the observations in order to produce theoretically meaningful results. This gives serious bounds on the accuracy of the observations of the large-scale solar corona in future satellite missions such a Solar-B or Stereo. Title: Dipped Magnetic Field Configurations Associated with Solar Filaments Authors: Mackay, D. H.; Longbottom, A. W. Bibcode: 1999ESASP.448..451M Altcode: 1999mfsp.conf..451M; 1999ESPM....9..451M No abstract at ADS Title: On the Comparison of Filament Chirality and Axial Magnetic Fields Deduced from a Flux Transport Model Authors: Mackay, D. H.; Gaizauskas, V.; van Ballegooijen, A. A. Bibcode: 1999ESASP.448..507M Altcode: 1999mfsp.conf..507M; 1999ESPM....9..507M No abstract at ADS Title: On the location of energy release and temperature profiles along coronal loops Authors: Galsgaard, K.; Mackay, D. H.; Priest, E. R.; Nordlund, Å. Bibcode: 1999SoPh..189...95G Altcode: Several mechanisms have been suggested to contribute to the heating of the solar corona, each of which deposits energy along coronal loops in a characteristic way. To compare the theoretical models with observations one has to derive observable quantities from the models. One such parameter is the temperature profile along a loop. Here numerical experiments of flux braiding are used to provide the spatial distribution of energy deposition along a loop. It is found that braiding produces a heat distribution along the loop which has slight peaks near the footpoints and summit and whose magnitude depends on the driving time. Using different examples of the heat deposition, the temperature profiles along the loop are determined assuming a steady state. Along with this, different methods for providing average temperature profiles from the time-series have been investigated. These give summit temperatures within approximately 10% of each other. The distribution of the heating has a significant impact on both the summit temperature and the temperature distribution along the loop. In each case the ratio between the heat deposited and radiation provides a scaling for the summit temperature. Title: Dipped Magnetic Field Configurations Associated with Filaments and Barbs Authors: Mackay, D. H.; Longbottom, A. W.; Priest, E. R. Bibcode: 1999SoPh..185...87M Altcode: In this paper, three-dimensional linear force-free field configurations that can be associated with filaments are considered. It is assumed that the field configurations are suitable to represent filaments if they contain magnetic dips. With the photospheric flux distribution chosen to be an arcade with a dextral/sinistral axial component, it is found that dipped configurations exist only for large values of alpha (where, ∇×B=αB). The dips always lie above the polarity inversion line in the centre of the channel between the flux regions. When the dips are viewed from above to a depth of 1 Mm they resemble closely the shape of filaments viewed in absorption on the solar disk. As the magnitude of alpha increases, the horizontal and vertical extent of the dips also increases, giving active-region filaments for low values of alpha and quiescient filaments for high values of alpha. Dextral filaments only form for negative values of alpha and sinistral filaments for positive values of alpha. The portion of the field line that is dipped is always of inverse polarity and the magnitude of the field in the dipped region increases with height, both of which are consistent with Leroy, Bommier, and Sahal-Bréchot (1983). Overlying the region of dips there are arcades of normal polarity which have the correct left-bearing/right-bearing orientation for dextral/sinistral filaments. When the hypothesis of barbs occurring in dipped field lines is used, barbs that branch out of the main axis and to the right/left for dextral/sinistral filaments can be formed around minority polarity elements on either side of the polarity inversion line. No barbs are found around normal polarity elements. The model reproduces many of the observed features of filament channels, filaments and their barbs. Title: Role of Helicity in the Formation of Intermediate Filaments Authors: Mackay, D. H.; Priest, E. R.; Gaizauskas, V.; van Ballegooijen, A. A. Bibcode: 1998SoPh..180..299M Altcode: In the last few years new observations have shown that solar filaments and filament channels have a surprising hemispheric pattern. To explain this pattern, a new theory for filament channel and filament formation is put forward. The theory describes the formation of a specific type of filament, namely the `intermediate filament' which forms either between active regions or at the boundary of an active region. It describes the formation in terms of the emergence of a sheared activity complex. The complex then interacts with remnant flux and, after convergence and flux cancellation, the filament forms in the channel. A key feature of the model is the net magnetic helicity of the complex. With the correct sign a filament channel can form, but with the opposite sign no filament channel forms after convergence. It is shown how the hemispheric pattern of helicity in emerging flux regions produces the observed hemispheric pattern for filaments. Title: Force-Free Models of a Filament Channel in Which a Filament Forms Authors: Mackay, D. H.; Gaizauskas, V.; Priest, E. R. Bibcode: 1998ASPC..150..286M Altcode: 1998npsp.conf..286M; 1998IAUCo.167..286M No abstract at ADS Title: Preliminary Results for Coronal Magnetic Fields as Suggested by MDI Magnetograms Authors: Walsh, R. W.; Ireland, J.; Mackay, D. H.; Galsgaard, K.; Longbottom, A. W. Bibcode: 1998ASPC..155..371W Altcode: 1998sasp.conf..371W No abstract at ADS Title: The Skew of Polar Crown X-ray Arcades Authors: McAllister, A. H.; Hundhausen, A. J.; Mackay, D.; Priest, E. Bibcode: 1998ASPC..150..430M Altcode: 1998npsp.conf..430M; 1998IAUCo.167..430M No abstract at ADS Title: Force-free and Potential Models of a Filament Channel in Which a Filament Forms Authors: Mackay, D. H.; Gaizauskas, V.; Rickard, G. J.; Priest, E. R. Bibcode: 1997ApJ...486..534M Altcode: Few examples of the creation of a filament channel or filament have ever been documented. In a recent paper, Gaizauskas and coworkers observed the early stages of creation of such a channel and then the formation of a filament in it. The filament channel was born when a new activity complex emerged near an old, decaying bipolar active region. The filament itself then formed after convergence of flux in the channel.

In this paper, force-free models are constructed for two phases of the channel's development. For the early days, the models show that the formation of the filament channel seen in Hα is due to the emerging activity complex. The field lines that give the best comparison to the fibril observations are low-lying and have a strong horizontal component. Later, when the activity complex has matured and a filament has formed between it and the adjacent decaying bipolar region, the models give a good representation of the path of the filament in the channel. It is found that the presence of flat or dipped field lines and of converging flux are necessary but not sufficient conditions for filament formation. Furthermore, the magnetic field lines of the filament itself form a narrow, vertical, sheetlike flux-tube corridor that is flat and low-lying. It connects one particular magnetic source to a sink and is bounded by separatrix surfaces that separate the filament from the old remnant region and most of the newly emerged flux. Title: The Skew of Polar Crown X-ray Arcades Authors: McAllister, A. H.; Mackay, D.; Hundhausen, A. J.; Priest, E. Bibcode: 1997SPD....28.0255M Altcode: 1997BAAS...29..903M A one-to-one relationship between the chirality of filament channels and the skew (relative orientation) of the overlying coronal arcades, as seen with the Yohkoh Soft X-ray Telescope (SXT) was found by Martin and McAllister [1997]. The basis of the relationship is a sample of over 30 mid-and low-latitude filaments during a 6 month period in early 1992. This relationship can be coupled with the predictions for the axial component of polar crown filaments based on the work of Leroy et al. [1983] to predict the skew of polar crown arcades in the recent cycle 22. Thus the axial component of the filament fields along the southern polar crown is predicted to point to the west and a similar component in the corona will lead to right skewed arcades. As has been pointed out in the past, this orientation is inconsistent with the action of photospheric differential rotation on an east-west arcade [Ballegooijen and Martens, 1990]. In this poster we report on the results of a recent survey of the SXT images over the whole declining phase of cycle 22 (Oct. 1991 to June 1995). These results are not in general agreement with those expected based on the past filament observations. They show highly left skewed polar arcades rather than the predicted right skew. The observations are, however, in general agreement with the effects of differential rotation and with recent numerical simulations of polar crown structures, which we will also briefly present. This posses an unexpected and challenging problem and we will discuss some possible ways of reconciling the different observational results. Leroy, Bommier, and Sahal-Brechot, The Magnetic Field in Prominences of the Polar Crown, Solar Physics, 83, 135-142, 1983. Martin and McAllister, The Chirality of X-ray Coronal Arcades Overlying Quiescent Filaments, Astrophys. Journ., submitted, 1997. Ballegooijen and Martens, Magnetic Fields in Quiescent Prominences, ApJ, 361, 283-289, 1990. Title: Basic magnetic field configurations for filament channels and filaments Authors: Mackay, D. H.; Priest, E. R. Bibcode: 1997A&AT...13..111M Altcode: Recent observations of Martin et al. have revealed two new magnetic and structural classes for solar filaments and filament channels. The magnetic classes are called sinistral and dextral while the structural classes are left-bearing and right-bearing. A potential model of the magnetic field in a filament channel consistent with the observations is developed, including the magnetic sources of network flux on both sides of the channel and concentrations of flux along the channel. A particular filament channel is also modelled by a set of discrete magnetic sources and sinks approximating the observed flux of the channel. In addition, the bending of a filament as it passes between opposite polarity sources is modelled. Title: Basic magnetic field configurations for solar filament channels and filaments Authors: Mackay, Duncan H. Bibcode: 1997PhDT.......376M Altcode: The three-dimensional magnetic structure of solar filament channels and filaments is considered. A simple analytical potential model of a filament channel is setup with line sources representing the overlying arcades and point sources the flux of the filament. A possible explanation of the distinct upper and lower bounds of a filament is given. A more detailed numerical force-free model with discrete flux sources is then developed and the effect of magnetic shear on the separatrix surface explored. Dextral channels are shown to exist for a wider range of negative values of the force-free alpha and sinistral channels for positive values of alpha. Potential models of a variety of coronal structures are then considered. The bending of a filament is modelled and a method of determining the horizontal component of a filament's magnetic field is proposed. Next, the observed opposite skew of arcades lying above switchbacks of polarity inversion lines is shown to be produced by a local flux imbalance at the corner of the switchback. Then, the magnetic structure of a particular filament in a filament channel is modelled using observations from a photospheric magnetogram. It is shown that dips in the filaments magnetic field could result from opposite polarity fragments lying below the filament. Finally, the formation of a specific filament channel and filament is modelled. The formation of the channel is shown to be due to the emergence of new flux in a sheared state. It is shown that convergence and reconnections between the new flux and old remnant flux is required for the filament to form. The field lines that represent the filament form a thin vertical sheet of flux. The changing angle of inclination of the sheet gives the appearance of twist. The method of formation is then generalised to other cases and it is shown that a hemispheric pattern consistent with the results of Martin et al. (1995) can be obtained. Title: A Potential-Field Model for Dextral and Sinistral Filament Channels Authors: Mackay, D. H.; Priest, E. R. Bibcode: 1996SoPh..167..281M Altcode: Recent observations of Martin, Bilimoria, and Tracadas (1995) have revealed two new magnetic and structural classes for solar filaments and filament channels. The magnetic classes are called sinistral and dextral, while the structural classes are left-bearing and right-bearing. Dextral filaments dominate in the northern hemisphere and sinistral in the southern. A model consistent with the observations is developed with magnetic sources that represent the network flux on both sides of the channel and extra concentrations of flux that produce the strong field component along the channel. We suggest that it is the imbalance of flux locations along the channel that creates the field of a filament channel. The resulting separatrix surfaces have distinct upper and lower boundaries that may produce the upper boundary of the filament cavity or filament and the lower boundary of the filament. The model is applied to a specific filament channel, with discrete sources and sinks that represent the flux observed in a photospheric magnetogram. The resulting three-dimensional field lines near the filament location are low-lying and possess dips. Title: A Model for Dextral and Sinistral Prominences Authors: Priest, E. R.; van Ballegooijen, A. A.; Mackay, D. H. Bibcode: 1996ApJ...460..530P Altcode: In a recent paper Martin and coworkers have discussed several striking facts about the structure of solar prominences and the filament channels in which they lie. They form two classes, called dextral and sinistral. In a dextral (sinistral) prominence, an observer viewing a prominence or filament channel from the positive-polarity side would see the magnetic field point to the right (left) along the axis of the filament channel, whereas an observer viewing from above would see the prominence feet bear off the axis to the right (left). Furthermore, dextral prominences dominate the northern hemisphere and sinistral the southern hemisphere, regardless of the cycle. Fibrils in the filament channels do not cross the prominence but usually stream from or to plagettes parallel to the prominence axis.

These pioneering observations suggest that there is a coherent organizational principle orchestrating the global nature of prominences, and they have led us to reexamine the standard paradigms of contemporary prominence theory, such as that (1) prominences form in a sheared force-free arcade, (2) formation is by radiative instability, (3) the prominence material is static, and (4) eruption occurs when the shear or twist is too great. We propose a new model which accounts for the above new observational features in a natural way, replaces many of the above paradigms, and explains the previously puzzling feet of a prominence. It is a dynamic model in which a prominence is maintained by the continual input of mass and magnetic flux. The correct global dextral and sinistral patterns for high-latitude east-west prominences (such as those in the polar crown) are created by an organizational principle that includes the combined effects of differential rotation on subphotospheric flux, its subsequent emergence by magnetic buoyancy, and its rearrangement by flux reconnection to form a filament channel with magnetic flux oriented along its axis. Continual emergence and reconnection creates a prominence as a flux tube along the filament channel axis and filled with cool plasma which is lifted up from the photosphere and chromosphere by the reconnection process. Prominences at low latitudes are in this model formed in a similar way, except that it is a general subphotospheric flow (rather than differential rotation) which acts and so may produce either dextral or sinistral structures, depending on the sense of the flow. The effect of neighboring plagettes in avoiding the prominence and making it snake its way along the filament channel is modeled. It is suggested that feet are short-lived structures caused by the interaction of nearby magnetic fragments with the prominence field and may represent either the addition or the extraction of mass from the prominence.