Author name code: zacharias ADS astronomy entries on 2022-09-14 author:"Zacharias, Pia" ------------------------------------------------------------------------ Title: High-resolution observations of the solar photosphere, chromosphere, and transition region. A database of coordinated IRIS and SST observations Authors: Rouppe van der Voort, L. H. M.; De Pontieu, B.; Carlsson, M.; de la Cruz Rodríguez, J.; Bose, S.; Chintzoglou, G.; Drews, A.; Froment, C.; Gošić, M.; Graham, D. R.; Hansteen, V. H.; Henriques, V. M. J.; Jafarzadeh, S.; Joshi, J.; Kleint, L.; Kohutova, P.; Leifsen, T.; Martínez-Sykora, J.; Nóbrega-Siverio, D.; Ortiz, A.; Pereira, T. M. D.; Popovas, A.; Quintero Noda, C.; Sainz Dalda, A.; Scharmer, G. B.; Schmit, D.; Scullion, E.; Skogsrud, H.; Szydlarski, M.; Timmons, R.; Vissers, G. J. M.; Woods, M. M.; Zacharias, P. Bibcode: 2020A&A...641A.146R Altcode: 2020arXiv200514175R NASA's Interface Region Imaging Spectrograph (IRIS) provides high-resolution observations of the solar atmosphere through ultraviolet spectroscopy and imaging. Since the launch of IRIS in June 2013, we have conducted systematic observation campaigns in coordination with the Swedish 1 m Solar Telescope (SST) on La Palma. The SST provides complementary high-resolution observations of the photosphere and chromosphere. The SST observations include spectropolarimetric imaging in photospheric Fe I lines and spectrally resolved imaging in the chromospheric Ca II 8542 Å, Hα, and Ca II K lines. We present a database of co-aligned IRIS and SST datasets that is open for analysis to the scientific community. The database covers a variety of targets including active regions, sunspots, plages, the quiet Sun, and coronal holes. Title: Disentangling flows in the solar transition region Authors: Zacharias, P.; Hansteen, V. H.; Leenaarts, J.; Carlsson, M.; Gudiksen, B. V. Bibcode: 2018A&A...614A.110Z Altcode: 2018arXiv180407513Z Context. The measured average velocities in solar and stellar spectral lines formed at transition region temperatures have been difficult to interpret. The dominant redshifts observed in the lower transition region naturally leads to the question of how the upper layers of the solar (and stellar) atmosphere can be maintained. Likewise, no ready explanation has been made for the average blueshifts often found in upper transition region lines. However, realistic three-dimensional radiation magnetohydrodynamics (3D rMHD) models of the solar atmosphere are able to reproduce the observed dominant line shifts and may thus hold the key to resolve these issues.
Aims: These new 3D rMHD simulations aim to shed light on how mass flows between the chromosphere and corona and on how the coronal mass is maintained. These simulations give new insights into the coupling of various atmospheric layers and the origin of Doppler shifts in the solar transition region and corona.
Methods: The passive tracer particles, so-called corks, allow the tracking of parcels of plasma over time and thus the study of changes in plasma temperature and velocity not only locally, but also in a co-moving frame. By following the trajectories of the corks, we can investigate mass and energy flows and understand the composition of the observed velocities.
Results: Our findings show that most of the transition region mass is cooling. The preponderance of transition region redshifts in the model can be explained by the higher percentage of downflowing mass in the lower and middle transition region. The average upflows in the upper transition region can be explained by a combination of both stronger upflows than downflows and a higher percentage of upflowing mass. The most common combination at lower and middle transition region temperatures are corks that are cooling and traveling downward. For these corks, a strong correlation between the pressure gradient along the magnetic field line and the velocity along the magnetic field line has been observed, indicating a formation mechanism that is related to downward propagating pressure disturbances. Corks at upper transition region temperatures are subject to a rather slow and highly variable but continuous heating process.
Conclusions: Corks are shown to be an essential tool in 3D rMHD models in order to study mass and energy flows. We have shown that most transition region plasma is cooling after having been heated slowly to upper transition region temperatures several minutes before. Downward propagating pressure disturbances are identified as one of the main mechanisms responsible for the observed redshifts at transition region temperatures.

The movie associated to Fig. 3 is available at http://www.aanda.org Title: New insights on mass flows in and out of the solar transition region Authors: Zacharias, Pia Bibcode: 2017psio.confE..56Z Altcode: No abstract at ADS Title: Tracing Flows in the Solar Atmosphere Using the Bifrost Stellar Atmosphere Code Authors: Zacharias, P. Bibcode: 2015AGUFMSH31B2409Z Altcode: All energy that heats the solar corona must pass through the transition region between the chromosphere and corona. Observations of transition region emission lines reveal the presence of redshifts up to temperatures of about 200,000 K and blueshifts for higher temperatures. The apparent large downward flows in the lower transition region would lead to an emptying of the corona, in contrast to what is being observed, thus some mechanism must be responsible for maintaining the mass balance between the photosphere and corona. We use the Bifrost stellar atmosphere code to perform 3D radiation MHD simulations of the solar atmosphere. The focus of this study is on the temporal evolution of mass flows into and out of the solar corona. By adding tracer particles to the simulations and analyzing their paths over time, we can provide new insights on the physical processes driving these mass flows and on their role in the chromosphere-corona mass cycle. Title: Analysis of mass and energy flows in coronal loops using the Bifrost stellar atmosphere code Authors: Zacharias, Pia; Leenaarts, Jorritt Bibcode: 2014cosp...40E3750Z Altcode: Identifying and quantifying processes that lead to the regulation of the mass and energy supply from the chromosphere to the outer layers of the solar atmosphere is key to advancing our understanding of the coupling between the solar chromosphere and corona. The combination of large-scale numerical simulations of the rapidly evolving detailed physical processes occurring in the solar atmosphere and high-resolution observations from instruments like IRIS, Hinode and SDO makes this undertaking more and more feasible. Using the Bifrost stellar atmosphere code, we have performed 3D radiation MHD simulations of the solar atmosphere extending from the convection zone to the corona to study the evolution of magnetic field structures and the underlying dynamics. By adding tracer particles to the simulation, we are able to follow the magnetic field lines properly. A detailed analysis of the plasma properties along those field lines and of the generation and propagation of waves travelling into the corona will be presented. By tracking the evolution of the observed perturbations, we provide new insights on the physical processes driving them and on their role in the chromosphere-corona mass cycle. Title: Studies of the dynamics and energetics of cool plasma ejections into the corona Authors: Zacharias, Pia; Bingert, Sven; Peter, Hardi Bibcode: 2013enss.confE.142Z Altcode: The corona is highly dynamic and shows transient events on various scales in space and time. Most of these features are related to changes in the magnetic field structure or impulsive heating caused by the conversion of magnetic to thermal energy. We are applying three-dimensional magnetohydrodynamic models in order to investigate the structure and dynamics in the upper solar atmosphere above a small active region. Emission line spectra are synthesized from the model and compared to spectra and images observed by current space-based instruments, such as the EUV Imaging Spectrometer (EIS) onboard the Hinode satellite and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory. We investigate mass and energy flows between the solar chromosphere and corona and discuss possible scenarios for a mass cycle between the lower and upper solar atmosphere. In particular, we have studied the processes that lead to the formation and ejection of a confined plasma ejection into the solar corona. A description of the nature of this particular feature will be presented which is found to be a hydrodynamic phenomenon triggered by a heating event above the chromosphere. A detailed analysis of 1D coronal loop models has been performed to understand how the plasma responds to a heating pulse. The results confirm the formation mechanism of the blob observed in the 3D model. This raises the question if other small-scale ejection features seen on the Sun could also be based on hydrodynamic processes instead of being plasmoid-type phenomena as it is usually assumed. Title: Mass flows between the chromosphere and corona - comparison of 1D and 3D coronal loop models Authors: Zacharias, P.; Bingert, S.; Peter, H. Bibcode: 2012AGUFMSH33B2239Z Altcode: The ejection and return of cool transition region plasma into the corona will be discussed in the context of our three-dimensional magnetohydrodynamic (3D MHD) model of the solar corona. The dynamics of the ejection are investigated in more detail in a 1D loop model and are compared to observations from Hinode/EIS and SDO/AIA. Results from the 3D model analysis serve as input for the 1D loop model. In the 3D case, a heating pulse is the main driver of the ejection. To mimic the situation in 1D, a heating pulse is injected at different heights along the loop with varying amplitude and width. As a consequence, the heating rate is strongly increased in a localized area and leads to enhanced evaporation that causes the material to rise. We present results that show the successful reproduction of the ejection in a 1D loop model following the injection of a heating pulse. In contrast to earlier studies, where similar heating events lead to both redshifts in transition region emission lines and blueshifts in coronal emission lines, preliminary results of our parameter study show exclusively upflows along the loop and almost no downflows during the heating phase. We will discuss these findings in terms of the mass cycle between the chromosphere and corona. Title: Ejection of cool plasma into the corona - comparison of results from a 3D MHD model with results from AIA/SDO, EIS/Hinode and a 1D loop model Authors: Zacharias, Pia; Bingert, Sven; Peter, Hardi Bibcode: 2012decs.confE..48Z Altcode: The formation and subsequent ejection of cool plasma into the corona will be discussed, as observed in our three-dimensional magnetohydrodynamic (3D MHD) model of the solar atmosphere extending from the photosphere into the corona. The model accounts properly for the energy balance, especially for heat conduction and radiative losses, allowing us to reliably synthesize the profiles of optically thin extreme ultraviolet emission lines and compare them to existing observations. A detailed description of the nature of this particular phenomenon will be provided. The analysis of the various forces acting upon the plasma in the 3D model shows that the pressure gradient which is driving the ejection is due to Ohmic dissipation of currents resulting from the braiding of the magnetic field lines by photospheric plasma motions. Preliminary results of a parameter study on the reproduction of the phenomenon in a one-dimensional loop model support the scenario of a heating event that leads to the ejection of cool plasma into the corona in both, the 1D loop model and the 3D model. In addition, results of the numerical model will be compared to observations from the Extreme Ultraviolet Imaging Spectrometer (EIS) onboard Hinode and the Atmospheric Imaging Assembly (AIA) onboard SDO, where we have also found evidence of cool plasma ejecta that are moving along magnetic field lines. Title: Ejection of cool plasma into the hot corona Authors: Zacharias, P.; Peter, H.; Bingert, S. Bibcode: 2011A&A...532A.112Z Altcode: 2011arXiv1106.5972Z Context. The corona is highly dynamic and shows transient events on various scales in space and time. Most of these features are related to changes in the magnetic field structure or impulsive heating caused by the conversion of magnetic to thermal energy.
Aims: We investigate the processes that lead to the formation, ejection and fall of a confined plasma ejection that was observed in a numerical experiment of the solar corona. By quantifying physical parameters such as mass, velocity, and orientation of the plasma ejection relative to the magnetic field, we provide a description of the nature of this particular plasma ejection.
Methods: The time-dependent three-dimensional magnetohydrodynamic (3D MHD) equations are solved in a box extending from the chromosphere, which serves as a reservoir for mass and energy, to the lower corona. The plasma is heated by currents that are induced through field line braiding as a consequence of photospheric motions included in the model. Spectra of optically thin emission lines in the extreme ultraviolet range are synthesized, and magnetic field lines are traced over time. We determine the trajectory of the plasma ejection and identify anomalies in the profiles of the plasma parameters.
Results: Following strong heating just above the chromosphere, the pressure rapidly increases, leading to a hydrodynamic explosion above the upper chromosphere in the low transition region. The explosion drives the plasma, which needs to follow the magnetic field lines. The ejection is then moving more or less ballistically along the loop-like field lines and eventually drops down onto the surface of the Sun. The speed of the ejection is in the range of the sound speed, well below the Alfvén velocity.
Conclusions: The plasma ejection observed in a numerical experiment of the solar corona is basically a hydrodynamic phenomenon, whereas the rise of the heating rate is of magnetic nature. The granular motions in the photosphere lead (by chance) to a strong braiding of the magnetic field lines at the location of the explosion that in turn is causing strong currents which are dissipated. Future studies need to determine if this process is a ubiquitous phenomenon on the Sun on small scales. Data from the Atmospheric Imaging Assembly on the Solar Dynamics Observatory (AIA/SDO) might provide the relevant information.

Appendix and movie are available in electronic form at http://www.aanda.org Title: Investigation of mass flows in the transition region and corona in a three-dimensional numerical model approach Authors: Zacharias, P.; Peter, H.; Bingert, S. Bibcode: 2011A&A...531A..97Z Altcode: 2011arXiv1105.5491Z Context. The origin of solar transition region redshifts is not completely understood. Current research is addressing this issue by investigating three-dimensional magneto-hydrodynamic models that extend from the photosphere to the corona.
Aims: By studying the average properties of emission line profiles synthesized from the simulation runs and comparing them to observations with present-day instrumentation, we investigate the origin of mass flows in the solar transition region and corona.
Methods: Doppler shifts were determined from the emission line profiles of various extreme-ultraviolet emission lines formed in the range of T = 104-106 K. Plasma velocities and mass flows were investigated for their contribution to the observed Doppler shifts in the model. In particular, the temporal evolution of plasma flows along the magnetic field lines was analyzed.
Results: Comparing observed vs. modeled Doppler shifts shows a good correlation in the temperature range log (T/[K]) = 4.5-5.7, which is the basis of our search for the origin of the line shifts. The vertical velocity obtained when weighting the velocity by the density squared is shown to be almost identical to the corresponding Doppler shift. Therefore, a direct comparison between Doppler shifts and the model parameters is allowed. A simple interpretation of Doppler shifts in terms of mass flux leads to overestimating the mass flux. Upflows in the model appear in the form of cool pockets of gas that heat up slowly as they rise. Their low temperature means that these pockets are not observed as blueshifts in the transition region and coronal lines. For a set of magnetic field lines, two different flow phases could be identified. The coronal part of the field line is intermittently connected to subjacent layers of either strong or weak heating, leading either to mass flows into the loop (observed as a blueshift) or to the draining of the loop (observed as a redshift). Title: On the nature of coronal loops above the quiet sun network Authors: Bingert, S.; Zacharias, P.; Peter, H.; Gudiksen, B. V. Bibcode: 2010AdSpR..45..310B Altcode: The structure and dynamics of a box in a stellar corona can be modeled employing a 3D MHD model for different levels of magnetic activity. Depending on the magnetic flux through the surface the nature of the resulting coronal structures can be quite different. We investigate a model of an active region for two sunspots surrounded by magnetic field patches comparable in magnetic flux to the sunspots. The model results in emission from the model corona being concentrated in loop structures. In Gudiksen and Nordlund (2005) the loops seen in EUV and X-ray emission outline the magnetic field, following the general paradigm. However, in our model, where the magnetic field is far from a force-free state, the loops seen in X-ray emission do not follow the magnetic field lines. This result is of interest especially for loops as found in areas where the magnetic field emerging from active regions interacts with the surrounding network. Title: Spectral analysis of 3D MHD models of coronal structures Authors: Zacharias, Pia; Bingert, Sven; Peter, Hardi Bibcode: 2009AdSpR..43.1451Z Altcode: 2009arXiv0904.2312Z We study extreme-ultraviolet emission line spectra derived from three-dimensional magnetohydrodynamic models of structures in the corona. In order to investigate the effects of increased magnetic activity at photospheric levels in a numerical experiment, a much higher magnetic flux density is applied at the photosphere as compared to the Sun. Thus, we can expect our results to highlight the differences between the Sun and more active, but still solar-like stars. We discuss signatures seen in extreme-ultraviolet emission lines synthesized from these models and compare them to observed signatures in the spatial distribution and temporal evolution of Doppler shifts in lines formed in the transition region and corona. This is of major interest to test the quality of the underlying magnetohydrodynamic model to heat the corona, i.e. currents in the corona driven by photospheric motions (flux braiding). Title: Doppler shifts in the transition region and corona. Mass cycle between the chromosphere and the corona Authors: Zacharias, P.; Bingert, S.; Peter, H. Bibcode: 2009MmSAI..80..654Z Altcode: Emission lines in the transition region and corona show persistent line shifts. It is a major challenge to understand the dynamics in the upper atmosphere and thus these line shifts, which are a signature of the mass cycle between the chromosphere and the corona. We examine EUV emission line profiles synthesized from a 3D MHD coronal model of a solar-like corona, in particular of an active region surrounded by strong chromospheric network. This allows us to investigate the physical processes leading to the line Doppler shifts, since we have access to both, the synthetic spectra and the physical parameters, i.e. magnetic field, temperature and density in the simulation box. By analyzing the evolution of the flows along field lines together with the changing magnetic structure we can investigate the mass cycle. We find evidence that loops are loaded with mass during a reconnection process, leading to upflows. After the loops disconnect from the reconnection site, they cool and drain which leads to the observed redshifts. Previous 1D loop models (neglecting the 3D nature) assumed that heating leads to evaporation and upflows followed by a cooling phase after the heating stops. The scenario modeled here is quite different, as it shows that the continuously changing three-dimensional magnetic structure is of pivotal importance to understand the mass balance between the chromosphere and the corona. Title: Spectral Analysis of 3D MHD Models of Quiet Sun and Active Region Structures Authors: Zacharias, P.; Bingert, S.; Peter, H. Bibcode: 2008ESPM...12.3.39Z Altcode: We study EUV emission line spectra derived from 3D MHD models of structures in the corona, in particular of an active region surrounded by a strong chromospheric network. The 3D MHD models account properly for the energy balance, especially for heat conduction and radiative losses. This allows us to reliably synthesize the profiles of EUV emission lines observable with current EUV spectrometers, e.g. SUMER/SOHO and EIS/Hinode. We investigate the temporal evolution and spatial distribution of the Doppler shifts of the EUV emission lines synthesized from these models. This is of major interest for the underlying mechanism of the heating of the solar corona, i.e. dissipation of currents in the corona driven by photospheric motions (flux braiding). Based on the 3D MHD models we can also derive intensity maps as they will be observed through the coronal channels of the AIA-instrument onboard SDO and we can analyze how to process the AIA maps in order to derive physical quantities such as temperatures and densities. Since we have access not only to the synthetic spectra, but also to the magnetic field in the box we can explore how the magnetic field relates to the emission in various coronal lines. In the present paper we will show results on the evolution of spectral properties such as line shifts or widths in different modeled coronal structures and compare these to results from SUMER/SOHO as well as EIS/Hinode data. Title: On the Nature of Coronal Loops Authors: Bingert, S.; Zacharias, P.; Peter, H.; Gudiksen, B. Bibcode: 2008ESPM...12.3.29B Altcode: The structure and dynamics of a box in a stellar corona can be modeled employing a 3D MHD model for different levels of magnetic activity.

Depending on the magnetic flux through the surface the nature of the resulting coronal structures can be quite different.

We will compare two different models of an active region, one for two basically isolated sunspots, and another one for two sunspots surrounded by magnetic field patches similar to the chromospheric network.

The current paradigm is that these loops follow magnetic field lines as pearls on a string, and thus the majority of present corona models describe structures following the field lines.

Our study challenges this paradigm by showing through a three-dimensional model that coronal structures in complex magnetic field geometries might appear loop-like while they are not aligned with the magnetic field.

Using a forward model approach, both models result in emission from the corona being concentrated in loop structures.

In the first case the loops seen in EUV and X-ray emission are following the magnetic field.

However, in the second case, where the magnetic field is far from a force-free state, the loops seen in X-ray emission do not follow the magnetic field, but are more related to the current sheets formed in response to the footpoint motions of the magnetic field.

This result is of interest especially for loops as found in areas where the magnetic field emerging from active regions interacts with the surrounding network or in the complex magnetic structures within chromospheric network patches. Title: On the nature of coronal loops Authors: Bingert, Sven; Zacharias, Pia; Peter, Hardi Bibcode: 2008cosp...37..302B Altcode: 2008cosp.meet..302B The structure and dynamics of a box in a stellar corona can be modeled employing a 3D MHD model for different levels of magnetic activity. In these models we account for the mass, momentum and energy balance including heat conduction and radiative losses. The heating is through current dissipation in the corona driven by photospheric motions (flux braiding). Depending on the magnetic flux through the surface the nature of the resulting coronal structures can be quite different. We will compare two different models of an active region, one for two basically isolated sunspots, and another one for two sunspots surrounded by strong magnetic field patches mimicking a strong chromospheric network. Both models result in emission from the model corona being concentrated in loop structures. In the first case the loops seen in EUV and X-ray emission are aligned with the magnetic field, following the general paradigm. However, in the second case, where the magnetic field is far from a force-free state, the loops seen in X-ray emission do not follow the magnetic field, but are related to the current sheets formed in response to the footpoint motions of the magnetic field. For the Sun this result is of interest especially for loops as found in areas where the magnetic field emerging from active regions interacts with the surrounding network. These models are now ready to face detailed comparisons with EUV spectroscopic observations from Hinode and imaging from SDO/AIA. Title: 3D MHD models compared to EUV observations of quiet Sun and active region structures Authors: Zacharias, Pia; Bingert, Sven; Peter, Hardi Bibcode: 2008cosp...37.3579Z Altcode: 2008cosp.meet.3579Z We study EUV emission line spectra derived from 3D MHD models of structures in the corona, in particular of an active region surrounded by a strong chromospheric network. The 3D MHD models account properly for the energy balance, especially for heat conduction and radiative losses, which allows us to reliably synthesize the profiles of EUV emission lines observable with current EUV spectrometers, i.e. SUMER/SOHO and EIS/Hinode. Thus we can directly compare these synthesized spectra to real observations with these instruments. We will discuss differences of models with different levels of magnetic activity in terms of signatures seen in EUV lines synthesized from these models and compare them to signatures found, e.g., in the spatial distribution and temporal evolution of Doppler shifts of lines formed in the transition region and corona. This is of major interest to test the quality of the underlying model to heat the corona, i.e. currents in the corona driven by photospheric motions (flux braiding). Based on the 3D MHD model we can also derive intensity maps as they will be observed through the coronal channels of the AIA-instrument on SDO. Through this we can provide some guidance on how to process the AIA maps in order to derive physical quantities such as temperature and density through a combination of filters. Title: Asteroseismological Studies of Long-Period Variable Subdwarf B Stars. II. Two-Color Photometry of PG 1338+481 Authors: Randall, S. K.; Green, E. M.; Fontaine, G.; Brassard, P.; Terndrup, D. M.; Brown, N.; Fontaine, M.; Zacharias, P.; Chayer, P. Bibcode: 2006ApJ...645.1464R Altcode: We present the results of an observational campaign for the long-period variable subdwarf B star PG 1338+481. Seven continuous weeks of observing time at the Steward Observatory 1.55 m Kuiper telescope on Mount Bigelow, Arizona, and the 1.3 m MDM telescope at Kitt Peak rendered ~250 hr of simultaneous U/R time series photometry, as well as an extra ~70 hr of R-band-only data. The analysis of the combined light curves resulted in the extraction of 13 convincing periodicities in the 2100-7200 s range, with amplitudes up to ~0.3% and ~0.2% in the U and R, respectively. Comparing the ratios of amplitudes in the two wave bands to those predicted from theory suggests the presence of dipole modes, a notion that is further supported by the period spacing between the highest amplitude peaks. If confirmed, this poses a challenge to current nonadiabatic theory. At the quantitative level, we find that the distribution of the observed period spectrum is highly nonuniform and much sparser than that predicted from a representative model. We provide a possible interpretation in the text. The asteroseismological analysis attempted for PG 1338+481 on the basis of six observed periodicities believed to constitute consecutive dipole modes renders encouraging results. Fixing the effective temperature and surface gravity to the spectroscopic estimates, we successfully isolate just one family of optimal models that can reproduce the measured periods to better than 1%. While the stellar parameters thus inferred must be regarded as preliminary, the achieved fit bodes well for future asteroseismic analyses of long-period variable subdwarf B stars.

Some of the observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution. Title: Fluctuations in Babcock-Leighton Dynamos. I. Period Doubling and Transition to Chaos Authors: Charbonneau, Paul; St-Jean, Cédric; Zacharias, Pia Bibcode: 2005ApJ...619..613C Altcode: We present a large series of numerical simulations of the solar magnetic activity cycle based on the Babcock-Leighton mechanism for the regeneration of the solar poloidal magnetic field. While the primary cycle period changes very little as the dynamo number is increased, the model shows a well-defined transition to chaos through a sequence of period-doubling bifurcations, i.e., the sequential appearance of modulations of the primary cycle's amplitude, with associated periods equal to twice the periods characterizing the amplitude variations prior to a given bifurcation. This behavior arises through the unavoidable time delay built into this type of solar dynamo model, rather than through the effects of complex, nonlinear magnetic back-reaction on the fluid motions driving the dynamo process. It is noteworthy that a chaotic regime exists in this numerical model, given that the only nonlinearity present is a simple algebraic amplitude-quenching factor in one of the governing partial differential equations. The results also represent a rare instance in which the complex dynamical behavior of a spatially extended, diffusive solar dynamo model can be reproduced in detail on the basis of the simplest of low-order dynamical systems, namely a one-dimensional iterative map. The numerical results also demonstrate the central role of meridional circulation in setting the primary cycle period in this class of dynamo models; despite variations by many orders of magnitude in the dynamo number and concomitant large and sometimes even chaotic variations in amplitude, the cycle period remains tightly locked to the meridional circulation turnover time.