Author name code: faurobert ADS astronomy entries on 2022-09-14 author:"Faurobert, Marianne" ------------------------------------------------------------------------ Title: Solar-cycle variations of internetwork magnetic fields Authors: Faurobert, M. Bibcode: 2022fysr.confE..40F Altcode: Small-scale magnetic fields in the quiet Sun contain in total more flux than active regions and represent an important reservoir of magnetic energy. But the origin and evolution of these fields still remain largely unknown. We present a study of the solar-cycle and center-to-limb variations of the magnetic-flux structures at small scales in the solar internetwork. We used Hinode SOT/Spectropolarimetric data from the irradiance program from 2008 to 2016 and applied a deconvolution to the Stokes profiles to correct them from the smearing due the Point Spread Function of the telescope. Then we performed a Fourier spectral analysis of the spatial fluctuations of the magnetic-flux density in 10"x10" internetwork regions spanning a wide range of latitudes. At low and mid latitudes and away from the active latitudes present at solar maximum, the power spectra do not vary significantly with the solar cycle. At high latitudes variations in opposition of phase with the solar cycle are observed at granular scales. Whatever the latitude the power of the magnetic fluctuations at scales smaller than 0.5" remain constant throughout the solar cycle. These results are in favor of a small-scale dynamo that operates in the internetwork. Title: HiRISE - High-Resolution Imaging and Spectroscopy Explorer - Ultrahigh resolution, interferometric and external occulting coronagraphic science Authors: Erdélyi, Robertus; Damé, Luc; Fludra, Andrzej; Mathioudakis, Mihalis; Amari, T.; Belucz, B.; Berrilli, F.; Bogachev, S.; Bolsée, D.; Bothmer, V.; Brun, S.; Dewitte, S.; de Wit, T. Dudok; Faurobert, M.; Gizon, L.; Gyenge, N.; Korsós, M. B.; Labrosse, N.; Matthews, S.; Meftah, M.; Morgan, H.; Pallé, P.; Rochus, P.; Rozanov, E.; Schmieder, B.; Tsinganos, K.; Verwichte, E.; Zharkov, S.; Zuccarello, F.; Wimmer-Schweingruber, R. Bibcode: 2022ExA...tmp...21E Altcode: Recent solar physics missions have shown the definite role of waves and magnetic fields deep in the inner corona, at the chromosphere-corona interface, where dramatic and physically dominant changes occur. HiRISE (High Resolution Imaging and Spectroscopy Explorer), the ambitious new generation ultra-high resolution, interferometric, and coronagraphic, solar physics mission, proposed in response to the ESA Voyage 2050 Call, would address these issues and provide the best-ever and most complete solar observatory, capable of ultra-high spatial, spectral, and temporal resolution observations of the solar atmosphere, from the photosphere to the corona, and of new insights of the solar interior from the core to the photosphere. HiRISE, at the L1 Lagrangian point, would provide meter class FUV imaging and spectro-imaging, EUV and XUV imaging and spectroscopy, magnetic fields measurements, and ambitious and comprehensive coronagraphy by a remote external occulter (two satellites formation flying 375 m apart, with a coronagraph on a chaser satellite). This major and state-of-the-art payload would allow us to characterize temperatures, densities, and velocities in the solar upper chromosphere, transition zone, and inner corona with, in particular, 2D very high resolution multi-spectral imaging-spectroscopy, and, direct coronal magnetic field measurement, thus providing a unique set of tools to understand the structure and onset of coronal heating. HiRISE's objectives are natural complements to the Parker Solar Probe and Solar Orbiter-type missions. We present the science case for HiRISE which will address: i) the fine structure of the chromosphere-corona interface by 2D spectroscopy in FUV at very high resolution; ii) coronal heating roots in the inner corona by ambitious externally-occulted coronagraphy; iii) resolved and global helioseismology thanks to continuity and stability of observing at the L1 Lagrange point; and iv) solar variability and space climate with, in addition, a global comprehensive view of UV variability. Title: Solar-cycle variations of internetwork magnetic fields Authors: Faurobert, M.; Ricort, G. Bibcode: 2021sf2a.conf..218F Altcode: Small-scale magnetic fields in the quiet Sun contain in total more flux than active regions and represent an important reservoir of magnetic energy. But the origin and evolution of these fields still remain largely unknown. We present a study of the solar-cycle and center-to-limb variations of the magnetic-flux structures at small scales in the solar internetwork. We used Hinode SOT/Spectropolarimetric data from the irradiance program from 2008 to 2016 and applied a deconvolution to the intensity and polarization profiles to correct them from the smearing due the Point Spread Function of the telescope. Then we performed a Fourier spectral analysis of the spatial fluctuations of the magnetic-flux density in 10''x10'' internetwork regions spanning a wide range of latitudes. At low and mid latitudes and away from the active latitudes present at solar maximum, the power spectra do not vary significantly with the solar cycle. At high latitudes variations in opposition of phase with the solar cycle are observed at granular scales. Whatever the latitude the power of the magnetic fluctuations at scales smaller than 0.5'' remain constant throughout the solar cycle. These results are in favor of a small-scale dynamo that operates in the internetwork. Title: New boundary conditions for the approximate flux-limited diffusion radiative transfer in circumstellar environments. Test case study for spherically symmetric envelopes Authors: Perdigon, J.; Niccolini, G.; Faurobert, M. Bibcode: 2021A&A...653A.139P Altcode: 2021arXiv210713993P Context. In order to constrain the models describing circumstellar environments, it is necessary to solve the radiative transfer equation in the presence of absorption and scattering, coupled with the equation for radiative equilibrium. However, solving this problem requires much CPU time, which makes the use of automatic minimisation procedures to characterise these environments challenging.
Aims: In this context, the use of approximate methods is of primary interest. One promising candidate method is the flux-limited diffusion (FLD), which recasts the radiative transfer problem into a non-linear diffusion equation. One important aspect for the accuracy of the method lies in the implementation of appropriate boundary conditions (BCs). We present new BCs for the FLD approximation in circumstellar environments that we apply here to spherically symmetric envelopes.
Methods: At the inner boundary, the entering flux (coming from the star and from the envelope itself) may be written in the FLD formalism and provides us with an adequate BC. At the free outer boundary, we used the FLD formalism to constrain the ratio of the mean radiation intensity over the emerging flux. In both cases we derived non-linear mixed BCs relating the surface values of the mean specific intensity and its gradient. We implemented these conditions and compared the results with previous benchmarks and the results of a Monte Carlo radiative transfer code. A comparison with results derived from BCs that were previously proposed in other contexts is presented as well.
Results: For all the tested cases, the average relative difference with the benchmark results is below 2% for the temperature profile and below 6% for the corresponding spectral energy distribution or the emerging flux. We point out that the FLD method together with the new outer BC also allows us to derive an approximation for the emerging flux. This feature avoids additional formal solutions for the radiative transfer equation in a set of rays (ray-tracing computations).
Conclusions: The FLD approximation together with the proposed new BCs performs well and captures the main physical properties of the radiative equilibrium in spherical circumstellar envelopes. Title: Magnetic flux structuring of the quiet Sun internetwork. Center-to-limb analysis of solar-cycle variations Authors: Faurobert, M.; Ricort, G. Bibcode: 2021A&A...651A..21F Altcode: 2021arXiv210508657F Context. The small-scale magnetism of the quiet Sun has been investigated by various means in recent decades. It is now well established that the quiet Sun contains in total more magnetic flux than active regions and represents an important reservoir of magnetic energy. But the nature and evolution of these fields remain largely unknown.
Aims: We investigate the solar-cycle and center-to-limb variations of magnetic-flux structures at small scales in internetwork regions of the quiet Sun.
Methods: We used Hinode SOT/SP data from the irradiance program between 2008 and 2016. Maps of the magnetic-flux density are derived from the center-of gravity method applied to the circular polarization profiles in the FeI 630.15 nm and FeI 630.25 nm lines. To correct the maps from the instrumental smearing of the telescope, we applied a deconvolution method based on a principal component analysis of the line profiles and on a Richardson-Lucy deconvolution of their coefficients. We took defocus effects and the diffraction of the SOT telescope into account. We then performed a spectral analysis of the spatial fluctuations of the magnetic-flux density in 10″ × 10″ internetwork regions spanning a wide range of latitudes from ±70° to the equator.
Results: At low and mid latitudes the power spectra normalized by the mean value of the unsigned flux in the regions do not vary significantly with the solar cycle. However at solar maximum for one scan in the activity belt showing an enhanced network, a marginal increase in the power of the magnetic fluctuations is observed at granular and larger scales in the internetwork. At high latitudes, we observe variations at granular and larger scales where the power decreases at solar maximum. At all the latitudes the power of the magnetic fluctuations at scales smaller than 0.5″ remains constant throughout the solar cycle.
Conclusions: At the equator the unsigned flux density is related to the vertical component of the magnetic field, whereas at high latitudes this flux density is mainly related to the horizontal component and probe higher altitudes. Our results favor a small-scale dynamo that operates in the internetwork, but they show that the global dynamo also contributes to the internetwork fields. At solar maximum the high-latitude horizontal internetwork fields seem to be depleted from the structures at granular and larger scales that are seen at solar minimum, whereas the internetwork within enhanced network regions show more structures at those scales than at solar minimum. Title: A new spectroscopic method for measuring the temperature gradient in the solar photosphere. Generalized application in magnetized regions Authors: Faurobert, M.; Criscuoli, S.; Carbillet, M.; Contursi, G. Bibcode: 2020A&A...642A.186F Altcode: Context. The contribution of quiet-Sun regions to the solar irradiance variability is currently unclear. Certain solar-cycle variations of the quiet-Sun's physical structure, such as the temperature gradient, might affect the irradiance. Accurate measurements of this quantity over the course of the activity cycle would improve our understanding of long-term irradiance variations.
Aims: In a previous work, we introduced and successfully tested a new spectroscopic method for measuring the photospheric temperature gradient directly on a geometric scale in the case of non-magnetic regions. In this paper, we generalize this method for moderately magnetized regions that may be encountered in the quiet solar photosphere.
Methods: To simulate spectroscopic observations, we used synthetic Stokes profiles I and V of the magnetic FeI 630.15 nm line and intensity profiles of the non-magnetic FeI 709 nm line computed from realistic three-dimensional magneto-hydrodynamical simulations of the photospheric granulation and line radiative transfer under local thermodynamical equilibrium conditions. We then obtained maps at different levels in the line-wings by convolution with the instrumental point spread function (PSF) under various conditions of atmospheric turbulence - with and without correction by an adaptive optics (AO) system. The PSF were obtained with the PAOLA software and the AO performance is inspired by the system that will be operating on the Daniel K. Inouye Solar Telescope.
Results: We considered different conditions of atmospheric turbulence and photospheric regions with different mean magnetic strengths of 100 G and 200 G. As in non-magnetic cases studied in our previous work, the image correction by the AO system is mandatory for obtaining accurate measurements of the temperature gradient. We show that the non-magnetic line at 709 nm may be safely used in all the cases we have investigated. However, the intensity profile of the magnetic-sensitive line is broadened by the Zeeman effect, which would bias our temperature-gradient measurement. We thus implemented a correction procedure of the line profile for this magnetic broadening in the case of weakly magnetized regions. In doing so, we remarked that in the weak-field regime, the right- and left-hand (I + V and I - V) components have similar shapes, however, they are shifted in opposite directions due to the Zeeman effect. We thus reconstructed the intensity profile by shifting back the I + V and I - V profiles and by adding the re-centered profiles. The measurement then proceeds as in the non-magnetic case. We find that this correction procedure is efficient in regions where the mean magnetic strength is smaller or on the order of 100 G.
Conclusions: The new method we implement here may be used to measure the temperature gradient in the quiet Sun from ground-based telescopes equipped with an efficient AO system. We stress that we derive the gradient on a geometrical scale and not on an optical-depth scale as we would do with other standard methods. This allows us to avoid any confusion due to the effect of temperature variations on the continuum opacity in the solar photosphere. Title: Chapter 8 - Solar and Stellar Variability Authors: Faurobert, Marianne Bibcode: 2019sgsp.book..267F Altcode: The Sun, like many cool stars on the main sequence, is variable. Changing dark and bright features, sunspots, and faculae appear and disappear on its surface. These variations are cyclic and related to a dynamo mechanism operating in the solar interior. The basic principles of the dynamo theories were presented in the previous chapter within the formalism of the mean field theory and its two branches, the flux-transport dynamos and the tachocline dynamos. However, many important problems remain to be solved to understand the magnetic activity of the Sun and stars.

In this chapter, we focus on observational studies of solar and stellar variability. This subject has been evolving quickly within the past decades thanks to the development of new space-borne and ground-based instruments, which have provided us with a wealth of data of unprecedented quality for both the Sun and stars. We will emphasize how knowledge and methods developed in the context of solar physics can serve as guides for stellar investigations and how, in turn, observation of stellar activity offers us a unique possibility of testing the dynamo theories through varying stellar parameters.

Because magnetic activity affects the radiative output of stars, we will examine variations in solar and stellar irradiance and discuss their modeling. This problem is related to the hotly debated subject of the impact of solar activity on the terrestrial climate and also to stars hosting exoplanets regarding the issue of accessing their habitability conditions. Title: Temperature gradient in the solar photosphere. Test of a new spectroscopic method and study of its feasibility for ground-based telescopes Authors: Faurobert, M.; Carbillet, M.; Marquis, L.; Chiavassa, A.; Ricort, G. Bibcode: 2018A&A...616A.133F Altcode: 2018arXiv180900893F Context. The contribution of quiet-Sun regions to the solar irradiance variability is currently unclear. Some solar-cycle variations of the quiet-Sun physical structure, such as the temperature gradient, might affect the irradiance. The synoptic measurement of this quantity along the activity cycle would improve our understanding of long-term irradiance variations.
Aims: We intend to test a method previously introduced for measuring the photospheric temperature gradient from high-resolution spectroscopic observation and to study its feasibility with ground-based instruments with and without adaptative optics.
Methods: We used synthetic profiles of the FeI 630.15 nm obtained from realistic three-dimensional hydrodynamical simulations of the photospheric granulation and line radiative transfer computations under local thermodynamical equilibrium conditions. Synthetic granulation images at different levels in the line are obtained by convolution with the instrumental point spread function (PSF) under various conditions of atmospheric turbulence, with and without correction by an adaptative optics (AO) system. The PSF are obtained with the PAOLA software, and the AO performances are inspired by the system that will be operating on the Daniel K. Inouye Solar Telescope.
Results: We consider two different conditions of atmospheric turbulence, with Fried parameters of 7 cm and 5 cm, respectively. We show that the degraded images lead to both a bias and a loss of precision in the temperature-gradient measurement, and that the correction with the AO system allows us to drastically improve the measurement quality.
Conclusions: Long-term synoptic observations of the temperature gradient in the solar photosphere can be undertaken by implementing this method on ground-based solar telescopes that are equipped with an AO correction system. Title: Quiet Sun magnetic fields Authors: Faurobert, M. Bibcode: 2017POBeo..96...39F Altcode: No abstract at ADS Title: Inference of magnetic fields in inhomogeneous prominences Authors: Milić, I.; Faurobert, M.; Atanacković, O. Bibcode: 2017A&A...597A..31M Altcode: 2016A&A...597A..31M; 2016arXiv160904954M Context. Most of the quantitative information about the magnetic field vector in solar prominences comes from the analysis of the Hanle effect acting on lines formed by scattering. As these lines can be of non-negligible optical thickness, it is of interest to study the line formation process further.
Aims: We investigate the multidimensional effects on the interpretation of spectropolarimetric observations, particularly on the inference of the magnetic field vector. We do this by analyzing the differences between multidimensional models, which involve fully self-consistent radiative transfer computations in the presence of spatial inhomogeneities and velocity fields, and those which rely on simple one-dimensional geometry.
Methods: We study the formation of a prototype line in ad hoc inhomogeneous, isothermal 2D prominence models. We solve the NLTE polarized line formation problem in the presence of a large-scale oriented magnetic field. The resulting polarized line profiles are then interpreted (I.e. inverted) assuming a simple 1D slab model.
Results: We find that differences between input and the inferred magnetic field vector are non-negligible. Namely, we almost universally find that the inferred field is weaker and more horizontal than the input field.
Conclusions: Spatial inhomogeneities and radiative transfer have a strong effect on scattering line polarization in the optically thick lines. In real-life situations, ignoring these effects could lead to a serious misinterpretation of spectropolarimetric observations of chromospheric objects such as prominences. Title: Variation of the photospheric temperature gradient with magnetic activity Authors: Faurobert, Marianne Bibcode: 2017psio.confE..16F Altcode: No abstract at ADS Title: Variation of the temperature gradient in the solar photosphere with magnetic activity Authors: Faurobert, M.; Balasubramanian, R.; Ricort, G. Bibcode: 2016A&A...595A..71F Altcode: Context. The contribution of quiet-Sun regions to the solar irradiance variability is currently unclear. Some solar-cycle variations of the quiet-Sun physical structure, such as the temperature gradient or the photospheric radius, might affect the irradiance.
Aims: We intend to investigate possible variations of the photospheric temperature gradient with magnetic activity.
Methods: We used high-resolution center-to-limb observations of the FeI 630.15 nm line profile in the quiet Sun performed onboard the Hinode satellite on 2007, December 19, and on 2013, December 7, that is, close to a minimum and a maximum of magnetic activity, respectively. We analyzed samples of 10″ × 10″ internetwork regions. The wings of the FeI 630.15 nm line were used in a non-standard way to recover images at roughly constant continuum optical depths above the continuum formation level. The image formation height is derived from measuring its perspective shift with respect to the continuum image, both observed away from disk center. The measurement relies on a cross-spectral method that is not limited by the spatial resolution of the SOT telescope and does not rely on any radiative transfer computation. The radiation temperature measured in the images is related to the photospheric temperature at their respective formation height.
Results: The method allows us to investigate the temperature gradient in the low photosphere at altitudes of between 0 and 60 km above the 500 nm continuum formation height. In this layer the internetwork temperature gradient appears steeper in our 2013 sample than in the sample of 2007 in the northern hemisphere, whereas we detect no significant change in the southern hemisphere. We argue that this might be related to some strong hemispheric asymmetry of the magnetic activity at the solar maximum of cycle 24.
Conclusions: Structural changes have been observed in numerical simulations of the magneto-convection at the surface of the Sun where the increase of the ambient sub-surface magnetic fields leads to some steepening of the temperature gradient in the internetwork. Hemispheric asymmetry of the activity has been reported for the last solar cycles with successive dominant north and south hemisphere during the activity maximum. Our results seem consistent with this global physical picture, but need to be confirmed by additional studies. Title: Fast inversion of Zeeman line profiles using central moments. II. Stokes V moments and determination of vector magnetic fields Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M. Bibcode: 2016A&A...591A..64M Altcode: Context. In the case of unresolved solar structures or stray light contamination, inversion techniques using four Stokes parameters of Zeeman profiles cannot disentangle the combined contributions of magnetic and nonmagnetic areas to the observed Stokes I.
Aims: In the framework of a two-component model atmosphere with filling factor f, we propose an inversion method restricting input data to Q , U, and V profiles, thus overcoming ambiguities from stray light and spatial mixing.
Methods: The V-moments inversion (VMI) method uses shifts SV derived from moments of V-profiles and integrals of Q2, U2, and V2 to determine the strength B and inclination ψ of a magnetic field vector through least-squares polynomial fits and with very few iterations. Moment calculations are optimized to reduce data noise effects. To specify the model atmosphere of the magnetic component, an additional parameter δ, deduced from the shape of V-profiles, is used to interpolate between expansions corresponding to two basic models.
Results: We perform inversions of HINODE SOT/SP data for inclination ranges 0 <ψ< 60° and 120 <ψ< 180° for the 630.2 nm Fe I line. A damping coefficient is fitted to take instrumental line broadening into account. We estimate errors from data noise. Magnetic field strengths and inclinations deduced from VMI inversion are compared with results from the inversion codes UNNOFIT and MERLIN.
Conclusions: The VMI inversion method is insensitive to the dependence of Stokes I profiles on the thermodynamic structure in nonmagnetic areas. In the range of Bf products larger than 200 G, mean field strengths exceed 1000 G and there is not a very significant departure from the UNNOFIT results because of differences between magnetic and nonmagnetic model atmospheres. Further improvements might include additional parameters deduced from the shape of Stokes V profiles and from large sets of 3D-MHD simulations, especially for unresolved magnetic flux tubes. Title: ADAHELI: exploring the fast, dynamic Sun in the x-ray, optical, and near-infrared Authors: Berrilli, Francesco; Soffitta, Paolo; Velli, Marco; Sabatini, Paolo; Bigazzi, Alberto; Bellazzini, Ronaldo; Bellot Rubio, Luis Ramon; Brez, Alessandro; Carbone, Vincenzo; Cauzzi, Gianna; Cavallini, Fabio; Consolini, Giuseppe; Curti, Fabio; Del Moro, Dario; Di Giorgio, Anna Maria; Ermolli, Ilaria; Fabiani, Sergio; Faurobert, Marianne; Feller, Alex; Galsgaard, Klaus; Gburek, Szymon; Giannattasio, Fabio; Giovannelli, Luca; Hirzberger, Johann; Jefferies, Stuart M.; Madjarska, Maria S.; Manni, Fabio; Mazzoni, Alessandro; Muleri, Fabio; Penza, Valentina; Peres, Giovanni; Piazzesi, Roberto; Pieralli, Francesca; Pietropaolo, Ermanno; Martinez Pillet, Valentin; Pinchera, Michele; Reale, Fabio; Romano, Paolo; Romoli, Andrea; Romoli, Marco; Rubini, Alda; Rudawy, Pawel; Sandri, Paolo; Scardigli, Stefano; Spandre, Gloria; Solanki, Sami K.; Stangalini, Marco; Vecchio, Antonio; Zuccarello, Francesca Bibcode: 2015JATIS...1d4006B Altcode: Advanced Astronomy for Heliophysics Plus (ADAHELI) is a project concept for a small solar and space weather mission with a budget compatible with an European Space Agency (ESA) S-class mission, including launch, and a fast development cycle. ADAHELI was submitted to the European Space Agency by a European-wide consortium of solar physics research institutes in response to the "Call for a small mission opportunity for a launch in 2017," of March 9, 2012. The ADAHELI project builds on the heritage of the former ADAHELI mission, which had successfully completed its phase-A study under the Italian Space Agency 2007 Small Mission Programme, thus proving the soundness and feasibility of its innovative low-budget design. ADAHELI is a solar space mission with two main instruments: ISODY: an imager, based on Fabry-Pérot interferometers, whose design is optimized to the acquisition of highest cadence, long-duration, multiline spectropolarimetric images in the visible/near-infrared region of the solar spectrum. XSPO: an x-ray polarimeter for solar flares in x-rays with energies in the 15 to 35 keV range. ADAHELI is capable of performing observations that cannot be addressed by other currently planned solar space missions, due to their limited telemetry, or by ground-based facilities, due to the problematic effect of the terrestrial atmosphere. Title: Do the quiet sun magnetic fields vary with the solar cycle? Authors: Faurobert, Marianne; Ricort, Gilbert; Lites, Bruce Bibcode: 2015IAUS..305...22F Altcode: The quiet Sun observed in polarized light exhibits a rich and complex magnetic structuring which is still not fully resolved nor understood. The present work is intended to contribute to the debate about the origin of the quiet sun magnetic fields, in relation or not to the global solar dynamo. We present analysis of center-to-limb polarization measurements obtained with the SOT/SP spectropolarimeter onboard the Hinode satellite outside active regions, in 2007 and 2013, i.e. at a minimum and a maximum of the solar cycle, respectively. We compare the spatial fluctuation Fourier spectra of unsigned circular and linear polarization images after corrections for polarization bias and focus variations between the two data sets. The decay of active regions is clearly a source of magnetic fields in the quiet Sun. It leads to a global increase of the polarization fluctuation power spectrum in 2013 in the network. In the internetwork, we observe no variation of the polarization fluctuation power at mesogranular and granular scales, whereas it increases at sub-granular scales. We interpret these results in the following way. At the mesogranular and granular scales very efficient mechanisms of magnetic field removal are operating in the internetwork, that leads to a dissipation or a concentration of magnetic fields on smaller scales. So the cycle-invariant magnetic signal that we detect at mesogranular and granular scales must be continuously created by a dynamo mechanism which is independent of the solar cycle. Title: Solar-cycle variations of the internetwork magnetic field Authors: Faurobert, M.; Ricort, G. Bibcode: 2015A&A...582A..95F Altcode: Context. The quiet Sun exhibits a rich and complex magnetic structuring that is still not fully resolved or understood.
Aims: We intend to contribute to the debate about the origin of the internetwork magnetic fields and whether or not they are related to the global solar dynamo.
Methods: We analyzed center-to-limb polarization measurements obtained with the SOT/SP spectropolarimeter onboard the Hinode satellite outside active regions in 2007 and 2013, that is, at a minimum and a maximum of the solar cycle, respectively. We examined 10'' × 10'' maps of the unsigned circular and linear polarization in the FeI 630.25 nm line in regions located away from network elements. The maps were corrected for bias and focus variations between the two data sets. Then we applied a Fourier spectral analysis to examine wether the spatial structuring of the internetwork magnetic fields shows significant differences between the minimum and maximum of the cycle.
Results: Neither the mean values of the unsigned circular and linear polarizations in the selected 10'' × 10'' maps nor their spatial fluctuation power spectra show significant center-to-limb variations. For the unsigned circular polarization the power of the spatial fluctuations is lower in 2013 than in 2007, but the spectral slope is unchanged. The linear polarization spectra show no significant differences in 2013 and 2007, but the spectrum of 2013 is more strongly affected by noise.
Conclusions: The small-scale magnetic structuring in the internetwork is different in our 2013 and 2007 data. Surprisingly, we find a lower spatial fluctuation power at the solar maximum in the internetwork magnetic structuring. This indicates some complex interactions between the small-scale magnetic structures in the quiet Sun and the global dynamo, as predicted by recent numerical simulations. This result has to be confirmed by further statistical studies with larger data sets. Title: Inhomogeneity and velocity fields effects on scattering polarization in solar prominences Authors: Milić, I.; Faurobert, M. Bibcode: 2015IAUS..305..238M Altcode: One of the methods for diagnosing vector magnetic fields in solar prominences is the so called "inversion" of observed polarized spectral lines. This inversion usually assumes a fairly simple generative model and in this contribution we aim to study the possible systematic errors that are introduced by this assumption. On two-dimensional toy model of a prominence, we first demonstrate importance of multidimensional radiative transfer and horizontal inhomogeneities. These are able to induce a significant level of polarization in Stokes U, without the need for the magnetic field. We then compute emergent Stokes spectrum from a prominence which is pervaded by the vector magnetic field and use a simple, one-dimensional model to interpret these synthetic observations. We find that inferred values for the magnetic field vector generally differ from the original ones. Most importantly, the magnetic field might seem more inclined than it really is. Title: New view on exoplanet transits. Transit of Venus described using three-dimensional solar atmosphere STAGGER-grid simulations Authors: Chiavassa, A.; Pere, C.; Faurobert, M.; Ricort, G.; Tanga, P.; Magic, Z.; Collet, R.; Asplund, M. Bibcode: 2015A&A...576A..13C Altcode: 2015arXiv150106207C Context. An important benchmark for current observational techniques and theoretical modeling of exoplanet atmospheres is the transit of Venus (ToV). Stellar activity and, in particular, convection-related surface structures, potentially cause fluctuations that can affect the transit light curves. Surface convection simulations can help interpreting the ToV as well as other transits outside our solar system.
Aims: We used the realistic three-dimensional (3D) radiative hydrodynamical (RHD) simulation of the Sun from the Stagger-grid and synthetic images computed with the radiative transfer code Optim3D to predict the transit of Venus (ToV) in 2004 that was observed by the satellite ACRIMSAT.
Methods: We computed intensity maps from the RHD simulation of the Sun and produced a synthetic stellar disk image as an observer would see, accounting for the center-to-limb variations. The contribution of the solar granulation was considered during the ToV. We computed the light curve and compared it to the ACRIMSAT observations as well as to light curves obtained with solar surface representations carried out using radial profiles with different limb-darkening laws. We also applied the same spherical tile imaging method as used for RHD simulation to the observations of center-to-limb solar granulation with Hinode.
Results: We explain ACRIMSAT observations of 2004 ToV and show that the granulation pattern causes fluctuations in the transit light curve. We compared different limb-darkening models to the RHD simulation and evaluated the contribution of the granulation to the ToV. We showed that the granulation pattern can partially explain the observed discrepancies between models and data. Moreover, we found that the overall agreement between real and RHD solar granulation is good, either in terms of depth or ingress/egress slopes of the transit curve. This confirms that the limb-darkening and granulation pattern simulated in 3D RHD of the Sun represent well what is imaged by Hinode. In the end, we found that the contribution of the Venusean aureole during ToV is ~10-6 times less intense than the solar photosphere, and thus, accurate measurements of this phenomena are extremely challenging.
Conclusions: The prospects for planet detection and characterization with transiting methods are excellent with access to large a amount of data for stars. Being able to consistently explain the data of 2004 ToV is a new step forward for 3D RHD simulations, which are becoming essential for detecting and characterizing exoplanets. They show that granulation has to be considered as an intrinsic uncertainty (as a result of stellar variability) on precise measurements of exoplanet transits of, most likely, planets with small diameters. In this context, it is mandatory to obtain a comprehensive knowledge of the host star, including a detailed study of the stellar surface convection. Title: Scattering line polarization in rotating, optically thick disks Authors: Milić, I.; Faurobert, M. Bibcode: 2014A&A...571A..79M Altcode: 2014arXiv1409.2654M Context. To interpret observations of astrophysical disks, it is essential to understand the formation process of the emitted light. If the disk is optically thick, scattering dominated and permeated by a Keplerian velocity field, non-local thermodynamic equilibrium (NLTE) radiative transfer modeling must be done to compute the emergent spectrum from a given disk model.
Aims: We investigate NLTE polarized line formation in different simple disk models and aim to demonstrate the importance of both radiative transfer effects and scattering, as well as the effects of velocity fields.
Methods: We self-consistently solve the coupled equations of radiative transfer and statistical equilibrium for a two-level atom model by means of Jacobi iteration. We use the short characteristics method of formal solution in two-dimensional axisymmetric media and compute scattering polarization, that is Q/I and U/I line profiles, using the reduced intensity formalism. We account for the presence of Keplerian velocity fields by casting the radiative transfer equation in the observer's frame.
Results: Relatively simple (homogeneous and isothermal) disk models show complex intensity profiles that owe their shape to the interplay of multidimensional NLTE radiative transfer and the presence of rotation. The degree of scattering polarization is significantly influenced not only by the inclination of the disk with respect to observer, but also by the optical thickness of the disk and the presence of rotation. Stokes U/I shows double-lobed profiles with amplitude that increases with the disk rotation.
Conclusions: Our results suggest that the line profiles, especially the polarized ones, emerging from gaseous disks differ significantly from the profiles predicted by simple approximations. Even in the case of the simple two-level atom model, we obtain line profiles that are diverse in shape, but typically symmetric in Stokes Q and antisymmetric in Stokes U. A clear indicator of disk rotation is the presence of Stokes U, which might prove to be a useful diagnostic tool. We also demonstrate that, for moderate rotational velocities, an approximate treatment can be used, where NLTE radiative transfer is done in the velocity field-free approximation, and Doppler shift is applied in the process of spatial integration over the whole emitting surface. Title: Possible measurements of the magnetic field in eruptive prominences using the PROBA-3 coronagraph Authors: Serge, Koutchmy; Zhukov, Andrei; Dolla, Laurent; Heinzel, Petr; Lamy, Philippe; Bazin, Cyrille; Bommier, Veronique; Faurobert, Marianne Bibcode: 2014cosp...40E2971S Altcode: The PROBA-3 mission will fly a spacecraft put in the shadow of a precisely occulting sister satellite orbiting “in formation” at a distance of 150 m in front of it to make artificial total eclipses. The region right above the solar limb will be studied for the first time over a coronal background not polluted by any spurious light. Although the priority will be the high-resolution fast imaging of the dynamic white-light corona, the use of a narrow filter centered on a low excitation D3 line of He I, is planned for imaging prominences. Adding the linear polarization analysis would permit the measurements of the magnetic field using the Hanle effect. We evaluate the possibility offered during the eruptive phase of a CME with prominence material inserted inside, for studying the associated magnetic field changes related to both the heating process and the ejection of material. The background highly polarized K-corona is taken into account. Sequences of quasi- simultaneous white-light processed images at high resolution are an additional feature of great interest for interpreting the overall magnetic structure. Title: Multidimensional and inhomogeneity effects on scattering polarization in solar prominences Authors: Milić, Ivan; Faurobert, Marianne Bibcode: 2014IAUS..300..453M Altcode: Measurements of magnetic fields in solar prominences via Hanle effect usually assume either single scattering approximation or simple, one-dimensional, slab model in order to perform an inversion and find the unknown magnitude and the orientation of the magnetic field from spectropolarimetric observations. Here we perform self-consistent NLTE modeling of scattering polarization in inhomogeneous 2D slab, illuminated from its sides by the solar continuum radiation. We show that even in the absence of a magnetic field, in the non-optically thin regime, significant non-zero Stokes U is to be expected. Neglecting these effects, in principle, could cause systematic errors in spectropolarimetric inversions, in the case when the prominence is optically thick. Title: Distribution of magnetic fields in the quiet Sun Authors: Faurobert, M.; Ricort, G. Bibcode: 2013A&A...560A..62F Altcode: Context. The distribution of magnetic fields in the atmosphere of the quiet Sun has been extensively studied with various methods, but it is still a matter of debate. Previous analyses mostly rely on the inversion of spectro-polarimetric data and different methods lead to somewhat different results.
Aims: Here we do not intend to determine the magnetic field vector, but we use total polarization images as tracers of the magnetic field distribution and we study their cross-correlations with granulation and reversed-granulation images.
Methods: We used high-resolution spectro-polarimetric scans obtained in the 630 nm FeI line pair at varying heliocentric angles along the north-south polar axis of the Sun, with the Solar Optical Telescope (SOT) onboard Hinode. We obtain polarization images by summing the total polarization (linear and circular) in each line. We compute the 2D correlation of polarization images and their cross-correlations with images of the granulation observed simultaneously in the line wings and with the reversed granulation observed in the line cores, and we examine their center-to-limb variations.
Results: The correlation-widths of polarization images have on the average, the same value (1.3'') as the correlation-width of the granulation, showing that the granular scale is a characteristic scale of the quiet Sun magnetic field distribution. At disk center the cross-correlation between total polarization and the granulation shows a negative peak. Out of disk-center both a negative and a positive peak are detected. The cross-correlation of polarization images with the reversed granulation always shows a positive peak. We assign these cross-correlation signals to the presence of two kinds of magnetized regions spatially separated, one of them is located in the intergranular lanes (anti-correlated with the granulation), the other one lies within the bright granules. For images obtained out of disk center, the correlation and anti-correlation peaks are shifted along the north-south direction and the shifts measured at the same limb-distance in the southern and northern hemispheres have opposite values. A consistent interpretation of these shifts is proposed in terms of a perspective effect arising when two images formed at different heights are observed at an angle. We were able to measure the perspective effect for the magnetic component correlated with the reversed granulation. Its polarization signals observed in the FeI 630.25 nm line and in the 630.15 nm line, are formed respectively 100 km and 150 km below the bright features seen at line centers. Title: Boundary conditions for polarized radiative transfer with incident radiation Authors: Faurobert, M.; Milić, I.; Atanacković, O. Bibcode: 2013A&A...559A..68F Altcode: 2013arXiv1309.4160F Context. Polarized radiative transfer in the presence of scattering in spectral lines and/or in continua may be cast in a reduced form for six reduced components of the radiation field. In this formalism, the six components of the reduced source function are angle-independent quantities. It thus drastically reduces the storage requirement of numerical codes and it is very well suited to solving polarized non-local thermodynamic equilibrium radiative transfer problems in 3D media.
Aims: This approach encounters a fundamental problem when the medium is illuminated by a polarized incident radiation, because there is a priori no way of relating the known (and measurable) Stokes parameters of the incident radiation to boundary conditions for the reduced equations. The origin of this problem is that there is no unique way of deriving the radiation-reduced components from its Stokes parameters (only the inverse operation is clearly defined). The method proposed here aims at enabling to work with arbitrary incident radiation field (polarized or unpolarized).
Methods: In previous studies, an ad-hoc treatment of the boundary conditions, applied to cases where the incident radiation is unpolarized, has been used. In this paper, we show that it is possible to account for the incident radiation in a rigorous way without any assumption on its properties by expressing the radiation field as the sum of a directly transmitted radiation and of a diffuse radiation. This approach was first used by Chandrasekhar to solve the problem of diffuse reflection by planetary atmospheres illuminated by their host star.
Results: The diffuse radiation field obeys a transfer equation with no incident radiation that may be solved in the reduced form. The first scattering of the incident radiation introduces primary creation terms in the six components of the reduced source function. Once the reduced polarized transfer problem is solved for the diffuse radiation field, its Stokes parameters can be computed. The full radiation field is then obtained by adding the directly transmitted radiation field computed in the Stokes formalism.
Conclusions: In the case of an unpolarized incident radiation, the diffuse field approach allows us to validate the previously introduced ad-hoc expressions. The diffuse field approach however leads to more accurate computation of the source terms in the case where the incident radiation is anisotropic. It is the only possible approach when the incident radiation field is polarized. We perform numerical computations of test cases, showing that the emergent line-polarization may be significantly affected by the polarization of the incident radiation. Title: Empirical determination of the temperature stratification in the photosphere of the quiet Sun Authors: Faurobert, M.; Ricort, G.; Aime, C. Bibcode: 2013A&A...554A.116F Altcode: Context. Detailed realistic 3D simulations of the photosphere of the Sun are now available, but 1D models of the average quiet-Sun photosphere are still widely used, in particular for spectro-polarimetric inversions.
Aims: Here we present an empirical determination of the average radiation temperature variations as a function of the geometrical height above the continuum formation level in the solar photosphere.
Methods: We used high resolution spectroscopic scans in the 630 nm Fe i line pair at varying heliocentric angles along the north-south polar axis of the Sun, made with SOT onboard Hinode. Implementing a new method for image reconstruction, we obtained images of the photospheric granulation at constant continuum opacity levels, from the upper photosphere seen at line centers to the low photosphere. The Fourier cross-spectra of images at different opacity levels were computed, and we derived the formation depths of images without referring to any atmospheric model, by measuring the slope of the cross-spectrum phase.
Results: A modified Milne-Eddington model for the line formation was tested by comparing it with the average line-intensity profiles observed at solar disk center. It yields consistent results for the FeI 630.2 nm line, whereas the FeI line at 630.1 nm is not well reproduced by the model. We ascribe this discrepancy to non-LTE effects in the line formation processes. The average image intensities at the different FeI 630.2 nm levels were used to determine the depth-variation of the temperature for an average 1D model of the quiet photosphere. We compared our empirical temperature model with the widely used FALC model. Both models agree well for the temperature variations with the continuum optical depth. But in the low photosphere, the temperature gradient we measure with respect to the geometrical height is significantly softer than in Model C. We argue that some of the assumptions used to solve the pseudohydrostatic equilibrium in semi-empirical models are probably at fault. We also derived empirical values for the 630 nm continuum absorption coefficient as a function of the geometrical height in the low photosphere. Finally, we were able to measure the altitude of the base of the granulation contrast inversion layer, which is found at about 130 km above the base of the photosphere, in agreement with 3D MHD simulations. Title: A cross-correlation method for measuring line formation heights in the solar photosphere Authors: Faurobert, M.; Ricort, G.; Aime, C. Bibcode: 2012A&A...548A..80F Altcode: Context. Detailed 3D-simulations of magneto-convection in the solar photosphere are now available. They intend to capture the main physical mechanisms at play in this boundary layer, where complex physical phenomena, such as convective overshooting and small scale magnetic dynamo take place. But numerical limitations in spatial resolution and in box-size are likely to affect the description of some relevant physical scales, so simulations need to be compared to independent observations allowing us to explore the full height range of the photosphere.
Aims: Here we focus on a model-independent method for measuring line formation depths. We construct images of the photosphere at constant continuum opacity levels from the low to the upper photosphere and we show how they can be used to measure systematic displacements of granular structures with height. The method is applied to determine the formation height of the 630 nm Fe i line pair. We compare our measurements to the results of 3D simulations.
Methods: We analyze high resolution spectroscopic scans obtained in the 630 nm Fe i line pair at varying heliocentric angles along the north-south polar axis of the Sun, with SOT onboard Hinode. We implement a new strategy for correcting the images observed at different line cords from spurious Doppler effects. The cross-correlations between continuum images and line core images show a clear anti-correlation peak due to the contrast inversion of the granulation in the upper photosphere, as predicted by magnetohydrodynamic (MHD) simulations.
Results: The anti-correlation peak is shifted by the perspective effect and by horizontal velocity effects. Both effects may be distinguished because they have different center-to-limb variations. The measurement of the perspective shift allows us to determine the line core formation heights and their center-to-limb variations. The results are in good agreement with 3D- MHD simulations for images close to disk center, but close to the solar limb we measure larger formation heights than what is predicted by the simulations, which seem to fail in modeling properly the upper layers of the photosphere. As the granulation contrast inversion is observed at line centers, we can safely conclude that the height of the contrast inversion layer is smaller than 200 km. Title: Searching For Weak Solar Magnetic Fields. What Can We Learn From the Hanle Effect? Authors: Faurobert, M. Bibcode: 2012POBeo..91...35F Altcode: Many dynamical phenomena taking place in the solar atmosphere, such as flares and coronal mass ejections, are driven by the interplay between the magnetic field and the turbulent solar plasma. Long standing questions on the physical origin of coronal heating and solar wind acceleration are also probably related to magnetic mechanisms. So the issue of how to measure magnetic fields in the solar atmosphere, from the photosphere up to the corona, is of crucial importance in solar physics. Because of the high value of the Reynolds magnetic number in the solar atmosphere, magnetic structures may develop from large to very small spatial scales, typically ranging from the scale of the solar diameter down to few tens of kilometers. The magnetic field strength also shows a broad dispersion from several thousands of Gauss in active regions like sunspots, down to a few Gauss in the quiet Sun. The amount of magnetic energy stored in magnetic structures is still unkown, and, according to recent numerical simulations, a significant fraction may be stored in weak, small scale fields, which cover a large fraction of the solar surface. However these field are hardly detectable in magnetograms based on the Zeeman effect because of their limited performances both in terms of polarimetric sensitivity and of spatial resolution. The Hanle effect is a valuable alternative for the diagnostics of weak fields with mixed polarity at small scales. It affects the linear polarization of spectral lines formed by scattering of photons in the solar atmosphere. I will present how weak magnetic fields investigations have changed our vision of the solar magnetism and discuss future research directions, in the context of solar polarimetry projects with ground based or space based intruments. Title: The quiet Sun magnetism: What can we learn from the Hanle effect? Authors: Faurobert, M. Bibcode: 2012IAUSS...6E.301F Altcode: The physics of the outer layers of the Sun is mostly driven by magnetic phenomena. This is the reason why high resolution investigations of the magnetic fields in the hot and dilute outer atmosphere of the Sun, from the photosphere to the chromosphere and corona, are the major objectives of future large solar telescopes, such as the Advanced Technology Solar Telescope (ATST), or the European Solar Telescope (EST). The so-called "quiet Sun" is filled in with magnetic fields distributed in strengths and over a wide range of spatial scales. The magnetic energy content of this distribution of fields is a crucial issue, related to the long standing questions of the coronal and chromospheric heatings. Zeeman diagnostics of the magnetic fields depend crucially on the spatial resolution of the observations, whereas diagnostics based on the Hanle effect do provide valuable information on the average field strength even if the magnetic structures are not resolved. However, they rely on the precise radiative transfer modeling of polarized lines formed under non-LTE conditions. The use of the differential Hanle effect on lines with different magnetic sensitivities is a method of choice to obtain model-independent diagnostics. Another promissing way explored nowdays is to make use of the complementary diagnostics provided by both the Zeeman and Hanle effects when they can be observed in the same lines. Title: Resonance Line Polarization in Moving Optically Thick Structures Authors: Milic, I.; Faurobert, M. Bibcode: 2012POBeo..91...45M Altcode: We compute the scattering polarization of lines formed in moving slabs of moderate optical thickness (τ=1 and τ=10) illuminated by a linearly polarized radiation field showing a broad absorption feature. Slabs are one-dimensional and horizontal, placed at a finite height H above a semi-infinite atmosphere. This model is an academic case which represents the formation of emergent radiation in solar filaments. The slabs have a macroscopic velocity in the radial direction with respect to the atmosphere, and are observed at different angles (i.e. at different locations over the solar disk). We investigate the sensitivity of the outgoing polarization to the slab velocity and observing angle. We show that outgoing polarization profiles are at least as sensitive to macroscopic velocity as are intensity profiles. Title: Hanle diagnostics of weak solar magnetic fields: . Inversion of scattering polarization in C2 and MgH molecular lines Authors: Milić, I.; Faurobert, M. Bibcode: 2012A&A...547A..38M Altcode: Context. The quiet Sun magnetism has been intensively investigated in recent years by various observational techniques. But several issues, such as the question of the isotropy and of the energy density spectrum of the mixed polarity turbulent magnetic fields, are still under debate.
Aims: Here we present an inversion method that allows us to constrain the depth-dependence of the magnetic field strength. We use the center-to-limb variations of linear scattering polarization measured in molecular lines of C2 and MgH molecules with different sensitivities to the Hanle effect. We consider six C2-triplets and one MgH line in the spectral range between 515.7 nm and 516.1 nm observed with the THEMIS Telescope.
Methods: One of the delicate problems with Hanle diagnostics is to disentangle the effects of elastic depolarizing collisions from the depolarization due to the Hanle effect of the magnetic field. By making use of the different sensitivities of the molecular lines in our spectral range to microturbulent magnetic fields and, by using a non-LTE radiative transfer modeling of the line formation, we are able to determine both the depolarizing collision cross-section and the magnetic strength. We use a standard 1D quiet Sun atmospheric model and we invert the full set of center-to-limb polarization rates measured at line centers, with a depth-dependent magnetic field described by three free parameters. The depolarizing collision cross-section is also treated as a free parameter. A downhill simplex method is used to find the best-fitting values for the collisional and magnetic strength parameters.
Results: For the elastic depolarizing collisions cross-section for the C2 lines we obtain α(2) = 1.6 ± 0.4 × 10-9 cm3 s-1, which is within an order of magnitude of the value previously obtained for MgH lines from a differential Hanle effect analysis. The observational constraints provided by the MgH and C2 line polarization give access to the altitude range between z = 200 km and z = 400 km above the base of the photosphere. We find that the turbulent magnetic field strength decreases from 95 Gauss at the altitude z = 200 km to 5 Gauss at z = 400 km.
Conclusions: The turbulent magnetic field strength that we derive from the Hanle effect shows a strong vertical gradient in the upper photosphere. We point out that this behavior may explain why very different turbulent magnetic field strengths have been inferred from the interpretation of Hanle depolarization when using different lines formed at different altitudes. We notice that the presence of a strong depth gradient is not compatible with the assumption of isotropy of the turbulent field. Title: Numerical modeling of the linear polarization in molecular lines of the solar flash spectrum Authors: Milić, I.; Faurobert, M. Bibcode: 2012EAS....55...65M Altcode: Molecular lines formed in the upper photosphere of the Sun show significant degree of linear scattering polarization, when one observes close to the solar limb. Those lines prove to be important tools for turbulent magnetic field diagnostic via the Hanle effect. In order to correctly model the line formation in regions close to the Solar limb, one has to take into account the sphericity of the atmosphere and to model depolarizing collisions and NLTE line formation in details. We present computations of scattering polarization in C2 lines in a 1D spherically symmetric medium described by FALC and FALX models, and compare those computations to observations of the Solar flash spectrum. Title: Extinction and Sky Brightness at Dome C Authors: Faurobert, M.; Arnaud, J.; Vernisse, Y. Bibcode: 2012EAS....55..365F Altcode: We have installed a small telescope to monitor the sky brightness around the sun at the French-Italian station Concordia at Dome C in Antarctica. Previous campaigns have been performed with the same instrument at Haleakala in Hawai and Sunspot in New Mexico. We compare here the results of the first year of the campaign at Dome C (2008) to the purest sky observed at Haleakala. We show that Dome C is an outstanding site for coronal observations. Compared to Haleaka, it appears to be more transparent, and to contain less aerosols. Its water vapour content is also significantly smaller. These results still have to be confirmed by the analysis of the 2009 and 2010 data. Title: Height of the granulation contrast inversion layer derived from a cross-correlation method Authors: Ricort, G.; Faurobert, M.; Aime, C.; Roudon, S. Bibcode: 2012EAS....55...79R Altcode: Using spectroscopic data from Hinode/SOT we have obtained monochromatic images of the solar granulation at different levels in the Fe i 603 nm lines. The granulation contrast inversion is clearly detected as a negative peak in the cross-correlation of images at the continuum level and at line center levels. Taking advantage of the perspective effect which appears in images taken out of the solar disk center, we were able to measure the formation heights of the lines and the height of the contrast inversion layer. Title: Inversion of Zeeman Line Profiles Using Central Moments Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M. Bibcode: 2012EAS....55...83M Altcode: A new inversion method derived from central moments of Zeeman line profiles (ICM), is used to determine magnetic field vectors (Mein et al. 2011). Two quantities A1 and A2 combining moments of profiles I ± S (S = Q,U,V) are nearly linear functions of the longitudinal and transverse components and lead to the field components through very fast iterations. Optimized exponents reduce noise effects. The ICM inversion does not require Milne Eddington approximation and can be used in a wide range of solar models. Title: Foreword Authors: Faurobert, M.; Fang, C.; Corbard, T. Bibcode: 2012EAS....55....1F Altcode: No abstract at ADS Title: ESCAPE : a first step to high resolution solar coronagraphy in Antarctica Authors: Damé, L.; Abe, L.; Faurobert, M.; Fineschi, S.; Kuzin, S.; Lamy, P.; Meftah, M.; Vives, S. Bibcode: 2012EAS....55..359D Altcode: The Dome C high plateau is unique for coronagraphic observations: sky brightness is reduced, water vapour is low, seeing is excellent and continuity of observations on several weeks is possible. ESCAPE (the Extreme Solar Coronagraphy Antarctic Program Experiment) will perform 2-dimensional spectroscopy of the forbidden line of FeXIV at 530.285 nm: precise line profile analysis will allow the diagnostic of the nature of waves by simultaneous measurements of velocities and intensities in the corona. ESCAPE is proposed to Institut Paul-Emile Victor (IPEV) for a campaign in 2012-2013 at Dome C/Concordia since all subsystems are available in particular thanks to an ESA STARTIGER 2010 R&D "Toward a New Generation of Formation Flying Coronagraph". Using state-of-the-art technologies developed for Space missions (a Three Mirrors Anastigmat telescope, the TMA, a 4 stages Liquid Crystal Tunable-filter Polarimeter, the LCTP) allows us to propose an automated Coronal Green Line full-field Polarimeter for unique observations (waves nature and intensity to address coronal heating) with the best possible performances on Earth and for preparing and testing the technologies for the next steps in Space. No other site would allow such coronagraphic performances (the sky brightness is a factor 2 to 4 better than in Hawaï) and with high spatial resolution (better than an arcsec is possible). Title: Understanding Solar Activity: Advances and Challenges Authors: Faurobert, M.; Fang, C.; Corbard, T. Bibcode: 2012EAS....55.....F Altcode: No abstract at ADS Title: Modeling scattering polarization in molecular solar lines in spherical geometry Authors: Milić, I.; Faurobert, M. Bibcode: 2012A&A...539A..10M Altcode: Context. The atmosphere of the Sun is permeated by a vast amount of magnetic flux that remains invisible in magnetograms based on the Zeeman effect. A model-independent way of measuring weak hidden magnetic fields makes use of the differential Hanle effect on the scattering polarization of molecular lines with different sensitivities to magnetic fields.
Aims: The observed line scattering polarization steeply increases at the solar limb. Here we are interested in interpreting observations performed at the solar limb, where plane-parallel semi-infinite geometry is not valid. The main reason is that the sphericity of the atmosphere means that the line-of-sight optical path intersects only a finite part of the solar atmosphere. In this paper we revisit the modeling of scattering polarization in two molecular lines of C2 and MgH in the spectral range from 515.60 nm to 516.20 nm, where observations performed both inside and above the solar limb are available.
Methods: The solar atmosphere is described by a one-dimensional, spherically symmetric medium following either the FALC or the FALX quiet Sun model. Both the line and background continuum scattering polarizations are computed by means of the "along-the-ray" approach. We assume a two-level atom formalism for the line source function, and we compute the molecule number densities and line opacities assuming LTE. We estimate the elastic and inelastic collision rates by fitting the line intensity and linear polarization in several couples of lines of the Second Solar Spectrum Atlas.
Results: The limb variations of scattering polarization, both in the lines and in the continuum, are strongly modified when the sphericity of the solar atmosphere is accounted for. We show that the line polarization goes through a maximum at 0.4'' above the limb, for both MgH and C2 lines. The contribution of the line rapidly goes to zero at a larger limb distance, but continuum polarization keeps increasing. The maximum polarization rates have an amplitude of 2% to 2.5% when the FALC model is used, which agrees with previous observations, whereas the FALX model leads to much higher rates. We then investigate the Hanle effect of microturbulent magnetic fields on the C2 line linear polarization. We show that polarization observed close to the limb would provide valuable diagnostics of weak magnetic fields in the region of the temperature minimum. Title: Scattering polarization of molecular lines at the solar limb Authors: Milić, I.; Faurobert, M. Bibcode: 2011sf2a.conf..401M Altcode: Molecular lines formed in the upper photosphere of the Sun show linear scattering polarization, when one observes close to the solar limb. This provides us with a diagnostic tool for measuring weak magnetic fields in the solar photosphere through the differential Hanle effect in these lines. However, in order to interpret polarization ratio measured in different lines of different optical thickness, one has to model accurately enough the line formation processes. Observations performed close to and above the solar limb give access to the still poorly known region of the temperature minimum between the photosphere and the chromosphere. The modeling of such observations requires to account for the spherical geometry of the solar atmosphere. Here we revisit the modeling of molecular solar line scattering polarization in spherical geometry and we investigate its diagnostics potential. Title: Fast inversion of Zeeman line profiles using central moments Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M. Bibcode: 2011A&A...535A..45M Altcode: Context. Many inversion techniques derive vector magnetic fields and other parameters of the solar atmosphere from Stokes profiles with an iterative process.
Aims: We propose a new inversion method, using functions derived from central moments (ICM), to determine magnetic field vectors with very few iterations.
Methods: Two quantities A1 and A2 that combine moments of profiles I ± S (S = Q,U,V) are proposed. They are nearly linear functions of the longitudinal and transverse components of the magnetic field, and lead to estimates of the field components through a least-squares polynomial fit. A third quantity AD can be used to interpolate between expansions that correspond to two basic models. Exponents β1 and β2 in the moment expressions are adjusted to minimize the sensitivity to data noise.
Results: Inversion coefficients are computed for magnetic fields up to 3000 G in the case of the 630.2 Fe i line by forward modeling in two selected 1D model atmospheres (FALC and MALTM). After inversion of synthetic profiles computed with four models at disk center (FALA, FALC, FALF, MALTM), the mean standard deviations with respect to the input fields do not exceed 5 G for both components over the full range 0-3000 G. A comparison of ICM results with inversion by the UNNOFIT code of profiles observed with THEMIS/MTR shows good agreement. The typical computing time for a solar map of 100 000 points is less than 30 s.
Conclusions: The ICM inversions are almost insensitive to thermodynamic properties and solve for vector magnetic fields in a wide range of solar conditions, ranging from plage to spot, with very little computational effort. They are, therefore, extremely suitable for large data sets. Further improvements should take into account instrumental profiles and effects of limited spatial resolution by using filling factors. Extensions using more parameters and models with large departures from the Milne Eddington approximation could also be considered. Title: Measurement of Line Formation Depths from a Super Resolving Analysis of Photospheric Layers Authors: Faurobert, M.; Aime, C.; Ricort, G.; Uitenbroek, H.; Grec, C. Bibcode: 2011ASPC..437...51F Altcode: We present the results of an experiment aimed at measuring the formation depths of the Fe I line pair at 630 nm in the solar photosphere. We use images of the granulation obtained at different levels in the lines, from line center up to the continuum level. When we observe out of disc center their difference in formation depths is projected into a radial shift of the images by the perspective effect. We measure this shift by implementing a cross-spectral method similar to a technique previously developed for stellar applications (Aime et al. 1984). The signal-to-noise ratio is increased by averaging the cross spectra over a large number of images. This technique allows us to measure very small displacements, below the telescope resolution.

We show results we obtained on HINODE/SP observations and compare them to numerical simulations. The difference of formation depths between the two line cores is determined with a very high accuracy and compares quite well to LTE model calculation using either 1D solar model or full 3D calculations in snapshots of the granulation. However it shows significant variations in magnetic regions. The difference between line core and continuum formation depths is more difficult to measure precisely because line core and continuum images are not well correlated, due to contrast inversion and depth-dependence of granular structures. We solve this problem by measuring the perspective shifts between similar enough images taken at successive steps along the line profile, and by integrating the shifts from the continuum level to the line center forming layer. Title: Measuring line formation depths by cross-spectral analysis. Numerical simulations for the 630 nm Fe I line pair Authors: Grec, C.; Uitenbroek, H.; Faurobert, M.; Aime, C. Bibcode: 2010A&A...514A..91G Altcode: Context. Numerical three-dimensional simulations of the solar photosphere have progressed greatly in the last 15 years. Observational tests are needed to independently verify the realism of these simulations.
Aims: We aim to measure the perspective shift between monochromatic images at different wavelengths taken away from disk center. We investigate the feasibility of our method by applying it to simulated spectra of the Fe i line pair at 630.15 and 630.25 nm calculated from several snapshots of a three-dimensional simulation of solar magneto-convection.
Methods: We present a method to determine line formation depths from spectroscopic observations without relying on assumptions about an atmospheric model. Our method is based on the measurement of a perspective shift, which is detected as a linear phase term in the cross-spectrum of the images. In principle this detection is independent of the spatial resolution of the observations, and provides a valuable test for numerical simulations of the solar photosphere.
Results: To obtain accurate formation heights we need to correct spectra for convective Doppler shifts, and we need to accumulate successive phase shifts between images in nearby wavelengths, rather than compare images from the continuum and core directly. The comparison of images provides large dissimilarities, which result from the temperature contrast inversion in the granulation with height. We verify that the cross-spectrum phase of the simulated images shows the expected linear behavior with spatial frequency when considering two close enough wavelengths in a spectral line profile. This linear behavior is however only obtained at small spatial frequencies, i.e. for large granular structures. Derived line formation heights of the two lines range from 239 and 287 km above the continuum formation height for the 630.15 nm line, and from 138 to 201 km for the 630.25 nm line, with significant variation between snapshots. Formation height estimates from optical depth unity give on average 319 km and 244 km respectively.
Conclusions: Our numerical tests validate measurements of line formation depths from cross-spectra between images at different wavelengths and stress the value of measuring the phase of the cross-spectra as an important test for numerical simulations. Title: Solar chromospheric and coronal magnetic structure: science cases for Dome C Authors: Faurobert, M. Bibcode: 2010EAS....40..467F Altcode: Magnetic fields play a crucial role for the physics of the dilute and hot upper parts of the solar atmosphere, from the low chromosphere up to the outer corona. Numerical modeling of these regions by MHD codes and 3D radiative transfer in spectral lines has started, we urgently need direct measurement of the magnetic and velocity fields in order to confirm and improve such modeling. Direct measurements of the magnetic field vector rely on spectro-polarimetric observations of the Hanle or Zeeman effects in spectral lines. In the upper solar atmosphere the magnetic field strength tends to decrease with height and lines are broaedened both thermally and by turbulent and wave motions. The sensitivity of spectral lines to Zeeman effect is thus low under such conditions, but it increases linearly with wavelength. The infrared is the domain of choice for Zeeman observations in chromospheric and coronal lines. Moreover, as chromospheric and coronal structures develop on a broad range of spatial scales, from very fine to large scales, high spatial resolution observations are required. These observations are very demanding in photometric sensitivity, together with spatial and temporal resolution. Dome C conditions of both very good day-time seeing and high coronal quality are unique and make it a site of choice for a possible breakthrough in our understanding of the physical mechanisms at play in the outer solar atmosphere. Title: Direct measurement of the formation height difference of the 630 nm Fe I solar lines Authors: Faurobert, M.; Aime, C.; Périni, C.; Uitenbroek, H.; Grec, C.; Arnaud, J.; Ricort, G. Bibcode: 2009A&A...507L..29F Altcode: Context: Spectral lines formed over a limited height range in either a stellar or planetary atmosphere provide us with information about the physical conditions within this height range. In this context, an important quantity is the so-called line formation depth. It is usually determined from numerical calculation of the atmospheric opacity in the line of interest and then converted into geometrical depth by using atmospheric models.
Aims: We develop a radically different approach, which allows us to measure directly line formation depths from spectroscopic observations without relying on assumptions about an atmospheric model. This method requires spatially resolved observations, which up to now have been available only for solar or planetary studies. We apply this method to images of the solar granulation.
Methods: The method was presented and tested numerically in previous papers. It is based on the measurement of the perspective shift between images at different wavelengths, formed at different heights, when they are observed away from disk center. Because of the Fourier transform properties, this shift gives rise to a deterministic linear phase term in the cross spectrum of the images.
Results: The method is applied to observations of solar quiet regions performed with the SOT spectropolarimeter on HINODE in the Fe i line pair at 630.15 and 630.25 nm. We derive the difference in formation heights between the two lines and its center-to-limb variations. We show that the high sensitivity of the measurements allows us to detect variations in the line formation heights between magnetized and non-magnetized regions of the solar atmosphere.
Conclusions: Our results are the first direct measurements of line formation depths in the solar photosphere. Cross spectral analysis provides us with a new observable quantity, which may be measured with an accuracy well bellow the spatial resolution of the observations. We recall that the Fe i line pair at 630.15 and 630.25 nm is often used to determine solar magnetic fields by spectropolarimetric observations and inversion methods. The difference in the line formation heights that we measure should be taken into account in the inversion procedures. Title: Non-LTE Modeling of the Ba II D2 Line Resonance Polarization Authors: Faurobert, M.; Bommier, V.; Derouich, M. Bibcode: 2009ASPC..405...35F Altcode: The Ba II resonance line at 455.4 nm is formed in the low solar chromosphere. It shows significant linear polarization outside active regions close to the solar limb. This so-called resonance polarization is sensitive to the Hanle effect of weak magnetic fields. We report on numerical simulations of the intensity and resonance polarization center-to-limb variations in the line and in the adjacent continuum, in a quiet solar atmosphere and we compare them to observations performed at THEMIS in August 2007. In the simulations we take into account non-LTE multilevel coupling, multiple scattering and partial frequency redistribution, and we neglect the hyperfine structure of the odd isotopes of Barium. As resonance polarization and partial frequency redistribution effects are very sensitive to elastic collisions with hydrogen atoms we use accurate depolarizing collisional rates recently computed for this line by a semi-classical method. Our radiative transfer calculations allow us to model the central part of the line core and the wings quite well. We show that the line polarization depends very much indeed on partial frequency redistribution effects. Then we investigate its diagnostic potential for weak unresolved magnetic fields in the low chromosphere. We find that the observed polarization rates are in good agreement with the simulations if we take into account the Hanle effect due to an isotropic turbulent magnetic field of the order of 30 Gauss at the altitude where the line core is formed, i.e. between 900 km and 1300 km above the basis of the photosphere. Title: Hanle effect in the solar Ba II D2 line: a diagnostic tool for chromospheric weak magnetic fields Authors: Faurobert, M.; Derouich, M.; Bommier, V.; Arnaud, J. Bibcode: 2009A&A...493..201F Altcode: 2008arXiv0811.1180F Context: The physics of the solar chromosphere depends in a crucial way on its magnetic structure. However there are presently very few direct magnetic field diagnostics available for this region.
Aims: Here we investigate the diagnostic potential of the Hanle effect on the Ba II D2 line resonance polarization for the determination of weak chromospheric turbulent magnetic fields.
Methods: The line formation is described with a non-LTE polarized radiative transfer model taking into account partial frequency redistribution with an equivalent two-level atom approximation, in the presence of depolarizing collisions and the Hanle effect. We investigate the line sensitivity to temperature variations in the low chromosphere and to elastic collision with hydrogen atoms. We compare center-to-limb variations of the intensity and linear polarization profiles observed at THEMIS in 2007 to our numerical results.
Results: We show that the line resonance polarization is very strongly affected by partial frequency redistribution effects both in the line central peak and in the wings. Complete frequency redistribution cannot reproduce the polarization observed in the line wings. The line is weakly sensitive to temperature differences between warm and cold components of the chromosphere. The effects of elastic collisions with hydrogen atoms and of alignment transfer due to multi-level coupling with the metastable ^2D{5/2} levels have been studied in a recent paper showing that they depolarize the ^2P{3/2} level of the line. In the conditions where the line is formed we estimate the amount of depolarization due to this mechanism as a factor of 0.7 to 0.65. If we first neglect this effect and determine the turbulent magnetic field strength required to account for the observed line polarization, we obtain values between 20 G and 30 G. We show that this overestimates the magnetic strength by a factor between 1.7 and 2. Applying these correction factors to our previous estimates, we find that the turbulent magnetic field strength is between 10 G and 18 G.
Conclusions: Because of its low sensitivity to temperature variations, the solar Ba II D2 line appears as a very good candidate for the diagnosis of weak magnetic fields in the low chromosphere (z ≥ 900 km) by means of the Hanle effect. Title: Apodized apertures for solar coronagraphy Authors: Carlotti, Alexis; Aime, Claude; Arnaud, Jean; Faurobert, Marianne; Ferrari, André; Grec, Catherine; Ricort, Gilbert Bibcode: 2008SPIE.7014E..15C Altcode: 2008SPIE.7014E..38C An apodized aperture should make it possible to observe the solar corona without the need of a Lyot coronagraph. We show in this communication that Sonine functions are much better apodizers for the observation of the solar corona than the generalized prolate spheroidal functions previously proposed. For a perfect circular aperture of diameter unity operated in space, a simple Sonine apodization of the form (1 - 4r2), with |r| <= 1/2 should sufficiently reduce the diffraction halo produced by the solar disc to observe the corona very close to the solar limb (a few arcsec). The throughput is just one third of the clear aperture. Title: Apodized apertures for solar coronagraphy Authors: Aime, C.; Arnaud, J.; Carlotti, A.; Faurobert, M.; Ferrari, A.; Grec, C.; Ricort, G. Bibcode: 2007sf2a.conf..574A Altcode: The solar corona cannot be studied without the help of a coronagraph. A telescope with an apodized aperture is, as described by Aime (2007), an alternative to the classical Lyot coronagraph. A spheroidal prolate apodization will modify the PSF of the telescope and optimize the energy concentration in the focal plane. A strong apodization (prolatness parameter c ≈ 10) would reduce the diffraction halo by a factor 10^5 at a cost of intensity throughput reduced at 10 %. In a site with outstanding daytime seeing, like Dome C, this method should allow to observe the corona extremely close to the solar limb and also, much better than otherwise, the rich chromospheric weak emission spectrum. Title: Resonance polarization of the solar 455.4 nm BaII line: diagnostics of chromospheric magnetic fields Authors: Michel, C.; Faurobert, M.; Arnaud, J.; Malherbe, J. M. Bibcode: 2007sf2a.conf..607M Altcode: The BaII resonance line at 455.4 nm is formed in the low solar chromopshere. It is significantly linearly polarized outside active regions and close to the solar limb. This so-called resonance polarization is sensitive to the Hanle effect of weak magnetic fields. We report on numerical simulations of the intensity and resonance polarization profiles in the line and in the adjacent continuum, in the quiet solar atmosphere and we compare them to observations performed at the Jean Rosch refractor at the Pic du Midi Observatory. In the simulations we take into account non-LTE multilevel coupling, multiple scattering and partial frequency redistribution, and we neglect the hyperfine structure of the odd isotopes. This allows to model the central part of the line core and the wings quite well. Then we investigate the diagnostic potential of the line core polarization for weak unresolved magnetic fields in the low chromosphere. We find that the observed polarization rates are in good agreement with the simulations if we take into account the Hanle effect of weak magnetic fields on the order of 60 to 75 Gauss. Title: The Prolate Apodized Solar Coronagraph Authors: Aimé, C.; Arnaud, J.; Carlotti, A.; Faurobert, M.; Ferrari, A.; Grec, C.; Ricort, G. Bibcode: 2007lyot.confE..40A Altcode: We present the project of a new solar coronagraph that makes it possible to observe the solar corona very close to the solar limb, without using Lyot's mask and stop technique. The high dynamic capability is obtained using a strongly apodized aperture. A good choice for the aperture transmission is the generalized prolate spheroidal function of prolateness coefficient c on the order of 10. Such an instrument operated in space, could reduce the diffraction halo produced by the Sun by a factor 100 000, at the cost of an intensity throughput of 10 %. The classical resolution, in terms of equivalent width of the PSF, is reduced by a factor of about 1.7 while the MTF of the telescope becomes similar to a Gaussian function with unchanged cut-off frequency D/lambda. The telescope design is an unobstructed circular aperture and the variable transmission produced directly at the entrance window. This concept, although demanding in terms of mechanical and optical achievements, is preferred to the more classical re-imaging of a clear aperture and subsequent apodisation, for image quality concerns. It does not need a wide field telescope and may take advantage of adaptive optics for ground based observations. It is expected that such a system should give much better images than the classical Lyot coronagraph very close to the solar limb. Such observations should give access to coronal heating processes expected to occur close to the solar surface, and provide information on Coronal Mass Ejections mechanisms at work in the very low corona. Title: Differential speckle interferometry: in-depth analysis of the solar photosphere Authors: Grec, C.; Aime, C.; Faurobert, M.; Ricort, G.; Paletou, F. Bibcode: 2007A&A...463.1125G Altcode: Aims:We present the results of an experiment performed at the solar telescope THEMIS in 2002 to measure the depth over which the solar granulation extends in the photosphere.
Methods: Observations made in the 523.3 nm and 557.6 nm photospheric non-magnetic iron lines were correlated with images in the continuum using spectrograms. The difference in depth between the different levels in the photosphere is projected into a difference of position along the slit of the spectrograph, using a perspective effect similar to the well-known Wilson effect for sunspots. This requires measuring displacements, ones much smaller than the telescope resolution. This is made possible by using a differential speckle interferometric technique, cross-correlating images taken in the continuum and the line. The method is not adapted to following displacements of structures in the core of strong lines, due to their difference in shapes with the structures observed in the continuum. In this case, a sequential cross-spectrum method is developed to cross-correlate images taken at close wavelengths.
Results: The raw results are surprising: displacements measured in the blue and the red wings of a line have opposite signs! North and South observations, however, clearly show the expected behavior attributed to a perspective effect. After a description of the observations, we give a first interpretation of the results. The main part of the observed displacement comes from the effect of unresolved Doppler shifts produced by horizontal velocities in the solar photosphere. The perspective effect we seek appears as a second-order term; we find that its amplitude is 2 or 3 times larger than predicted by theoretical 1D models. In the core of strong lines we detect a contrast inversion that also shows up in the cross-correlation function as an anti-correlation peak at line center.
Conclusions: .This first use of the differential speckle interferometry technique on the Sun is quite promising for 3D studies at high spatial resolution. Further observations with very good image quality are needed to take advantage of this new technique.

THEMIS is operated on the Island of Tenerife by CNRS-CNR in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: Magnetic flux tubes observed with THEMIS/MSDP Authors: Mein, P.; Mein, N.; Faurobert, M.; Aulanier, G.; Malherbe, J. -M. Bibcode: 2007A&A...463..727M Altcode: Aims:We use spectro-polarimetric THEMIS/MSDP data to investigate the 3D structure of solar magnetic-flux tubes across the upper photosphere.
Methods: Profiles of the sodium D1 line 589.6 nm are analysed by the bisector method at different wavelengths from the core to the wings, for several bright features. They are compared to synthetic profiles derived from 2D magnetic models of flux tubes and from the MULTI code for NLTE line profiles. Three different magnetic models of flux tubes are investigated. Model (I) consists of a single flux tube that compensates for the horizontal Lorentz forces exactly, while model (II) uses a compromise between horizontal and vertical components. Model (III), a conglomerate of thinner flux tubes, leads to the best agreement with observations.
Results: (1) The combination of seeing effects (small filling factor) with slopes of line profiles, which are different in the flux tubes and the neighbouring quiet sun, account for the decrease in observed magnetic field from line core to line wings in central parts of magnetic features, as well as the decrease in magnetic fluxes integrated over the whole magnetic features. (2) The expansion with height of single magnetic flux tubes (models I and II) accounts for the increase in the size of magnetic features from line wings to line core. (3) Pure thermodynamical criteria characterising Dopplershifts and line-intensity fluctuations of magnetic and non-magnetic features have been proven by observations.
Conclusions: . We could account for differential Zeeman effects along the D1 line profile by combining expansion of flux tubes with height, low gas pressure inside flux tubes, and small filling factor due to seeing effects. Better agreement with observations, in particular with respect to magnetic field amplitudes, will probably need 3D models that take velocity fields and horizontal gradients of temperature into account. Title: Magnetic flux tubes observed with THEMIS/MSDP . Authors: Mein, P.; Mein, N.; Faurobert, M.; Aulanier, G.; Malherbe, J. -M. Bibcode: 2007MmSAI..78...92M Altcode: We use 2D spectro-polarimetric data of the NaD1 line to investigate magnetic flux tubes at several levels of the solar photosphere:

- magnetic and non-magnetic bright features can be discriminated by simple criteria of intensities and dopplershifts.

- 2D magnetic models and NLTE line profiles are compared to observations : combination of seeing effects and departures between slopes of line profiles in flux tubes and neighbouring photosphere account for vertical gradients of line-of-sight (LOS) magnetic field measurements.

- Best qualitative agreements are obtained with clusters of magnetic flux tubes. Title: Dome C: An exceptional site for solar observations . Authors: Arnaud, J.; Faurobert, M.; Fossat, E. Bibcode: 2007MmSAI..78..105A Altcode: Dome C, on the Antarctica plateau, may be the best site on Earth for astronomy, thanks to outstanding image quality and very pure and cold atmosphere. This is of particular interest for solar physics, namely for very high-resolution studies of the solar surface and for magnetometry of the innermost solar corona. Here we review Dome C unique atmospheric properties and present two projects aimed at quantitatively qualify this site for solar observations. Title: Solar Coronagraphy at Dome C: Site Testing and Prospects Authors: Arnaud, J.; Faurobert, M.; Grec, G.; Renaud, C. Bibcode: 2007EAS....25...81A Altcode: Progress in our understanding of solar magnetism and activity rest to a large part on our ability to improve spatial resolution for resolving the solar surface magnetic fields fine structure. The solar corona is permeated by magnetic fields emerging from the sun and, in turn, ejects particules and magnetic field into the heliosphere. It is of prime importance to measure the coronal magnetic field to understand mechanisms at work in the corona. We explain why Dome C is expected to be an outstanding site for such observations and describe the Solar Brightness Monitor we prepare to probe sky background and aerosols levels at this site. We also discuss coronal observations DomeC could allow to obtain. Title: Contrast inversion in the 557.6 nm line detected with differential speckle interferometry Authors: Grec, C.; Aime, C.; Faurobert, M.; Ricort, G.; Paletou, F. Bibcode: 2007MmSAI..78...48G Altcode: We report on some aspects of the use of a Differential speckle interferometry technique on the Sun. The method consists in cross-correlating images of the granulation taken in the line absorption and in the continuum, outside the solar disk center. Due to a perspective effect, the difference in depth between different photospheric levels results in a difference in position along the spectrograph slit. Observations were done in 2002, 2005 and 2006, at the telescope THEMIS in the 557.6 nm iron line. As expected from the perspective effect, we obtain opposite results at opposite latitudes on the Sun disk. Surprisingly, the displacements measured in the blue and the red wings of the line have opposite signs. This may be the result of unresolved Doppler shifts produced by horizontal granular velocity fields. We also detect an anti-correlation peak in the core of strong lines, that is the signature of a contrast inversion. Title: Preliminary results from the March 29, 2006 total eclipse observations in Egypt Authors: Koutchmy, S.; Daniel, J. -Y.; Mouette., J.; Vilinga, J.; Noëns, J. -C.; Damé, L.; Faurobert, M.; Dara, H.; Hady, A.; Semeida, M.; Sabry, M.; Domenech, A.; Munier, J. -M.; Jimenez, R.; Legault, Th.; Viladrich, Ch.; Kuzin, S.; Pertsov, A.; O. A. Team Bibcode: 2006sf2a.conf..547K Altcode: A coordinated effort has been carried in the framework of the French-Egyptian scientific cooperation to permit joined simultaneous eclipse observations of the solar corona during the total solar eclipse of March 29, 2006. Spaceborne EIT and Lasco (SoHO) observations were also planned at the same time and were successfully collected. Scientists from other countries collaborated on different experiments. The synthetic image showing the magnetic coronal structure of this quasi-minimum corona seen in W-L is given. Some preliminary results are presented; a White Light (W.L.) movie has been also taken during the totality. Title: Solar Magnetometry: recent advances Authors: Faurobert, M. Bibcode: 2005sf2a.conf....7F Altcode: Magnetic fields play a crucial role in the phenomena related to solar and stellar activity. However the determination of magnetic fields in astrophysical plasma is very often a difficult task, which relies on spectro-polarimetric methods. The PNST (Programme National Soleil-Terre) supports the collaboration of several groups investigating solar magnetic fields with various methods. I present some results recently obtained by PNST groups using dedicated instruments, such as THEMIS. Title: Coronal Magnetometry Authors: Arnaud, J.; Faurobert, M.; Grec, G.; Vial, J. -C. Bibcode: 2005EAS....14...95A Altcode: Magnetic fields emerging in the solar atmosphere control the structure, dynamics and heating of the solar corona. Those fields remain essentially unattainable with present low corona instrumentation. We present the most direct way of magnetic field remote measurements in the internal corona, namely visible and infrared coronal emission lines magnetometry and we explain why Dome C should be investigated as a likely outstanding site for such observations. We develop a strategy towards a large aperture coronal magnetometer at Dome C in the context of the other main instrumental projects underway for solar physics. Title: Center-to-limb variation of scattering polarization in molecular solar lines: Observations and modeling Authors: Faurobert, M.; Arnaud, J. Bibcode: 2003A&A...412..555F Altcode: We present center-to-limb measurements of the scattering polarization observed in molecular lines of C2 and MgH in the spectral range between 515.7 and 516.1 nm, together with a radiative transfer model for the formation of these lines. The observations were performed in July 2000 with THEMIS inside the south polar limb. We were able to measure the polarization at distances between 1 arcsec and 50 arcsec from the solar limb. The lines appear as very weak absorption features in the intensity spectrum but their linear polarization clearly dominates in the polarization spectrum. We introduce here a simple radiative transfer model which allows to interpret the observed center-to-limb variations of both the intensity and linear polarization. The basic assumption is that molecular lines are formed higher in the photosphere than the continuous photospheric radiation. Molecules are thus illuminated by the polarized continuum photospheric radiation field. We account for a possible Hanle effect due to weak unresolved magnetic fields but we neglect depolarizing collisions. The model depends on four parameters which are determined by fitting both the intensity and polarization in 9 molecular lines of the observed spectral domain. Making use of the differential Hanle effect in the different lines of C2 we show that the C2 lines are affected by the Hanle effect due to a weak unresolved magnetic field. Its mean strength is on the order of 15 Gauss in the upper photosphere and increases to values on the order of 50 Gauss at larger depths. These results are in good agreement with those derived previously (Faurobert et al. \cite{Faurobert1}) from the linear polarization of the SrI 460.7 nm line which was observed simultaneously. Such a weak field has almost no effect on the MgH lines. Title: Molecular lines observations with THEMIS Authors: Arnaud, J.; Faurobert, M.; Raouafi, N. -E.; Solanki, S. K. Bibcode: 2003sf2a.conf..111A Altcode: 2003sf2a.confE..39A Lines of molecules like MgH, C2, TiO, ... represent powerful tools for the study of the solar atmosphere. Their observations on the Sun can also help to constrain the polarizability and Lande factors calculations which are much more complex than for atomic lines. We will present THEMIS polarimetric observations of these lines to illustrate some aspects of their use for solar physics. Title: Diagnostics of Solar Magnetic fields based on the Hanle effect Authors: Faurobert, M. Bibcode: 2003EAS.....9...77F Altcode: The Hanle effect was first used in solar physics to determine weak magnetic fields in prominences (see Leroy [CITE]). More recently the development of a new generation of very accurate spectro-polarimeters has open a new window for the diagnostics of weak magnetic fields in the solar photosphere and chromosphere, based on the Hanle effect. I present here such recent research programs performed with the solar telescope THEMIS and with other polarimeters such as ZIMPOL and the LOCARNO polarimeter. Title: Second Solar Spectrum Observations at THEMIS Authors: Faurobert, M.; Arnaud, J. Bibcode: 2003ASPC..307..431F Altcode: No abstract at ADS Title: Hanle effect with angle-dependent partial redistribution Authors: Nagendra, K. N.; Frisch, H.; Faurobert, M. Bibcode: 2002A&A...395..305N Altcode: The polarized line transfer equation for the Hanle effect is solved in the framework of an exact partial frequency redistribution (PRD) theory developed by Bommier (1997a,b). In that theory the effect of collisions on the Hanle effect is considered self-consistently. We follow that approach in the line transfer computations presented here. The theory formulated by Bommier clearly recognizes two levels of approximations for exact PRD, in order to facilitate the solution of the line transfer equation. The second level employs angle-dependent redistribution functions, and numerically represents a more difficult problem compared to the third level, which involves only the use of angle-averaged frequency redistribution functions. We present a method which can solve the problem in both the levels of approximation. The method is based on a perturbative approach to line polarization. Although computationally expensive, it offers the only practical means of solving the angle-dependent Hanle PRD problem. We discuss the numerical aspects of assembling the so called ``frequency domain dependent redistribution matrices'', and also an efficient way of computing the scattering integral. Some examples are presented to illustrate the interesting aspects of the Hanle-PRD problem with angle-dependent frequency redistribution. A comparison of the emergent profiles computed under angle-averaged and angle-dependent redistribution is carried out, and the effect of collisions is investigated. We show that it is necessary to incorporate an angle-dependent redistribution mechanism especially in the computation of the Stokes U parameter. We demonstrate that the use of simple frequency domains is good enough in practical applications of the Hanle PRD theory. Title: Scattering polarization of molecular emission lines in the quiet solar chromosphere Authors: Faurobert, M.; Arnaud, J. Bibcode: 2002A&A...382L..17F Altcode: We present scattering polarization measurements performed with THEMIS in July 2000 near the south polar limb. The low level of scattered light at THEMIS, which is the only large solar telescope to include a superpolished primary mirror, allows, in good seeing conditions, to observe the emission spectrum of the low chromosphere above the limb. These are, as far as we know, the first high spectral resolution observations of the intensity and the first measurements of the polarization of C2 and MgH molecular lines in emission above the limb. Molecules are present in a thin layer in the region of the temperature minimum between the photosphere and the chromosphere. We present a very simple model for the formation of the polarized lines and we relate the observed polarization rates to the so-called intrinsic line polarizability coefficients W2. Those quantities may be derived from quantum mechanical computations involving the solution of the Schrödinger equation for the molecular potential. Solar observations provide a direct way of checking these heavy computations and contribute to the improvement of our knowledge in molecular physics. Nine C2 molecular transitions and two MgH transitions are present in our spectral window; we find that for the C2 transitions, the polarizability is between 0.13 and 0.26 and that it takes higher values, namely 0.41 and 0.46, for the two MgH transitions. Title: Polarimetric Imaging of The Solar Corona During The 21 June 2001 Total Solar Eclipse Authors: Habbal, S. R.; Arnaud, J.; Arndt, M.; Ene, A.; Esser, R.; Faurobert, M.; Hale, J.; Hegwer, S.; Johnson, J.; Woo, R. Bibcode: 2002EGSGA..27.6098H Altcode: We report on the first successful simultaneous eclipse measurements of the inten- sity and polarization brightness of the K-Corona and the near-infrared Fe XIII 1074.7 nm emission line. Those observations were obtained during the total solar eclipse of 21 June 2001. The technique used for those observations will be presented. Coronal emission lines polarization measurements are the only tools to date that can yield the direction of the coronal magnetic field. Title: Vertical structure of sunspots from THEMIS observations Authors: Eibe, M. T.; Aulanier, G.; Faurobert, M.; Mein, P.; Malherbe, J. M. Bibcode: 2002A&A...381..290E Altcode: We have analysed two-dimensional spectro-polarimetric data taken with the MSDP observing mode of THEMIS in the Na I D1 line to investigate the height variation of the magnetic field in sunspot umbrae. From the Zeeman-induced circular polarization measured at individual MSDP channels within the line profile, maps of the longitudinal magnetic field have been computed. A method based on Response Functions has been developed to estimate the depth in the atmosphere at which the Zeeman measurements are originated, thus providing the line-of-sight field at different altitudes in the photosphere. The magnetogram corresponding to the deepest level has served as a boundary condition to perform the potential field extrapolation into the corona. We have found that the spatial distribution of vertical field gradient contours predicted from extrapolation is in qualitatively good agreement with that inferred from observations. Quantitatively, however, the longitudinal field gradients obtained with both methods differ about one order of magnitude, being larger for observations. The origin of this discrepancy has been discussed with respect to possible observation biases, as well as to idealizations used for field extrapolation. This is a crucial problem to be addressed in future work, and may have important implications for the physics of how the magnetic field evolves through sunspots and how the flux is distributed in the corona. Title: Polarized Intensity Measurements of the Corona during the 21 June 2001 Total Solar Eclipse Authors: Habbal, S. R.; Arnaud, J.; Johnson, J.; Hegwer, S.; Ene, A.; Hale, J.; Esser, R.; Arndt, M.; Kohl, J. L.; Daw, A.; Faurobert, M.; Woo, R.; Habbal, F.; Havasy, R.; Alford, J. N. Bibcode: 2001AGUFMSH11C0716H Altcode: We report on the first successful simultaneous polarimetric measurements of the brightness of the Thompson-scattered white light and intensity of the near-infrared Fe XIII 10747 Å line, the strongest of the coronal iron forbidden lines. These observations which extended out to 3 Rs in the corona were obtained during the total solar eclipse of 21 June 2001. The novel technique used to acquire these measurements will be presented. Polarized intensity measurements of the resonantly scattered component of coronal emission lines are the only tools to date that can yield the direction of the coronal magnetic field. Through these simultaneous measurements, we show how the direction of the coronal magnetic field can be placed in the context of coronal density structures. We also discuss the implications of these simultaneous measurements for the source of the solar wind. Title: Investigation of weak solar magnetic fields. New observational results for the SrI 460.7 nm linear polarization and radiative transfer modeling Authors: Faurobert, M.; Arnaud, J.; Vigneau, J.; Frisch, H. Bibcode: 2001A&A...378..627F Altcode: Scattering polarization measurements were obtained with THEMIS in July 2000, close to the solar south Pole and to the east Equator and in a period of maximum solar activity. Using the THEMIS multi-lines spectro-polarimetric mode (MTR), we observed simultaneously four spectral domains containing the 460.7 nm Sr i line, several molecular lines around 515.9 nm and the Na i D1 and Na i D2 lines. This allows us to scan different altitudes in the solar atmosphere at the same time and provides us with a large set of constraints to study the behaviour of the magnetic field. This paper is devoted to the Sr i line which exhibits quite a strong linear polarization peak outside active regions. A detailed radiative transfer modeling is performed in order to interpret the observed center-to-limb variations of the line intensity and polarization. It was shown previously (Faurobert-Scholl \cite{Faurobert-Scholl1}) that this line, which is sensitive to the Hanle effect, can be used as a diagnostic tool for the presence of weak turbulent magnetic fields in the solar photosphere outside active regions. The line polarization rates that we measured in July 2000 are 25% lower than what has been reported previously, for observations near the minimum, or in the increasing phase, of the activity cycle (Stenflo et al. \cite{Stenflo1}). They are in agreement with other observations performed with a different observational set-up in August 2000 (Bommier & Molodij \cite{Bommier4}). We show that they are consistent with the presence of a weak turbulent magnetic field with an average strength between 20 G and 30 G in the upper solar photosphere. This is about twice the value which was derived from previous observations. This result raises the possiblity of a long-term variation of the turbulent photospheric magnetic field with the activity cycle. Title: Investigation of temperature and velocity fluctuations through the solar photosphere with the Na I D lines Authors: Eibe, M. T.; Mein, P.; Roudier, Th.; Faurobert, M. Bibcode: 2001A&A...371.1128E Altcode: In this work we explore the diagnostic properties of the Na I D resonance lines by calculating the response functions of their line profiles to temperature and velocity perturbations in the atmosphere. We propose a method to transform spectral line intensity fluctuations measured at several wavelengths into temperature and velocity disturbances at different height levels. Results from tests done with several theoretical models of perturbations are discussed. Perturbations that vary as linear functions of depth are efficiently reproduced. The method also provides good estimations for exponential models. As an example we present an application to solar granulation data obtained with Multichannel Subtractive Double Pass (MSDP) spectroscopy. Title: Temporal height properties of the exploding granules Authors: Roudier, Th.; Eibe, M. T.; Malherbe, J. M.; Rieutord, M.; Mein, P.; Mein, N.; Faurobert, M. Bibcode: 2001A&A...368..652R Altcode: Based on time series of 2D MSDP spectrograms, taken at the Turret Dome in Pic du Midi, we present the temporal evolution of exploding granules in intensity and Doppler velocity through the solar photosphere. We describe the penetration of exploding granules in the solar photosphere during their lifes and the related phenomena like the ``Bright Plumes'' located in the downflowing plasma just on the edge of the granule. We suggest a possible scenario of the exploding granule evolution in the solar photosphere. Title: Scattering Polarization and Hanle Effect: On the Importance of Angle-Dependent Frequency Redistribution Authors: Faurobert, M.; Frisch, H.; Nagendra, K. N. Bibcode: 2001ASPC..248..145F Altcode: 2001mfah.conf..145F No abstract at ADS Title: Scattering Induced Polarization and Hanle Effect Observations with THEMIS Authors: Arnaud, J.; Faurobert, M.; Vigneau, J.; Paletou, F. Bibcode: 2001ASPC..248...93A Altcode: 2001mfah.conf...93A No abstract at ADS Title: Using the Na I D resonance lines to probe the solar photosphere Authors: Eibe, M. T.; Mein, P.; Faurobert, M.; Roudier, Th. Bibcode: 2001ESASP.464..199E Altcode: 2001soho...10..199E Observational techniques in helioseismology are often based on measurements made in the Na I D resonance lines. A good knowledge of their spectral profiles is crucial for the purposes of calibration and interpretation of data. Here we explore their diagnostic properties by calculating response functions of the D1 and D2 line profiles to temperature and velocity perturbations in the atmosphere. We propose a method to transform spectral line intensity fluctuations measured at several wavelenths into temperature and velocity disturbances at different height levels. The possibilities of such a procedure to trace the vertical structure of the photosphere are discussed. Title: The Hanle Effect with Angle Dependent Redistribution Functions Authors: Frisch, H.; Faurobert, M.; Nagendra, K. N. Bibcode: 2001ASPC..236..197F Altcode: 2001aspt.conf..197F No abstract at ADS Title: Scattering Polarization Measurements with THÉMIS Authors: Arnaud, J.; Vigneau, J.; Faurobert, M.; Paletou, F. Bibcode: 2001ASPC..236..151A Altcode: 2001aspt.conf..151A No abstract at ADS Title: Hanle Effect of Weak Solar Magnetic Fields Authors: Faurobert, M. Bibcode: 2000ASPC..205..156F Altcode: 2000ltse.conf..156F The Hanle effect provides a diagnostic tool for weak magnetic fields, which do not give rise to a measurable Zeeman effect, such as turbulent fields or magnetic canopies in the chromosphere. The lines which are sensitive to the Hanle effect are formed under non-LTE conditions by scattering of photons. After a brief description of the physical mechanism at hand, I present some approximate expressions for the linear polarization of such lines in the presence of a weak magnetic field and show how the Hanle effect may be used for the diagnostics of magnetic canopies. Title: Investigating the Vertical Structure of the Solar Granulation with the Sodium D2 Line Authors: Eibe, M. T.; Roudier, Th.; Mein, P.; Faurobert, M. Bibcode: 2000ESASP.463..309E Altcode: 2000sctc.proc..309E No abstract at ADS Title: Fast Numerical Methods for Polarized Line Radiative Transfer in the Presence of Hanle Effect Authors: Faurobert, M.; Frisch, H.; Nagendra, K. N. Bibcode: 1999ASPC..184...28F Altcode: The Hanle effect provides a diagnostic tool for weak magnetic fields which do not give rise to a measurable Zeeman effect, such as turbulent fields or magnetic canopies. The lines which are sensitive to the Hanle effect are formed under non-LTE conditions, by scattering of photons. Inversion methods for such diagnostics require to solve the non-LTE polarized transfer equation for a large number of magnetic configurations. Fast numerical methods are thus highly required. We present an Approximate Lambda Iteration method to treat the Hanle effect for lines formed with complete frequency redistribution. Referred to as PALI-H, this method is an extension of ALI methods first developed for non polarized line transfer. The starting point is to recast the polarized transfer equation into a vectorial integral equation for a 6-component source function. We show that the convergence of the method is independent of the strength and direction of the magnetic field. The method is very fast and allows to handle any type of depth-dependent magnetic field. Title: An operator perturbation method for polarized line transfer IV: Applications to the Hanle effect with partial frequency redistribution Authors: Nagendra, K. N.; Paletou, F.; Frisch, H.; Faurobert-Scholl, M. Bibcode: 1999ASSL..243..127N Altcode: 1999sopo.conf..127N No abstract at ADS Title: Polarized radiation transfer in 2D geometry Authors: Paletou, F.; Bommier, V.; Faurobert-Scholl, M. Bibcode: 1999ASSL..243..189P Altcode: 1999sopo.conf..189P No abstract at ADS Title: Polarized redistribution matrix for Hanle effect: Numerical tests Authors: Faurobert-Scholl, M.; Paletou, F.; Bommier, V. Bibcode: 1999ASSL..243..115F Altcode: 1999sopo.conf..115F No abstract at ADS Title: An operator perturbation method for polarized line transfer. III. Applications to the Hanle effect in 1D media Authors: Nagendra, K. N.; Frisch, H.; Faurobert-Scholl, M. Bibcode: 1998A&A...332..610N Altcode: In this paper we present an Approximate Lambda Iteration method to treat the Hanle effect (resonance scattering in the presence of a weak magnetic field) for lines formed with complete frequency redistribution. The Hanle effect is maximum in the line core and goes to zero in the line wings. Referred to as PALI-H, this method is an extension to non-axisymmetric radiative transfer problems of the PALI method presented in Faurobert-Scholl et al. (1997), hereafter referred to as Paper I. It makes use of a Fourier decomposition of the radiation field with respect to the azimuthal angle which is somewhat more general than the decomposition introduced in Faurobert-Scholl (1991, hereafter referred to as FS91). The starting point of the method is a vector integral equation for a six-component source vector representing the non-axisymmetric polarized radiation field. As in Paper I, the Approximate Lambda operator is a block diagonal matrix. The convergence rate of the PALI-H method is independent of the polarization rate and hence of the strength and direction of the magnetic field. Also this method is more reliable than the perturbation method used in FS91. The PALI-H method can handle any type of depth-dependent magnetic field. Here it is used to examine the dependence of the six-component source vector on the co-latitude, azimuthal angle and strength of the magnetic field. The dependence of the surface polarization on the direction of the line-of-sight and on the magnetic field is illustrated with polarization diagrams showing Q/I versus U/I at line center. The analysis of the results show that the full six-dimension problem can be approximated by a two-component modified resonance polarization problem, producing errors of at most 20% on the surface polarization at line center. Title: An operator perturbation method for polarized line transfer. II. Resonance polarization with partial frequency redistribution effects Authors: Paletou, Frederic; Faurobert-Scholl, Marianne Bibcode: 1997A&A...328..343P Altcode: The effects of partial frequency redistribution are implemented in the Polarized Accelerated Lambda Iteration (PALI) method of Faurobert-Scholl et al. (1997). The numerical scheme is an extension of the core-wing technique of Paletou & Auer (1995) originally developed for non-polarized line transfer problems. Using a new code, we validate theoretical results against those given by a Feautrier type code. Title: An operator perturbation method for polarized line transfer. I. Non-magnetic regime in 1D media. Authors: Faurobert-Scholl, M.; Frisch, H.; Nagendra, K. N. Bibcode: 1997A&A...322..896F Altcode: In this paper we generalize an Approximate Lambda Iteration (ALI) technique developed for scalar transfer problems to a vectorial transfer problem for polarized radiation. Scalar ALI techniques are based on a suitable decomposition of the Lambda operator governing the integral form of the transfer equation. Lambda operators for scalar transfer equations are diagonally dominant, offering thus the possibility to use iterative methods of the Jacobi type where the iteration process is based on the diagonal of the Lambda operator (Olson et al., 1986, JQSRT 35, 431). Here we consider resonance polarization, created by the scattering of an anisotropic radiation field, for spectral lines formed with complete frequency redistribution in a 1D axisymmetric medium. The problem can be formulated as an integral equation for a 2-component vector (Rees, 1978PASJ...30..455R) or, as shown by Ivanov (1995A&A...303..621I), as an integral equation for a (2x2) matrix source function which involves the same generalized Lambda operator as the vector integral equation. We find that this equation holds also in the presence of a weak turbulent magnetic field. The generalized Lambda operator is a (2x2) matrix operator. The element {11} describes the propagation of the intensity and is identical to the Lambda operator of non-polarized problems. The element {22} describes the propagation of the polarization. The off-diagonal terms weakly couple the intensity and the polarization. We propose a block Jacobi iterative method and show that its convergence properties are controlled by the propagator for the intensity. We also show that convergence can be accelerated by an Ng acceleration method applied to each element of the source matrix. We extend to polarized transfer a convergence criterion introduced by Auer et al. (1994A&A...292..599A) based on the grid truncation error of the converged solution. Title: On the use of CA I triplet lines as luminosity indicators. Authors: Cayrel, R.; Faurobert-Scholl, M.; Feautrier, N.; Spielfieldel, A.; Thevenin, F. Bibcode: 1996A&A...312..549C Altcode: Many strong lines formed in stellar atmospheres are well known to be dominated by pressure broadening, therefore their wings are a precious help for determining the surface gravities of dwarf or subgiant stars. In this paper, we explore the possibility for using the wings of the Ca I triplet lines 6102, 6122, 6162A for which recent theoretical computations of the damping are available. A NLTE code for radiative transfer was used to check these new computations against the integrated Solar Spectrum. We report here that (i) there is a spectacular improvement in the fit of the computed profile with the observed one when the new quantum mechanical computations are used instead of the classical Unsoeld's expression of the Van der Waals damping constant (ii) the departures from LTE in the computation of the wings of these lines are negligible, and this justifies the use of LTE computations for the determination of the surface gravities of G type stars, by this method. Title: Transfert de rayonnement hors-ETL et applications en physique solaire. Authors: Faurobert-Scholl, M.; Paletou, F.; Frisch, H. Bibcode: 1996JAF....53...24F Altcode: No abstract at ADS Title: Diagnostics with the Hanle Effect Authors: Faurobert-Scholl, M. Bibcode: 1996SoPh..164...79F Altcode: The Hanle effect has been extensively used for the determination of the magnetic field strength and direction in solar prominences. Here we address the problem of the diagnostics of weak magnetic fields in the solar photosphere and chromosphere by means of their Hanle effect in some selected absorption lines. As this is a relatively new area we will focus on the diagnostic methods and summarize some results that relate to the presence of a weak, turbulent magnetic field in the photosphere and to the chromospheric magnetic canopy. Finally we will outline some directions for future work. Title: Turbulent magnetic fields in the solar photosphere: diagnostics and interpretation. Authors: Faurobert-Scholl, M.; Feautrier, N.; Machefert, F.; Petrovay, K.; Spielfiedel, A. Bibcode: 1995A&A...298..289F Altcode: Turbulent magnetic fields in the solar photosphere may be determined by their depolarizing Hanle effect on the linear polarization of some solar absorption lines formed outside active regions (Stenflo 1982). In Faurobert-Scholl (1993) the center-to-limb variation of the linear polarization in the SrI 4607 A line was analyzed. It was shown that it is affected by the Hanle effect due to a weak magnetic field with mixed polarity at small scales. The accurate determination of the turbulent magnetic field strength requires radiative transfer calculations taking into account the effect of collisions and magnetic fields on the frequency and angular redistribution of the light. Here we present the different steps in the theory of redistribution, together with the first precise quantum calculations of the collisional cross-sections between hydrogen and SrI and CaI atoms. These new results are then used to perform a more accurate determination of the turbulent magnetic field strength in the solar photosphere. It is shown that the center-to-limb variation of the linear polarization in the SrI line is mainly sensitive to the average value of the field strength between the altitudes 200 and 400km. According to the observations this average value is between 20 and 10G. A theoretical interpretation is given in terms of a one-dimensional passive magnetic field transport equilibrium model with first-order smoothing. The resulting <|B_x_|>(z) equilibrium distribution reproduces the observations rather well, but the uncertainty in the amplitude, height-dependence and interpretation of microturbulence suggests that the present model could be brought to an even better agreement with the observations if a microturbulence different from the VAL3C model is used. It is finally pointed out that in the upper photosphere the turbulent field becomes force-free instead of being passively transported. It is found that this does not seriously modify our conclusions. Title: Hanle effect of magnetic canopies in the solar chromosphere Authors: Faurobert-Scholl, M. Bibcode: 1994A&A...285..655F Altcode: The center-to-limb variations of the linear polarization observed by Stenflo et al. (1980) outside active regions, in the resonance lines of CaI at 4227 A and of SrII at 4078 A, are analyzed. Both lines are formed in the low chromosphere by multiple scattering. Their linear polarization is a consequence of the coherent scattering of the anisotropic radiation field by the atoms. It is very sensitive to partial frequency redistribution, depolarizing collisions, turbulent velocity fields and to the Hanle effect due to weak magnetic fields. The rates of depolarizing collisions may be determined by fitting the polarization profiles observed in the line wings, which are not affected by the Hanle effect. The quadratic mean of the turbulent velocity field is adjusted in order to recover the observed line core intensity. It is then possible to estimate the resonance polarization in the line cores. These estimates are in good agreement with the observations performed close to the solar limb (at heliocentric angles larger than about 70deg). Closer to disk center the observed polarization rates are significantly larger than what is expected in the absence of a magnetic field. We investigate the Hanle effect of an almost horizontal magnetic field of random azimuthal orientation lying in the chromosphere, which may constitute the base of a magnetic canopy. If the base of the canopy lies slightly below the depth where the line core is formed, i.e. between 700km and 1000km above τ_5000_=1, then the line core polarization close to disk center is actually enhanced as compared to its non-magnetic value. This surprising effect is a consequence of multiple scattering of line photons in the chromosphere. The enhancement is however somewhat smaller than what is required to fit the observations. In contrast, the polarization is reduced when the canopy base lies in the region where the line core is formed, i.e. between 1000km and 1300km above τ_5000_=1; it becomes insensitive to any horizontal magnetic field lying higher in the chromosphere. Title: Diagnostics of turbulent magnetic fields in the solar photosphere Authors: Faurobert-Scholl, M. Bibcode: 1994smf..conf..331F Altcode: No abstract at ADS Title: Diagnostics of Magnetic Canopies in the Solar Chromosphere Authors: Faurobert-Scholl, M. Bibcode: 1994emsp.conf...69F Altcode: No abstract at ADS Title: Investigation of microturbulent magnetic fields in the solar photosphere by their Hanle effect in the Sr I 4607 angstroms line. Authors: Faurobert-Scholl, M. Bibcode: 1993A&A...268..765F Altcode: A detailed analysis is made of the center-to-limb variations of the Sr I 4607 A line, recorded by Stenflo et al. (1980). The effect of multiple scattering, depolarizing collisions, and partial frequency redistribution are fully taken into account. We find that the observed polarization rates are hard to explain without depolarizing effects, which following Stenflo (1982) we ascribe to a weak turbulent magnetic field producing depolarization by Hanle effect. As the spatial scale of a weak turbulent magnetic field is likely to be smaller than 300 km, the effect of the turbulent magnetic field is treated in the microturbulent limit. In the transfer equation for the Stokes parameters, the Hanle phase matrix is thus replaced by its average over the magnetic field distribution. We show that the center-to-limb observations of the Sr I 4607 A line polarization indicate the presence in the photosphere of a depth-dependent turbulent magnetic field. Its intensity decreases from values in the range 30 G to 60 G at the altitude z = 150 km above tau 5000 = 1, to values in the range l0 G to 30 G at the altitude z = 250 km. It then remains roughly constant at higher altitudes. Title: Hanle effect with partial frequency redistribution. II - Linear polarization of the solar CA I 4227 A line Authors: Faurobert-Scholl, M. Bibcode: 1992A&A...258..521F Altcode: An interpretation is presented of observations of the linear polarization in the resonance line of Ca I at 4227 A over solar active and nonactive regions performed by Stenflo (1982) and Stenflo et al. (1980). Theoretical polarization profiles of the Ca I line are calculated by solving a non-LTE polarized transfer problem with a two-level atom interative method which takes into account partial frequency redistribution and the Hanle effect. For Ca I depolarization is caused by collisions with neutral hydrogen atoms, and the collision rate is determined by gamma(vw), the van der Waals coefficient of neutral calcium. Comparisons of the theoretical line wing polarization with observational data from nonmagnetic regions suggest an empirical value for gamma(vw) which is in agreement with the results of previous theoretical calculations. Title: Hanle effect with partial frequency redistribution. I. Numerical methods and first applications. Authors: Faurobert-Scholl, M. Bibcode: 1991A&A...246..469F Altcode: The Hanle effect on optically thick resonance lines formed with partial frequency redistribution is investigated. In order to take into account partial frequency redistribution, two numerical methods were used for solving directly the vectorial transfer equation with Hanle effect for a two-level atom in a 1D medium: (1) a generalization of the Feautrier method and (2) a method that relies on a Fourier expansion of the radiation field with respect to the azimuth of the direction of propagation. Complete and partial frequency redistribution results are compared, and the effect of partial frequency redistribution on the determination of magnetic fields by means of the Hanle effect is evaluated. Title: Quelques problèmes de transfert en physique solaire. Authors: Frisch, H.; Faurobert-Scholl, M. Bibcode: 1991sed..conf..151F Altcode: (1) Introduction. (2) Formation ETL des raies: (2.1) Intensité du rayonnement et équation de transfert. (2.2) Approximation de diffusion. (2.3) Equation de transfert ETL pour les raies. (3) Formation non-ETL des raies: (3.1) Fonction source d'un atome à deux niveaux. (3.2) Fonction de redistribution. (3.3) Equation de transfert non-ETL. (3.4) Analyse asymptotique. (3.5) Transfert non-ETL dans une couche plane. (3.6) Probabilité d'échappement. (3.7) Méthodes numériques en transfert non-ETL. (3.8) Construction de modèles d'atmosphères. (4) Transfert de rayonnement polarisé. (4.1) Les paramètres de Stokes. (4.2) Mécanismes de polarisation des raies spectrales. (4.3) Equation de transfert d'un rayonnement polarisé. (4.4) Effet Hanle. (4.5) Effet Zeeman. Title: Hanle Effect with Partial Frequency Redistribution Authors: Faurobert-Scholl, M. Bibcode: 1990PDHO....7..264F Altcode: 1990dysu.conf..264F; 1990ESPM....6..264F The author investigates the Hanle effect on optically thick lines formed by multiple scattering of photons. In particular the importance of the correlation between the frequencies of the absorbed and reemitted photons at each scattering event (partial frequency redistribution) is outlined. Title: Asymptotic analysis of resonance polarization and escape probability approximations Authors: Faurobert-Scholl, M.; Frisch, H. Bibcode: 1989A&A...219..338F Altcode: Polarized transfer asymptotic and first order escape probability methods developed for the nonpolarized case are generalized to include linear polarization produced by the scattering of anisotropic radiation in the absence of magnetic fields. The analyses are based on a coupled integral equation for two-angle-dependent source functions. Some general properties, such as the order of magnitude of the surface polarization and approximations for the source functions, are deduced. The escape probability approximations are compared with exact solutions and found to be more accurate than first order perturbation techniques for lines of moderate optical thickness in solar isothermal prominences. Title: A Model for the Penetration of Lyman Alpha in the Solar Chromosphere Authors: Faurobert, M.; Frisch, H.; Skumanich, A. Bibcode: 1988ApJ...328..856F Altcode: A multilevel calculation of the hydrogen spectrum by Skumanich and Lites, followed by a two-level representation of each transition, shows that all the solar Lyα photons are created in an optically thick layer in the high chromosphere above τ0 ≈ 102. The authors give a simplified model that demonstrates the penetration of Lyα into the lower chromosphere below the creation region, i.e., for τ0 > 102. A second-order escape probability approximation yields a simple analytical expression which accurately reproduces the behavior of the Lyα source function for 102 ⪉ τ0 ⪉ 5×106 provided the destruction probability, ɛ is set close to 10-6. Title: Linear polarization of resonance lines in the absence of magnetic fields. II - Semi-infinite atmospheres Authors: Faurobert, M. Bibcode: 1988A&A...194..268F Altcode: Polarization profiles of resonance lines formed in magnetic free semiinfinite atmospheres having either a uniform temperature or a chromospheric-type temperature rise are considered. In the isothermal case, a comparison is made between profiles calculated with the angle- and frequency-dependent R(II) partial redistribution and those given by the angle-averaged form of R(II), which is a simplified version of it introduced by Ayres (1985) and the Kneer (1975) approximation. It is found that, in chromospheric models, a maximum of polarization perpendicular to the surface appears at frequencies which are formed in the region of the temperature rise. Title: Transfert de rayonnement polarisé et non-polarisé avec redistribution en fréquence : méthodes asymptotiques et applications Title: Transfert de rayonnement polarisé et non-polarisé avec redistribution en fréquence : méthodes asymptotiques et applications Title: Transfer of polarized and non-polarized radiation with frequency redistribution: asymptotic methods and applications; Authors: Faurobert, Marianne Bibcode: 1988PhDT........83F Altcode: No abstract at ADS Title: Linear polarization of resonance lines in the absence of magnetic fields. I - Slabs of finite optical thickness Authors: Faurobert, M. Bibcode: 1987A&A...178..269F Altcode: Effects of partial frequency redistribution on resonance polarization of spectral lines in the absence of magnetic fields are studied for resonance lines formed in finite slabs. The emphasis is on testing the validity (for polarization calculations) of various approximate forms of the so-called RII frequency redistribution function which describes the formation of resonance lines formed in dilute media. Polarization profiles obtained with the angle-dependent RII are compared to profiles calculated with the angle-averaged form of RII and its approximate versions proposed by Kneer and Ayres. A comparison with complete frequency redistribution polarization profiles is also presented. Title: The Lyman α line in the solar chromosphere: penetrative model andapproximations. Authors: Faurobert, M.; Frisch, H.; Skumanich, A. Bibcode: 1987PAICz..66..205F Altcode: 1987eram....1..205F The authors present a model for the formation of Lyman α in the chromosphere below the creation region. The hydrogen atom is treated as a two-level atom and the chromosphere as a semi-infinite medium free of primary sources and illuminated by an isotropic and frequency independent radiation field at r0 ≅ 102. Title: A numerical investigation of approximation procedures for optically thick resonance lines. Authors: Faurobert, M. Bibcode: 1986A&A...158..191F Altcode: This paper concerns approximation procedures which can replace the full transfer equation with RII partial frequency redistribution. Existing asymptotic analyses of the formation of optically thick resonance lines in dilute media show that the interior radiation field (away from boundaries) can be approximated by the solution of a space and frequency diffusion equation and provide an expression of the emergent radiation field, away from line center, in terms of the interior solution. Here an approximation for the angle-averaged intensity, to be used at all optical depths, is constructed by adding the solution of the interior diffusion equation to the surface value of the angle-averaged intensity. The validity of this approximation is tested by comparison with the solution of the full transfer equation, in the case where the probability of collisional deexcitation and the Doppler width of the line are uniform. The diffusion equation has then an analytical solution. The tests are performed first for a two-level atom, considering a wide range of optical thicknesses and densities, and also for the Lyα line under physical conditions typical of the quasar broad emission line regions. In the latter case, the validity of a mean escape probability approximation has also been examined. Title: Line transfer with complete frequency redistribution in an absorbing medium - Scaling laws and approximation Authors: Faurobert, M.; Frisch, H. Bibcode: 1985A&A...149..372F Altcode: This paper discusses the influence of a continuous absorption produced by dust grains or photoionization on subordinate or weak resonance lines. The lines are being formed with complete Doppler or Voigt frequency redistribution in a one dimensional slab of finite thickness. An asymptotic analysis in the limit of small β (ratio of continuum to line opacity coefficient) shows that the large scale behaviour of the radiation field is described by a singular integral equation identical to that obtained by Frisch and Frisch (1977) for collisional destruction, but with an exponentially decreasing kernel in the case of the Voigt profile. Asymptotic scaling laws for the mean path length, the mean number of scatterings and the fraction of created photons which escapes the medium are given in the limits of weak and strong absorption. A first order escape probability method is used to evaluate net radiative brackets and line cooling rates, taking into account a possible emission by the continuum in the frequency domain of the line. Finally, a definition of the mean number of scatterings properly incorporating this emission term is proposed. Title: Boundary layer conditions for the transport of radiation in stars Authors: Frisch, H.; Faurobert, M. Bibcode: 1984A&A...140...57F Altcode: An expansion technique used by Larsen et al. (1983) for describing coherent scattering is applied to characterizing an outer thermal boundary condition for radiation transport in stellar interiors. Modifications are introduced to cover conditions of non-gray radiative equilibrium, which is analyzed asymptotically. An expansion parameter is defined in terms of coupled transfer and energy equations and carried out to first order to obtain a ratio of the photon free path to the stellar characteristic dimension. The ratio provides a scale for the space variable with which a singular perturbation problem is solved for interior and boundary conditions, the latter being in the stellar atmosphere and the sum of the interior solution and the boundary layer correction. A Robin boundary condition results which is only 5 percent higher in temperature than the interior in the case of a gray opacity coefficient.