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. <BR /> 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. <BR /> 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. <BR />
  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). <BR />
  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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <P />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. <P />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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR
  /> 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. <BR
  /> 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. <BR /> 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. <BR /> Aims:
  We intend to investigate possible variations of the photospheric
  temperature gradient with magnetic activity. <BR /> 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. <BR /> 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. <BR />
  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. <BR /> 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. <BR /> Methods: The V-moments inversion (VMI) method uses
  shifts S<SUB>V</SUB> derived from moments of V-profiles and integrals
  of Q<SUP>2</SUP>, U<SUP>2</SUP>, and V<SUP>2</SUP> 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. <BR /> Results:
  We perform inversions of HINODE SOT/SP data for inclination ranges 0
  &lt;ψ&lt; 60° and 120 &lt;ψ&lt; 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR
  /> 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. <BR /> 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<SUP>-6</SUP> times less intense than the
  solar photosphere, and thus, accurate measurements of this phenomena
  are extremely challenging. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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). <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR
  /> 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. <BR
  /> 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 C<SUB>2</SUB> 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. <BR /> 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 C<SUB>2</SUB> and MgH
  molecules with different sensitivities to the Hanle effect. We consider
  six C<SUB>2</SUB>-triplets and one MgH line in the spectral range
  between 515.7 nm and 516.1 nm observed with the THEMIS Telescope. <BR
  /> 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. <BR /> Results: For the elastic depolarizing collisions
  cross-section for the C<SUB>2</SUB> lines we obtain α<SUP>(2)</SUP>
  = 1.6 ± 0.4 × 10<SUP>-9</SUP> cm<SUP>3</SUP> s<SUP>-1</SUP>, 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 C<SUB>2</SUB> 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. <BR /> 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 A<SUB>1</SUB> and A<SUB>2</SUB> 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&amp;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. <BR /> 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 C<SUB>2</SUB> 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. <BR /> 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. <BR
  /> 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 C<SUB>2</SUB> 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 C<SUB>2</SUB> 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. <BR /> Aims: We propose a new inversion method, using
  functions derived from central moments (ICM), to determine magnetic
  field vectors with very few iterations. <BR /> Methods: Two quantities
  A<SUB>1</SUB> and A<SUB>2</SUB> 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 A<SUB>D</SUB> can be used to interpolate between
  expansions that correspond to two basic models. Exponents β<SUB>1</SUB>
  and β<SUB>2</SUB> in the moment expressions are adjusted to minimize
  the sensitivity to data noise. <BR /> 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. <BR /> 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. <P />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. <BR /> 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. <BR /> 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. <BR /> 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. <BR /> 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. <BR />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. <BR />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. <BR />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. <BR />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. <BR />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. <BR />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. <BR />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. <BR />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 -
  4r<SUP>2</SUP>), with |r| &lt;= 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. <BR />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. <BR />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. <BR />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. <P />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. <BR
  />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. <BR />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. <BR />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: <P />-
  magnetic and non-magnetic bright features can be discriminated by simple
  criteria of intensities and dopplershifts. <P />- 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. <P />- 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 C<SUB>2</SUB> 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 C<SUB>2</SUB> we show that the
  C<SUB>2</SUB> 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 C<SUB>2</SUB> 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
  W<SUB>2</SUB>. 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 C<SUB>2</SUB> molecular
  transitions and two MgH transitions are present in our spectral window;
  we find that for the C<SUB>2</SUB> 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 D<SUB>1</SUB>
  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 R<SUB>s</SUB> 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 D<SUB>1</SUB> and Na i
  D<SUB>2</SUB> 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
  &amp; 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 D<SUB>1</SUB> and D<SUB>2</SUB>
  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 D<SUB>2</SUB> 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 &amp; 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&amp;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&amp;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 &lt;|B_x_|&gt;(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 τ<SUB>0</SUB> ≈ 10<SUP>2</SUP>. The
  authors give a simplified model that demonstrates the penetration of
  Lyα into the lower chromosphere below the creation region, i.e., for
  τ<SUB>0</SUB> &gt; 10<SUP>2</SUP>. A second-order escape probability
  approximation yields a simple analytical expression which accurately
  reproduces the behavior of the Lyα source function for 10<SUP>2</SUP>
  ⪉ τ<SUB>0</SUB> ⪉ 5×10<SUP>6</SUP> provided the destruction
  probability, ɛ is set close to 10<SUP>-6</SUP>.

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 R<SUB>II</SUB> frequency redistribution function
  which describes the formation of resonance lines formed in dilute
  media. Polarization profiles obtained with the angle-dependent
  R<SUB>II</SUB> are compared to profiles calculated with the
  angle-averaged form of R<SUB>II</SUB> 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 r<SUB>0</SUB> ≅ 10<SUP>2</SUP>.

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 R<SUB>II</SUB> 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.

