Author name code: bommier ADS astronomy entries on 2022-09-14 author:"Bommier, Veronique" ------------------------------------------------------------------------ Title: On Identifying and Mitigating Bias in Inferred Measurements for Solar Vector Magnetic Field Data Authors: Leka, K. D.; Wagner, Eric L.; Griñón-Marín, Ana Belén; Bommier, Véronique; Higgins, Richard Bibcode: 2022arXiv220711572L Altcode: The problem of bias, meaning over- or underestimation, of the component perpendicular to the line-of-sight, Bperp, in vector magnetic field maps is discussed. Previous works on this topic have illustrated that the problem exists; here we perform novel investigations to quantify the bias, fully understand its source(s), and provide mitigation strategies. First, we develop quantitative metrics to measure the Bperp bias and quantify the effect in both local (physical) and native image-plane components. Second we test and evaluate different inversion options and data sources, to systematically characterize the impacts of choices, including explicitly accounting for the magnetic fill fraction ff. Third we deploy a simple model to test how noise and different models of the bias may manifest. From these three investigations we find that while the bias is dominantly present in under-resolved structures, it is also present in strong-field pixel-filling structures. Noise in the magnetograms can exacerbate the problem, but it is not the primary cause. We show that fitting ff explicitly provides significant mitigation, but that other considerations such as choice of chi^2 weights and optimization algorithms can impact the results as well. Finally, we demonstrate a straightforward "quick fix" that can be applied post-facto but prior to solving the 180deg ambiguity in Bperp, and which may be useful when global-scale structures are, e.g., used for model boundary input. The conclusions of this work support the deployment of inversion codes that explicitly fit ff or, as with the new SyntHIA neural-net, that are trained on data that did so. Title: Mini solar flare and jet due to small scale surface motions Authors: Joshi, Reetika; Vilmer, Nicole; Chandra, Ramesh; Heinzel, Petr; Bommier, Veronique; Schmieder, Brigitte; Aulanier, Guillaume; Tomin, James Bibcode: 2022cosp...44.2535J Altcode: Here we present the study of the fine structure and dynamics of the plasma at a jet base forming a mini-flare between two emerging magnetic fluxes (EMFs) observed with Interface Region Imaging Spectrograph (IRIS) and the Solar Dynamics Observatory instruments. This active region is an outcome of the collapse of two EMFs overlaid by arch filament systems. We observed that, before the jet an extension of the flux rope was present and a part of it was detached and formed a small bipole with a bald patch region, which dynamically became an X-current sheet over the dome of one EMF where the reconnection took place. At the time in the site of reconnection, the IRIS C II, Si IV, and Mg II line profiles present bi directional flows in a tiny region. These types of spectra are typically associated with twist, rotation, or the presence of plasma in helical structures. The tilt observed in our spectra can be explained by the presence of a helical structure at the jet base during the reconnection process due to a transfer of the twist from a flux rope in the vicinity of the jet. We also combined the observations of the Balmer continuum obtained with the IRIS (spectra and SJIs 2832 Å). The calibrated Balmer continuum was compared to non-local thermodynamic equilibrium radiative transfer flare models and the radiated energy was estimated. Assuming thick target HXR emission, we calculated the energy of the non thermal electrons detected by the Fermi/GBM and compared it to the radiated energy. The electron-beam flux estimated from Fermi/GBM between 10$ ^{9}$ and 10$ ^{10}$ erg s$ ^{-1}$ cm$ ^{-2}$ is consistent with the beam flux required in non-LTE radiative transfer models to obtain the excess of Balmer continuum emission observed in this IRIS spectra. We conclude that the bombardment of electrons could be in a region smaller than the IRIS spatial resolution. Title: Electron thermal escape inside the Sun Authors: Bommier, V. Bibcode: 2021sf2a.conf..181B Altcode: No abstract at ADS Title: Empirical atmosphere model in a mini flare during magnetic reconnection Authors: Schmieder, Brigitte; Joshi, Reetika; Chandra, Ramesh; Aulanier, Guillaume; Tei, Akiko; Heinzel, Petr; Tomin, James; Vilmer, Nicole; Bommier, Veronique Bibcode: 2021arXiv211206790S Altcode: A spatio-temporal analysis of IRIS spectra of MgII, CII, and SiIV ions allows us to study the dynamics and the stratification of the flare atmosphere along the line of sight during the magnetic reconnection phase at the jet base. Strong asymmetric MgII and CII line profiles with extended blue wings observed at the reconnection site are interpreted by the presence of two chromospheric temperature clouds: one explosive cloud with blueshifts at 290 km/s and one cloud with smaller Doppler shift (around 36 km/s). Simultaneously at the same location a mini flare was observed with strong emission in multi temperatures (AIA), in several spectral IRIS lines (e.g. Oiv and Siiv, Mgii), absorption of identified chromospheric lines in Siiv line profile, enhancement of the Balmer continuum and X-ray emission by FERMI/GBM. With the standard thick-target flare model we calculate the energy of non thermal electrons observed by FERMI and compare it to the energy radiated by the Balmer continuum emission. We show that the low energy input by non thermal electrons above 20 keV was still sufficient to produce the excess of Balmer continuum. Title: 24 synoptic maps of average magnetic field in 296 prominences measured by the Hanle effect during the ascending phase of solar cycle 21 Authors: Bommier, V.; Leroy, J. L.; Sahal-Bréchot, S. Bibcode: 2021A&A...647A..60B Altcode: 2020arXiv200708219B
Aims: We present 24 synoptic maps of solar filaments, in which the average unambiguous magnetic field vectors of 296 prominences were determined with Pic-du-Midi observations between 1974 and 1982. This was the ascending phase of cycle 21.
Methods: The magnetic field was determined by interpreting the Hanle effect, which is observed in the He I D3 line. Previous results for the prominence field polarity and prominence chirality were applied to solve the fundamental ambiguity. The measurements were averaged in each prominence for accuracy reasons.
Results: The result is twofold. First, alternating field directions can be observed from one neutral line to the next. Second, a general field alignment is found along a solar north-south field that is distorted by the differential rotation effect.

The 296 prominences solar coordinates and magnetic field vector data are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/647/A60 Title: Electron thermal escape in the Sun Authors: Bommier, V. Bibcode: 2021csss.confE...4B Altcode: Magnetic field vector observations in the solar photosphere have generally revealed a non-zero value of the divergence: the vertical field component gradient is found on the order of 3 G/km when the horizontal field component gradient is of 0.3 G/km only. This has first to be assigned to the fact that the measured quantity is the magnetic field H, which is related to the divergence-free magnetic induction B by the law B=µ0(H+M), where M is the magnetization. In plasmas like the solar photosphere, magnetization results from plasma diamagnetism and spiral movement of charged particles about the magnetic field. The usually admitted but very indirect electron density leads to weak magnetization. However, it can be observed that in the solar interior the electron thermal velocity is much larger than the escape velocity. The attractive effect of the protons does not completely prevent the electrons from escaping. A model of this will be presented. The electrons escape from lower layers in a quasi-static spreading, and accumulate in the photosphere. Therefore, the electron density at surface is increased but decreases with height at surface, which enables the observed values because divH = -divM. Such a structure is probably at play in the solar-type stars. Title: Twist transfer to a solar jet from a big flux rope detected in the HMI magnetogram Authors: Joshi, Reetika; Schmieder, Brigitte; Aulanier, Guillaume; Chandra, Ramesh; Bommier, Veronique Bibcode: 2021cosp...43E1752J Altcode: Solar jets often have a helical structure containing both hot and cool ejected plasma. Different mechanisms are proposed to trigger jets by magnetic reconnection between the emergence of magnetic flux and environment, or induced by twisted photospheric motions bringing the system to instability. Multi-wavelength observations of a twisted jet observed with the AIA and IRIS is presented to understand how the twist was injected in the jet from a flux rope, fortunately, IRIS spectrographic slit was just crossing the reconnection site. This active region is a result of the collapse of two emerging magnetic fluxes (EMFs) overlaid by arch filament systems. In the magnetic field maps, we evidenced the pattern of a long sigmoidal flux rope along the polarity inversion line between the two EMFs which is the site of the reconnection. Before the jet, there was an extension of the flux rope, and a part of it was detached and formed a small bipole with a bald patch region which dynamically became an X-current sheet over the dome of one EMF where the reconnection took place. At the time of the reconnection, the Mg II spectra exhibited a strong extension of the blue wing which is decreasing over a distance of 10 Mm (from -300 km/s to a few km/s). This is the signature of the transfer of the twist to the jet. Comparison with numerical magnetohydrodynamics simulations confirmed the existence of the long flux rope in the neighborhood of the jet. We conjecture that there is a transfer of twist to the jet during the extension of the flux rope to the reconnection site without the flux rope eruption. The reconnection would start in the low atmosphere in the bald patch reconnection region and extend at an X-point along the current sheet formed above. Title: VizieR Online Data Catalog: Prominence average magnetic fields in cycle XXI (Bommier+, 2021) Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S. Bibcode: 2021yCat..36470060B Altcode: From our full sample of 3297 measurements achieved in 379 quiescent prominences observed in HeI D3 at the Pic-du-Midi during the ascending phase of Cycle XXI (1974-1982), we discarded those prominences for which the identification of the neutral line is doubtful (64 prominences).

As a result, we obtained unambiguous average horizontal magnetic field vectors of 296 prominences each associated to a filament observed eight days before (W limb) or after (E limb).

(1 data file). Title: Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. VI. Application to the second solar spectrum of the Na I D1 and D2 lines: convergence Authors: Bommier, Véronique Bibcode: 2020A&A...644A..65B Altcode: 2020arXiv200708226B Context. This paper presents a numerical application of a self-consistent theory of partial redistribution in nonlocal thermodynamical equilibrium conditions, developed in previous papers of the series.
Aims: The code was described in IV of this series. However, in that previous paper, the numerical results were unrealistic. The present paper presents an approximation able to restore the reliability of the outgoing polarization profiles.
Methods: The convergence of the results is also proved. It is demonstrated that the step increment decreases like 1/Nα, with α > 1.
Results: Thanks to these additions, the results series behaves like a Riemann series, which is absolutely convergent. However, convergence is not fully reached in line wings within the allocated computing time. Development of efficient acceleration methods would be desirable for future work.
Conclusions: Agreement between the computed and observed linear polarization profiles remains qualitative only. The discrepancy is assigned to the plane parallel atmosphere model, which is insufficient to describe the chromosphere, where these lines are formed. As all the integrals are numerical in the code, it could probably be adapted to more realistic and higher dimensional model atmospheres. However, this is time consuming for lines with a hyperfine structure, as in the Na I D lines. The net linear polarization observed in Na I D1 with the Zürich Imaging Polarimeter ZIMPOL mounted on the McMath-Pierce telescope at Kitt Peak is not confirmed by the present calculations and could be an artefact of instrumental polarization. The presence of instrumental polarization could be confirmed by the higher linear polarization degree observed by this instrument in the Na I D2 line center with respect to the present calculation result where the magnetic field is not accounted for. At this precise point, the Hanle effect acts as a depolarizing effect in the second solar spectrum. The observed linear polarization excess is found to be of the same order of magnitude in both line centers, namely 0.1%, which is also comparable to the instrumental polarization compensation level of this experiment. Title: The role of small-scale surface motions in the transfer of twist to a solar jet from a remote stable flux rope Authors: Joshi, Reetika; Schmieder, Brigitte; Aulanier, Guillaume; Bommier, Véronique; Chandra, Ramesh Bibcode: 2020A&A...642A.169J Altcode: 2020arXiv200806887J Context. Jets often have a helical structure containing ejected plasma that is both hot and also cooler and denser than the corona. Various mechanisms have been proposed to explain how jets are triggered, primarily attributed to a magnetic reconnection between the emergence of magnetic flux and environment or that of twisted photospheric motions that bring the system into a state of instability.
Aims: Multi-wavelength observations of a twisted jet observed with the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory and the Interface Region Imaging Spectrograph (IRIS) were used to understand how the twist was injected into the jet, thanks to the IRIS spectrographic slit fortuitously crossing the reconnection site at that time.
Methods: We followed the magnetic history of the active region based on the analysis of the Helioseismic and Magnetic Imager vector magnetic field computed with the UNNOFIT code. The nature and dynamics of the jet reconnection site are characterised by the IRIS spectra.
Results: This region is the result of the collapse of two emerging magnetic fluxes (EMFs) overlaid by arch filament systems that have been well-observed with AIA, IRIS, and the New Vacuum Solar Telescope in Hα. In the magnetic field maps, we found evidence of the pattern of a long sigmoidal flux rope (FR) along the polarity inversion line between the two EMFs, which is the site of the reconnection. Before the jet, an extension of the FR was present and a part of it was detached and formed a small bipole with a bald patch (BP) region, which dynamically became an X-current sheet over the dome of one EMF where the reconnection took place. At the time of the reconnection, the Mg II spectra exhibited a strong extension of the blue wing that is decreasing over a distance of 10 Mm (from -300 km s-1 to a few km s-1). This is the signature of the transfer of the twist to the jet.
Conclusions: A comparison with numerical magnetohydrodynamics simulations confirms the existence of the long FR. We conjecture that there is a transfer of twist to the jet during the extension of the FR to the reconnection site without FR eruption. The reconnection would start in the low atmosphere in the BP reconnection region and extend at an X-point along the current sheet formed above.

Movies attached to Figs. 1, 3, 4, and 7 are available at https://www.aanda.org Title: Solar photosphere magnetization Authors: Bommier, Véronique Bibcode: 2020A&A...634A..40B Altcode: 2019arXiv190706476B Context. A recent review shows that observations performed with different telescopes, spectral lines, and interpretation methods all agree about a vertical magnetic field gradient in solar active regions on the order of 3 G km-1, when a horizontal magnetic field gradient of only 0.3 G km-1 is found. This represents an inexplicable discrepancy with respect to the divB = 0 law.
Aims: The objective of this paper is to explain these observations through the law B = μ0(H + M) in magnetized media.
Methods: Magnetization is due to plasma diamagnetism, which results from the spiral motion of free electrons or charges about the magnetic field. Their usual photospheric densities lead to very weak magnetization M, four orders of magnitude lower than H. It is then assumed that electrons escape from the solar interior, where their thermal velocity is much higher than the escape velocity, in spite of the effect of protons. They escape from lower layers in a quasi-static spreading, and accumulate in the photosphere. By evaluating the magnetic energy of an elementary atom embedded in the magnetized medium obeying the macroscopic law B = μ0(H + M), it is shown that the Zeeman Hamiltonian is due to the effect of H. Thus, what is measured is H.
Results: The decrease in density with height is responsible for non-zero divergence of M, which is compensated for by the divergence of H, in order to ensure div B = 0. The behavior of the observed quantities is recovered.
Conclusions: The problem of the divergence of the observed magnetic field in solar active regions finally reveals evidence of electron accumulation in the solar photosphere. This is not the case of the heavier protons, which remain in lower layers. An electric field would thus be present in the solar interior, but as the total charge remains negligible, no electric field or effect would result outside the star. Title: Magnetic field vector ambiguity resolution in a quiescent prominence observed on two consecutive days Authors: Kalewicz, T.; Bommier, V. Bibcode: 2019A&A...629A.138K Altcode: 2019arXiv190401816K Context. Magnetic field vector measurements are always ambiguous, that is, two or more field vectors are solutions of the observed polarisation.
Aims: The aim of the present paper is to solve the ambiguity by comparing the ambiguous field vectors obtained in the same prominence observed on two consecutive days. The effect of the solar rotation is to modify the scattering angle of the prominence radiation, which modifies the symmetry of the ambiguous solutions. This method, which is a kind of tomography, was successfully applied in the past to the average magnetic field vector of 20 prominences observed at the Pic du Midi. The aim of the present paper is to apply this method to a prominence observed with spatial resolution at the THÉMIS telescope (European site at Izaña, Tenerife Island).
Methods: The magnetic field vector is measured by interpretation of the Hanle effect observed in the He I D3 5875.6 Å line, within the horizontal field vector hypothesis for simplicity. The ambiguity is first solved by comparing the two pairs of solutions obtained for a "big pixel" determined by averaging the observed Stokes parameters in a large region at the prominence centre. Each pixel is then disambiguated by selecting the closest solution in a propagation from the prominence centre to the prominence boundary.
Results: The results previously obtained on averaged prominences are all recovered. The polarity is found to be inverse with a small angle of about -21° between the magnetic field vector and the long axis of the filament. The magnetic field strength of about 6 G is found to slightly increase with height, as previously observed. The new result is the observed decrease with height, of the absolute value of the angle between the magnetic field vector and the long axis of the filament.
Conclusions: This result is in excellent agreement with prominence magnetohydrodynamical models. Title: Self-consistent Multilevel PRD Authors: Bommier, Véronique Bibcode: 2019ASPC..519...39B Altcode: After having recalled what are the physical components of frequency partial redistribution (PRD), this paper presents a new multilevel theoretical formalism based on non-markovian master equation theory for describing the atom-radiation interaction. As an application, this paper present final results of a modeling, based on this theory, of the second solar spectrum of the Na I D lines, which is the spectrum of the linear polarisation formed by scattering and observed close to the solar limb. Title: Collisional Line Broadening and Collisional Depolarization of Spectral Lines: Similarities and Differences Authors: Sahal-Bréchot1, S.; Bommier, V. Bibcode: 2019ASPC..526...35S Altcode: The collisional width of a spectral line takes part in the frequency redistribution of the scattered radiation in the line. Within the impact approximation, collisional line broadening parameters (widths and shifts), depolarization and polarization transfer rates seem very similar: both include the effect of collisional transitions between the Zeeman sublevels of a given level, or between fine or hyperfine structure levels of a given term. However, there are important differences. On the one hand, for line broadening, the two levels connected by the radiative transition contribute to the broadening. There is also an interference term between the two levels of the line, which can be very important for collisions with neutral hydrogen. On the other hand, only one level or two close levels are concerned in the depolarization. Another difference lies in the fact that elastic cross-sections of the two levels contribute to the line broadening, whereas they do not contribute to the depolarization. The possibility to find some theoretical relationships concerning depolarization versus collisional broadening will be shown to be impossible. The perturbation expansion of the collisional S matrix and the Van der Waals interaction potential are recalled to be unsuitable, since all the derived parameters are too small (by approximately a factor 2). Finally, in the light of a very recent paper, numerical relationships between line widths and level depolarization rates will be quoted. Title: Non-Perturbative Theory of Radiative Scattering in the Weak Radiation Field Limit: Resolution of Egidio Landi's "Paradox" Authors: Bommier, V. Bibcode: 2019ASPC..526...17B Altcode: No abstract at ADS Title: Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. V. The two-term atom (Corrigendum) Authors: Bommier, Véronique Bibcode: 2018A&A...619C...1B Altcode: No abstract at ADS Title: Interpretation of Hanle effect measurements in the Solar Corona: promises and difficulties Authors: Bommier, Veronique Bibcode: 2018cosp...42E.395B Altcode: After having recalled the main features of the Hanle effect, and of its application to coronal lines, the promises and difficulties of the measurement interpretation in terms of magnetic field vector diagnostics, will be investigated, based on Bommier, V., Leroy, J.L., and Sahal-Bréchot, S., 1981, A&A, 100, 231, and in the light of the new instrumentation presently available or in project, as well as data-driven modeling present possibilities. The feasibility of measuring the Coronal magnetic field by interpretation of the Zeeman effect observed in the infrared, will also be investigated. Title: Disambiguated magnetic field measurements in a quiescent prominence Authors: Bommier, Veronique; Kalewicz, Thomas Bibcode: 2018cosp...42E.396B Altcode: The magnetic field vector was measured in a prominence by interpretation of the Hanle effect, following the method described in Bommier, V., Leroy, J.L., and Sahal-Bréchot, S., 1981, A&A, 100, 231, but with the difference that the measurements were spatially resolved in the prominence body, because the prominence was observed with the French THEMIS telescope (Izaña, Tenerife, Canarias). The prominence was observed on two following days, and the measurement ambiguity was resolved by selecting the closest pair in the ambiguous solutions, whose symmetry changes along the days due to solar rotation. The method successfully worked. The observed line was He I D3. The polarisation was integrated along the line profile for accuracy purposes, and the two line components were not resolved. The magnetic field was then assumed to be horizontal, as shown by Athay et al. (1983, Solar Phys. 89, 3). The magnetic field strength and the α angle between the field vector and the prominence long axis were unambiguously obtained for nearly each pixel. A vertical gradient of +0.5e-4 G/km (increasing with height) is found above h=34 Mm, in excellent agreement with Leroy et al. (1983, Sol. Phys. 83, 135). The new result is that the α angle is found to decrease with height, in accordance with the theoretical model by Aulanier & Démoulin (2003, A&A, 402, 769). The second new result is that measurements are now obtained close to the solar limb, lower than 20 Mm. In these regions, the magnetic field strength gradient is found negative -0.6e-4 G/km (decreasing with height), contrarily to the model. In this region, the α angle is also found decreasing with height, but in a quicker manner and with more scattered values. The prominence is found of Inverse Polarity at all heights. Title: Ion traps at the Sun: observational evidence Authors: Musset, Sophie; Fleishman, Gregory D.; Bommier, Veronique; Glesener, Lindsay Bibcode: 2018tess.conf20955M Altcode: Our understanding of thermal processes in the solar atmosphere relies in particular on diagnostics of the plasma emission in ultraviolet and extreme ultraviolet (EUV). These emissions are produced by heavy ions in various ionization states and depend on the amount of these ions and on the plasma temperature and density. Any non-uniformity of the distribution of elements can therefore affect our thermal diagnostics of the solar atmosphere. Using a simple model of ion propagation in current carrying magnetic loops, we theoretically predicted a concentration (depletion) of ions in regions of the solar atmosphere associated with upward-directed (downward-directed) current densities. We present here the data analysis that leads to observational evidence supporting this prediction. We analyze the distribution of EUV emission from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamic Observatory (SDO) in regard to positive and negative vertical current densities calculated at the photospheric level using the spectropolarimetric data from the Helioseismic Magnetic Imager (SDO/HMI). A statistical analysis of these distributions was performed for several active regions and at several times, for several EUV wavelengths. We found a significant excess in EUV brightness in the areas with positive (i.e. upward) current densities rather than negative. We call such areas of heavy ion concentrations the "ion traps". We will discuss the implication of our result for the first ionization potential (FIP) effect in particular, as well as the next theoretical and observational developments foreseen to deepen our understanding of this effect in the dynamic coronal environment during and between solar flares. Title: Ion Traps at the Sun: Implications for Elemental Fractionation Authors: Fleishman, Gregory D.; Musset, Sophie; Bommier, Véronique; Glesener, Lindsay Bibcode: 2018ApJ...857...85F Altcode: 2018arXiv180302851F Why the tenuous solar outer atmosphere, or corona, is much hotter than the underlying layers remains one of the greatest challenges for solar modeling. Detailed diagnostics of the coronal thermal structure come from extreme ultraviolet (EUV) emission. The EUV emission is produced by heavy ions in various ionization states and depends on the amount of these ions and on plasma temperature and density. Any nonuniformity of the elemental distribution in space or variability in time affects thermal diagnostics of the corona. Here we theoretically predict ionized chemical element concentrations in some areas of the solar atmosphere, where the electric current is directed upward. We then detect these areas observationally, by comparing the electric current density with the EUV brightness in an active region. We found a significant excess in EUV brightness in the areas with positive current density rather than negative. Therefore, we report the observational discovery of substantial concentrations of heavy ions in current-carrying magnetic flux tubes, which might have important implications for the elemental fractionation in the solar corona known as the first ionization potential effect. We call such areas of heavy ion concentration the “ion traps.” These traps hold enhanced ion levels until they are disrupted by a flare, whether large or small. Title: Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. V. The two-term atom Authors: Bommier, Véronique Bibcode: 2017A&A...607A..50B Altcode: 2017arXiv170805579B Context. In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution).
Aims: This paper provides theoretical expressions of the redistribution function for the two-term atom. This redistribution function includes both coherent (RII) and incoherent (RIII) scattering contributions with their branching ratios.
Methods: The expressions were derived by applying the formalism outlined above. The statistical equilibrium equation for the atomic density matrix is first formally solved in the case of the two-term atom with unpolarized and infinitely sharp lower levels. Then the redistribution function is derived by substituting this solution for the expression of the emissivity.
Results: Expressions are provided for both magnetic and non-magnetic cases. Atomic fine structure is taken into account. Expressions are also separately provided under zero and non-zero hyperfine structure.
Conclusions: Redistribution functions are widely used in radiative transfer codes. In our formulation, collisional transitions between Zeeman sublevels within an atomic level (depolarizing collisions effect) are taken into account when possible (I.e., in the non-magnetic case). However, the need for a formal solution of the statistical equilibrium as a preliminary step prevents us from taking into account collisional transfers between the levels of the upper term. Accounting for these collisional transfers could be done via a numerical solution of the statistical equilibrium equation system. Title: Interpretation of Hanle effect measurements in the Solar Corona: promises and difficulties Authors: Bommier, Veronique Bibcode: 2016cosp...41E.227B Altcode: After having recalled the main features of the Hanle effect, and of its application to coronal lines, the promises and difficulties of the measurement interpretation in terms of magnetic field vector diagnostics, will be investigated, based on Bommier, V., Leroy, J.L., and Sahal-Bréchot, S., 1981, A&A, 100, 231, and in the light of the new instrumentation presently available or in project, as well as data-driven modeling present possibilities. Title: Enabling Solar Flare Forecasting at an Unprecedented Level: the FLARECAST Project Authors: Georgoulis, Manolis K.; Pariat, Etienne; Massone, Anna Maria; Vilmer, Nicole; Jackson, David; Buchlin, Eric; Csillaghy, Andre; Bommier, Veronique; Kontogiannis, Ioannis; Gallagher, Peter; Gontikakis, Costis; Guennou, Chloé; Murray, Sophie; Bloomfield, D. Shaun; Alingery, Pablo; Baudin, Frederic; Benvenuto, Federico; Bruggisser, Florian; Florios, Konstantinos; Guerra, Jordan; Park, Sung-Hong; Perasso, Annalisa; Piana, Michele; Sathiapal, Hanna; Soldati, Marco; Von Stachelski, Samuel; Argoudelis, Vangelis; Caminade, Stephane Bibcode: 2016cosp...41E.657G Altcode: We attempt a brief but informative description of the Flare Likelihood And Region Eruption Forecasting (FLARECAST) project, European Commission's first large-scale investment to explore the limits of reliability and accuracy for the forecasting of major solar flares. The consortium, objectives, and first results of the project - featuring an openly accessible, interactive flare forecasting facility by the end of 2017 - will be outlined. In addition, we will refer to the so-called "explorative research" element of project, aiming to connect solar flares with coronal mass ejections (CMEs) and possibly pave the way for CME, or eruptive flare, prediction. We will also emphasize the FLARECAST modus operandi, namely the diversity of expertise within the consortium that independently aims to science, infrastructure development and dissemination, both to stakeholders and to the general public. Concluding, we will underline that the FLARECAST project responds squarely to the joint COSPAR - ILWS Global Roadmap to shield society from the adversities of space weather, addressing its primary goal and, in particular, its Research Recommendations 1, 2 and 4, Teaming Recommendations II and III, and Collaboration Recommendations A, B, and D. The FLARECAST project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 640216. Title: Evolution of flare ribbons, electric currents, and quasi-separatrix layers during an X-class flare Authors: Janvier, M.; Savcheva, A.; Pariat, E.; Tassev, S.; Millholland, S.; Bommier, V.; McCauley, P.; McKillop, S.; Dougan, F. Bibcode: 2016A&A...591A.141J Altcode: 2016arXiv160407241J Context. The standard model for eruptive flares has been extended to three dimensions (3D) in the past few years. This model predicts typical J-shaped photospheric footprints of the coronal current layer, forming at similar locations as the quasi-separatrix layers (QSLs). Such a morphology is also found for flare ribbons observed in the extreme ultraviolet (EUV) band, and in nonlinear force-free field (NLFFF) magnetic field extrapolations and models.
Aims: We study the evolution of the photospheric traces of the current density and flare ribbons, both obtained with the Solar Dynamics Observatory instruments. We aim to compare their morphology and their time evolution, before and during the flare, with the topological features found in a NLFFF model.
Methods: We investigated the photospheric current evolution during the 06 September 2011 X-class flare (SOL2011-09-06T22:20) occurring in NOAA AR 11283 from observational data of the magnetic field obtained with the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory. We compared this evolution with that of the flare ribbons observed in the EUV filters of the Atmospheric Imager Assembly. We also compared the observed electric current density and the flare ribbon morphology with that of the QSLs computed from the flux rope insertion method-NLFFF model.
Results: The NLFFF model shows the presence of a fan-spine configuration of overlying field lines, due to the presence of a parasitic polarity, embedding an elongated flux rope that appears in the observations as two parts of a filament. The QSL signatures of the fan configuration appear as a circular flare ribbon that encircles the J-shaped ribbons related to the filament ejection. The QSLs, evolved via a magnetofrictional method, also show similar morphology and evolution as both the current ribbons and the EUV flare ribbons obtained several times during the flare.
Conclusions: For the first time, we propose a combined analysis of the photospheric traces of an eruptive flare, in a complex topology, with direct measurements of electric currents and QSLs from observational data and a magnetic field model. The results, obtained by two different and independent approaches 1) confirm previous results of current increase during the impulsive phase of the flare and 2) show how NLFFF models can capture the essential physical signatures of flares even in a complex magnetic field topology.

A movie associated to Fig. 1 is available in electronic form at http://www.aanda.org Title: Energetic electrons and photospheric electric currents during solar flares Authors: Musset, Sophie; Vilmer, Nicole; Bommier, Veronique Bibcode: 2016cosp...41E1373M Altcode: It is currently admitted that solar flares are powered by magnetic energy previously stored in the coronal magnetic field. During magnetic reconnection processes, this energy is transferred to particle acceleration, plasma motion and plasma heating. Magnetic energy release is likely to occur on coronal currents sheets along regions of strong gradient of magnetic connectivity. These coronal current sheets can be traced by their footprints at the surface on the Sun, i.e. by photospheric current ribbons. We aim to study the relation between these current ribbons observed at the photospheric level, tracing the coronal current sheets, and the flare energetic electrons traced by their X-ray emissions. The photospheric magnetic field and vertical current density have been calculated from SDO/HMI spectropolarimetric data with the UNNOFIT inversion and Metcalf disambiguation codes, while the X-ray images and spectra have been reconstructed from RHESSI data. In a first case, the GOES X2.2 flare of February 15, 2011, a spatial correlation is observed between the photospheric current ribbons and the coronal X-ray emissions from energetic electrons. Moreover, a conjoint evolution of both the photospheric currents and the X-ray emission is observed during the course of the flare. Both results are interpreted as consequences of the magnetic reconnection in coronal current sheets, and propagation of the reconnection sites to new structures during the flare, leading to new X-ray emission and local increase of the photospheric currents (Musset et al., 2015). We shall discuss here similar results obtained for other X-class flares. Title: Evidence of flux rope and sigmoid in Active Regions prior eruptions Authors: Schmieder, Brigitte; Aulanier, Guillaume; Janvier, Miho; Bommier, Veronique; Dudik, Jaroslav; Gilchrist, Stuart; Zhao, Jie Bibcode: 2016cosp...41E1750S Altcode: In the solar corona, the magnetic field is dominant, and the current density vector is nearly aligned with the magnetic field lines for strong and stressed field regions. Stressed and highly twisted flux ropes are at the origin of eruptive events such as flares and coronal mass ejections, which inject material into the interplanetary medium. The standard three dimensional (3D) flare model predicts the complex evolution of flare loops and the flux rope before the eruption. Flux ropes are not directly observed in the corona, however it has started to be possible to detect their footprints in the photosphere. Recent high spatial and temporal resolution spectro-polarimeters have allowed us to compute the photospheric electric currents and follow their evolution. Characteristics pattern like J-shaped ribbons indicate the presence of a flux rope before the flare. The results confirm the predictions of the 3D MHD standard model of eruptive flares. It is interesting to compare the magnetic helicity of the ejected flux rope with the in situ measurements of the corresponding ICME at L1. We will show some examples (February 15 2011, July 12 2012, Sept 10 2014). Title: Milne-Eddington inversion for unresolved magnetic structures in the quiet Sun photosphere Authors: Bommier, Véronique Bibcode: 2016JGRA..121.5025B Altcode: This paper is first devoted to present our method for modeling unresolved magnetic structures in the Milne-Eddington inversion of spectropolarimetric data. The related definitions and other approaches and different used inversion algorithms are recalled for comparison. In a second part, we apply our method to quiet Sun data outside active regions. We obtain the quiet Sun photospheric magnetic field as composed of unresolved opening and connected magnetic flux tubes, which form a loop carpet of field lines. We then analyze the spatial correlation, which we also observed for the magnetic field vector, in terms of flux tube diameter, distance, and field strength. We find that different observations with the Zurich imaging polarimeter and THEMIS polarimeter mounted on the THEMIS telescope give very close results, and we add results also very close derived from HINODE/Solar Optical Telescope/spectropolarimeter observations analyzed with the same method. We obtain a mean flux tube diameter of 30 km, a mean flux tube distance of 230 km, and a mean flux tube magnetic field of 1.3 kG. Title: Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. III. Theory for the multilevel atom Authors: Bommier, Véronique Bibcode: 2016A&A...591A..59B Altcode: Context. We discuss the case of lines formed by scattering, which comprises both coherent and incoherent scattering. Both processes contribute to form the line profiles in the so-called second solar spectrum, which is the spectrum of the linear polarization of such lines observed close to the solar limb. However, most of the lines cannot be simply modeled with a two-level or two-term atom model, and we present a generalized formalism for this purpose.
Aims: The aim is to obtain a formalism that is able to describe scattering in line centers (resonant scattering or incoherent scattering) and in far wings (Rayleigh/Raman scattering or coherent scattering) for a multilevel and multiline atom.
Methods: The method is designed to overcome the Markov approximation, which is often performed in the atom-photon interaction description. The method was already presented in the two first papers of this series, but the final equations of those papers were for a two-level atom.
Results: We present here the final equations generalized for the multilevel and multiline atom. We describe the main steps of the theoretical development, and, in particular, how we performed the series development to overcome the Markov approximation.
Conclusions: The statistical equilibrium equations for the atomic density matrix and the radiative transfer equation coefficients are obtained with line profiles. The Doppler redistribution is also taken into account because we show that the statistical equilibrium equations must be solved for each atomic velocity class. Title: Fast inversion of Zeeman line profiles using central moments. II. Stokes V moments and determination of vector magnetic fields Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M. Bibcode: 2016A&A...591A..64M Altcode: Context. In the case of unresolved solar structures or stray light contamination, inversion techniques using four Stokes parameters of Zeeman profiles cannot disentangle the combined contributions of magnetic and nonmagnetic areas to the observed Stokes I.
Aims: In the framework of a two-component model atmosphere with filling factor f, we propose an inversion method restricting input data to Q , U, and V profiles, thus overcoming ambiguities from stray light and spatial mixing.
Methods: The V-moments inversion (VMI) method uses shifts SV derived from moments of V-profiles and integrals of Q2, U2, and V2 to determine the strength B and inclination ψ of a magnetic field vector through least-squares polynomial fits and with very few iterations. Moment calculations are optimized to reduce data noise effects. To specify the model atmosphere of the magnetic component, an additional parameter δ, deduced from the shape of V-profiles, is used to interpolate between expansions corresponding to two basic models.
Results: We perform inversions of HINODE SOT/SP data for inclination ranges 0 <ψ< 60° and 120 <ψ< 180° for the 630.2 nm Fe I line. A damping coefficient is fitted to take instrumental line broadening into account. We estimate errors from data noise. Magnetic field strengths and inclinations deduced from VMI inversion are compared with results from the inversion codes UNNOFIT and MERLIN.
Conclusions: The VMI inversion method is insensitive to the dependence of Stokes I profiles on the thermodynamic structure in nonmagnetic areas. In the range of Bf products larger than 200 G, mean field strengths exceed 1000 G and there is not a very significant departure from the UNNOFIT results because of differences between magnetic and nonmagnetic model atmospheres. Further improvements might include additional parameters deduced from the shape of Stokes V profiles and from large sets of 3D-MHD simulations, especially for unresolved magnetic flux tubes. Title: Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. IV. Application to the second solar spectrum of the Na I D1 and D2 lines Authors: Bommier, Véronique Bibcode: 2016A&A...591A..60B Altcode: Context. The spectrum of the linear polarization, which is formed by scattering and observed on the solar disk close to the limb, is very different from the intensity spectrum and thus able to provide new information, in particular about anisotropies in the solar surface plasma and magnetic fields. In addition, a large number of lines show far wing polarization structures assigned to partial redistribution (PRD), which we prefer to denote as Rayleigh/Raman scattering. The two-level or two-term atom approximation without any lower level polarization is insufficient for many lines.
Aims: In the previous paper of this series, we presented our theory generalized to the multilevel and multiline atom and comprised of statistical equilibrium equations for the atomic density matrix elements and radiative transfer equation for the polarized radiation. The present paper is devoted to applying this theory to model the second solar spectrum of the Na I D1 and D2 lines.
Methods: The solution method is iterative, of the lambda-iteration type. The usual acceleration techniques were considered or even applied, but we found these to be unsuccessful, in particular because of nonlinearity or large number of quantities determining the radiation at each depth.
Results: The observed spectrum is qualitatively reproduced in line center, but the convergence is yet to be reached in the far wings and the observed spectrum is not totally reproduced there.
Conclusions: We need to investigate noniterative resolution methods. The other limitation lies in the one-dimensional (1D) atmosphere model, which is unable to reproduce the intermittent matter structure formed of small loops or spicules in the chromosphere. This modeling is rough, but the computing time in the presence of hyperfine structure and PRD prevents us from envisaging a three-dimensional (3D) model at this instant. Title: Energetic electrons and photospheric electric currents during solar flares Authors: Musset, S.; Vilmer, N.; Bommier, V. Bibcode: 2015AGUFMSH52A..06M Altcode: Solar flares are among the most energetic events in the solar system. Magnetic energy previously stored in the coronal magnetic field is transferred to particle acceleration, plasma motion and plasma heating. Magnetic energy release is likely to occur in coronal currents sheets associated with regions of strong gradient of magnetic connectivity. Coronal current sheets can be traced by their footprints at the surface on the Sun, in e.g. photospheric current ribbons. We aim to study the relationship between the current ribbons observed at the photospheric level which trace coronal current sheets, and the flare energetic electrons traced by their X-ray emissions. The photospheric magnetic field and vertical current density are calculated from SDO/HMI spectropolarimetric data using the UNNOFIT inversion and Metcalf disambiguation codes, while the X-ray images and spectra are reconstructed from RHESSI data. In a first case (the GOES X2.2 flare of February 15, 2011), a spatial correlation is observed between the photospheric current ribbons and the coronal X-ray emissions from energetic electrons (Musset et al., 2015). Moreover, a conjoint evolution of both the photospheric currents and the X-ray emission is observed during the course of the flare. Both results are interpreted as consequences of the magnetic reconnection in coronal current sheets. Propagation of the reconnection sites to new structures during the flare results in new X-ray emission sites and local increase of the photospheric currents We will examine in this contribution whether similar results are obtained for other X-class flares. Title: Solar Surface Anisotropy effect on the Magnetic Field Authors: Bommier, Véronique Bibcode: 2015IAUS..305...28B Altcode: Within the literature there are at least 15 references indicating that the horizontal magnetic flux does not exactly balance vertical flux in sunspots, leading to the surprising result that div B would depart from zero. Intuitively, this has to be related to the stratification at the surface of the star, due to which horizontal and vertical typical lengths are different. This surface anisotropy results from gravity, but how does gravity influence the magnetic field? To answer this question, a scenario has been proposed in two recent publications, based on anisotropic Debye shielding. The presentation reported in this paper was devoted to investigate the possibility and causes of a non-zero div B. A scaling law associated with the anisotropy is able to reestablish the nullity of div B, which would lead to a renewed MHD in the solar photosphere layer. An eventual observation in the laboratory is also reported. Title: Hard X-ray emitting energetic electrons and photospheric electric currents Authors: Musset, S.; Vilmer, N.; Bommier, V. Bibcode: 2015A&A...580A.106M Altcode: 2015arXiv150602724M Context. The energy released during solar flares is believed to be stored in non-potential magnetic fields associated with electric currents flowing in the corona. While no measurements of coronal electric currents are presently available, maps of photospheric electric currents can now be derived from SDO/HMI observations. Photospheric electric currents have been shown to be the tracers of the coronal electric currents. Particle acceleration can result from electric fields associated with coronal electric currents. We revisit here some aspects of the relationship between particle acceleration in solar flares and electric currents in the active region.
Aims: We study the relation between the energetic electron interaction sites in the solar atmosphere, and the magnitudes and changes of vertical electric current densities measured at the photospheric level, during the X2.2 flare on February 15, 2011, in AR NOAA 11158.
Methods: X-ray images from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) are overlaid on magnetic field and electric current density maps calculated from the spectropolarimetric measurements of the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) using the UNNOFIT inversion and Metcalf disambiguation codes. X-ray images are also compared with extreme ultraviolet (EUV) images from the SDO Atmospheric Imaging Assembly (AIA) to complement the flare analysis.
Results: Part of the elongated X-ray emissions from both thermal and non-thermal electrons overlay the elongated narrow current ribbons observed at the photospheric level. A new X-ray source at 50-100 keV (produced by non-thermal electrons) is observed in the course of the flare and is cospatial with a region in which new vertical photospheric currents appeared during the same period (an increase of 15%). These observational results are discussed in the context of the scenarios in which magnetic reconnection (and subsequent plasma heating and particle acceleration) occurs at current-carrying layers in the corona. Title: The auroral red line polarisation: modelling and measurements Authors: Lilensten, Jean; Bommier, Véronique; Barthélemy, Mathieu; Lamy, Hervé; Bernard, David; Idar Moen, Joran; Johnsen, Magnar Gullikstad; Løvhaug, Unni Pia; Pitout, Frédéric Bibcode: 2015JSWSC...5A..26L Altcode: In this work, we model the polarisation of the auroral red line using the electron impact theory developed by <xref ref-type="bibr" rid="R5">Bommier et al. (2011)</xref>. This theory enables the computation of the distribution of the Degree of Linear Polarisation (DoLP) as a function of height if the flux of precipitated electrons is provided as input. An electron transport code is used to infer the stationary electron flux at each altitude in the ionosphere as a function of energy and pitch angle. Using adequate cross-sections, the integral of this electron flux over energy and pitch angle provides an anisotropy parameter from which the theoretical local DoLP can be computed at each altitude. The modelled DoLP is then derived by integrating along the line-of-sight. Depending on the integration length, the modelled DoLP ranges between 0.6% for a very long integration length and 1.8% for a very short integration length localised around an altitude of 210 km. A parametric study is performed to check how the characteristics of the local DoLP (maximum value, altitude of the maximum, integrated height profile) vary. It is found that the polarisation is highly sensitive to the scattering function of the electrons, to the electron precipitation and to the geomagnetic activity. We compare these values to measured ones obtained during an observational campaign performed in February 2012 from Svalbard. The measured DoLP during the campaign was 1.9% ± 0.1%. The comparison between this value and the theoretical one is discussed. Discrepancies may be due to the poor constraint of the input parameters (thermosphere and ionosphere), to the fact that only electron precipitation is considered in this approach (and not proton precipitation for instance) and to the difficulty in constraining the exact width of the emission layer in the thermosphere. Title: XTAT: A New Multilevel-Multiline Polarized Radiative Transfer Code with PRD Authors: Bommier, V. Bibcode: 2014ASPC..489..195B Altcode: This work is intended to the interpretation of the so-called "Second Solar Spectrum" (Stenflo 1996), which is the spectrum of the linear polarization formed by scattering and observed close to the solar internal limb. The lines are also optically thick, and the problem is to solve in a coherent manner, the statistical equilibrium of the atomic density matrix and the polarized radiative transfer in the atmosphere. Following Belluzzi & Landi Degl'Innocenti (2009), 30 % of the solar visible line linear polarization profiles display the M-type shape typical of coherent scattering effect in the far wings. A new theory including both coherent (Rayleigh) and resonant scatterings was developed by Bommier (1997a,b). Raman scattering was later added (Bommier 1999, SPW2). In this theory, which is straightly derived from the Schrödinger equation for the atomic density matrix, the radiative line broadening appears as a non-Markovian process of atom-photon interaction. The collisional broadening is included. The Rayleigh (Raman) scattering appears as an additional term in the emissivity from the fourth order of the atom-photon interaction perturbation development. The development is pursued and finally summed up, leading to a non-perturbative final result. In this formalism, the use of redistribution functions is avoided. The published formalism was limited to the two-level atom without lower level alignment. But most of the solar lines are more complex. We will present how the theory has to be complemented for multi-level atom modeling, including lower level alignment. The role of the collisions as balancing coherent and resonant scatterings is fully taken into account. Progress report will be given about the development of a new code for the numerical iterative solution of the statistical equilibrium and polarized radiative transfer equations, for multi-level atoms and their multi-line spectrum. Fine and hyperfine structures, and Hanle, Kemp (Kemp et al. 1984), Zeeman, incomplete Paschen-Back effects, are included. Doppler redistribution is fully taken into account, by solving the statistical equilibrium for each velocity class of the atoms. In the presentation, a particular attention will be devoted to the depolarizing collisions and their rate estimation. Title: Collisional line broadening versus collisional depolarization: Similarities and differences Authors: Sahal-Bréchot, S.; Bommier, V. Bibcode: 2014AdSpR..54.1164S Altcode: Within the impact approximation, collisional line broadening parameters and depolarizing and polarization transfer (population, orientation, alignment transfer) rates are complementary: both include the effect of collisional transitions between the Zeeman sublevels of a given level, or between fine or hyperfine structure levels of a given term. However, there are several differences: in line broadening, the two levels connected by the radiative transition contribute to the broadening, and there is also an interference term between these two levels, whereas only one level or two close levels are concerned in the depolarization. Another difference lies in the fact that purely elastic collisions contribute also to the line broadening, whereas they do not contribute to the depolarization. The nature of these two kinds of coefficients are recalled. Then the possibility to find some relationships or systematic trends concerning depolarization versus collisional broadening is considered. This is to answer some current questions which come from the polarization community. Title: Optical characterization of the breadboard narrowband prefilters for Solar Orbiter PHI Authors: Dominguez-Tagle, Carlos; Appourchaux, Thierry; Ruiz de Galarreta, Claudia; Fourmond, Jean-Jacques; Philippon, Anne; Le Clec'h, Jean-Christophe; Bouzit, Mehdi; Bommier, Véronique; Le Cocguen, Regis; Crussaire, Daniel; Malherbe, Jean-Marie Bibcode: 2014SPIE.9143E..5GD Altcode: The Polarimetric and Helioseismic Imager (PHI) on board of Solar Orbiter will observe the Sun to measure the photospheric vector magnetic field and the line-of-sight velocity. It will employ a narrowband filtergraph (FG) to scan the FeI 6173 Å absorption line. At different spectral positions, the polarization state of the incoming light will be analyzed. The FG will provide a tuning range to scan the line, the continuum, and to compensate for the spacecraft radial velocity, as it will approach to the Sun down to 0.28 AU. The FG includes a Fabry-Perot etalon and two narrowband prefilters. The bandpass of the narrowest one has a nominal Full Width at Half Maximum (FWHM) of 2.7 Å. The measurement of the prefilters characteristics is essential for the instrument calibration. Here we present the results of the breadboard prefilters characterization, which is an important milestone in the development of the instrument. Title: Electric Currents in Flare Ribbons: Observations and Three-dimensional Standard Model Authors: Janvier, M.; Aulanier, G.; Bommier, V.; Schmieder, B.; Démoulin, P.; Pariat, E. Bibcode: 2014ApJ...788...60J Altcode: 2014arXiv1402.2010J We present for the first time the evolution of the photospheric electric currents during an eruptive X-class flare, accurately predicted by the standard three-dimensional (3D) flare model. We analyze this evolution for the 2011 February 15 flare using Helioseismic and Magnetic Imager/Solar Dynamics Observatory magnetic observations and find that localized currents in J-shaped ribbons increase to double their pre-flare intensity. Our 3D flare model, developed with the OHM code, suggests that these current ribbons, which develop at the location of extreme ultraviolet brightenings seen with Atmospheric Imaging Assembly imagery, are driven by the collapse of the flare's coronal current layer. These findings of increased currents restricted in localized ribbons are consistent with the overall free energy decrease during a flare, and the shapes of these ribbons also give an indication of how twisted the erupting flux rope is. Finally, this study further enhances the close correspondence obtained between the theoretical predictions of the standard 3D model and flare observations, indicating that the main key physical elements are incorporated in the model. 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: Relation between electric current densities and X-ray emissions from particles accelerated during solar flares Authors: Musset, Sophie; Vilmer, Nicole; Bommier, Veronique Bibcode: 2014cosp...40E2209M Altcode: The energy released during solar flares is believed to be stored in non-potential magnetic fields associated with electric currents. This energy is partially transferred to particle acceleration. We studied for several X-class flares located near the solar disk center the relation between the location of the X-ray emissions produced by energetic electrons accelerated in the corona and the magnetic field and vertical component of the electric current density in the photosphere. The study is based on X-ray images with data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and magnetic field maps and current density maps calculated with the UNNOFIT inversion and Metcalf disambiguation codes from the spectropolarimetric measurements of the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO). A comparison between X-ray and Extreme Ultraviolet (EUV) images from the SDO Atmospheric Imaging Assembly (AIA) complete the study. We shall present preliminary conclusions on the link between particle acceleration and the presence of electric currents in the active region. Title: 24 synoptic maps 1974-1982 (ascending phase of cycle XXI) of 323 prominence average magnetic fields measured by the Hanle effect Authors: Bommier, Véronique Bibcode: 2014IAUS..300..397B Altcode: The poster was made of 323 average prominence magnetic fields reported on 24 synoptic maps. The paper first resumes the methods for the field derivation, and the different results of the whole program of these second generation Hanle effect observations. From their conclusions, it was possible to derive a unique field vector for each of the 323 prominences. The maps put in evidence a large scale structure of the prominence magnetic field, probably distorted by the differential rotation, which leads to a systematically small angle (on the order of 30°) between the field vector and the prominence long axis. Title: Reconciliating the Vertical and Horizontal Gradients of the Sunspot Magnetic Field Authors: Bommier, V. Bibcode: 2013PRI..2013E...1B Altcode: 2013PhyRI2013E...1B In the literature, we found 15 references showing that the sunspot photospheric magnetic field vertical gradient is on the order of 3-4 G/km, with field strength decreasing with height, whereas the horizontal gradient is nine times weaker on the order of 0.4-0.5 G/km. This is confirmed by our recent THEMIS observations. As a consequence, the vanishing of divB is not realized. In other words, a loss of magnetic flux is observed with increasing height, which is not compensated for by an increase of the horizontal flux. We show that the lack of spatial resolution, vertical as well as horizontal, cannot be held responsible for the nonvanishing observed divB. The present paper is devoted to the investigation of this problem. We investigate how the magnetic field is influenced by the plasma anisotropy due to the stratification, which is responsible for an "aspect ratio" between horizontal and vertical typical lengths. On the example of our THEMIS observations, made of two spectral lines formed at two different depths, which enables the retrieval of the three components entering divB, it is shown that once this aspect ratio is applied, the rescaled divB vanishes, which suggests a new methodology for MHD modeling in the photosphere. Title: Polarisation of the auroral red line in the Earth's upper atmosphere: a review (Invited) Authors: Lamy, H.; Barthelemy, M.; Lilensten, J.; Bommier, V.; Simon Wedlund, C. Bibcode: 2013AGUFM.P42B..03L Altcode: Polarisation of light is a key observable to provide information about asymmetry or anisotropy within a radiative source. Polarimetry of auroral emission lines in the Earth's upper atmosphere has been overlooked for decades. However, the bright red auroral line (6300Å) produced by collisional impact with electrons precipitating along magnetic field lines is a good candidate to search for polarisation. This problem was investigated recently with observations obtained by Lilensten et al (2008), Barthélemy et al (2011) and Lilensten et al (2013) with a photopolarimeter. Analysis of the data indicates that the red auroral emission line is polarised at a level of a few percent. The results are compared to theoretical predictions of Bommier et al (2011) that were obtained for a collimated beam. The comparison suggests the existence of depolarization processes whose origin will be discussed. A new dedicated spectropolarimeter currently under development will also be presented. This instrument will cover the optical spectrum from approximately 400 to 700 nm providing simultaneously the polarisation of the red line and of other interesting auroral emission lines such as N2+ 1NG (4278Å), other N2 bands, etc... The importance of these polarisation measurements in the context of upper atmosphere modelling and geomagnetic activity will be discussed. Lilensten, J. et al, Polarization in aurorae: A new dimension for space environments studies, Geophys. Res. Lett., 26, 269, 2008 Barthélemy M. et al, Polarisation in the auroral red line during coordinated EISCAT Svalbard Radar/optical experiments, Annales Geophysicae, Volume 29, Issue 6, 2011, 1101-1112, 2011. Bommier V. et al, The Theoretical Impact Polarization of the O I 6300 Å Red Line of Earth Auroræ, Annales Geophysicae, Volume 29, Issue 1, 2011, 71-79, 2011 Lilensten, J. et al, The thermospheric auroral red line polarization: confirmation of detection and first quantitative analysis, Journal of Space Weather and Space Climate, Volume 3, 12, 2013. Title: Longitudinal magnetic field and velocity gradients in the photosphere inferred from THEMIS multiline observations Authors: Molodij, G.; Bommier, V.; Rayrole, J. Bibcode: 2013A&A...552A..50M Altcode: We present multiline observations taken with the French-Italian telescope THEMIS operated by CNRS and CNR on the island of Tenerife. Several spectral lines are observed simultaneously to study magnetic phenomena at different altitudes of line formation, comprising the Fe i 5250.65 Å, Cr i 5247.57 Å, Fe i 5250.22 Å, Fe i 6301.51 Å, Fe i 6302.50 Å, and Fe i 6151.62 Å lines. The observations were analyzed using Milne-Eddington inversion algorithms modified to allow for non-normal Zeeman triplet lines, and to take additionally into account the vertical velocity gradient. We show the self-consistency of the solutions found from the inversion and those obtained from the quantitative bisector method. Results from the different lines observed simultaneously yield the height dependence of the magnetic field strength. From modeling the line formation heights applied on selected points with a longitudinal magnetic field between 200 and 1000 G, we determine the gradient of the vertical component (absolute value) of the magnetic field to be - 1.18 G/km. Title: Behavior of the vertical current during the X2 flare of 2011 February 15 observed by SDO/HMI, compared to a line-tied zero-beta resistive MHD simulation Authors: Bommier, Veronique; Aulanier, Guillaume Bibcode: 2013enss.confE..79B Altcode: The level-1 data of SDO/HMI have been inverted with the UNNOFIT inversion code (Bommier et al., 2007, A&A, 464, 323), which differs from VFISV about the magnetic filling factor modeling. More realistic field inclinations are obtained outside the active region. The spatial resolution seems to be also better. UNNOFIT is enabled for the taking into account of gradients of radial velocity, responsible for asymmetry of the Stokes profiles (Molodij et al., 2011, A&A, 531, A139). The ambiguity has been solved with the ME0 code of Metcalf, Leka, Barnes & Crouch. We present the movie of 4 hours of observation, the flare occurring at middle. Two current ribbons of opposite polarity are visible along the magnetic neutral line, in the vertical density current map. The negative one strengthens and radially expands from the flare center at the eruption moment. A similar current ribbon pair is visible in a 3D line-tied zero-beta resistive MHD flare simulation with the OHM code (Aulanier et al. , 2012, A&A, 543, A110). The two ribbons part from the flare center during the flare, similarly to what observed on 2011 February 15 at 02:00 with SDO/HMI. Title: The thermospheric auroral red line polarization: confirmation of detection and first quantitative analysis Authors: Lilensten, Jean; Barthélémy, Mathieu; Amblard, Pierre-Olivier; Lamy, Hervé; Simon Wedlund, Cyril; Bommier, Véronique; Moen, Joran; Rothkaehl, Hanna; Eymard, Julien; Ribot, Jocelyn Bibcode: 2013JSWSC...3A..01L Altcode: The thermospheric atomic oxygen red line is among the brightest in the auroral spectrum. Previous observations in Longyearbyen, Svalbard, indicated that it may be intrinsically polarized, but a possible contamination by light pollution could not be ruled out. During the winter 2010/2011, the polarization of the red line was measured for the first time at the Polish Hornsund polar base without contamination. Two methods of data analysis are presented to compute the degree of linear polarization (DoLP) and angle of linear polarization (AoLP): one is based on averaging and the other one on filtering. Results are compared and are in qualitative agreement. For solar zenith angles (SZA) larger than 108° (with no contribution from Rayleigh scattering), the DoLP ranges between 2 and 7%. The AoLP is more or less aligned with the direction of the magnetic field line, in agreement with the theoretical predictions of <xref ref-type="bibr" rid="R2">Bommier et al. (2010)</xref>. However, the AoLP values range between ±20° around this direction, depending on the auroral conditions. Correlations between the polarization parameters and the red line intensity I were considered. The DoLP decreases when I increases, confirming a trend observed during the observations in Longyearbyen. However, for small values of I, DoLP varies within a large range of values, while for large values of I, DoLP is always small. The AoLP also varies with the red line intensity, slightly rotating around the magnetic field line. Title: Reconstruction of 3D Coronal Magnetic Structures from THEMIS/MTR and Hinode/SOT Vector Maps Authors: Schmieder, B.; Guo, Y.; Aulanier, G.; Démoulin, P.; Török, T.; Bommier, V.; Wiegelmann, T.; Gosain, S. Bibcode: 2012ASPC..454..363S Altcode: Coordinated campaigns using THEMIS, Hinode, and other instruments have allowed us to study the magnetic fields of faculae, filaments, and active regions. In a first case, we modelled the 3D magnetic field in a flaring active region with a nonlinear force-free field extrapolation, using magnetic vectors observed by THEMIS/MTR as boundary condition. In order to construct a consistent bottom boundary for the model, we first removed the 180 degree ambiguity of the transverse fields and minimized the force and torque in the observed vector fields. We found a twisted magnetic flux rope, well aligned with the polarity inversion line and a part of an Hα filament, and located where a large flare is initiated about two hours later. In a second case, Hinode/SOT allowed us to detect fine flux concentrations in faculae, while MTR provided us with magnetic information at different levels in the atmosphere. The polarimetry analysis of the MTR and SOT data gave consistent results, using both UNNOFIT and MELANIE inversion codes. Title: Inversion of Zeeman Line Profiles Using Central Moments Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M. Bibcode: 2012EAS....55...83M Altcode: A new inversion method derived from central moments of Zeeman line profiles (ICM), is used to determine magnetic field vectors (Mein et al. 2011). Two quantities A1 and A2 combining moments of profiles I ± S (S = Q,U,V) are nearly linear functions of the longitudinal and transverse components and lead to the field components through very fast iterations. Optimized exponents reduce noise effects. The ICM inversion does not require Milne Eddington approximation and can be used in a wide range of solar models. Title: Magnetic field distribution in the quiet and active photosphere Authors: Bommier, V. Bibcode: 2012EAS....55...49B Altcode: The presentation is intended to describe results obtained with the UNNOFIT inversion of spectropolarimetric data. Quiet regions of the Sun are studied on the one hand, where the structure of the magnetic field remains unresolved and is approached via a magnetic filling factor. It is got that the field is structured in thin flux tubes connected by loops at any altitude in the solar atmosphere. The fluxtube diameter size is evaluated. On the other hand, active regions are studied, in particular sunspots where the magnetic field horizontal gradient is found one order of magnitude weaker than the vertical gradient, as in other observations reported in the literature. This is a difficulty to ensure divB=0. Before entering the results, the particular features of the UNNOFIT inversion are recalled, which concern essentially the magnetic filling factor modeling. Title: Electric current density and related sigmoid in an active region Authors: Joulin, V.; Schmieder, B.; Aulanier, G.; Bommier, V. Bibcode: 2012EAS....55..143J Altcode: Using THEMIS vector magnetograms we measured vertical electric current density in the leading sunspot of NOAA 11127 active region during its disk passage. The current structures evolve versus time. MHD modelling allows us to explain the spiral pattern by torsion. We found observational visible counterparts in the SDO/AIA 335 A images. The field lines are visible as loops in the AIA images. When the torsion is increasing, a sigmoid is observed. In the present event observed on November 24th 2010, we find that reconnection is also necessary to explain their sigmoidal shape. Title: Magnetic Field Structures in a Facular Region Derived from THEMIS and Hinode Vector Magnetic Field Authors: Guo, Y.; Schmieder, B.; Bommier, V.; Mein, P. Bibcode: 2012ASPC..456...55G Altcode: In order to compare vector magnetic fields obtained by two spectral polarimeters (THEMIS/MTR and Hinode SOT/SP) and two inversion codes (UNNOFIT and MELANIE), we observed a facular region in the active region NOAA 10996 on 2008 May 23. We found that they give consistent results concerning the distributions of field strengths, azimuth and inclination angles. SOT/SP could resolve small magnetic polarities with sizes of 1'' to 2'', and detect convergence and divergence of the horizontal components of magnetic fields in the facular cells. These findings support the models suggesting the existence of flux tube bundles in faculae. With this model and multi spectral line observations, we could infer the relative formation heights of those spectral lines. Title: Solar magnetism eXplorer (SolmeX). Exploring the magnetic field in the upper atmosphere of our closest star Authors: Peter, Hardi; Abbo, L.; Andretta, V.; Auchère, F.; Bemporad, A.; Berrilli, F.; Bommier, V.; Braukhane, A.; Casini, R.; Curdt, W.; Davila, J.; Dittus, H.; Fineschi, S.; Fludra, A.; Gandorfer, A.; Griffin, D.; Inhester, B.; Lagg, A.; Landi Degl'Innocenti, E.; Maiwald, V.; Sainz, R. Manso; Martínez Pillet, V; Matthews, S.; Moses, D.; Parenti, S.; Pietarila, A.; Quantius, D.; Raouafi, N. -E.; Raymond, J.; Rochus, P.; Romberg, O.; Schlotterer, M.; Schühle, U.; Solanki, S.; Spadaro, D.; Teriaca, L.; Tomczyk, S.; Trujillo Bueno, J.; Vial, J. -C. Bibcode: 2012ExA....33..271P Altcode: 2011arXiv1108.5304P; 2011ExA...tmp..134P The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona—that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200 m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. SolmeX integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations. Title: Hanle effect from a dipolar magnetic structure: the case of the solar corona and the case of a star Authors: Bommier, V. Bibcode: 2012A&A...539A.122B Altcode: Context. The context is the magnetic field measurement in external solar or stellar layers by interpreting line polarization measurements and the Hanle effect.
Aims: The aim is to model the Hanle effect depolarization by integrating upon a star on the one hand, and by integrating along a line-of-sight through the solar corona on the other hand.
Methods: The formalism of the atomic density matrix is recalled. Particular attention was devoted to the four axis rotations necessary to transform the magnetic field reference frame into that of the line-of-sight.
Results: In the stellar case, the discrepancy between the results by López Ariste et al. (2011, A&A, 527, A120) and the symmetry considerations by Ignace etal. (2011, A&A, 530, A82) is resolved. In the solar case, the computations of the hydrogen Lyα polarization by Derouich et al. (2010, A&A, 511, A7) are revisited, owing to symmetry considerations.
Conclusions: In the stellar case, we confirm that the effect integrated on a star leads to a non-vanishing magnetic depolarization due to the high non-linearity of the Hanle effect. In the solar case, we find that the Hanle sensitivity of hydrogen Lyβ and Lyγ could be better adapted to the measurement of the coronal background magnetic field. They form a pair of lines of different and complementary sensitivity, which makes it possible to determine the full vector. Lyα would be instead adapted to the coronal loop magnetic field measurement, because this field is stronger and suited to the Lyα Hanle sensitivity. Title: Multi-wavelength observations to understand the solar magnetic activity and its feedback on the interplanetary medium Authors: Molodij, G.; Schmieder, B.; Bommier, V. Bibcode: 2012mfu3.conf...93M Altcode: No abstract at ADS Title: Polarisation of auroral emission lines in the Earth's upper atmosphere : first results and perspectives Authors: Lamy, H.; Barthelemy, M.; Simon Wedlund, C.; Lilensten, J.; Bommier, V. Bibcode: 2011AGUFM.P14C..03L Altcode: Polarisation of light is a key observable to provide information about asymmetry or anisotropy within a radiative source. Following the pioneering and controversial work of Duncan in 1959, the polarisation of auroral emission lines in the Earth's upper atmosphere has been overlooked for a long time, even though the red intense auroral line (6300Å) produced by collisional impacts with electrons precipitating along magnetic field lines is a good candidate to search for polarisation. This problem was investigated again by Lilensten et al (2006) and observations were obtained by Lilensten et al (2008) confirming that the red auroral emission line is polarised. More recent measurements obtained by Barthélemy et al (2011) are presented and discussed. The results are compared to predictions of the theoretical work of Bommier et al (2011) and are in good agreement. Following these encouraging results, a new dedicated spectropolarimeter is currently under construction between BIRA-IASB and IPAG to provide simultaneously the polarisation of the red line and of other interesting auroral emission lines such as N2+ 1NG (4278Å), other N2 bands, etc... Perspectives regarding the theoretical polarisation of some of these lines will be presented. The importance of these polarisation measurements in the framework of atmospheric modeling and geomagnetic activity will be discussed. Title: Fast inversion of Zeeman line profiles using central moments Authors: Mein, P.; Uitenbroek, H.; Mein, N.; Bommier, V.; Faurobert, M. Bibcode: 2011A&A...535A..45M Altcode: Context. Many inversion techniques derive vector magnetic fields and other parameters of the solar atmosphere from Stokes profiles with an iterative process.
Aims: We propose a new inversion method, using functions derived from central moments (ICM), to determine magnetic field vectors with very few iterations.
Methods: Two quantities A1 and A2 that combine moments of profiles I ± S (S = Q,U,V) are proposed. They are nearly linear functions of the longitudinal and transverse components of the magnetic field, and lead to estimates of the field components through a least-squares polynomial fit. A third quantity AD can be used to interpolate between expansions that correspond to two basic models. Exponents β1 and β2 in the moment expressions are adjusted to minimize the sensitivity to data noise.
Results: Inversion coefficients are computed for magnetic fields up to 3000 G in the case of the 630.2 Fe i line by forward modeling in two selected 1D model atmospheres (FALC and MALTM). After inversion of synthetic profiles computed with four models at disk center (FALA, FALC, FALF, MALTM), the mean standard deviations with respect to the input fields do not exceed 5 G for both components over the full range 0-3000 G. A comparison of ICM results with inversion by the UNNOFIT code of profiles observed with THEMIS/MTR shows good agreement. The typical computing time for a solar map of 100 000 points is less than 30 s.
Conclusions: The ICM inversions are almost insensitive to thermodynamic properties and solve for vector magnetic fields in a wide range of solar conditions, ranging from plage to spot, with very little computational effort. They are, therefore, extremely suitable for large data sets. Further improvements should take into account instrumental profiles and effects of limited spatial resolution by using filling factors. Extensions using more parameters and models with large departures from the Milne Eddington approximation could also be considered. Title: Observed difference between the vertical and horizontal magnetic field gradients in sunspots Authors: Bommier, Veronique Bibcode: 2011sdmi.confE...6B Altcode: A difference (larger than the measurements uncertainties) was observed between the vertical and horizontal gradients of the magnetic field in sunspots. This difference was observed with multiline recordings achieved with the THEMIS telescope and the HINODE/SOT/SP instrument. The multiline feature corresponds to a depth probing. This difference was already present in the literature, which will be discussed in details. The method for interpreting the spectropolarimetric data in terms of magnetic field will be also detailed. Title: A filament supported by different magnetic field configurations Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.; Aulanier, G.; Török, T.; Bommier, V. Bibcode: 2011IAUS..273..328G Altcode: A nonlinear force-free magnetic field extrapolation of vector magnetogram data obtained by THEMIS/MTR on 2005 May 27 suggests the simultaneous existence of different magnetic configurations within one active region filament: one part of the filament is supported by field line dips within a flux rope, while the other part is located in dips within an arcade structure. Although the axial field chirality (dextral) and the magnetic helicity (negative) are the same along the whole filament, the chiralities of the filament barbs at different sections are opposite, i.e., right-bearing in the flux rope part and left-bearing in the arcade part. This argues against past suggestions that different barb chiralities imply different signs of helicity of the underlying magnetic field. This new finding about the chirality of filaments will be useful to associate eruptive filaments and magnetic cloud using the helicity parameter in the Space Weather Science. Title: Vector magnetic field and vector current density in and around the δ-spot NOAA 10808† Authors: Bommier, Véronique; Landi Degl'Innocenti, Egidio; Schmieder, Brigitte; Gelly, Bernard Bibcode: 2011IAUS..273..338B Altcode: The context is that of the so-called ``fundamental ambiguity'' (also azimuth ambiguity, or 180° ambiguity) in magnetic field vector measurements: two field vectors symmetrical with respect to the line-of-sight have the same polarimetric signature, so that they cannot be discriminated. We propose a method to solve this ambiguity by applying the ``simulated annealing'' algorithm to the minimization of the field divergence, added to the longitudinal current absolute value, the line-of-sight derivative of the magnetic field being inferred by the interpretation of the Zeeman effect observed by spectropolarimetry in two lines formed at different depths. We find that the line pair Fe I λ 6301.5 and Fe I λ 6302.5 is appropriate for this purpose. We treat the example case of the δ-spot of NOAA 10808 observed on 13 September 2005 between 14:25 and 15:25 UT with the THEMIS telescope. Besides the magnetic field resolved map, the electric current density vector map is also obtained. A strong horizontal current density flow is found surrounding each spot inside its penumbra, associated to a non-zero Lorentz force centripetal with respect to the spot center (i.e., oriented towards the spot center). The current wrapping direction is found to depend on the spot polarity: clockwise for the positive polarity, counterclockwise for the negative one. This analysis is made possible thanks to the UNNOFIT2 Milne-Eddington inversion code, where the usual theory is generalized to the case of a line (Fe I λ 6301.5) that is not a normal Zeeman triplet line (like Fe I λ 6302.5). Title: Network velocity gradients in the photosphere. I. Modeling Authors: Molodij, G.; Bommier, V.; Rayrole, J. Bibcode: 2011A&A...531A.139M Altcode: We present an extension of the Unno-Rachkovsky solution that provides the theoretical profiles coming out of a Milne-Eddington atmosphere imbedded in a magnetic field, and that then takes a vertical velocity gradient into account. Thus, the theoretical profiles may display asymmetries as do the observed profiles, which facilitates the inversion based on the Unno-Rachkovsky theory, and leads to the additional determination of the vertical velocity gradient. We present UNNOFIT inversion on synthetic data and spectropolarimetric observations performed on an active region of the Sun with the French-Italian telescope THEMIS operated by CNRS and CNR on the island of Tenerife. Title: Inclusion of velocity gradients in the Unno solution for magnetic field diagnostic from spectropolarimetric data Authors: Molodij, Guillaume; Bommier, Véronique Bibcode: 2011IAUS..274..291M Altcode: We present an extension of the Unno-Rachkovsky solution that provides the theoretical profiles coming out of a Milne-Eddington atmosphere imbedded in a magnetic field, to the additional taking into account of a vertical velocity gradient. Thus, the theoretical profiles may display asymmetries as do the observed profiles, which facilitates the inversion based on the Unno-Rachkovsky theory, and leads to the additional determination of the vertical velocity gradient. We present UNNOFIT inversion on spectropolarimetric data performed on an active region of the Sun with the french-italian telescope THEMIS operated by CNRS and CNR on the island of Tenerife. Title: The quiet Sun magnetic field: statistical description from THEMIS observations Authors: Bommier, V. Bibcode: 2011A&A...530A..51B Altcode: Context. The pioneer interpretation of Hanle-effect depolarization observed at the limb was the one of a turbulent nature for the solar internetwork photospheric magnetic field. In the present paper, we propose an alternative interpretation of these measurements, which are now complemented with Zeeman-effect observations to allow one to conclude on the properties of weak fields.
Aims: In a previous paper, we presented an internetwork field diagnostic from data obtained with the ZIMPOL II polarimeter mounted on the THEMIS telescope. In the present paper, we present the results obtained with the THEMIS polarimeter with ten times more pixels. The agreement between the results obtained with the two polarimeters confirm the goodness of both the THEMIS polarimeter measurements and our data treatment.
Methods: The Zeeman-effect measurements are interpreted via a 2-component model, which has a field-free component and a magnetized one, filling a fraction of the analyzed pixel equal to 1 - α and α, respectively. We determine this α parameter independently of the magnetic inversion. We already applied these methods to the previous interpretation of the ZIMPOL/THEMIS data.
Results: The magnetic field strength and magnetic field inclination are not independent, because the strongest fields are more vertical and the weakest fields are more horizontal, both in ZIMPOL/THEMIS and THEMIS/THEMIS data.
Conclusions: This suggests that the photospheric internetwork field has the structure of scattered narrow fluxtubes consisting in a vertical field, which weakens in opening - widening with individual field line bending - with height. The weakest fields then have a 2D horizontal structure, instead of the usually admitted 3D turbulent one. This does not contradict the previous Hanle-effect observations, because it is insensitive to vertical fields. The number of fluxtubes inside each pixel (which was 0.21 arcsec for the THEMIS/THEMIS and 0.53 arcsec for the ZIMPOL/THEMIS data) should, however, remain small. We could make a conclusion about this after observing a non-zero spatial correlation of the magnetic field orientation, with an estimated correlation length of 250 km.

Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: The Quiet Sun Magnetic Field Structure Derived from a Full Vector Determination Authors: Bommier, V. Bibcode: 2011ASPC..437..471B Altcode: The magnetic field vector of the quiet Sun has been first determined by usual Milne-Eddington inversion of ZIMPOL/THEMIS data. But such an inversion provides the local average field only, i.e. the product of the field strength by the magnetic filling factor. To discriminate between both quantities, an additional method has to be provided. We proposed a direct but approached determination of the filling factor in the spectropolarimetric data themselves. Then we were able to derive the inhomogeneous magnetic field strength (i.e. disambiguated from the filling factor). The methods and results from the ZIMPOL/THEMIS data are now published (Bommier et al. 2009). The present paper is intended to show that the THEMIS/THEMIS data, 10 times more numerous, give the same results, validating thus the THEMIS polarimeter results with the ZIMPOL ones. But the main new result is that finally the inhomogeneous field strength is found clearly dependent on the field inclination angle, thus ruling out the hypothesis of a turbulent field. The corresponding field organization could be: thin scattered vertical tubes of strong field opening and weakening with height (in the photosphere). Thus the weak fields would be horizontally (2D) distributed rather than following their generally admitted 3D turbulent structure. This distribution is not incompatible with the Hanle effect observations, because the Hanle effect is insensitive to the vertical field. The distribution of the thin opening tubes remains to be quantized, but spatial horizontal correlations were observed, which suggests that their size would not be very small with respect to the observation pixel size of 0.2-0.5 arcsec. Title: Polarized Radiative Transfer: from Solar Applications to Laboratory Experiments Authors: Landi Degl'Innocenti, E.; Belluzzi, L.; Bommier, V. Bibcode: 2011ASPC..437...45L Altcode: The theory of radiative transfer for polarized radiation, developed from Quantum Electrodynamics for the interpretation of solar observations, predicts the existence of a variety of physical phenomena that, in many cases, would deserve being directly tested through laboratory experiments, also in view of possible practical applications. In this report we will focus on the description of some of these atomic-physics phenomena that have been disregarded, or overlooked, in terrestrial laboratories. Title: Magnetic Field, Density Current, and Lorentz Force Full Vector Maps of the NOAA 10808 Double Sunspot: Evidence of Strong Horizontal Current Flows in the Penumbra Authors: Bommier, V.; Landi Degl'Innocenti, E.; Schmieder, B.; Gelly, B. Bibcode: 2011ASPC..437..491B Altcode: The context is that of the so-called “fundamental ambiguity” (also azimuth ambiguity, or 180° ambiguity) in magnetic field vector measurements: two field vectors symmetrical with respect to the line-of-sight have the same polarimetric signature, so that they cannot be discriminated. We propose a method to solve this ambiguity by applying the “simulated annealing” algorithm to the minimization of the field divergence, added to the longitudinal current absolute value, the line-of-sight derivative of the magnetic field being inferred by the interpretation of the Zeeman effect observed by spectropolarimetry in two lines formed at different depths. We find that the line pair Fe I λ 6301.5 and Fe I λ 6302.5 is appropriate for this purpose. We treat the example case of the δ-spot of NOAA 10808 observed on 13 September 2005 between 14:25 and 15:25 UT with the THEMIS telescope. Besides the magnetic field resolved map, the electric current density vector map is also obtained. A strong horizontal current density flow is found surrounding each spot inside its penumbra, associated to a non-zero Lorentz force centripetal with respect to the spot center (i.e., oriented towards the spot center). The current wrapping direction is found to depend on the spot polarity: clockwise for the positive polarity, counterclockwise for the negative one. This analysis is made possible thanks to the UNNOFIT2 Milne-Eddington inversion code, where the usual theory is generalized to the case of a line Fe I λ 6301.5) that is not a normal Zeeman triplet line (like Fe I λ 6302.5). Title: The Theoretical Impact Polarization of the O I 6300 Å Red Line of Earth Auroræ Authors: Bommier, V.; Sahal-Bréchot, S.; Dubau, J.; Cornille, M. Bibcode: 2011ASPC..437...73B Altcode: We present a semi-classical theory of the impact polarization due to a quadrupolar electric excitation, well-suited to this forbidden line. In addition, this line is also radiatively forbidden being a triplet-singlet transition. This is overcome by scaling the semi-classical result to a full quantum calculation at a single energy value. The cross-section and impact polarization are thus obtained as a function of energy (with good agreement with the quantum calculated cross-section), and the behavior of the impact polarization is found quite different of the usual one of the dipolar electric interaction. Denoting as radial the polarization parallel to the incident beam or magnetic field, and as tangential the perpendicular polarization, the dipolar interaction (permitted lines) leads to radial polarization at low energy, and tangential polarization at high energy, the polarization vanishing at energy about twelve times the threshold energy. In the case of the quadrupolar electric interaction, we get a quite different behavior, the vanishing point being much closer to the threshold energy. This leads to reanalyze the auroræ red line polarization observation by Lilensten et al. (2008), and to conclude that the line is only weakly radially polarized and only during the auroral events. The weak polarization level leads to consider the competing depolarization by collisions with the neighboring O atoms, whose density could then be diagnosed with further measurements and calculations. Title: Coexisting Flux Rope and Dipped Arcade Sections Along One Solar Filament Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.; Aulanier, G.; Török, T.; Bommier, V. Bibcode: 2010ApJ...714..343G Altcode: We compute the three-dimensional magnetic field of an active region in order to study the magnetic configuration of active region filaments. The nonlinear force-free field model is adopted to compute the magnetic field above the photosphere, where the vector magnetic field was observed by THEMIS/MTR on 2005 May 27. We propose a new method to remove the 180° ambiguity of the transverse field. Next, we analyze the implications of the preprocessing of the data by minimizing the total force and torque in the observed vector fields. This step provides a consistent bottom boundary condition for the nonlinear force-free field model. Then, using the optimization method to compute the coronal field, we find a magnetic flux rope along the polarity inversion line. The magnetic flux rope aligns well with part of an Hα filament, while the total distribution of the magnetic dips coincides with the whole Hα filament. This implies that the magnetic field structure in one section of the filament is a flux rope, while the other is a sheared arcade. The arcade induced a left-bearing filament in the magnetic field of negative helicity, which is opposite to the chirality of barbs that a flux rope would induce in a magnetic field of the same helicity sign. The field strength in the center of the flux rope is about 700 G, and the twist of the field lines is ~1.4 turns. Title: Magnetic Field Structures in a Facular Region Observed by THEMIS and Hinode Authors: Guo, Y.; Schmieder, B.; Bommier, V.; Gosain, S. Bibcode: 2010SoPh..262...35G Altcode: 2010SoPh..tmp...30G; 2010arXiv1002.4355G The main objective of this paper is to build and compare vector magnetic maps obtained by two spectral polarimeters, i.e. THEMIS/MTR and Hinode SOT/SP, using two inversion codes (UNNOFIT and MELANIE) based on the Milne - Eddington solar atmosphere model. To this end, we used observations of a facular region within active region NOAA 10996 on 23 May 2008, and found consistent results concerning the field strength, azimuth and inclination distributions. Because SOT/SP is free from the seeing effect and has better spatial resolution, we were able to resolve small magnetic polarities with sizes of 1″ to 2″, and we could detect strong horizontal magnetic fields, which converge or diverge in negative or positive facular polarities. These findings support models which suggest the existence of small vertical flux tube bundles in faculae. A new method is proposed to get the relative formation heights of the multi-lines observed by MTR assuming the validity of a flux tube model for the faculae. We found that the Fe I 6302.5 Å line forms at a greater atmospheric height than the Fe I 5250.2 Å line. Title: Fast imaging spectroscopy with MSDP spectrometers. Vector magnetic maps with THEMIS/MSDP Authors: Mein, P.; Mein, N.; Bommier, V. Bibcode: 2009A&A...507..531M Altcode: Context: Multichannel subtractive double pass (MSDP) spectrometers produce 3D data cubes (x, y, λ) simultaneously across several line profiles. They do not suffer from image convolution by any slit width, and synchronous observations across all wavelengths avoid differential seeing effects. They are very suitable for fast 2D spectroscopy.
Aims: (1) We review specifications and capabilities of some existing MSDP spectrometers with respect to high-cadence observations. (2) THEMIS/MSDP is designed for the spectropolarimetry of strong lines. We propose new data reductions also suitable for the spectropolarimetry of photospheric lines.
Methods: An off-line algorithm is described as a way to increase the spectral resolution. Taking the opportunity of 3D data, spatial interpolations are used around each solar point by only assuming that intensity gradients partial I(x, y, λ)/partial x are constant in the range (x± ɛ_x,λ ± ɛ_λ). The UNNOFIT inversion is used to compare vector magnetic maps deduced from THEMIS/MSDP and slit-spectropolarimetry THEMIS/MTR data.
Results: Both results are in good agreement. In active regions, the rms of the MSDP noise, calculated over 1 arcsec^2, is less than 24 G for the LOS magnetic field and less than 52 G for Bx and 32 G for B_y. The MSDP scanning speed is 10 times the speed of slit-spectropolarimetry.
Conclusions: THEMIS/MSDP can provide vector magnetic maps with typical temporal resolutions that are less than 1 min for small fields-of-view and 10 min for active regions. This allows addressing a number of fast events. In the future, MSDP instruments should efficiently complement single-slit spectroscopy and tunable filters. Their main capabilities should be the multiline aspect and the high temporal and spatial resolutions. New optical devices, such as image slicers, should substantially increase the signal-to-noise ratio. For polarimetric measurements, various compromises are possible between speed, spatial resolution, and SNR. A-posteriori image restorations, either using wide band proxies or bursts of multi-wavelength short exposures, should help improving signal-to-noise ratio and spatial resolution.

Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: The quiet Sun magnetic field observed with ZIMPOL on THEMIS. I. The probability density function Authors: Bommier, V.; Martínez González, M.; Bianda, M.; Frisch, H.; Asensio Ramos, A.; Gelly, B.; Landi Degl'Innocenti, E. Bibcode: 2009A&A...506.1415B Altcode: Context: The quiet Sun magnetic field probability density function (PDF) remains poorly known. Modeling this field also introduces a magnetic filling factor that is also poorly known. With these two quantities, PDF and filling factor, the statistical description of the quiet Sun magnetic field is complex and needs to be clarified.
Aims: In the present paper, we propose a procedure that combines direct determinations and inversion results to derive the magnetic field vector and filling factor, and their PDFs.
Methods: We used spectro-polarimetric observations taken with the ZIMPOL polarimeter mounted on the THEMIS telescope. The target was a quiet region at disk center. We analyzed the data by means of the UNNOFIT inversion code, with which we inferred the distribution of the mean magnetic field α B, α being the magnetic filling factor. The distribution of α was derived by an independent method, directly from the spectro-polarimetric data. The magnetic field PDF p(B) could then be inferred. By introducing a joint PDF for the filling factor and the magnetic field strength, we have clarified the definition of the PDF of the quiet Sun magnetic field when the latter is assumed not to be volume-filling.
Results: The most frequent local average magnetic field strength is found to be 13 G. We find that the magnetic filling factor is related to the magnetic field strength by the simple law α = B_1/B with B1 = 15 G. This result is compatible with the Hanle weak-field determinations, as well as with the stronger field determinations from the Zeeman effect (kGauss field filling 1-2% of space). From linear fits, we obtain the analytical dependence of the magnetic field PDF. Our analysis has also revealed that the magnetic field in the quiet Sun is isotropically distributed in direction.
Conclusions: We conclude that the quiet Sun is a complex medium where magnetic fields having different field strengths and filling factors coexist. Further observations with a better polarimetric accuracy are, however, needed to confirm the results obtained in the present work.

Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Present address: Instituto de Astrofísica de Canarias, vía Láctea s/n, 38205 La Laguna, Tenerife, Spain. 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: The Height Dependence of the Magnetic Vector Field in Sunspots Authors: Balthasar, H.; Bommier, V. Bibcode: 2009ASPC..405..229B Altcode: A complex active region was observed simultaneously with the solar telescopes VTT and THEMIS on Tenrife in May 2005. Spatial scans across the sunspot group were performed at both telescopes. The full Stokes-vector was recorded in several photospheric spectral lines, i.~e. at the VTT in a group of iron and silicon lines in the near infrared and at THEMIS in iron and chromium lines in the visible. Inversions were carried out independently for the different lines in order to derive the magnetic field strength, its inclination and azimuth together with the temperature stratification. Thus we obtained the three-dimensional structure of the magnetic field. Selected locations in the penumbra and in light bridges were considered in detail. We find a general tendency that the magnetic field is weaker and less inclined in higher layers. Title: Atomic and Molecular Depolarizing Collision Rates Authors: Bommier, V. Bibcode: 2009ASPC..405..335B Altcode: This paper is divided in three parts: after having recalled the different types of collisions with the different types of perturbers and having provided rough orders of magnitude of the collision rates, three cases are discussed. Although the most frequent type of depolarizing collision is the one of the collisions with the surrounding Hydrogen atoms, we discuss in the first part a particular case where the depolarizing collision effect is due to collisions with electrons and protons. This is the case of the Hydrogen lines observed in solar prominences. We recall how the interpretation of polarization observations in two lines has led to the joint determination of the magnetic field vector and the electron and proton density, and we show that this density determination gives results in agreement with the densities determined by interpretation of the Stark effect, provided that this last effect be evaluated in the impact approximation scheme which is indeed more valid than the quasistatic approach at these densities. In the second part, we describe a method that has been recently developed for the computation of the depolarizing rates in the case of collisions with the neutral Hydrogen atom. The case of molecular lines is less favourable, because, even if depolarizing collision rates computation may be soon expected and begin to be done inside the ground level of the molecule, calculations inside the excited states are far from the present ability. In the third part, we present an example where the excited state depolarizing rates were evaluated together with the magnetic field through the differential Hanle effect interpretation, based on the fact that the molecule provides a series of lines of different sensitivities that can be compared. This led to an experimental/observational determination of these rates, waiting for future theoretical computations for comparison. Title: Evidence for a Pre-Eruptive Twisted Flux Rope Using the Themis Vector Magnetograph Authors: Canou, A.; Amari, T.; Bommier, V.; Schmieder, B.; Aulanier, G.; Li, H. Bibcode: 2009ApJ...693L..27C Altcode: Although there is evidence that twisted structures form during large-scale eruptive events, it is not yet clear whether these exist in the pre-eruptive phase as twisted flux ropes (TFRs) in equilibrium. This question has become a major issue since several theoretical mechanisms can lead to the formation of TFRs. These models consider either the evolution of a coronal configuration driven by photospheric changes or the emergence of TFR from the convection zone. We consider as a target for addressing this issue the active region NOAA AR 10808 known at the origin of several large-scale eruptive phenomena, and associated with the emergence of a δ-spot. Using the THEMIS vector magnetogram as photospheric boundary conditions for our nonlinear force-free reconstruction model of the low corona and without any other assumption, we show that the resulting pre-eruptive configuration exhibits a TFR above the neutral line of the emerging δ-spot. In addition, the free magnetic energy of this configuration could even be large enough to explain such resulting large-scale eruptive events. Title: The Solar Magnetic Field: Surface and Upper Layers, Network and Internetwork Field Authors: Bommier, V. Bibcode: 2009LNP...765..231B Altcode: After having presented the magnetic field effects on the radiation emitted in an atomic or molecular line (Zeeman effect, Hanle effect), we present two applications: (i) the measurement of the magnetic field vector in solar prominences during the ascending phase of Cycle XXI. By transferring the results on synoptic maps of the filaments, a general organization of the large-scale surface field becomes visible; (ii) the measurements of the surface magnetic field made by recent spectropolarimeters like THEMIS. The result is the division of the surface magnetic field into two classes: (a) the network field, nearly vertical and 100 G or more (local average value), located in active regions and at the frontiers of supergranules; (b) the internetwork field, turbulent in direction with an horizontal trend, with a local average value of 20 Gauss or less. Title: Hanle effect in the solar Ba II D2 line: a diagnostic tool for chromospheric weak magnetic fields Authors: Faurobert, M.; Derouich, M.; Bommier, V.; Arnaud, J. Bibcode: 2009A&A...493..201F Altcode: 2008arXiv0811.1180F Context: The physics of the solar chromosphere depends in a crucial way on its magnetic structure. However there are presently very few direct magnetic field diagnostics available for this region.
Aims: Here we investigate the diagnostic potential of the Hanle effect on the Ba II D2 line resonance polarization for the determination of weak chromospheric turbulent magnetic fields.
Methods: The line formation is described with a non-LTE polarized radiative transfer model taking into account partial frequency redistribution with an equivalent two-level atom approximation, in the presence of depolarizing collisions and the Hanle effect. We investigate the line sensitivity to temperature variations in the low chromosphere and to elastic collision with hydrogen atoms. We compare center-to-limb variations of the intensity and linear polarization profiles observed at THEMIS in 2007 to our numerical results.
Results: We show that the line resonance polarization is very strongly affected by partial frequency redistribution effects both in the line central peak and in the wings. Complete frequency redistribution cannot reproduce the polarization observed in the line wings. The line is weakly sensitive to temperature differences between warm and cold components of the chromosphere. The effects of elastic collisions with hydrogen atoms and of alignment transfer due to multi-level coupling with the metastable ^2D{5/2} levels have been studied in a recent paper showing that they depolarize the ^2P{3/2} level of the line. In the conditions where the line is formed we estimate the amount of depolarization due to this mechanism as a factor of 0.7 to 0.65. If we first neglect this effect and determine the turbulent magnetic field strength required to account for the observed line polarization, we obtain values between 20 G and 30 G. We show that this overestimates the magnetic strength by a factor between 1.7 and 2. Applying these correction factors to our previous estimates, we find that the turbulent magnetic field strength is between 10 G and 18 G.
Conclusions: Because of its low sensitivity to temperature variations, the solar Ba II D2 line appears as a very good candidate for the diagnosis of weak magnetic fields in the low chromosphere (z ≥ 900 km) by means of the Hanle effect. Title: Photospheric flows around a quiescent filament at Large and small scale and their ffects on filament destabilization Authors: Roudier, Th.; Malherbe, J. M.; Švanda, M.; Molodij, G.; Keil, S.; Sütterlin, P.; Schmieder, B.; Bommier, V.; Aulanier, G.; Meunier, N.; Rieutord, M.; Rondi, S. Bibcode: 2008sf2a.conf..569R Altcode: We study the influence of large and small scales photospheric motions on the destabilization of an eruptive filament, observed on October 6, 7, and 8, 2004 as part of an international observing campaign (JOP 178). Large-scale horizontal flows are invetigated from a series of MDI/SOHO full-disc Dopplergrams and magnetograms from THEMIS. Small-scale horizontal flows were derived using local correlation tracking on TRACE satellite, Dutch Open Telescope (DOT) and The Dunn Solar telescope (DST) data. The topology of the flow field changed significantly during the filament eruptive phase, suggesting a possible coupling between the surface flow field and the coronal magnetic field. We measured an increase of the shear below the point where the eruption starts and a decrease in shear after the eruption. We conclude that there is probably a link between changes in surface flow and the disappearance of the eruptive filament. Title: Topological Departures from Translational Invariance along a Filament Observed by THEMIS Authors: Dudík, J.; Aulanier, G.; Schmieder, B.; Bommier, V.; Roudier, T. Bibcode: 2008SoPh..248...29D Altcode: 2008SoPh..tmp...53D We study the topology of the 3D magnetic field in a filament channel to address the following questions: Is a filament always formed in a single flux tube? How does the photospheric magnetic field lead to filament interruptions and to feet formation? What is the relation between feet-related field lines and the parasitic polarities? What can topological analyses teach us about EUV filament channels? To do so, we consider a filament observed on 6 October 2004 with THEMIS/MTR, in Hα with the full line profile simultaneously and cospatially with its photospheric vector magnetic field. The coronal magnetic field was calculated from a "linear magnetohydrostatic" extrapolation of a composite THEMIS-MDI magnetogram. Its free parameters were adjusted to get the best match possible between the distribution of modeled plasma-supporting dips and the Hα filament morphology. The model results in moderate plasma β≤1 at low altitudes in the filament, in conjunction with non-negligible departures from force-freeness measured by various metrics. The filament here is formed by a split flux tube. One part of the flux tube is rooted in the photosphere aside an observed interruption in the filament. This splitted topology is due to strong network polarities on the edge of the filament channel, not to flux concentrations closer to the filament. We focus our study to the northwest portion of the filament. The related flux tube is highly fragmented at low altitudes. This fragmentation is due to small flux concentrations of two types. First, some locally distort the tube, leading to noticeable thickness variations along the filament body. Second, parasitic polarities, associated with filament feet, result in secondary dips above the related local inversion line. These dips belong to long field lines that pass below the flux tube. Many of these field lines are not rooted near the related foot. Finally, the present model shows that the coronal void interpretation cannot be ruled out to interpret the wideness of EUV filament channels. Title: Large-scale horizontal flows in the solar photosphere. III. Effects on filament destabilization Authors: Roudier, T.; Švanda, M.; Meunier, N.; Keil, S.; Rieutord, M.; Malherbe, J. M.; Rondi, S.; Molodij, G.; Bommier, V.; Schmieder, B. Bibcode: 2008A&A...480..255R Altcode: 2007arXiv0711.3112R Aims:We study the influence of large-scale photospheric motions on the destabilization of an eruptive filament, observed on October 6, 7, and 8, 2004, as part of an international observing campaign (JOP 178).
Methods: Large-scale horizontal flows were investigated from a series of MDI full-disc Dopplergrams and magnetograms. From the Dopplergrams, we tracked supergranular flow patterns using the local correlation tracking (LCT) technique. We used both LCT and manual tracking of isolated magnetic elements to obtain horizontal velocities from magnetograms.
Results: We find that the measured flow fields obtained by the different methods are well-correlated on large scales. The topology of the flow field changed significantly during the filament eruptive phase, suggesting a possible coupling between the surface flow field and the coronal magnetic field. We measured an increase in the shear below the point where the eruption starts and a decrease in shear after the eruption. We find a pattern in the large-scale horizontal flows at the solar surface that interact with differential rotation.
Conclusions: We conclude that there is probably a link between changes in surface flow and the disappearance of the eruptive filament. Title: Magnetic Causes of the Eruption of a Quiescent Filament Authors: Schmieder, B.; Bommier, V.; Kitai, R.; Matsumoto, T.; Ishii, T. T.; Hagino, M.; Li, H.; Golub, L. Bibcode: 2008SoPh..247..321S Altcode: 2007SoPh..tmp..213S During the JOP178 campaign in August 2006, we observed the disappearance of our target, a large quiescent filament located at S25°, after an observation time of three days (24 August to 26 August). Multi-wavelength instruments were operating: THEMIS/MTR ("MulTi-Raies") vector magnetograph, TRACE ("Transition Region and Coronal Explorer") at 171 Å and 1600 Å and Hida Domeless Solar telescope. Counter-streaming flows (+/−10 km s−1) in the filament were detected more than 24 hours before its eruption. A slow rise of the global structure started during this time period with a velocity estimated to be of the order of 1 km s−1. During the hour before the eruption (26 August around 09:00 UT) the velocity reached 5 km s−1. The filament eruption is suspected to be responsible for a slow CME observed by LASCO around 21:00 UT on 26 August. No brightening in Hα or in coronal lines, no new emerging polarities in the filament channel, even with the high polarimetry sensitivity of THEMIS, were detected. We measured a relatively large decrease of the photospheric magnetic field strength of the network (from 400 G to 100 G), whose downward magnetic tension provides stability to the underlying stressed filament magnetic fields. According to some MHD models based on turbulent photospheric diffusion, this gentle decrease of magnetic strength (the tension) could act as the destabilizing mechanism which first leads to the slow filament rise and its fast eruption. Title: Magnetic Field Vector Measurements with THEMIS Authors: Bommier, V.; González, M. J. M.; Schmieder, B.; Landi Degl'Innocenti, E. Bibcode: 2008ASPC..383..123B Altcode: The aim of the present work is twofold: a) to validate the Milne-Eddington UNNOFIT inversion by comparing its results with those of the SIR inversion, which is in LTE but does not assumes the Milne-Eddington atmosphere; b) to present a decrease of the network local average magnetic field strength in the vicinity of a filament/prominence, observed before its disppearance, suggesting that the disappearance results from a weakening of the magnetic support. Title: Interaction of magnetic field systems leading to an X1.7 flare due to large-scale flux tube emergence Authors: Li, H.; Schmieder, B.; Song, M. T.; Bommier, V. Bibcode: 2007A&A...475.1081L Altcode: Aims:The aim of this paper is to understand the magnetic configuration and evolution of an active region, which permitted an X1.7 flare to be observed during the decaying phase of a long-duration X1.5 flare on 2005 September 13.
Methods: We performed a multi-wavelength analysis using data from space-borne (Solar and Heliospheric Observatory (SOHO), Transition Region and Coronal Explorer (TRACE), Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI), GOES) and ground-based (the French-Italian THEMIS telescope and the Huairou Video Vector Magnetograph (HVVM)) instruments. We coaligned all the data in order to study the origin of the flare by comparing the observed magnetic field structures with the emissions detected by different instruments.
Results: Reconstructed RHESSI images show three hard X-ray (HXR) sources. In TRACE 195 Å images, two loops are seen: a short bright loop and a longer one. Five ribbons are identified in Hα images, with two of them remnant ribbons of the previous flare. We propose the following scenario to explain the X1.7 flare. A reconnection occurs between the short loop system and the longer loops (TRACE 195 Å). Two X-ray sources could be the footpoints of the short loop, while the third one between the two others is the site of the reconnection. The Hα ribbons are the footprints in the chromosphere of the reconnected loops. During the reconnection, the released energy is principally nonthermal according to the RHESSI energy spectrum analysis (two orders of magnitude higher than the maximum thermal energy). The proposed scenario is confirmed by a nonlinear force-free field (NLFFF) extrapolation, which shows the presence of short sheared magnetic field lines before the eruption and less sheared ones after the reconnection, and the connectivity of the field lines involved in the flaring activity is modified after the reconnection process. The evolution of the photospheric magnetic field over a few days shows the continuous emergence of a large-scale magnetic flux tube, the tongue-shape of the two main polarities of the active region being the signature of such an emergence. After the previous X1.5 flare, the emergence of the tube continues and favors new magnetic energy storage and the onset of the X1.7 flare. Title: Fast vector magnetographs: THEMIS/MSDP and EST project Authors: Mein, P.; Bommier, V.; Mein, N. Bibcode: 2007sf2a.conf..601M Altcode: Imaging spectro-polarimetry with Multichannel Subtractive Double Pass (MSDP) is able to provide vector magnetic fields with high temporal resolution. We present some results obtained with THEMIS and reduced with the UNNOFIT code, as well as a new method to achieve off-line the required spectral resolution. Performances of slit- and imaging-spectroscopy are briefly compared, together with the high capabilities expected from the EST project. Title: Photospheric flows around a quiescent filament Authors: Rondi, S.; Roudier, Th.; Molodij, G.; Bommier, V.; Keil, S.; Sütterlin, P.; Malherbe, J. M.; Meunier, N.; Schmieder, B.; Maloney, P. Bibcode: 2007A&A...467.1289R Altcode: Context: The horizontal photospheric flows below and around a filament are one of the components in the formation and evolution of filaments. Few studies exist because they require multiwalength time sequences at high spatial resolution.
Aims: Our objective is to measure the horizontal photospheric flows associated with the evolution and eruption of a filament.
Methods: We present observations obtained in 2004 during the international JOP 178 campaign which involved eleven instruments both in space and at ground based observatories. We use TRACE WL, DOT and DST observation to derive flow maps which are then coaligned with intensity images and with the vector magnetic field map obtained with THEMIS/MTR.
Results: Several supergranulation cells cross the Polarity Inversion Line (PIL) and can transport magnetic flux through the PIL, in particular parasitic polarities. We present a detailed example of the formation of a secondary magnetic dip at the location of a filament footpoint. Large-scale converging flows, which could exist along the filament channel and contribute to its formation, are not observed. Before the filament's eruptive phase, we observe both parasitic and normal polarities being swept by a continuously diverging horizontal flow located in the filament gap. The disappearance of the filament initiates in this gap. Such purely horizontal motions could lead to destabilization of the filament and could trigger the sudden filament disappearance. Title: A generalized √ɛ-law. The role of unphysical source terms in resonance line polarization transfer and its importance as an additional test of NLTE radiative transfer codes Authors: Stepán, J.; Bommier, V. Bibcode: 2007A&A...468..797S Altcode: 2007arXiv0704.1573S Context: A derivation of a generalized √ɛ-law for nonthermal collisional rates of excitation by charged perturbers is presented.
Aims: Aim of this paper is to find a more general analytical expression for a surface value of the source function which can be used as an additional tool for verification of the non-LTE radiative transfer codes.
Methods: Under the impact approximation hypothesis, static, one-dimensional, plane-parallel atmosphere, constant magnetic field of arbitrary strength and direction, two-level atom model with unpolarized lower level and stimulated emission neglected, we introduce the unphysical terms into the equations of statistical equilibrium and solve the appropriate non-LTE integral equations.
Results: We derive a new analytical condition for the surface values of the source function components expressed on the basis of irreducible spherical tensors. Title: Is the Solar Intranetwork Field a Resolved Turbulent Field? Authors: Bommier, V.; Landi Degl'Innocenti, E.; Landolfi, M.; Molodij, G. Bibcode: 2007ASPC..370...81B Altcode: The spectropolarimetric map observed below an active region filament on 7 December 2003 in the Fe I 6302.5 Å line has been inverted by using the UNNOFIT code of Landolfi et al. (1984), improved by the introduction of a magnetic filling factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, are derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved. The results make clearly appear two regimes, corresponding to two ranges of filling factors: (a) the network zone extended to spatially broad lanes, having a field about 20°-30° from the vertical, with a homogeneous azimuth. In this zone the filling factor may be high, typically 10%-20% on the network itself and decreasing on both sides. (b) the intranetwork zone, where the field is turbulent and the filling factor typically 2% as expected by several authors. In both regions the field strength is found of the order of 1 kGauss. No clear difference in field strength is found between both zone types, they differ only by field direction homogeneity and filling factor. The turbulent nature of the intranetwork field has been confirmed by an independent inversion of Fe I 6301.5 Å. Title: Multipole rates for atomic polarization studies: the case of complex atoms in non-spherically symmetric states colliding with atomic hydrogen Authors: Sahal-Bréchot, S.; Derouich, M.; Bommier, V.; Barklem, P. S. Bibcode: 2007A&A...465..667S Altcode: Context: Interpretation of linearly polarized parameters of the lines of complex atoms for the second solar spectrum needs a lot of collisional coefficients which are often poorly known.
Aims: We provide general and simple formulae giving the coefficients of the atomic master equation (depolarization, polarization transfer, population transfer, and relaxation coefficients) for the case of any atomic level (but not a spherically symmetric) that is perturbed by collisions with hydrogen atoms.
Methods: We use the theory of the density matrix and the theory of atomic collisions with a few assumptions (frozen core and spin neglected during the collision). We only study collisional transitions between levels of the same configuration with no equivalent electrons in the external shell, and with the rest of the configuration (the core) frozen. We use the basis of the Tkq irreducible spherical tensor operators.
Results: The formulae giving the depolarization and polarization transfer coefficients due to collisions with neutral hydrogen for l ≠ 0 levels of complex atoms can be expressed as a linear combination of the k-pole depolarization and elastic collisional rate coefficients obtained for simple atoms.
Conclusions: .It should be possible to apply this method for fast calculation of multipole rates for any level having an external shell l ≠ 0. Title: UNNOFIT inversion of spectro-polarimetric maps observed with THEMIS Authors: Bommier, V.; Landi Degl'Innocenti, E.; Landolfi, M.; Molodij, G. Bibcode: 2007A&A...464..323B Altcode: Aims:We inverted a spectropolarimetric scan of an active region and a filament (240× 340 arcsec) achieved with THEMIS on 7 December 2003 in the two lines Fe I 6302.5 and 6301.5 Å.
Methods: The inversion was achieved for each line separately by using the UNNOFIT code of Landolfi and Landi Degl'Innocenti, and was improved by introducing a magnetic filling-factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, were derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved.
Results: The tests run with UNNOFIT show that the magnetic field strength B and the magnetic filling factor α cannot be separately recovered by the inversion in Fe I 6302.5, but that their product α B, which is the local average magnetic field, is recovered. The magnetic flux is only its longitudinal component. In addition, the results make two regimes clearly appear, corresponding to two ranges of local average magnetic field strength as measured in 6302.5: (a) the network, having a field inclined of about 20°-30° from the vertical in 6302.5 (spread more but non-horizontal in 6301.5), with a homogeneous azimuth. In this zone the local average field strength in 6302.5 is higher than 45 Gauss; (b) the internetwork, where the field is turbulent (with a horizontal trend, spread more at lower altitudes), and the 6302.5 local average field strength is lower than 45 Gauss (about 20 Gauss).
Conclusions: .The two lines display coherent results, in particular for the magnetic-field azimuth. From this coherence we conclude that the turbulence of the 20 Gauss internetwork field has a solar origin.

Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: Fast vector magnetic maps with imaging spectroscopy Authors: Mein, P.; Mein, N.; Bommier, V. Bibcode: 2007MmSAI..78..160M Altcode: We present a new observing mode of THEMIS / MSDP which can provide fast vector magnetic maps of the solar photosphere in the 610.27 Ca line. Title: Simultaneous polarimetric observations with VTT and THEMIS Authors: Balthasar, H.; Bommier, V. Bibcode: 2007msfa.conf..229B Altcode: Spectro-polarimetric observations of sunspot groups have been performed simultaneously with the VTT and with THEMIS. At the VTT we observed a group of iron and silicon lines at 1078 nm with the Tenerife Infrared Polarimeter, and at THEMIS we observed in five spectral channels (MTRmode): Fe 630 nm, Na D, Hα, Fe 557.6 nm and alternatively Cr 578 nm or Fe 525 nm. The inversion of the Stokes-profiles was done with the SIR-code for the infrared lines and for Fe 630 nm, for the other spectral ranges the inversion is still pending. So far we derived that the magnetic field strength decreases with height at most locations inside the spots, in contrast to some recently published results of other investigations. Title: Solar magnetism and dynamics and THEMIS users meeting Authors: Bommier, V.; Sahal-Bréchot, S. Bibcode: 2007MmSAI..78....5B Altcode: No abstract at ADS Title: Photospheric flows around a quiescent filament and CALAS first results . Authors: Rondi, S.; Roudier, Th.; Molodij, G.; Bommier, V.; Malherbe, J. M.; Schmieder, B.; Meunier, N.; Rieutord, M.; Beigbeder., F. Bibcode: 2007MmSAI..78..114R Altcode: The horizontal photospheric flows below and around a filament are one of the components in the formation and evolution of filaments. Few studies have been done so far because this requires multiwalength time sequences with high spatial resolution. We present observations obtained in 2004 during the international JOP 178 campaign in which eleven instruments were involved, from space and ground based observatories. Several supergranulation cells are crossing the Polarity Inversion Line (PIL) allowing the transport of magnetic flux through the PIL, in particular the parasitic polarities. Before the filament eruptive phase, parasitic and normal polarities are swept by a continuous diverging horizontal flow located in the filament gap where the disappearance of the filament starts. In the future, observations at high spatial resolution on a large field-of-view would be very useful to study filaments, as they are very large structures. We also present the first images obtained with the use of our new 14 MPixel camera CALAS (CAmera for the LArge Scales of the Solar Surface) (10 arcmin× 6.7 arcmin) . These are the first large-scale and high-resolution images of the solar surface ever made. Title: Multipole rates for atomic polarization studies: the case of complex atoms in non-spherically symmetric states colliding with atomic hydrogen. Authors: Sahal-Bréchot, S.; Derouich, M.; Bommier, V.; Barklem, P. S. Bibcode: 2007MmSAI..78..197S Altcode: Interpretation of linearly polarized parameters of the spectral lines of the second solar spectrum permits to obtain information about the magnetic field vector of the medium where the spectral lines are formed, provided suitable theoretical and numerical methods be applied to extract the physical information. This linear polarization is modified by the magnetic field and by collisions. In this context, with a few approximations, we provide in the present paper general and simple formulae giving the coefficients of the atomic master equation (depolarization, polarization transfer, population transfer and relaxation coefficients) for the case of an atom in any (but not spherically symmetric) level, perturbed by collisions with hydrogen atoms. It would be possible to apply this method for fast calculation of multipole rates for any level having an external shell l ≠q 0 . Title: Some THEMIS tip-tilt images . Authors: Bommier, V. Bibcode: 2007MmSAI..78...23B Altcode: In the MTR (`MulTiRaies', i.e. multiline spectropolarimetry) mode of THEMIS, a map is the result of a reconstruction from a scan of the solar image on the spectrograph entrance slit. The result of image motion appears as zigzags along non-vertical lines or structures in the map. As an image stabilization system, the new tip-tilt acts in reducing such zigzags. A map is presented obtained with the tip-tilt ON where nearly no zigzag is visible. Title: The granular magnetic field as observed with THEMIS Authors: Bommier, V.; Molodij, G.; Meunier, N. Bibcode: 2007MmSAI..78...65B Altcode: The search for correlation along the slit in THEMIS spectropolarimetric observations of a quiet region shows a positive autocorrelation of the magnetic field direction with a pixel size of 0.45 arcsec. Accordingly, the magnetic field appears as partially resolved with such a pixel size. Further spectropolarimetric observations have been performed by scanning a quiet region with THEMIS tip-tilt ON, in order to investigate a possible relationship between the granulation and the magnetic field vector which is known in each pixel of this observation (pixel size of 0.25 arcsec). As a result, we see a very clear correlation between the granulation observed in the continuum and the longitudinal velocity field observed via the Doppler effect, but the granulation and the magnetic field vector (strength and direction) appear us as uncorrelated, by looking at their respective maps. These quantities (velocity and magnetic field) have been derived from spectropolarimetric observations of the Fe I 6302.5 line, to which UNNOFIT inversion has been applied to derive the magnetic field vector. Title: Second Spectrum of Na I D1 Observed with THEMIS Authors: Bommier, V.; Molodij, G. Bibcode: 2006ASPC..358..231B Altcode: The second solar spectrum (spectrum of the linear polarization observed near the solar limb in a quiet region) of Na I D1 has always been found antisymmetrical when observed with THEMIS tep{b12 TB01,b12 BM02}.

The same holds also for atlas of tet{b12 Ga00}.

On the contrary, tet{b12 SK97} and tet{b12 St00}

observed a differently shaped profile, showing a central peak. We investigated in depth our treatment of THEMIS data, in particular looking for possible beam misalignments, by observing other unpolarized lines, but we have failed to put in evidence any misalignment. We discuss these complementary observations. In addition, we present a structure in the V/I profile of Na I D1 and D2, which we have repeatedly observed, and which we suggest be due to the Kemp effect (the alignement-to-orientation transfer that occurs in the transition from the Zeeman effect to the Paschen-Back effect). Title: UNNOFIT Inversion of Spectro-Polarimetric Maps Observed with THEMIS Authors: Bommier, V.; Landi Degl'Innocenti, E.; Landolfi, M.; Molodij, G. Bibcode: 2006ASPC..358..119B Altcode: This paper presents the inversion of a spectro-polarimetric scan (240 arcsec×340 arcsec) of an active region and a filament, obtained with THEMIS, on December 7, 2003, in the two Fe I lines at 6302.5 Å and 6301.5 Å. The inversion was applied to each line separately, using the UNNOFIT code of tet{b13 La84}, improved by the introduction of a magnetic filling factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, are derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved. The tests run with UNNOFIT show that the magnetic field strength, B, and the magnetic filling factor, α, cannot be separately recovered by the inversion of Fe I 6302.5 Å, but that their product, α B, which is the local average magnetic field, is recovered. The magnetic flux is only its longitudinal component. Our results also reveal two distinct regimes, corresponding to two different ranges of local average magnetic field strength as inferred from Fe I 6302.5 Å: a) The network, having a field inclined of about 20°-30° from the vertical in Fe I 6302.5 Å (more spreaded, but non-horizontal in Fe I 6301.5 Å), with a homogeneous azimuth. In this zone, the local average field strength in Fe I 6302.5 Å is larger than 45 G. b) The internetwork, where the field is turbulent (with a horizontal trend, more spreaded at lower altitudes), and with local average field strength in Fe I 6302.5 Å smaller than 45 G. The two lines gives coherent results, in particular in magnetic field azimuth. From this we conclude that the turbulence of the internetwork field is of solar origin. This work has been presented in detail by tet{b13 Bo06}. Title: Multi-Line Determination of the Turbulent Magnetic Field from the Second Solar Spectrum of MgH Authors: Bommier, V.; Landi Degl'Innocenti, E.; Molodij, G. Bibcode: 2006ASPC..358..317B Altcode: This paper presents an analysis of the Q1,2(6{-}12) lines of the Q band of the A2Π-X2Σ+ (0,0) transition of MgH, whose linear polarization was measured with THEMIS, on November 21, 2004, in a quiet region of the Sun (North pole), 4 arcsec inside the solar limb. This analysis is performed as follows: a) The Hanle effect parameter, ΓH, is derived by applying the differential Hanle effect method between the two extreme pairs of lines. Assuming no depolarizing collisions, a magnetic field strength follows, which is found to be 9.2 G, in agreement with previous observations of the same kind. b) This ΓH parameter is entered in a code solving the non-LTE polarized radiative transfer equations, and the other depolarizing parameter, namely the depolarizing collision rate, is then derived by adjusting the computed polarization to the observed one. Thus an average value of the rate per colliding hydrogen atom α(2)=1.20×10-9 cm3 s-1 is obtained for the upper levels of the 12 lines (with a standard deviation of 0.21×10-9 cm3 s-1). The corresponding model-dependent depolarizing rate is D(2)=(4.2 ± 0.7)×107 s-1 at h=200 km. c) This depolarizing rate is now introduced in the conversion of the ΓH parameter in terms of magnetic field strength: an average turbulent field strength of 29 ± 12 G is derived as the final value, at a height h=200 ± 80 km where the polarization is formed. The Hönl-London factors of the lines under interest have been recalculated, leading to detect an error of a factor 2 in the recent literature. The derived value B=29 ± 12 G at h=200 ± 80 km is in fairly good agreement with previous determinations based on the interpretation of the Sr I 4607 Å limb polarization, which has led to fields in the range 35-60 G. Given the error bars, it seems unnecessary to put forward different formation regions for the Sr I and MgH lines. This work has been presented in detail by tet{b14 Bo06}, under the title ``Collisional influence on the differential Hanle effect method applied to the second solar spectrum of the A2Π-X2Σ+ (0,0) band of MgH.'' Title: Semi-Classical Collision Formalism with Energy and Momentum Transfer Authors: Bommier, V. Bibcode: 2006ASPC..358..245B Altcode: As expected, the semi-classical theory of atom-electron and atom-ion collisions ( tealt{b11 Se62}; see also tealt{b11 SB96})

leads to incorrect results when it is applied to impact polarization computations. This is due to the fact that, near the threshold, the Δ M=± 1 transitions between Zeeman sublevels remain open, even though the momentum conservation law tep{b11 PS58}

implies that they should be forbidden at the exact threshold. An approximate model of momentum transfer is proposed, which corrects this behavior, leading to a fairly good agreement with observed impact polarization for several target atoms. The agreement is improved also for the total cross-section, because the Δ M=± 1 cross-sections were previously overestimated. Comparison with experimental results are shown, for electron-atom impact polarization and total cross-section. As a second step, energy transfer is also taken into account, by splitting the collision process in two halves: the first half is modeled within the initial conditions, while the second half is modeled within the final conditions. Title: Interpretation of the Second Solar Spectrum of the Sr I 4607 Å Line Observed at THEMIS and Pic-du-Midi Authors: Derouich, M.; Bommier, V.; Malherbe, J. -M.; Landi Degl'Innocenti, E.; Molodij, G.; Sahal-Bréchot, S. Bibcode: 2006ASPC..358..120D Altcode: The Hanle effect is the only tool available for measuring turbulent (i.e., spatially unresolved) magnetic fields at the surface of the quiet Sun. The Hanle-effect diagnostics relies on the discrepancy between the linear polarization calculated in the absence of a magnetic field and the observed polarization. We interpreted the linear polarization of the Sr I 4607 Å line, observed at THEMIS (December 7-9, 2002) and Pic-du-Midi (May 14, 2004), in terms of the Hanle effect. We present here the main results of this study. In particular, we stress the importance of a proper adjustment of the theoretical intensity profile to the observed one, through the application of a zero-field model, the magnetic field being determined in a second step from the line-center polarization degree. With the spatial resolution

and coverage of the Pic-du-Midi data (1 arcsec resolution, 132 distances from the limb), we can also attain depth probing of the turbulent magnetic strength, and we discuss whether this can vary within the range of heights of formation for the line center. Title: Collisional influence on the differential Hanle effect method applied to the second solar spectrum of the A2Π-X2Σ+ (0, 0) band of MgH Authors: Bommier, V.; Landi Degl'Innocenti, E.; Feautrier, N.; Molodij, G. Bibcode: 2006A&A...458..625B Altcode: Aims.This paper presents an analysis of the Q1,2(6-12) lines of the Q band of the A2Π-X2Σ+ (0, 0) transition of MgH, whose linear polarization was measured 4 arcsec inside the solar limb in a quiet region (North Pole) with THEMIS on 21 November 2004.
Methods: .This analysis is performed as follows: a) the Hanle effect ΓH parameter is derived by applying the differential Hanle effect method between the two extreme pairs of lines. Assuming no depolarizing collisions, a magnetic field strength follows, which is found to be 9.2 Gauss, in agreement with previous observations of the same kind; b) this ΓH parameter is entered in a code solving the NLTE polarized radiative transfer equations, and the other depolarizing parameter, namely the depolarizing collision rate, is then derived by adjusting the computed polarization to the observed one. Thus an average value of the rate per colliding hydrogen atom α(2)=1.20 × 10-9 cm3 s-1 is obtained for the upper levels of the 12 lines (standard deviation 0.21 × 10-9 cm3 s-1). The corresponding model-dependent depolarizing rate is D(2)=(4.2 ± 0.7) × 107 s-1 at h=200 km; c) this depolarizing rate is now introduced in the conversion of the ΓH parameter in terms of magnetic field strength: an average turbulent field strength of 29 ± 12 Gauss is derived as the final value, at height h=200 ± 80 km where the polarization is formed. The Hönl-London factors of the lines under interest have been recalculated, leading to detect an error of a factor 2 in the recent literature.
Results: .The derived value B=29 ± 12 Gauss at h=200 ± 80 km is in fairly good agreement with the previous determinations based on the interpretation of the Sr I 4607 Å limb polarization, which has led to fields in the range 35-60 Gauss.
Conclusions: .Given the error bars, it seems unnecessary to put forward different formation regions for the Sr I and MgH lines. Title: Second solar spectrum of the Sr I 4607 Å line: depth probing of the turbulent magnetic field strength in a quiet region Authors: Derouich, M.; Bommier, V.; Malherbe, J. M.; Landi Degl'Innocenti, E. Bibcode: 2006A&A...457.1047D Altcode: Aims.This paper is devoted to an interpretation of Quiet-Sun, spatially-resolved spectropolarimetric observations of the Hanle effect in terms of turbulent weak magnetic field determination.
Methods: . Observations: the slit was positioned perpendicular to the limb, and the spatial resolution along the slit was 1 arcsec, leading to a depth probing along 132 different limb distances. The new polarimeter of the Pic-du-Midi Turret Dome was used on May 14, 2004 to observe a quiet region at the East limb equator in the resonance line of neutral Strontium at 4607 Å.
Results: . For each limb distance, we properly adjusted the theoretical intensity profile obtained by applying a zero-field model to the observed one. Micro- and macroturbulent velocities were thus derived (average values v{micro}=1.77 km s-1 and v{macro}=1.95 km s-1). The magnetic field was determined in a second step by interpreting the Hanle effect on the line center linear polarization degree. The depolarizing collisions with neutral hydrogen were taken fully into account through a semi-classical calculation of their rates. An average value of B=38 Gauss was thus derived. Finally, error bars on the magnetic field values were evaluated from a) the polarimetric inaccuracy, b) the limb distance determination inaccuracy, and c) the uncertainty on our theoretical collisional depolarizing rates that we evaluated. This combination leads to 10-20% as total relative error on the magnetic field determination by the Hanle effect method. Since the inaccuracy due to the model itself was hard to properly evaluate, it was ignored. An uncertainty of ±60 km on the line formation depth was, however, derived from the contribution functions. The magnetic field is found to increase slowly with height in the height range 220-300 km above τ5000=1 and then decrease in the height range 300-370 km.
Title: Predictions on the application of the Hanle effect to map the surface magnetic field of Jupiter Authors: Ben-Jaffel, L.; Harris, W.; Bommier, V.; Roesler, F.; Ballester, G. E.; Jossang, J. Bibcode: 2005Icar..178..297B Altcode: In this paper we evaluate the possibility of detecting, for the first time, the surface magnetic field of Jupiter (∼1 bar level) by observing the change of linear polarization induced by the Hanle effect on the H Lyman-alpha (Ly α) emission line of the planet. We find that, indeed, the Hanle effect, which results from the interaction between a local magnetic field and the atomic polarization induced by absorption of anisotropic radiation, is sensitive to relatively weak values of the strength of the magnetic fields expected on planets. First, we show that for the Ly α emission backscattered by atomic H in the presence of a magnetic field, the Hanle effect is polarizing. This new result is in total contrast to the depolarizing effect predicted and observed for emission lines scattered at right angles in solar prominences. Additionally, to estimate the polarization rate for the case of Jupiter, we have considered three magnetic field models: a dipole field for reference, an O based model [Connerney, J.E.P., 1981. The magnetic field of Jupiter—A generalized inverse approach. J. Geophys. Res. 86, 7679-7693], and finally, an O based model [Khurana, K.K., 1997. Euler potential models of Jupiter's magnetospheric field. J. Geophys. Res. 102, 11295-11306]. In all models, we show that for the jovian backscattered Ly α line, the Hanle effect does enhance the Ly α linear polarization; the polarization rate may exceed 2% at specific regions of the jovian disc, making detection possible either remotely or from an orbiter around Jupiter. In general, depending on the instrumental sensitivity and the observing strategy used, we show that accurate mapping of the linear polarization rate at the planetary surface (thermosphere) or off-disc (corona) may provide a rather accurate estimate of the jovian total magnetic field strength on large area scales. Title: Vector magnetic field map at the photospheric level below and around a solar filament (neutral line) Authors: Bommier, V.; Rayrole, J.; Eff-Darwich, A. Bibcode: 2005A&A...435.1115B Altcode: We present a vector magnetic field map obtained on 7 December 2003, below and around a filament located not so far from the active region NOAA 517, whose one spot is also found on the map of 240× 340 arcsec. This region was itself located near the disk center, so that the longitudinal (resp. transverse) field is nearly the vertical (resp. horizontal) one. The THEMIS telescope was used in its spectropolarimetric multiline mode MTR ("MulTiRaies"). The noise level is 5-10 Gauss in the longitudinal field and 50-100 Gauss in the transverse field, while the pixel size is 0.45 arcsec. Fundamental ambiguity is not solved, and the atmosphere is assumed to be homogeneous. The magnetic field derivation method described in this paper was validated on eight test points submitted to the UNNOFIT inversion code, and the results are found in agreement within 14% discrepancy. Two main results appear on the map: (i) a strong spatial correlation between the longitudinal and transverse field resulting in an inclined field vector (making a most probable angle of 60° or 120° with the line-of-sight in the filament region); and (ii) homogeneity of the field direction (inclination and azimuth) in the filament region. Parasitic polarities were also detected: first those located at the filament feet, as theoretically expected, on the one hand; and then weak opposite polarity regular patterns that appear between the network field (strong field at the frontiers of supergranules), on the other. The exact superimposition of the magnetic field map derived from the Fe I 6302.5 Å line and of the Hα map, which enabled association of the parasitic polarities with the filament feet, was possible because these two maps were simultaneously obtained, thanks to a unique facility available in the multiline mode of THEMIS. Title: Interpretation of second solar spectrum observations of the Sr I 4607 Å line in a quiet region: Turbulent magnetic field strength determination Authors: Bommier, V.; Derouich, M.; Landi Degl'Innocenti, E.; Molodij, G.; Sahal-Bréchot, S. Bibcode: 2005A&A...432..295B Altcode: This paper presents and interprets some observations of the limb polarization of Sr I 4607 Å obtained with the spectropolarimeter of the French-Italian telescope THEMIS in quiet regions close to the solar North Pole on 2002 December 7-9. The linear polarization was measured for a series of limb distances ranging from 4 to 160 arcsec, corresponding to heights of optical depth unity in the line core ranging from about 330 to 220 km, respectively, above the τ5000=1 level. To increase the polarimetric sensitivity, the data were averaged along the spectrograph slit (one arcmin long) set parallel to the solar limb. Since the data show no rotation of the linear polarization direction with respect to the limb direction, the observed depolarization is ascribed to the Hanle effect of a turbulent weak magnetic field, the zero-field polarization being derived from a model. The interpretation is performed by means of an algorithm which describes the process of line formation in terms of the atomic density matrix formalism, the solar atmosphere being described by an empirical, plane-parallel model. The collisional rates entering the model (inelastic collisions with electrons, elastic depolarizing collisions with neutral hydrogen), have been computed by applying fast semi-classical methods having a typical accuracy of the order of 20% or better (see Derouich [CITE]), leading to 6% inaccuracy on the magnetic field strength determination. We assume a unimodal distribution for the intensity of the turbulent field. The computed intensity profile has been adjusted to the observed one in both depth and width, by varying both microturbulent and macroturbulent velocities. The best adjustment is obtained for respectively 1.87 km s-1 (micro) and 1.78 km s-1 (macro). The evaluation of the magnetic depolarization leads then to the average value of 46 Gauss for the turbulent magnetic field strength, with a gradient of -0.12 Gauss/km. Our results are in very good agreement with the value of 60 Gauss determined at large μ, in the volume-filling field case, by Trujillo Bueno et al. ([CITE], Nature, 430, 326), using a 3D magneto-convective simulation. This validates our method.

Based on observations made with the french-italian telescope THEMIS operated by CNRS and CNR on the island of Tenerife in the spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: Second solar spectrum observed at the Pic-du-Midi: depth probing of the turbulent magnetic field intensity in a quiet region. Authors: Derouich, M.; Malherbe, J. M.; Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Bréchot, S. Bibcode: 2004sf2a.conf..113D Altcode: 2004sf2a.confE.346D The installation of a new polarimeter at the Turret Dome of the Pic-du-Midi has permitted new observations of the "second solar spectrum" (which is the spectrum of the linear polarization observed near the solar limb), having a spatial resolution. On 2003 October 25, we have observed a quiet region located at the East limb equator, in the resonance line of neutral strontium at 4607 Å. The slit was positioned perpendicular to the limb: recording various limb distances provides a depth probing of the solar atmosphere. The intensity of the turbulent magnetic field has been derived from the Hanle effect interpretation, which is actually the only method for vectorial weak field determination. The theoretical profiles to be compared to the observed ones have been obtained by applying the atomic density matrix formalism (Landi Degl'Innocenti E., Bommier V., & Sahal-Bréchot S., 1990). The various collisional coefficients have been computed by applying semi-classical methods that are accurate to 20% or better: the one from Seaton (1962) and Sahal-Bréchot (1969a, 1969b) for the collisions with electrons, responsible for the inelastic transitions, and the one developed by Anstee & O'Mara (1991, 1995) for line broadening computations, generalized to the collisional depolarization by Derouich et al. (2003; see also Derouich, 2004), for the elastic collisions with neutral hydrogen atoms. The results have been found in full agreement with those previously obtained with THEMIS without any spatial resolution (at 9 limb distances). With the spatial resolution that we have now at the Pic-du-Midi (1 arcsec, 138 limb distances), it appears that the turbulent magnetic field intensity does not vary with depth, in the line formation region that ranges from ~200 to ~300 km above the tau5000=1 level. Title: The Partial Redistribution in the Atomic Density Matrix Formalism Authors: Bommier, V. Bibcode: 2003ASPC..307..213B Altcode: No abstract at ADS Title: Diagnostic of turbulent magnetic fields in solar quiet regions by their Hanle effect in the Sr I 4607Å line Authors: Derouich, M.; Bommier, V.; Landi Degl'Innocenti, E.; Molodij, G.; Sahal-Bréchot, S. Bibcode: 2003sf2a.conf..113D Altcode: 2003sf2a.confE..42D Stokes parameters of the resonance Sr I 4607 Å line were observed with the solar THEMIS telescope in December 2002, close to the limb of the sun at the North pole. They are interpreted in terms of turbulent magnetic field. The Interpretation requires a non-LTE radiative transfer calculations of the Stokes parameters. The contributions of depolarizing isotropic collisions with neutral hydrogen and inelastic collisions with electrons as well as the radiative processes are taken into account in the statistical equilibrium equations in order to identify weak magnetic fields by their depolarizing Hanle effect. The values of depth-dependent magnetic field, derived from observations at different distances from the solar limb, are given. These observations and the magnetic field results are in agreement with other measurements also obtained with THEMIS, and interpreted by using a different formalism (Faurobert M., Arnaud J., Vigneau J., Frisch H., 2001, A&A 378, 627). Title: Theoretical Study of the Collisional Depolarization and of the Hanle Effect in the Na I D2 Line Observed on the Solar Limb Authors: Bommier, V.; Kerkeni, B. Bibcode: 2003ASPC..307..284B Altcode: No abstract at ADS Title: The Hanle effect observed in solar prominences: interpretation of the 1974 1982 Pic-du-Midi observations, and new perspectives Authors: Bommier, V. Bibcode: 2003EAS.....9..197B Altcode: This paper is devoted to review the development and the results of the program “solar prominences" that has been aimed to observe the Hanle effect at the Pic-du-Midi during the ascending phase of Cycle XXI (1974 1982). This aim had been defined and the observations have been performed by Jean-Louis Leroy. The Hanle effect is the effect of a weak magnetic field on the scattering linear polarization: its main features are, for some field orientations, a depolarization and eventually a rotation of the polarization direction. The magnetic field diagnostic from polarization measurements requires a modelling of the polarized line formation, that has been achieved in Meudon in the well-adapted formalism of the atomic density matrix. It is shown how the program has been developed to determine the 3components of the field vector and the electron density, by setting multi-line polarimetric observations. Particular attention has been devoted on the solution of the 180degrees ambiguity, which has been solved by 3 independent methods. By using this solution, one unique average magnetic field vector has been determined in each of 296 quiescent prominences, leading to results on the field strength, direction, vertical gradient, cyclic variations. The future perspective opened by the low scattered light level of THEMIS and other spectropolarimeters is to increase the spatial resolution of the measurements. Title: Theoretical study of the collisional depolarization and of the Hanle effect in the Na I D2 line observed on the solar limb Authors: Kerkeni, B.; Bommier, V. Bibcode: 2002A&A...394..707K Altcode: In recent years, Landi Degl'Innocenti (\cite{Landi-98}, \cite{Landi-99}) has proposed a model of the polarization spectrum of the Na I D lines observed near the solar limb, based on lower level polarization effects. By so doing, he obtains a remarkable agreement between his model and the observations, so that he comes to a conclusion about a paradox, because the existence of lower level polarization is incompatible with a magnetic field strength higher than 10 mGauss (except vertical), and with possible depolarizing collision effects. In the present paper, we investigate the depolarizing collision effects (collisions with neutral hydrogen) by using the collisional rates computed with ab-initio and quantum chemistry methods by Kerkeni (\cite{Kerkeni-01}; see also Kerkeni et al. \cite{Kerkeni-etal-00}, and Kerkeni \cite{Kerkeni-02}). We solve the statistical equilibrium equations for the atomic density matrix, taking into account these depolarizing collisions. We investigate the effect of a weak magnetic field (Hanle effect). Our results indicate that the lower levels should be completely depolarized by the collisions at the depth where the Na I D lines are formed. Furthermore, large values of the lower level alignment such as those introduced by Landi Degl'Innocenti in his model to get a good theoretical fit of the observations, seem to us unlikely, as our computations confirm. Thus, as the agreement between the model by Landi Degl'Innocenti and the observations is however very convincing, the paradox is confirmed, reinforced and increased by our results. Title: Linear polarization of the O VI lambda 1031.92 coronal line. I. Constraints on the solar wind velocity field vector in the polar holes Authors: Raouafi, N. -E.; Sahal-Bréchot, S.; Lemaire, P.; Bommier, V. Bibcode: 2002A&A...390..691R Altcode: In the first part of the present work, we report on the determination of the linear polarization parameters of the O VI lambda1031 .92 coronal line (hereafter O VI D2). Spectropolarimetric observations done by the SUMER spectrometer on board the spacecraft SoHO during minimum activity of the solar cycle (March, 1996) in the south coronal hole were used to analyze the partial linear polarization of the D2 resonance line scattered by the O {VI} coronal ions. Widths of the O VI D2 and O VI 1037.61 (hereafter O VI D1) lines and limb-brightening determined from data observations of SUMER/SoHO are also presented. The second part of this work is devoted to the interpretation of the determined polarization parameters in terms of the macroscopic velocity field vector of the O VI coronal ions that can be assimilated to the solar wind velocity field. Numerical results of the linear polarization parameters of the O VI D2 coronal line are presented. Constraints on the strength and direction of the solar wind velocity vector are obtained by comparing the numerical and the observational results of the O VI D2 coronal line polarization parameters. In conclusion, the effect of the macroscopic velocity field vector of the scattering ions (Doppler redistribution) provides a first set of results compatible with the observations. However, the inclination of the derived set of compatible field vectors, with respect to the solar vertical, is higher than expected in a coronal hole. The result will be improved by the inclusion of the magnetic field effect (Hanle effect), which will be treated in a further paper. Title: Theoretical study of the collisional depolarization and of the Hanle effect in the line Na I D2 observed on the solar limb Authors: Bommier, V.; Kerkeni, B. Bibcode: 2002sf2a.conf..125B Altcode: Observations of the Na I D lines polarization in quiet regions near the solar limb have been recently achieved, in particular with THEMIS (Bommier V., Molodij G., 2002, AandA 381, 241). These observations are in very good agreement with a theoretical model developed by Landi Degl'Innocenti (1998, Nature 392, 256, and 1999, "Solar Polarization", K.N. Nagendra and J.O. Stenflo (eds.), ASSL 243, 61). However, this model, based on the existence of atomic polarization in the line lower level, leads to the so-called "Sodium paradox": the existence of this at omic polarization is incompatible with the existence of a magnetic field stronger than 5 mG (except vertical), and also with the existence of collisional depolarization. We have investigated this last point, by using the collisional coefficients recently computed by B. Kerkeni from a quantum chemistry model. We have solved the statistical equilibrium equations for the atomic density matrix in the last scattering approximation, in order to investigate the Na I D2 line polarization formation and destruction at the solar limb. We have obtained that the atomic polarization in the lower level is completely destroyed by the collisions with neutral hydrogen at the line formation depth, which results in a "paradox in the paradox". Title: Some THEMIS-MTR observations of the second solar spectrum (2000 campaign) Authors: Bommier, V.; Molodij, G. Bibcode: 2002A&A...381..241B Altcode: We report spectropolarimetric observations with the THEMIS telescope multi-lines operating mode (MTR) during the 2000 observational period from August 27th to September 1st. We measured the resonance polarization at the limb of a series of lines: Sr I 460.7 nm, Na I D1 589.6 nm and D2 589.0 nm, Ba Ii D1 493.4 nm and D2 455.4 nm, C I 493.2 nm. The data analysis method is mainly described in Bommier & Rayrole (\cite{Bommier-Rayrole-01}), and has been completed by using the beam exchange facility as available in 2000 THEMIS, i.e., in a single Stokes parameter. A so-called ``generalized beam exchange'' technique has been settled on, for the full Stokes vector measurement under this limitation. The observations have been devoted to the measurement of the scattering polarization which is a linear polarization observed near the limb of the Quiet Sun, eventually modified by a weak magnetic field (the so-called Hanle effect). The entrance slit of the spectrograph has been oriented parallel to the tangential direction of the solar limb, and data have been averaged in time and along the spatial direction of the slit in order to increase the polarimetric resolution. Two different cameras have been used to record simultaneously the two polarization states exiting the beam-splitter. The results of our polarization measurements are in good agreement with those given in the second spectrum solar atlas of Gandorfer (\cite{Gandorfer-00}), based on 1999-2000 observations. Nevertheless, with regard to a quantification of the polarization signal, we found that the signal is systematically smaller than previous results obtained during the 1994-96 observational period and was also observed as decreasing during the 1998 observational period, as if a 11-year cyclic variation of the limb polarization occured. This signal variability obviously requires further observational and interpretative investigations. We noticed other differences to previous results, in particular, the linear polarization shape of the Na I D1 line that also requires further observational investigation. Based on observations made with THEMIS operated on the island of Tenerife by CNRS-CNR in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: Search for polarimetric sensitivity in the first observations with THEMIS spectropolarimetric mode MTR (August 1998 campaign) Authors: Bommier, V.; Rayrole, J. Bibcode: 2002A&A...381..227B Altcode: The present paper is devoted to the search for the polarimetric sensitivity level in observations of the Fe I 5576 Å line performed with the THEMIS spectropolarimetric mode MTR on August 23 1998. This line is insensitive to the Zeeman effect and the present work is thus useful to calibration purposes. The upper level of the line is unpolarizable (J=0) and insensitive to the Hanle effect, and the observations have been performed at disk center to avoid any scattering polarization of lower level atomic polarization origin. In the present paper, we describe the steps of a method that is the basis of a data reduction code implemented on systems at the Meudon Observatory for the interpretation of observations where a large number ( ~ 150) of images are averaged, and where the signal is in addition averaged along the slit. First, we describe the numerical methods used to determine the line position in the images, and to perform operations on the profiles by FFT techniques (such as translation, dilation, defocusing, apodization). Then, the preprocessing steps are described: dark current subtraction, destretching and flat-field correction. The polarization analysis is then performed, based on the idea that, as the flat-field images are unpolarized, they can be used to correct spurious polarization occuring in the observations. As a result, the observed line is found to be unpolarized, and a sensitivity of 2-4x 10-4 is found for the polarization degree in the neighboring continuum. Title: Polarization of the hydrogen Hα line in solar flares. Contribution of the local polarized radiation field and effect of the spectral index of the proton energy distribution Authors: Vogt, E.; Sahal-Bréchot, S.; Bommier, V. Bibcode: 2001A&A...374.1127V Altcode: Linear polarization of the hydrogen Hα line was observed during solar flares. The polarization vector is directed towards disk center and its degree is of the order of 5%. The best explanation for this polarization is anisotropic collisional excitation of the n = 3 level of hydrogen by vertical beams of protons with an energy greater than a few keV. However, previous calculations gave an expected polarization degree of 2.5% or less, a factor of two below the observations. In this paper, the theoretical model for the formation of the line polarization has been refined, including the effect of polarization in the local radiation field that is created by hydrogen proton anisotropic excitation. We have also increased the spectral index of the proton energy distribution from 4 to 5, giving more weight to the low energy protons which are the most efficient for impact polarization, without ionizing the atmosphere too much. It is found that the inclusion of the polarization of the local radiation field does not increase the Hα polarization very significantly; however, going from a spectral index of 4 to 5 results in an expected polarization degree of 4.5%, compatible with the observations. Title: Full-Stokes spectropolarimetry of solar prominences Authors: Paletou, F.; López Ariste, A.; Bommier, V.; Semel, M. Bibcode: 2001A&A...375L..39P Altcode: We report on first spectropolarimetric observations of solar prominences made at THEMIS. Hereafter we shall emphasis on the preliminary analysis of He I D3 full-Stokes observations. Our measurements clearly show manifestations of both the Hanle and Zeeman effects. More generally, we demonstrate the very favourable performances of the THEMIS multi-line spectropolarimetric mode for further new investigations of the magnetic field in solar prominences. Based on observations made at THEMIS, operated on the Island of Tenerife by CNRS-CNR in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Title: Partial frequency redistribution with Hanle and Zeeman effects. Non-perturbative classical theory Authors: Bommier, V.; Stenflo, J. O. Bibcode: 1999A&A...350..327B Altcode: A theory for the scattering of polarized radiation with partial frequency redistribution and coherence effects in the presence of magnetic fields of arbitrary strength and direction is developed within a classical framework. The time-dependent equation for a classical oscillator is solved. While the oscillator is being excited, it is also damped by emission of radiation and subject to phase-destroying collisions. Fourier transformation of the emitted wave train with phase-scrambling collisions leads to the partial-redistribution expressions for the relation between the polarization and frequencies of the incident and scattered radiation. While previous treatments of partial redistribution have been based on quantum perburbation theory, the classical theory has the advantage of being fully non-perturbative. It is therefore conceptually more transparent and leads itself to direct physical interpretation. The classical and quantum theories give identical results for a J=0-> 1-> 0 transition. Title: Doppler redistribution of resonance polarization of the O VI 103. 2 nm line observed above a polar hole Authors: Raouafi, N. -E.; Sahal-Bréchot, S.; Lemaire, P.; Bommier, V. Bibcode: 1999ASSL..243..349R Altcode: 1999sopo.conf..349R No abstract at ADS Title: The density matrix theory for polarized radiation redistribution: Extensions for multilevel atom model and quantum Doppler effect Authors: Bommier, V. Bibcode: 1999ASSL..243...43B Altcode: 1999sopo.conf...43B 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: Doppler redistribution of anisotropic radiation and resonance polarization in moving scattering media. I. Theory revisited in the density matrix formalism Authors: Sahal-Brechot, S.; Bommier, V.; Feautrier, N. Bibcode: 1998A&A...340..579S Altcode: Under the light of recent developments of the theory of matter-radiation interaction in the presence of magnetic field applied to non-LTE spectropolarimetry in astrophysics, we have revisited the theory of anisotropic resonance line scattering in moving media by means of the density-matrix formulation. This has led us to present a theoretical method of determination of the matter velocity field vector in the solar wind acceleration region. The example of the O Vi 103.2 nm line has been chosen for putting this theory into operation. It has been observed by the ultraviolet spectrograph \textsc{Sumer} of \textsc{Soho} in different regions of the solar wind acceleration region; it is partially formed by resonance scattering of the incident underlying transition region radiation which competes (and can predominate) with electron collisional excitation at the low densities which prevail at these high altitudes. The theory which is developed hereafter not only shows that this line is shifted and its intensity dimmed by the Doppler effect, due to the matter velocity field of the solar wind, but also predicts that it is linearly polarized, owing to the anisotropy of the incident radiation field; its two linear polarization parameters, degree and direction of polarization, are sensitive to the matter velocity field vector. Our results show that the interpretation of polarimetric data, associated to the shift and the Doppler-dimming effect, may offer a method of diagnostic of the complete velocity field vector, provided that the partial anisotropy of the incident radiation field be taken into account. In fact such a diagnostic is currently missing. Yet its interest is crucial to understand various problems in astrophysics, such as stellar winds, and especially the acceleration mechanisms of the solar wind. It is also essential for a dynamical modelling of solar structures. Title: Global Pattern of the Magnetic Field Vectors Above Neutral Lines from 1974 to 1982: Pic-du-Midi Observations of Prominences Authors: Bommier, V.; Leroy, J. L. Bibcode: 1998ASPC..150..434B Altcode: 1998npsp.conf..434B; 1998IAUCo.167..434B No abstract at ADS Title: Master equation theory applied to the redistribution of polarized radiation, in the weak radiation field limit. II. Arbitrary magnetic field case Authors: Bommier, V. Bibcode: 1997A&A...328..726B Altcode: This paper addresses the problem of partial redistribution of polarized radiation in the presence of a magnetic field of arbitrary strength. It is the continuation of a previous paper (\cite{Paper I}) devoted to the same problem, treated in the simpler case of vanishing magnetic field. In the present paper, we give the results of the derivation of the master equation for the atomic density matrix, and of the coefficients of the radiative transfer equation, following the method described in \cite{Paper I} (which makes use of the summation of the perturbation series development for the atom-radiation interaction), now applied to the case of a non-zero magnetic field of arbitrary strength. The other hypotheses underlying the derivation of \cite{Paper I} are maintained in the present paper, namely: (a) weak radiation field (stimulated emission is neglected with respect to spontaneous emission); (b) 2-level atom; (c) unpolarized lower level. The redistribution matrix, that relates the frequency, polarization and direction of the incident photon to those of the scattered photon, is derived in the presence of a magnetic field of arbitrary strength. 3 successive levels of approximation are proposed, in the case of a weak magnetic field, in order to derive simpler expressions for the redistribution matrix that might conveniently be used in radiative transfer calculations. Title: Master equation theory applied to the redistribution of polarized radiation, in the weak radiation field limit. I. Zero magnetic field case Authors: Bommier, V. Bibcode: 1997A&A...328..706B Altcode: This paper is devoted to describe the atom-radiation interaction in the formalism of non-relativistic quantum electrodynamics by means of a perturbative development extended to orders higher than 2. Atom and radiation are treated quantum mechanically, through the density matrix approach. Collision effects are also introduced, in the impact approximation. Polarization is taken into account. The following hypotheses are considered: (a) weak radiation field (stimulated emission is neglected with respect to spontaneous emission); (b) two-level atom; (c) unpolarized lower level; (d) atomic reference frame; (e) zero magnetic field. The perturbation series development has been summed. The result of the paper is twofold: (a) the profiles in the form of delta -functions obtained in ordinary theories extended up to order 2 in the series development are now replaced by realistic profiles: line-broadening is derived from the present formalism; (b) a new term (Rayleigh scattering term) appears at order 4 in the emissivity. This term is responsible for frequency coherence in scattering processes. Title: A Complex Diagnostic of Solar Prominences Authors: Heinzel, P.; Bommier, V.; Vial, J. C. Bibcode: 1996SoPh..164..211H Altcode: We use the polarimetric and intensity measurements of Hα and HeI D3 lines in solar prominences to derive the true geometrical thickness for several quiescent prominences. The electron densities, derived from the collisional depolarization in Hα by Bommier et al. (1994), are used to evaluate the thickness from the emission measure. The emission measure was obtained from the theoretical correlation with the Hα integrated intensity, according to Gouttebroze, Heinzel, and Vial (1993). Theoretical electron densities obtained by latter authors are also compared with those of Bommier et al. (1994) and we find a very good agreement between them. The prominence geometrical thickness exhibits a relatively large range of values from about 100 km up to a few 104 km. The plasma densities vary by almost two orders of magnitude in the observed structures, but the total column mass in the direction perpendicular to the prominence sheet seems to be fairly constant for the set of prominences studied. Title: Non-LTE Polarized Radiative Transfer in Intermediate Magnetic Fields: Numerical Problems and Results Authors: Bommier, V.; Landi Degl'Innocenti, E. Bibcode: 1996SoPh..164..117B Altcode: This paper presents some numerical results relative to a solution, based on the density matrix formalism, of the non-LTE, polarized radiative transfer problem for a two-level atom. The results concern the atomic upper level population and alignment, and the emergent radiation Stokes profiles, for a plane-parallel, static, isothermal atmosphere embedded in a magnetic field of intermediate strength, such that the Zeeman splitting has to be taken into account in the line profile. Zeeman coherences are neglected, whereas magneto-optical effects are taken into account, resulting in a full 4×4 absorption matrix. Induced emission is neglected and complete frequency redistribution, in the rest and laboratory frames, is assumed. Pure Doppler absorption profile (gaussian shape) has also been assumed. The presentation of the results is preceded by a brief discussion of their accuracy and of the numerical difficulties that were met in the solution of the problem. Title: Atomic Coherences and Level-Crossings Physics Authors: Bommier, Véronique Bibcode: 1996SoPh..164...29B Altcode: A synthesis work about the interaction of matter with polarized radiation, applied to solar magnetic field diagnostics, has recently been done by Stenflo (1994). This synthesis uses the classical theory of matter-radiation interaction - supplemented by the theory of partial redistribution of Omont, Smith, and Cooper (1972), on the one hand, and full quantum matter-radiation interaction theory, unable to take into account the partial frequency redistribution effects, on the other hand. The need of a full quantum approach taking into account the partial frequency redistribution effects appears as a unifying purpose; the present work, using the density matrix formalism, is a first attempt in this direction. Title: Complete determination of the magnetic field vector and of the electron density in 14 prominences from linear polarizaton measurements in the HeI D3 and Hα lines Authors: Bommier, Veronique; Landi Degl'Innocenti, Egidio; Leroy, Jean-Louis; Sahal-Brechot, Sylvie Bibcode: 1994SoPh..154..231B Altcode: The present paper is devoted to the interpretation of linear polarization data obtained in 14 quiescent prominences with the Pic-du-Midi coronagraph-polarimeter by J. L. Leroy, in the two lines HeI D3 andHα quasi-simultaneously. The linear polarization of the lines is due to scattering of the anisotropic photospheric radiation, modified by the Hanle effect due to the local magnetic field. The interpretation of the polarization data in the two lines is able to provide the 3 components of the magnetic field vector, and one extra parameter, namely the electron density, because the linear polarization of Hα is also sensitive to the depolarizing effect of collisions with the electrons and protons of the medium. Moreover, by using two lines with different optical thicknesses, namely HeI D3, which is optically thin, and Hα, which is optically thick (τ = 1), it is possible to solve the fundamental ambiguity, each line providing two field vector solutions that are symmetrical in direction with respect to the line of sight in the case of the optically thin line, and which have a different symmetry in the case of the optically thick line. Title: Resonance line polarization for arbitrary magnetic fields in optically thick media. III. A generalization of the ɛ^1/2^-law. Authors: Landi Degl'Innocenti, E.; Bommier, V. Bibcode: 1994A&A...284..865L Altcode: The well-known "ɛ^1/2^-law" - one of the few exact analytical results in the theory of radiative transfer - is generalized to the case of an isothermnal, plane-parallel atmosphere in the presence of a magnetic field vector of arbitrary intensity and direction and in the presence of depolarizing collisions. A compact expression is found, relating the squares of the surface value of the upper level components of the atomic density matrix in the representation of the irreducible spherical tensors to the value of the constant Planck function. By taking the appropriate limits, the usual ɛ^1/2^-law for unpolarized radiation, and its generalization to resonance scattering polarization in a non-magnetic atmosphere (Ivanov 1990), are recovered as particular cases. Title: A Spectroscopic Method for the Solution of the 180 degrees Azimuth Ambiguity in Magnetograms Authors: Landi Degl'Innocenti, Egidio; Bommier, Veronique Bibcode: 1993ApJ...411L..49L Altcode: A spectroscopic method is proposed for removing the azimuth ambiguity intrinsically present in vector magnetograms. The method is based on the idea that the polarization observed in resonance lines (typically formed at the chromospheric level) depends not only on the magnetic field vector, but also on the anisotropy of the radiation field that is illuminating the scattering atoms. An observational scheme is proposed. Title: Stokes parameters of the O VI 103.2 nm line as a probe of the matter velocity field vector in the solar wind acceleration region. Authors: Sahal-Brechot, S.; Feautrier, N.; Bommier, V.; Dekertanguy, A. Bibcode: 1992ESASP.344...81S Altcode: 1992spai.rept...81S The authors present a theoretical method of determination of the matter velocity field vector in the solar wind acceleration region that they have currently developed. The O VI 103.2 nm line should be observed high in the corona in the solar wind acceleration region; it would be formed by resonance scattering of the incident underlying transition region radiation which competes (and can predominate) with electron collisional excitation at these low densities which prevail at these high altitudes. This line will not only be shifted and its intensity dimmed by the Doppler effect but it will be also linearly polarized, owing to the anisotropy of the incident radiation field; its two polarization parameters, degree and direction of polarization, should be sensitive to the matter velocity field vector. Preliminary results show that the interpretation of polarimetric data, associated to the shift and the Dopplerdimming effect, provided that the partial anisotropy of the incident radiation field be taken into account, should offer a method of diagnostic of the complete velocity field vector. Title: Derivation of the master equation for the atomic density matrix for line polarization studies in the presence of magnetic field and depolarizing collisions in astrophysics. Authors: Bommier, V.; Sahal-Bréchot, S. Bibcode: 1991AnPh...16..555B Altcode: The authors derive in a coherent manner the master equation for the density matrix of an atom interacting with a bath of perturbers and photons, in the presence of a weak magnetic field. This paper has been inspired by astrophysical purposes: the interpretation of line polarization induced by anisotropic excitation of the levels, eventually modified by the local magnetic field (the Hanle effect); the polarization can be due to scattering of the incident anisotropic radiation, as in solar prominences, or to impact polarization, as in solar flares. The physical conditions are then those of numerous astrophysical media: any directions of polarization and magnetic field, two-level atom approximation not valid, weak radiation field, weak density of perturbers. The master equation for the atomic density matrix has been derived in the framework of the impact approximation. Title: Derivation of the radiative transfer equation for line polarization studies in the presence of magnetic field in astrophysics. Authors: Bommier, V. Bibcode: 1991AnPh...16..599B Altcode: In the preceding paper (063.110), the master equation for the atomic density matrix has been derived in the framework of the impact approximation. In the present paper, the author obtains the spontaneous emission 4-vector and absorption and stimulated emission 4×4 matrices entering the transfer equation for polarized radiation, as functions of the absorbed and emitted radiation polarization tensors, themselves functions of the Zeeman coherences of the atomic density matrix. Line profiles have been ignored. Title: Stark broadening of spectral lines of multicharged ions of astrophysical interest. I - C IV lines. II - SI IV lines Authors: Dimitrijevic, M. S.; Sahal-Brechot, S.; Bommier, V. Bibcode: 1991A&AS...89..581D Altcode: Results are presented on calculations of the electron-, proton-, and ionized helium-impact line widths and shifts for 31 C IV multiplets and 40 Si IV multiplets. These data are compared with observations and are used to investigate the Stark broadening parameter regularities within the spectral series. For both the C IV and Si IV multiplets, a gradual change of the Stark widths was obtained. The reason for this is discussed. Title: Stark broadening parameter tables for spectral lines of multicharged ions of astrophysical interest. II. Si IV lines. Authors: Dimitrijević, M. S.; Sahal-Bréchot, S.; Bommier, V. Bibcode: 1991BOBeo.144...81D Altcode: Using a semiclassical approach, the authors have calculated electron-, proton-, and ionized helium-impact line widths and shifts for 39 Si IV multiplets as a function of temperature for perturber densities 1015cm-3 and 1018- 1821cm-3. Title: Stark broadening parameter tables for spectral lines of multicharged ions of astrophysical interest. I: C IV lines. Authors: Dimitrijević, M. S.; Sahal-Bréchot, S.; Bommier, V. Bibcode: 1991BOBeo.144...65D Altcode: Using a semiclassical approach, the authors have calculated electron-, proton-, and ionized helium-impact line widths and shifts for 39 C IV multiplets as a function of temperature for perturber densities 1015cm-3 and 1018- 1821cm-3. Title: Stark Broadening of Spectral Lines of Multicharged Ions of Astrophysical Interest - Part Two - Si IV Lines Authors: Dimitrijevic, M. S.; Sahal-Brechot, S.; Bommier, V. Bibcode: 1991A&AS...89..591D Altcode: Using a semi-classical approach, we have calculated electron-, proton-, and ionized helium-impact line widths and shifts for 40 Si IV multiplets. The comprehensive set of obtained data has also been used for investigation of Stark broadening parameter regularities within spectral series. Title: Resonance line polarization and the Hanle effect in optically thick media. II - Case of a plane-parallel atmosphere Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1991A&A...244..383B Altcode: The results of computations of resonance polarization and the Hanle effect (weak magnetic field) for a two-level atom in a plane-parallel optically thick atmosphere and numerical methods for solving them are presented. The findings are compared with results yielded by other methods, of the differential method type, in zero magnetic field and under the hypothesis of complete frequency redistribution, and a good agreement is obtained. The novel computation method, called the 'global' method, is applied to test the validity of the results obtained by the iterative method. The result of the computations are finally presented in the form of Hanle diagrams for some magnetic field and line-of-sight geometries. Title: Resonance line polarization for arbitrary magnetic fields in optically thick media. I - Basic formalism for a 3-dimensional medium. Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1991A&A...244..391L Altcode: We present in this paper a general formalism to describe resonance line polarization for a two-level atom in an optically thick three-dimensional medium embedded in a magnetic field of arbitrary strength and irradiated by an arbitrary radiation field. The results contained in the present paper generalize those derived in a previous paper (Landi Degl'Innocenti et al. 1990) that were restricted to weak magnetic fields (νL ≪ ΔνD, with νL the Larmor frequency and ΔνD the Doppler broadening of the line). Here the restriction νL ≪ ΔνD is released, which makes the present formulation capable of describing, in a unified framework, resonance polarization, the Hanle effect and the Zeeman effect. Analogously to our previous paper, neglecting atomic polarization in the lower level and stimulated emission, we derive an integral equation for the multipole moments of the density matrix of the upper level by coupling the statistical equilibrium equations for the density matrix with the radiative transfer equations for polarized radiation. The final equation accounts for the effect of the magnetic field and for the role of inelastic and elastic (or depolarizing) collisions. Obviously, in the limiting case of weak magnetic fields (νL ≪ ΔνD), the results of our previous paper are recovered. Title: Resonance Line Polarization for Arbitrary Magnetic Fields in Optically Thick Media - Part Two - Case of a Plane-Parallel Atmosphere and Absence of Zeeman Coherences Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1991A&A...244..401L Altcode: The general problem of resonance scattering for a two-level atom in a magnetized plane-parallel atmosphere is formulated by using the irreducible tensor representation of the atomic density matrix. A more general formalism presented in a previous paper (Paper I), convenient for taking into account arbitrary magnetic field effects (Zeeman effect as well as Hanle effect), is particularized in the present paper to the case of a "strong" magnetic field (Zeeman splitting much larger than the natural width of the upper level), and to the case of a unidimensional medium. A system of coupled integral equations, relating the density matrix elements at different depths in the atmosphere, is derived, and the properties of the relative kernels are discussed. It is shown that, in the limiting case of weak magnetic fields (VL ≪ ΔνD), the presence of atomic polarization induces a breakdown in the usual formula V(ν) = -gνL(dI/dν), that is commonly used for measuring magnetic fields from magnetograph-type observations. Title: Diagnostic of the magnetic field vector using the atomic density matrix formalism. Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Bréchot, S. Bibcode: 1991sopo.work..434B Altcode: The authors present the work which has been done and which is being done using the atomic density matrix formalism, for the interpretation of linear polarization measurements, leading to the magnetic field diagnostic in astrophysical media. This formalism has been used for interpreting polarization data from solar prominences, leading to original results on the prominence magnetic field obtained through the Hanle effect. An attempt is made to solve the coupled problem of polarized radiative transfer and statistical equilibrium in the case of weak, intermediate and strong magnetic fields, using a method of the integral method type; the advantages of this method, with respect to other methods, of the differential method type, are briefly discussed. Title: Resonance line polarization and the Hanle effect in optically thick media. Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1990A&A...235..459L Altcode: A general formalism is presented to describe resonance line polarization for a two-level atom in an optically thick, three-dimensional medium embedded in an arbitrary varying magnetic field and irradiated by an arbitrary radiation field. The magnetic field is supposed sufficiently small to induce a Zeeman splitting much smaller than the typical line width. By neglecting atomic polarization in the lower level and stimulated emission, an integral equation is derived for the multipole moments of the density matrix of the upper level. This equation shows how the multipole moments at any assigned point of the medium are coupled to the multipole moments relative at a different point as a consequence of the propagation of polarized radiation between the two points. The equation also accounts for the effect of the magnetic field, described by a kernel locally connecting multipole moments of the same rank, and for the role of inelastic and elastic (or depolarizing) collisions. After having given its formal derivation for the general case, the integral equation is particularized to the one-dimensional and two-dimensional cases. For the one-dimensional case of a plane parallel atmosphere, neglecting both the magnetic field and depolarizing collisions, the equation here derived reduces to a previous one given by Rees (1978). Title: Linear polarization of the hydrogen H-alpha line in filaments. I - Theoretical investigation Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1989A&A...211..230B Altcode: Results are presented of theoretical calculations of the expected linear polarization in H-alpha from a filament observed at different positions over the solar disk. The geometry of the filament is represented by an infinite cylinder with an elliptical cross section, standing horizontally over the solar surface. The calculation results indicate a clear effect of a magnetic field; it was found that the polarization degrees in the presence of a magnetic field can reach values of the order of 2 percent. In addition, there was an optical thickness effect on the polarization degree and direction. These results suggest that it is possible to use the observations of the H-alpha line from filaments to determine the magnetic field vector. Title: Linear Polarization of Hydrogen H-alpha Line in Filaments: Method and Results of Computation Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1989HvaOB..13..339B Altcode: No abstract at ADS Title: Linear polarization of hydrogen Balmer lines in optically thick prominences: theoretical investigation. Authors: Bommier, V.; Landi Degl'Innocenti, E.; Sahal-Bréchot, S. Bibcode: 1988dssp.conf...41B Altcode: The expected linear polarization in Hα for a filament observed at different positions over the solar disk is investigated from a theoretical point of view. The filament is schematized as an infinite cylinder with an elliptical cross-section standing horizontally on the solar surface. The emerging linear polarization is calculated according to a perturbative scheme introduced in a preceding paper (Landi Degl'Innocenti et al., 1987). The role of depolarizing collisions and the influence of local magnetic fields (Hanle effect) is fully accounted for. Typical results are presented for the expected Hα polarization across filaments observed at various positions and skew angles over the solar disk. Title: Linear polarization of hydrogen Balmer lines in optically thick quiescent prominences Authors: Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1987A&A...186..335L Altcode: The linear polarization of H-alpha and H-beta in quiescent prominences having a nonnegligible optical thickness in H-alpha is theoretically deduced, starting from a zero-order self-consistent model obtained by solving the conventional non-LTE problem in prominences. The results show that the fractional linear polarization in zero magnetic field decreases with increasing optical thickness of the prominence and is rotated a small angle with respect to the solar limb when the prominence is seen at a sharp angle with respect to its plane. They also show that the polarization diagrams have a less symmetrical shape with respect to the analogous diagrams obtained for the limiting case of negligible optical thickness. Title: Linear Polarization of Hydrogen Balmer Lines in Optically Thick Prominences - Theoretical Investigation Authors: Bommier, V.; Landi degl'Innocenti, E.; Sahal-Brechot, S. Bibcode: 1987dssp.work...41B Altcode: 1987ASSL..150...41B No abstract at ADS Title: Magnetic field vector and electron density diagnostics from linear polarization measurements in 14 solar prominences. Authors: Bommier, V. Bibcode: 1986NASCP2442..209B Altcode: 1986copp.nasa..209B The Hanle effect is the modification of the linear polarization parameters of a spectral line due to the effect of the magnetic field. It has been successfully applied to the magnetic field vector diagnostic in solar prominences. The magnetic field vector is determined by comparing the measured polarization to the polarization computed, taking into account all the polarizing and depolarizing processes in line formation and the depolarizing effect of the magnetic field. The method was applied to simultaneous polarization measurements in the Helium D3 line and in the hydrogen beta line in 14 prominences. Four polarization parameters are measured, which lead to the determination of the three coordinates of the magnetic field vector and the electron density, owing to the sensitivity of the hydrogen beta line to the non-negligible effect of depolarizing collisions with electrons and protons of the medium. A mean value of 1.3 x 10 to the 10th power cu. cm. is derived in 14 prominences. Title: The polarization of the O VI 1032 Å line as a probe for measuringthe coronal vector magnetic field via the Hanle effect. Authors: Sahal-Brechot, S.; Malinovsky, M.; Bommier, V. Bibcode: 1986A&A...168..284S Altcode: Recent works have shown the possibility of detecting resonance lines of moderately ionized lithium-like ions (especially O VI 1032 Å) of the chromosphere-corona transition region at high altitudes in the solar corona (up to several solar radii). Since these lines would be partially formed by resonance scattering of the anisotropic underlying transition region radiation field, they are expected to be partially linearly polarized; moreover this polarization should be modified by the local magnetic field (e.g. the Hanle effect). The aim of the present paper is to calculate the expected linear polarization and its modification by the coronal local magnetic field and to provide analytical formulae, in order to investigate the possibility of measuring coronal vector magnetic fields via the interpretation of the Hanle effect. Title: The Linear Polarization of Hydrogen H-Beta Radiation and the Joint Diagnostic of Magnetic Field Vector and Electron Density in Quiescent Prominences - Part Two - the Electron Density Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S. Bibcode: 1986A&A...156...90B Altcode: Fourteen quiescent prominences of considerable height over the Solar surface have been observed simultaneously in the helium D3 and hydrogen Hβ lines: the linear polarization measurements which have been performed at the Pic-du-Midi Observatory have been interpreted by means of the Hanle effect theory (modification of polarization by the local magnetic field) and of the collisional depolarization theory. The present paper is devoted to the analysis of the results concerning the electron density Ne which have been obtained by this new method of diagnostic. Firstly, a straightforward interpretation of the measurements made by using the Hβ line polarization only has provided an upper limit for Ne, which remains lower than 7 1010 cm-3 in all cases. Secondly, by taking into account both the Hanle effect and the depolarization by collisions with the electrons and the protons of the medium, the actual electron density has been derived: it neighbours 1 1010 cm-3. As physically expected, Ne decreases with increasing height in prominences. Finally, our results have been compared to those obtained quite recently by different methods, which shows an evident tendency for Ne to get higher values in brighter prominences. Title: The linear polarization of hydrogen H-beta radiation and the joint diagnostic of magnetic field vector and electron density in quiescent prominences. I - The magnetic field. II - The electron density Authors: Bommier, V.; Sahal-Brechot, S.; Leroy, J. L. Bibcode: 1986A&A...156...79B Altcode: Quasi-simultaneous measurements of the linear polarization of the helium D3 and hydrogen Hβ lines have been achieved at the Pic-du-Midi coronagraph-polarimeter for fourteen quiescent prominences. Both lines are linearly polarized by resonant scattering of the anisotropic photospheric and chromospheric radiation field, and depolarized by the local magnetic field (i.e. the Hanle effect). The measurements show that another depolarizing mechanism has to be taken into account for the Hβ line: this is confirmed by the theory which predicts that Hβ is also depolarized by collisions with the electrons and protons of the medium. Therefore polarization measurements in those two lines provide a method for determining both the magnetic field B and the electron density Ne in prominences. Title: Effect of polarized radiative transfer on the Hanle magnetic field determination in prominences: Analysis of hydrogen H alpha line observations at Pic-du-Midi Authors: Bommier, V.; Landi Degl'Innocenti, E.; Leroy, J. L.; Sahal-Brechot, S. Bibcode: 1985svmf.nasa..335B Altcode: The linear polarization of the Hydrogen H alpha line of prominences has been computed, taking into account the effect of a magnetic field (Hanle effect), of the radiative transfer in the prominence, and of the depolarization due to collisions with the surrounding electrons and protons. The corresponding formalisms are developed in a forthcoming series of papers. In this paper, the main features of the computation method are summarized. The results of computation have been used for interpretation in terms of magnetic field vector measurements from H alpha polarimetric observations in prominences performed at Pic-du-Midi coronagraph-polarimeter. Simultaneous observations in one optically thin line (He I D(3)) and one optically thick line (H alpha) give an opportunity for solving the ambiguity on the field vector determination. Title: Magnetic field-vector measurements in quiescent prominences via the Hanle effect: Analysis of prominences observed at Pic-du-Midi and at Sacramento Peak Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S. Bibcode: 1985svmf.nasa..375B Altcode: The Hanle effect method for magnetic field vector diagnostics has now provided results on the magnetic field strength and direction in quiescent prominences, from linear polarization measurements in the He I E3 line, performed at the Pic-du-Midi and at Sacramento Peak. However, there is an inescapable ambiguity in the field vector determination: each polarization measurement provides two field vector solutions symmetrical with respect to the line-of-sight. A statistical analysis capable of solving this ambiguity was applied to the large sample of prominences observed at the Pic-du-Midi (Leroy, et al., 1984); the same method of analysis applied to the prominences observed at Sacramento Peak (Athay, et al., 1983) provides results in agreement on the most probable magnetic structure of prominences; these results are detailed. The statistical results were confirmed on favorable individual cases: for 15 prominences observed at Pic-du-Midi, the two-field vectors are pointing on the same side of the prominence, and the alpha angles are large enough with respect to the measurements and interpretation inaccuracies, so that the field polarity is derived without any ambiguity. Title: Vector Magnetic Fields in Prominences - Part Two Hei d3 Stokes Profiles Analysis for Two Quiescent Prominences Authors: Querfeld, C. W.; Smartt, R. N.; Bommier, V.; Landi Degl'Innocenti, E.; House, L. L. Bibcode: 1985SoPh...96..277Q Altcode: The Stokes components of He I D3 emission in two quiescent prominences, using full spectral profile measurements, are analyzed to derive vector magnetic fields. Two independently developed schemes, based on the Hanle effect, are used for interpretation. They involve solutions of the statistical equilibrium equations for the He I D3 multiplet, including the effect of coherency and full level crossing, which predict the magnetic field dependence of the observed polarization. Derived magnetic field vector solutions for each pair of linear polarization Stokes profiles corresponding to an observational point in the prominence are, intrinsically, not uniquely determined, and a set of possible solutions is usually obtained. However, mutual consistency of these solutions with those independently predicted by the form of the circular polarized component, allow, in almost all cases, rejection of all solutions of a set except one symmetrical pair. Of such a pair, a unique solution can be determined with a high confidence level by reference to independent potential field information. Field vectors are found usually to be close to horizontal and normal to the prominence surface, but extreme exceptions are found. Field values range from 6 G to 60 G. The derived vectorfield configurations and their magnitudes are briefly discussed relative to these prominences and to different quiescent prominence models. Title: Effect of polarized radiative transfer on the Hanle magnetic field determination in prominences: analysis of hydrogen Hα line obervations at Pic-du-Midi. Authors: Bommier, V.; Landi Degl'Innocenti, E.; Leroy, J. L.; Sahal-Bréchot, S. Bibcode: 1985NASCP2374..335B Altcode: The linear polarization of the hydrogen Hα line of prominences has been computed, taking into account the effect of a magnetic field (Hanle effect), of the radiative transfer in the prominence, and of the depolarization due to collisions with the surrounding electrons and protons. In this paper, the main features of the computation method are summarized. The results of computation have been used for interpretation in terms of magnetic field vector measurements from Hα polarimetric observations in prominences performed at Pic-du-Midi coronagraph-polarimeter (Leroy, 1981). Simultaneous observations in one optically thin line (He I D3) and one optically thick line (Hα) give an opportunity for solving the ambiguity on the field vector determination. Title: Magnetic field-vector measurements in quiescent prominences via the Hanle effect: analysis of prominences observed at Pic-du-Midi and at Sacramento Peak. Authors: Bommier, V.; Leroy, J. L.; Sahal-Bréchot, S. Bibcode: 1985NASCP2374..375B Altcode: No abstract at ADS Title: New data on the magnetic structure of quiescent prominences Authors: Leroy, J. L.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1984A&A...131...33L Altcode: Hanle-effect vector-magnetic-field measurements in the unresolved 5876-A D3 line of He and simultaneous H-alpha or H-beta polarization measurements obtained with the coronagraph polarimeter at Observatoire du Pic du Midi during 1974-1982 are reported for 256 solar prominences of medium and low latitude. The data are presented in graphs, tables, diagrams, and photographs and analyzed statistically to resolve the twofold ambiguity inherent in magnetic/polarimetric measurements of this type. Prominences with maximum heights lower than 30,000 km are found to have field-vector angles (alpha) about 20 deg and fields of about 20 G; those above 30,000 km have alpha 25 deg and fields 5-10 G; the structures correspond to the models proposed by Kippenhahn and Schlueter (1957) and by Kuperus and Raadu (1974), respectively. Title: Vector Magnetic Field Measurements in Quiescent Prominences via the Hanle Effect - Analysis of Prominences Observed at the Pic-Du and at Sacramento-Peak Authors: Bommier, V.; Leroy, J. L.; Sahal-Brechot, S. Bibcode: 1984apoa.conf...58B Altcode: No abstract at ADS Title: Vector Magnetic Fields in Prominences - Part Three - Hei d3 Stokes Profile Analysis for Quiescent and Eruptive Prominences Authors: Athay, R. G.; Querfeld, C. W.; Smartt, R. N.; Landi Degl'Innocenti, E.; Bommier, V. Bibcode: 1983SoPh...89....3A Altcode: Observations of linear polarization in two resolved components of HeI D3 are interpreted using the Hanle effect to determine vector magnetic fields in thirteen prominences. As in all vector magnetic field measurements, there is a two-fold ambiguity in field direction that is symmetric to a 180° rotation about the line-of-sight. The polar angles of the fields show a pronounced preference to be close to 90° from the local solar radius, i.e., the field direction is close to horizontal. Azimuth angles show internal consistency from point to point in a given prominences, but because of the rotational symmetry, the fields may be interpreted, in most cases, as crossing the prominence either in the same sense as the underlying photospheric fields or in the opposite sense. Title: The Magnetic Field in the Prominences of the Polar Crown Authors: Leroy, J. L.; Bommier, V.; Sahal-Brechot, S. Bibcode: 1983SoPh...83..135L Altcode: The Hanle effect method has been applied to the determination of the magnetic field in 120 prominences of the polar crown observed during the 1974-1980 period, which is the ascending phase of cycle XXI. The average field strength which was about 6 G at the beginning of the cycle reached twice this value just before the maximum. There is also a clear trend for a increase of the prominence field with the altitude. We confirm the fact that the magnetic vector makes a small angle (25 °) with the long axis of the prominence. As to the field orientation, we show that the most striking feature lies in the regular pattern of the component which is parallel to the axis of the filament; its direction seems to depend closely on the polarities of the high latitude photospheric field. Title: The Hanle Effect of the Coronal L-Alpha Line of Hydrogen - Theoretical Investigation Authors: Bommier, V.; Sahal-Brechot, S. Bibcode: 1982SoPh...78..157B Altcode: This paper is devoted to a computation of the effect of a magnetic field on the linear polarization of the coronal Lα line of hydrogen. Recent works (Gabriel et al., 1971) have shown that the linear polarization of this line is due to resonant scattering of the incident chromospheric Lα line. The Hanle effect is the modification of this linear polarization, due to the magnetic field. After having briefly recalled the main features of this effect and the conditions of the coronal Lα line formation, we present the theoretical formalism to be used for Hanle effect computations. The effect of the hyperfine structure of the line is included. Then the results of our computations are given in terms of linear polarization as a function of the magnetic field. We get that the effect of the hyperfine structure on these results is negligible, although this is not evident a priori. When the hyperfine structure is neglected, the line structure is simplified and the Hanle effect can be expressed with analytical formulae, which we give in the last part of this paper. After integration along the line of sight, these formulae could be used for magnetic field determination in the solar corona from measurements of the linear polarization of the Lα line. Title: Determination of the complete vector magnetic field in solar prominences, using the Hanle effect Authors: Bommier, V.; Sahal-Brechot, S.; Leroy, J. L. Bibcode: 1981A&A...100..231B Altcode: Various methods which are liable to provide the three components of the prominence magnetic field are investigated. It is noted that the methods consist in adding information supplementary to that which results from the Hanle effect analysis of linear polarization measurements of an emission line. This supplementary information can be (1) the linear polarization measurements of another line (which is thought to be the most reliable method), (2) the projection of the field direction onto the plane of the sky; or (3) the longitudinal field derived from Zeeman effect measurements. It is noted that all these methods lead to two magnetic field solutions. The way in which the varying scattering geometry due to the sun's rotation makes it possible to choose between them is described. Title: Quiescent Prominence Vector Magnetic Fields Inferred from He I D3 Polarization Authors: Querfeld, C. W.; Smartt, R. N.; Bommier, V.; Landi Degl'Innocenti, E. Bibcode: 1980BAAS...12..792Q Altcode: No abstract at ADS Title: Vector Magnetic Fields Inferred from He I D3 Polarization in the August 5, 1980 Eruptive Prominence Authors: Querfeld, C. W.; Smartt, R. N.; Bommier, V.; Landi Degl'Innocenti, E. Bibcode: 1980BAAS...12..913Q Altcode: No abstract at ADS Title: Quantum theory of the Hanle effect. II - Effect of level-crossings and anti-level-crossings on the polarization of the D3 helium line of solar prominences Authors: Bommier, V. Bibcode: 1980A&A....87..109B Altcode: In this paper, we present a generalization of the quantum formalism of the Hanle effect, including the case of level-crossings and anti-level-crossings of the Zeeman sublevels. The transition from the Zeeman effect to the Paschen-Back effect, which gives rise to the anti-level-crossings, is explicitly taken into account. As an application the calculation of the linear polarization parameters of the Helium D3 line of solar quiescent prominences, in the presence of a stationary magnetic field, has been performed. The results are reported and the effect of the level-crossings is discussed. These results extend our previous calculations which were valid only for weak magnetic fields (B < 10 G) because both the level-crossing and anti-level-crossing effects were neglected. Title: The Hanle Effect and the Determination of Magnetic Fields. Authors: Bommier, V.; Sahal-Brechot, S. Bibcode: 1979phsp.coll...87B Altcode: 1979IAUCo..44...87B; 1979phsp.conf...87B The determination of prominence magnetic fields by interpreting the two measured parameters that describe the linear polarization of spectral lines (the Hanle method) is discussed. The possibility of determining the three components of a prominence magnetic field by using simultaneous observations in two different lines is considered. Limitations on the Hanle method are summarized. It is shown that a complete determination of a prominence magnetic field may be possible with the Hanle method by observing the prominence of interest during rotation of the sun. Title: Theory of the Hanle Effect; Application to the Linear Polarization of the Helium Lines in Solar Prominences. Authors: Bommier, V. Bibcode: 1979phsp.coll...93B Altcode: 1979IAUCo..44...93B; 1979phsp.conf...93B No abstract at ADS Title: Quantum theory of the Hanle effect: calculations of the Stokes parameters of the D3 helium line for quiescent prominences. Authors: Bommier, V.; Sahal-Brechot, S. Bibcode: 1978A&A....69...57B Altcode: A formalism of the quantum theory of the Hanle effect is developed to obtain the Stokes parameters of the D3 line in quiescent prominences in the presence of a stationary magnetic field. The aim is to develop a method that can be used to determine the vector magnetic field in prominences. The quantum description of an ensemble of atoms or photons in terms of a density matrix is briefly recalled, and the evolution of the time-dependent density matrix of the atom is treated by means of a master equation in which the interaction between the scattering atom, the incident photons, and the magnetic field appears. The approximations leading to the master equation are discussed. The expression for the density matrix of the reemitted photons is given as a function of the atomic density matrix calculated for the steady state. The formalism has been used for explicit calculations of the D3 polarization in an earlier paper by Sahal-Brechot et al. (1977). Title: The Hanle effect and the determination of magnetic fields in solar prominences. Authors: Sahal-Brechot, S.; Bommier, V.; Leroy, J. L. Bibcode: 1977A&A....59..223S Altcode: The object of this paper is to investigate whether the determination of magnetic fields based on the interpretation of the linear polarization modified by the Hanle effect of the He I D3 line in quiescent prominences can be accurate and safe enough. It is shown that the observed depolarization and rotation of the vector polarization result only from magnetic effects. An account of the quantum theory used (a more detailed account will be published separately) for the calculations is given. The interpretation of the attached theoretical polarization diagrams, their use for the determination of magnetic fields, the limitations of the theory and the accuracy of the results are discussed. From this it can be concluded that the present method is very promising, especially for the weak magnetic fields (1-15 Gauss) which are typical of most quiescent prominences. Title: The polarization of the D3 emission line in prominences. Authors: Leroy, J. L.; Ratier, G.; Bommier, V. Bibcode: 1977A&A....54..811L Altcode: Over 1,000 polarization measurements pertaining to about 90 distinct solar prominences were taken on the D 3 triplet lines of helium at 5876 A. Most of the measurements were made on quiescent prominences at the polar latitude. A typical D 3 polarization measurement in a quiescent prominence yields a degree of polarization of about 0.020 and a polarization deviation of plus or minus 15 deg. Average height variations of the degree of polarization and angular deviation of polarization were also obtained. The observed polarizations fall below the theoretical maximum, and it is believed that in some cases one is dealing with prominence regions in which there is no nonmagnetic depolarization or no magnetic depolarization. Several possible nonmagnetic depolarization effects are likely to decrease in the uppermost part of prominences, so that magnetic depolarization must be larger at the top of quiescent prominences. Title: Quantum theory of the Hanle effect. Application to the determination of magnetic fields in quiescent prominences. Authors: Sahal-Brechot, S.; Bommier, V. Bibcode: 1977ROLun..12....5S Altcode: No abstract at ADS