Scattering line polarization in rotating, optically thick disks

To interpret observations of astrophysical disks it is essential to understand the formation process of the emitted light. If the disk is optically thick, scattering dominated and permeated by a Keplerian velocity field, Non-Local Thermodynamic Equilibrium radiative transfer modeling must be done to compute the emergent spectrum from a given disk model. We investigate Non-local thermodynamic equilibrium polarized line formation in different simple disk models and aim to demonstrate the importance of both radiative transfer effects and scattering as well as the effects of velocity fields. We self-consistently solve the coupled equations of radiative transfer and statistical equilibrium for a two level atom model by means of Jacobi iteration. We compute scattering polarization, that is Q/I and U/I line profiles. The degree of scattering polarization is significantly influenced by the inclination of the disk with respect to observer, but also by the optical thickness of the disk and the presence of rotation. Stokes U shows double-lobed profiles with amplitude which increases with the disk rotation. Our results suggest that the line profiles, especially the polarized ones, emerging from gaseous disks differ significantly from the profiles predicted by simple approximations. The profiles are diverse in shape, but typically symmetric in Stokes Q and antisymmetric in Stokes U. A clear indicator of disk rotation is the presence of Stokes U, which might prove to be a useful diagnostic tool. We also demonstrate that, for moderate rotational velocities, an approximate treatment can be used, where non-local thermodynamic equilibrium radiative transfer is done in the velocity field-free approximation and Doppler shift is applied in the process of spatial integration over the whole emitting surface.Comment: 16 pages; 12 figures; Accepted with revision for A&A. This is the version after first round of referee's suggestion

Polarized Line Formation in Multi-Dimensional Media.III. Hanle Effect with Partial Frequency Redistribution

In the previous two papers, namely, \citet{anuknn11} and \citet{anuetal11} we solved the polarized radiative transfer (RT) equation in multi-dimensional (multi-D) geometries, with partial frequency redistribution (PRD) as the scattering mechanism. We assumed Rayleigh scattering as the only source of linear polarization ($Q/I, U/I$) in both these papers. In this paper we extend these previous works to include the effect of weak oriented magnetic fields (Hanle effect) on line scattering. We generalize the technique of Stokes vector decomposition in terms of the irreducible spherical tensors $\mathcal{T}^K_Q$, developed in \citet{anuknn11}, to the case of RT with Hanle effect. A fast iterative method of solution (based on the Stabilized Preconditioned Bi-Conjugate-Gradient technique), developed in \citet{anuetal11}, is now generalized to the case of RT in magnetized three-dimensional media. We use the efficient short-characteristics formal solution method for multi-D media, generalized appropriately to the present context. The main results of this paper are the following: (1) A comparison of emergent $(I, Q/I, U/I)$ profiles formed in one-dimensional (1D) media, with the corresponding emergent, spatially averaged profiles formed in multi-D media, shows that in the spatially resolved structures, the assumption of 1D may lead to large errors in linear polarization, especially in the line wings. (2) The multi-D RT in semi-infinite non-magnetic media causes a strong spatial variation of the emergent $(Q/I, U/I)$ profiles, which is more pronounced in the line wings. (3) The presence of a weak magnetic field modifies the spatial variation of the emergent $(Q/I, U/I)$ profiles in the line core, by producing significant changes in their magnitudes.Comment: 31 pages, 14 figures, Submitted to ApJ, Under revie

Inference of magnetic fields in inhomogeneous prominences

Most of the quantitative information about the magnetic field vector in solar prominences comes from the analysis of the Hanle effect acting on lines formed by scattering. As these lines can be of non-negligible optical thickness, it is of interest to study the line formation process further. We investigate the multidimensional effects on the interpretation of spectropolarimetric observations, particularly on the inference of the magnetic field vector. We do this by analyzing the differences between multidimensional models, which involve fully self-consistent radiative transfer computations in the presence of spatial inhomogeneities and velocity fields, and those which rely on simple one-dimensional geometry. We study the formation of a prototype line in ad hoc inhomogeneous, isothermal 2D prominence models. We solve the NLTE polarized line formation problem in the presence of a large-scale oriented magnetic field. The resulting polarized line profiles are then interpreted (i.e. inverted) assuming a simple 1D slab model. We find that differences between input and the inferred magnetic field vector are non-negligible. Namely, we almost universally find that the inferred field is weaker and more horizontal than the input field. Spatial inhomogeneities and radiative transfer have a strong effect on scattering line polarization in the optically thick lines. In real-life situations, ignoring these effects could lead to a serious misinterpretation of spectropolarimetric observations of chromospheric objects such as prominences.Comment: 11 pages, 9 figure

On the Sensitivity of Partial Redistribution Scattering Polarization Profiles to Various Atmospheric Parameters

This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of several atmospheric parameters on the emergent fractional linear polarization profiles. The shapes of these $Q/I$ profiles are interpreted in terms of the anisotropy of the radiation field, which in turn depends on the source function gradient that sets the angular variation of the specific intensity. We define a suitable frequency integrated anisotropy factor for PRD that can be directly related to the emergent linear polarization. We show that complete frequency redistribution is a good approximation to model weak resonance lines. We also show that the emergent linear polarization profiles can be very sensitive to the thermal structure of the solar atmosphere and, in particular, to spatial variations of the damping parameter.Comment: 45 pages, 16 figures, accepted for publication in the Astrophysical Journal (2010

Hanle effect in the solar Ba II D2 line: a diagnostic tool for chromospheric weak magnetic fields

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. 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......Comment: In press in astronomy and astrophysic

Hanle effect in the CN violet system with LTE modeling

Weak entangled magnetic fields with mixed polarity occupy the main part of the quiet Sun. The Zeeman effect diagnostics fails to measure such fields because of cancellation in circular polarization. However, the Hanle effect diagnostics, accessible through the second solar spectrum, provides us with a very sensitive tool for studying the distribution of weak magnetic fields on the Sun. Molecular lines are very strong and even dominate in some regions of the second solar spectrum. The CN $B {}^{2} \Sigma - X {}^{2} \Sigma$ system is one of the richest and most promising systems for molecular diagnostics and well suited for the application of the differential Hanle effect method. The aim is to interpret observations of the CN $B {}^{2} \Sigma - X {}^{2} \Sigma$ system using the Hanle effect and to obtain an estimation of the magnetic field strength. We assume that the CN molecular layer is situated above the region where the continuum radiation is formed and employ the single-scattering approximation. Together with the Hanle effect theory this provides us with a model that can diagnose turbulent magnetic fields. We have succeeded in fitting modeled CN lines in several regions of the second solar spectrum to observations and obtained a magnetic field strength in the range from 10--30 G in the upper solar photosphere depending on the considered lines.Comment: Accepted for publication in Astronomy and Astrophysic

Steady-state signatures of radiation trapping by cold multilevel atoms

In this paper, we use steady-state measurements to obtain evidence of radiation trapping in an optically thick a cloud of cold rubidium atoms. We investigate the fluorescence properties of our sample, pumped on opened transitions. The intensity of fluorescence exhibits a non trivial dependence on the optical thickness of the media. A simplified model, based on rate equations self-consistently coupled to a diffusive model of light transport, is used to explain the experimental observations in terms of incoherent radiation trapping on one spectral line. Measurements of atomic populations and fluorescence spectrum qualitatively agree with this interpretation.Comment: 8 pages, 5 figure

A new view on exoplanet transits: Transit of Venus described using three-dimensional solar atmosphere Stagger-grid simulations

Stellar activity and, in particular, convection-related surface structures, potentially cause fluctuations that can affect the transit light curves. Surface convection simulations can help the interpretation of ToV. We used realistic three-dimensional radiative hydrodynamical simulation of the Sun from the Stagger-grid and synthetic images computed with the radiative transfer code Optim3D to provide predictions for the transit of Venus in 2004 observed by the satellite ACRIMSAT. We computed intensity maps from RHD simulation of the Sun and produced synthetic stellar disk image. We computed the light curve and compared it to the ACRIMSAT observations and also to the light curves obtained with solar surface representations carried out using radial profiles with different limb-darkening laws. We also applied the same spherical tile imaging method to the observations of center-to-limb Sun granulation with HINODE. We managed to explain ACRIMSAT observations of 2004 ToV and showed that the granulation pattern causes fluctuations in the transit light curve. We evaluated the contribution of the granulation to the ToV. We showed that the granulation pattern can partially explain the observed discrepancies between models and data. This confirms that the limb-darkening and the granulation pattern simulated in 3D RHD Sun represent well what is imaged by HINODE. In the end, we found that the Venus's aureole contribution during ToV is less intense than the solar photosphere, and thus negligible. Being able to explain consistently the data of 2004 ToV is a new step forward for 3D RHD simulations that are becoming essential for the detection and characterization of exoplanets. They show that the granulation have to be considered as an intrinsic incertitude, due to the stellar variability, on precise measurements of exoplanet transits of, most likely, planets with small diameters.Comment: Accepted for publication in Astronomy and Astrophysic

Determining the Magnetization of the Quiet Sun Photosphere from the Hanle Effect and Surface Dynamo Simulations

The bulk of the quiet solar photosphere is thought to be significantly magnetized, due to the ubiquitous presence of a tangled magnetic field at subresolution scales with an average strength ~ 100 G. This conclusion was reached through detailed three-dimensional (3D) radiative transfer modeling of the Hanle effect in the Sr I 4607 line, using the microturbulent field approximation and assuming that the shape of the probability density function of the magnetic field strength is exponential. Here we relax both approximations by modeling the observed scattering polarization in terms of the Hanle effect produced by the magnetic field of a 3D photospheric model resulting from a (state-of-the-art) magneto-convection simulation with surface dynamo action. We show that the scattering polarization amplitudes observed in the Sr I 4607 line can be explained only after enhancing the magnetic strength of the photospheric model by a sizable scaling factor, F=10, which implies = 130 G in the upper photosphere. We argue also that in order to explain both the Hanle depolarization of the Sr I 4607 line and the Zeeman signals observed in Fe I lines we need to introduce a height-dependent scaling factor, such that the ensuing = 160 G in the low photosphere and = 130 G in the upper photosphere.Comment: To appear in ApJ Letter

Magnetic flux in the inter-network quiet Sun from comparison with numerical simulations

Khomenko et al. estimate the mean magnetic field strength of the quiet Sun to be 20 G. The figure is smaller than several existing estimates, and it comes from the comparison between observed Zeeman polarization signals and synthetic signals from numerical simulations of magneto-convection. The numerical simulations require an artificially large magnetic diffusivity, which smears out magnetic structures smaller than the grid scale. Assuming a turbulent cascade for the unresolved artificially smeared magnetic fields, we find that their unsigned magnetic flux is at least as important as that explicitly shown in the simulation. The unresolved fields do not produce Zeeman polarization but contribute to the unsigned flux.Since they are not considered by Khomenko et al., their mean magnetic field strength has to be regarded as a lower limit. This kind of bias is not specific of a particular numerical simulation or a spectral line. It is to be expected when observed quiet Sun Zeeman signals are compared with synthetic signals from simulations.Comment: Accepted A&A. 4 pages, 0 figure