Theoretical formulation of Doppler redistribution in scattering polarization within the framework of the velocity-space density matrix formalism

Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.Comment: Accepted for publication in Astronomy & Astrophysic

Isotropic inelastic and superelastic collisional rates in a multiterm atom

The spectral line polarization of the radiation emerging from a magnetized astrophysical plasma depends on the state of the atoms within the medium, whose determination requires considering the interactions between the atoms and the magnetic field, between the atoms and photons (radiative transitions), and between the atoms and other material particles (collisional transitions). In applications within the framework of the multiterm model atom (which accounts for quantum interference between magnetic sublevels pertaining either to the same J-level or to different J-levels within the same term) collisional processes are generally neglected when solving the master equation for the atomic density matrix. This is partly due to the lack of experimental data and/or of approximate theoretical expressions for calculating the collisional transfer and relaxation rates (in particular the rates for interference between sublevels pertaining to different J-levels, and the depolarizing rates due to elastic collisions). In this paper we formally define and investigate the transfer and relaxation rates due to isotropic inelastic and superelastic collisions that enter the statistical equilibrium equations of a multiterm atom. Under the hypothesis that the atom-collider interaction can be described by a dipolar operator, we provide expressions that relate the collisional rates for interference between different J-levels to the usual collisional rates for J-level populations. Finally, we apply the general equations to the case of a two-term atom with unpolarized lower term, illustrating the impact of inelastic and superelastic collisions on scattering polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field.Comment: Accepted for publication in Astronomy & Astrophysic

The Magnetic Sensitivity of the Ba II D1 and D2 Lines of the Fraunhofer Spectrum

The physical interpretation of the spectral line polarization produced by the joint action of the Hanle and Zeeman effects offers a unique opportunity to obtain empirical information about hidden aspects of solar and stellar magnetism. To this end, it is important to achieve a complete understanding of the sensitivity of the emergent spectral line polarization to the presence of a magnetic field. Here we present a detailed theoretical investigation on the role of resonance scattering and magnetic fields on the polarization signals of the Ba II D1 and D2 lines of the Fraunhofer spectrum, respectively at 4934 \AA\ and 4554 \AA. We adopt a three-level model of Ba II, and we take into account the hyperfine structure that is shown by the $^{135}$Ba and $^{137}$Ba isotopes. Despite of their relatively small abundance (18%), the contribution coming from these two isotopes is indeed fundamental for the interpretation of the polarization signals observed in these lines. We consider an optically thin slab model, through which we can investigate in a rigorous way the essential physical mechanisms involved (resonance polarization, Zeeman, Paschen-Back and Hanle effects), avoiding complications due to radiative transfer effects. We assume the slab to be illuminated from below by the photospheric solar continuum radiation field, and we investigate the radiation scattered at 90 degrees, both in the absence and in the presence of magnetic fields, deterministic and microturbulent. We show in particular the existence of a differential magnetic sensitivity of the three-peak Q/I profile that is observed in the D2 line in quiet regions close to the solar limb, which is of great interest for magnetic field diagnostics.Comment: 40 pages, 1 table and 19 figures. Accepted for publication in The Astrophysical Journal (ApJ

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

Spatial variations of the Sr i 4607 {\AA} scattering polarization peak

Context. The scattering polarization signal observed in the photospheric Sr i 4607 {\AA} line is expected to vary at granular spatial scales. This variation can be due to changes in the magnetic field intensity and orientation (Hanle effect), but also to spatial and temporal variations in the plasma properties. Measuring the spatial variation of such polarization signal would allow us to study the properties of the magnetic fields at subgranular scales, but observations are challenging since both high spatial resolution and high spectropolarimetric sensitivity are required. Aims. We aim to provide observational evidence of the polarization peak spatial variations, and to analyze the correlation they might have with granulation. Methods. Observations conjugating high spatial resolution and high spectropolarimetric precision were performed with the Zurich IMaging POLarimeter, ZIMPOL, at the GREGOR solar telescope, taking advantage of the adaptive optics system and the newly installed image derotator. Results. Spatial variations of the scattering polarization in the Sr i 4607 {\AA} line are clearly observed. The spatial scale of these variations is comparable with the granular size. Small correlations between the polarization signal amplitude and the continuum intensity indicate that the polarization is higher at the center of granules than in the intergranular lanes.Comment: 5 pages, 4 figure

Atomic Scattering Polarization. Observations, Modeling, Predictions

This paper highlights very recent advances concerning the identification of new mechanisms that introduce polarization in spectral lines, which turn out to be key for understanding some of the most enigmatic scattering polarization signals of the solar visible spectrum. We also show a radiative transfer prediction on the scattering polarization pattern across the Mg ii h & k lines, whose radiation can only be observed from spac