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

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

Temporal Evolution of the Scattering Polarization of the CaII IR Triplet in Hydrodynamical Models of the Solar Chromosphere

Velocity gradients in a stellar atmospheric plasma have an impact on the anisotropy of the radiation field that illuminates each point within the medium, and this may in principle influence the scattering line polarization that results from the induced atomic level polarization. Here we analyze the emergent linear polarization profiles of the Ca II infrared triplet after solving the radiative transfer problem of scattering polarization in time-dependent hydrodynamical models of the solar chromosphere, taking into account the impact of the plasma macroscopic velocity on the atomic level polarization. We discuss the influence that the velocity and temperature shocks in the considered chromospheric models have on the temporal evolution of the scattering polarization signals of the Ca II infrared lines, as well as on the temporally averaged profiles. Our results indicate that the increase of the linear polarization amplitudes caused by macroscopic velocity gradients may be significant in realistic situations. We also study the effect of the integration time, the microturbulent velocity and the photospheric dynamical conditions, and discuss the feasibility of observing with large-aperture telescopes the temporal variation of the scattering polarization profiles. Finally, we explore the possibility of using the differential Hanle effect in the IR triplet of Ca II with the intention of avoiding the characterization of the zero-field polarization to infer magnetic fields in dynamic situations.Comment: 12 pages, 9 figures. Accepted for publication in ApJ. New figure added, typos correcte

Polynomial Approximants for the Calculation of Polarization Profiles in the \ion{He}{1} 10830 \AA Multiplet

The \ion{He}{1} multiplet at 10830 \AA is formed in the incomplete Paschen-Back regime for typical conditions found in solar and stellar atmospheres. The positions and strengths of the various components that form the Zeeman structure of this multiplet in the Paschen-Back regime are approximated here by polynomials. The fitting errors are smaller than $\sim10^{-2}$ m\AA in the component positions and $\sim10^{-3}$ in the relative strengths. The approximant polynomials allow for a very fast implementation of the incomplete Paschen-Back regime in numerical codes for the synthesis and inversion of polarization profiles in this important multiplet.Comment: ApJ Supplements (in press

A Substantial Amount of Hidden Magnetic Energy in the Quiet Sun

Deciphering and understanding the small-scale magnetic activity of the quiet solar photosphere should help to solve many of the key problems of solar and stellar physics, such as the magnetic coupling to the outer atmosphere and the coronal heating. At present, we can see only ${\sim}1$ of the complex magnetism of the quiet Sun, which highlights the need to develop a reliable way to investigate the remaining 99%. Here we report three-dimensional radiative tranfer modelling of scattering polarization in atomic and molecular lines that indicates the presence of hidden, mixed-polarity fields on subresolution scales. Combining this modelling with recent observational data we find a ubiquitous tangled magnetic field with an average strength of ${\sim}130$ G, which is much stronger in the intergranular regions of solar surface convection than in the granular regions. So the average magnetic energy density in the quiet solar photosphere is at least two orders of magnitude greater than that derived from simplistic one-dimensional investigations, and sufficient to balance radiative energy losses from the solar chromosphere.Comment: 21 pages and 2 figures (letter published in Nature on July 15, 2004

A conjugate gradient method for the solution of the non-LTE line radiation transfer problem

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and Successive Over-Relaxation (GS/SOR) schemes. Our study is indeed based on the application of a preconditioned bi-conjugate gradient method (BiCG-P). Standard tests, in 1D plane parallel geometry and in the frame of the two-level atom model, with monochromatic scattering, are discussed. Rates of convergence between the previously mentioned iterative schemes are compared, as well as their respective timing properties. The smoothing capability of the BiCG-P method is also demonstrated.Comment: Research note: 4 pages, 5 figures, accepted to A&

Using galaxy pairs as cosmological tracers

The Alcock-Paczynski (AP) effect uses the fact that, when analyzed with the correct geometry, we should observe structure that is statistically isotropic in the Universe. For structure undergoing cosmological expansion with the background, this constrains the product of the Hubble parameter and the angular diameter distance. However, the expansion of the Universe is inhomogeneous and local curvature depends on density. We argue that this distorts the AP effect on small scales. After analyzing the dynamics of galaxy pairs in the Millennium simulation, we find an interplay between peculiar velocities, galaxy properties and local density that affects how pairs trace cosmological expansion. We find that only low mass, isolated galaxy pairs trace the average expansion with a minimum "correction" for peculiar velocities. Other pairs require larger, more cosmology and redshift dependent peculiar velocity corrections and, in the small-separation limit of being bound in a collapsed system, do not carry cosmological information.Comment: 15 pages, 14 figures, 1 tabl