Some aspects of polarized line formation in magneto-turbulent media

Abstract

Observations and numerical simulations of magneto-convection show a highly variable solar magnetic field. Using a statistical approach, we analyze the effects of random magnetic fields on Stokes profiles of spectral lines. We consider the micro and macro-turbulent regimes, which provide bounds for more general random fields with finite scales of variations. The mean Stokes parameters are obtained in the micro-turbulent regime, by first averaging the Zeeman propagation matrix Φ ^ over the probability distribution function P( B ) of the magnetic field and then solving the concerned radiative transfer equation. In the macro-turbulent regime, the mean solution is obtained by averaging the emergent solution over P( B ). It is assumed that B has a Gaussian distribution defined by its mean field B 0, angular distribution and dispersion. Fluctuations parallel and perpendicular to B 0 are considered. Spectral lines are parameterized by their strength β, which is varied over the range 1–10 4. A detailed comparison of micro and macro-turbulent limit with mean field solution shows that differences are important for β ⩾ 10. When β increases, the saturation behavior of micro-turbulent profiles are significantly different from that of mean field profiles. The Stokes profiles shapes are explained in terms of the non-linear β-dependence of the Unno–Rachkovsky solution using approximate expressions for the mean absorption coefficients. These expressions when inserted in the Unno–Rachkovsky solution can predict Stokes profiles that match with the numerical result to a good approximation.