Frisch, H and Sampoorna, M and Nagendra, K N (2005) Stochastic polarized line formation I. Zeeman propagation matrix in a random magnetic field. In: Astronomy and Astrophysics, 442 (1). pp. 1128.

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Abstract
This paper considers the effect of a random magnetic field on Zeeman line transfer, assuming that the scales of fluctuations of the random field are much smaller than photon mean free paths associated to the line formation (microturbulent limit). The mean absorption and anomalous dispersion coefficients are calculated for random fields with a given mean value, isotropic or anisotropic Gaussian distributions azimuthally invariant about the direction of the mean field. Following Domke & Pavlov (1979, Ap&SS, 66, 47), the averaging process is carried out in a reference frame defined by the direction of the mean field. The main steps are described in detail. They involve the writing of the Zeeman matrix in the polarization matrix representation of the radiation field and a rotation of the line of sight reference frame. Three types of fluctuations are considered : fluctuations along the direction of the mean field, fluctuations perpendicular to the mean field, and isotropic fluctuations. In each case, the averaging method is described in detail and fairly explicit expressions for the mean coefficients are established, most of which were given in Dolginov & Pavlov (1972, Soviet Ast., 16, 450) or Domke & Pavlov (1979, Ap&SS, 66, 47). They include the effect of a microturbulent velocity field with zero mean and a Gaussian distribution. A detailed numerical investigation of the mean coefficients illustrates the two effects of magnetic field fluctuations: broadening of the \sigmacomponents by fluctuations of the magnetic field intensity, leaving the \picomponents unchanged, and averaging over the angular dependence of the \pi and \sigma components. For longitudinal fluctuations only the first effect is at play. For isotropic and perpendicular fluctuations, angular averaging can modify the frequency profiles of the mean coefficients quite drastically with the appearance of an unpolarized central component in the diagonal absorption coefficient, even when the mean field is in direction of the line of sight. A detailed comparison of the effects of the three types of fluctuation coefficients is performed. In general the magnetic field fluctuations induce a broadening of the absorption and anomalous dispersion coefficients together with a decrease of their values. Two different regimes can be distinguished depending on whether the broadening is larger or smaller than the Zeeman shift by the mean magnetic field. For isotropic fluctuations, the mean coefficients can be expressed in terms of generalized Voigt and FaradayVoigt functions $H^{(n)}$ and $F^{(n)}$introduced by Dolginov & Pavlov (1972, Soviet Ast., 16, 450). These functions are related to the derivatives of the Voigt and FaradayVoigt functions. A recursion relation is given in an Appendix for their calculation. A detailed analysis is carried out of the dependence of the mean coefficients on the intensity and direction of the mean magnetic field, on its root mean square fluctuations and on the Landé factor and damping parameter of the line.
Item Type:  Journal Article 

Additional Information:  Copyright of this article belongs to EDP Sciences 
Keywords:  Line: formation – polarization – magnetic fields – turbulence – radiative transfer; 
Department/Centre:  Division of Physical & Mathematical Sciences > Joint Astronomy Programme 
Date Deposited:  14 Feb 2007 
Last Modified:  19 Sep 2010 04:34 
URI:  http://eprints.iisc.ernet.in/id/eprint/9417 
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