The non-LTE transport equation for polarized radiation in the presence of magnetic fields. I - Formulation

Physics – Condensed Matter – Statistical Mechanics

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Nonequilibrium Thermodynamics, Polarized Light, Radiative Transfer, Stellar Magnetic Fields, Stokes Theorem (Vector Calculus), Boltzmann Transport Equation, Magnetic Field Configurations, Magnetic Stars, Matrix Theory, Quantum Mechanics, Statistical Mechanics, Stellar Atmospheres

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A formulation of the radiative transfer of polarized light under conditions departing from local thermodynamic equilibrium and accounting for the presence of a magnetic field is presented. The formulation is self-consistent in that the equations of statistical equilibrium for magnetic sublevels are also included. The quantum-mechanical derivation of the absorption matrix, the key to the presentation, is derived in detail utilizing the density matrix approach. The polarization of the radiation field is described in terms of the usual Stokes parameters, but the discussion of the Stokes parameters in this paper illustrates their quantum mechanical origin and interpretation. The equation of radiative transfer for the Stokes vector is cast in a form reminiscent of the nonlocal thermodynamic equilibrium (NLTE) scalar equation of transfer, except that the equation is now a vector equation in the Stokes parameters and the source function is a vector function containing the population of magnetic sublevels.

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