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A. Skumanich (High Altitude Obs - NCAR)
The presence of Stokes asymmetries imply the presence of line of sight velocity gradients in a magnetic atmosphere. Such gradients, as well as magnetic field gradients, prevents one from obtaining closed form analytic expressions for the emergent Stokes profiles. This is due to the fact that the absorption matrix is non-commutative at neighboring points. However closed form expresions are still possible if one uses a quasi-linearization technique to bootstrap from the constant matrix case to the variable case. We use such a bootstrap approach to derive analytic expressions for the gradients of velocity and field for the Milne-Eddinton atmosphere. Our expressions are more general than those derived by Sanchez Almeida & Lites (Ap J 398, 359, 1992) using the response matrix approach.
The National Center for Atmospheric Research (NCAR) is sponsored by the National Science Foundation.