Analytical maximum likelihood estimation of stellar magnetic fields

摘要: The polarized spectrum of stellar radiation encodes valuable information on the conditions atmospheres and magnetic fields that permeate them. In this paper, we give explicit expressions to estimate field vector its associated error from observed Stokes parameters. We study solar case where specific intensities are then case, receive flux. second concentrate expression for a slow rotator with dipolar geometry. Moreover, also formulae retrieve least-squares deconvolution (LSD) profiles without assuming mean values LSD artificial spectral line. have been obtained lines can be described in weak-field regime using maximum likelihood approach. errors recovered by means Hermitian matrix. bias estimators is analysed depth.