Estimating the magnetic field strength from magnetograms

Abstract

A properly calibrated longitudinal magnetograph is an instrument that measures circular polarization and gives an estimation of the magnetic flux density in each observed resolution element. This usually constitutes a lower bound of the field strength in the resolution element, given that it can be made arbitrarily large as long as it occupies a proportionally smaller area of the resolution element and/or becomes more transversal to the observer while still produce the same magnetic signal. However, we know that arbitrarily stronger fields are less likely - hG fields are more probable than kG fields, with fields above several kG virtually absent - and we may even have partial information about their angular distribution. Based on a set of sensible considerations, we derive simple formulae based on a Bayesian analysis to give an improved estimation of the magnetic field strength for magnetographs.