Estimating the magnetic field strength from magnetograms

TL;DR

This paper introduces Bayesian-based formulae to improve magnetic field strength estimates from magnetograms, accounting for the likelihood of different field strengths and orientations, thus refining traditional measurements.

Contribution

It presents novel Bayesian formulae that enhance magnetic field strength estimation from magnetograms by incorporating probabilistic considerations of field magnitude and orientation.

Findings

Provides a more accurate estimation method for magnetic fields.

Reduces bias in magnetic field measurements.

Incorporates prior knowledge about field distributions.

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 and still produce the same magnetic signal. Yet, 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 its 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.