Bayesian approach for modeling global magnetic parameters for the solar active region

Abstract

Context. Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux tubes. The presence of elongated magnetic polarities in line-of-sight (LOS) magnetograms indicates the existence of twist in the flux tubes that form them. These polarity elongations, referred to as magnetic tongues, bias the measurement of AR characteristics obtained during their emergence phase (e.g., their tilt angle and magnetic flux). In particular, obtaining a good estimation of the tilt angle evolution plays a key role in constraining flux-transport dynamo models. Aims. In this work, we aim to estimate the intrinsic properties of the twisted flux tubes, or flux ropes, that form ARs by quantitatively comparing observed LOS magnetograms with synthetic ones derived from a toroidal magnetic flux tube model. Methods. We developed a Bayesian inference method to obtain the statistical distributions of the inferred model parameters. As an example, we applied the method to NOAA AR 10268. Next, we tested the results using a synthetic-AR generator to quantify the effect of small-scale perturbations over the inferred parameter distributions. Results. We conclude that this method can significantly remove the effects of magnetic tongues on the derived AR global characteristics, providing a better understanding of the intrinsic properties of the emerging flux rope. Conclusions. These results provide a framework for future analyses of the physical properties of emerging ARs using Bayesian statistics.