Bayesian Modeling of Emerging Bipolar Active Regions from Solar Cycle 23

Active regions (ARs) are the photospheric manifestations of emerging magnetic flux ropes (FRs) formed in the solar interior. We analyze the emergence of 126 bipolar ARs during Solar Cycle 23 using a flux rope model, whose parameters are inferred through a Bayesian inference method. This approach allows us to estimate key sub-photospheric properties of FRs. We find that the Bayesian method effectively captures the global magnetic characteristics of ARs, with discrepancies primarily arising in the later stages of emergence. We examine the ability of a flux-balanced FR model with a symmetric circular cross-section to reproduce polarity shapes during these late stages. Additionally, we analyze how the inclination of the FR legs provides insight into the emergence stage. We propose an improved method for estimating the separation of polarities, which decreases projection effects and flux distribution biases. Furthermore, we confirm a strong correlation between the AR flux and the distance between the main polarities, as well as the evolution of their separation speed. Finally, we identify a characteristic ratio between the thickness of the FR and its curvature radius, suggesting an underlying physical mechanism governing this ratio.