Probability Density Functions to Represent Magnetic Fields at the Solar Surface

TL;DR

This paper investigates how different probability density functions (PDFs) can model the magnetic field at the solar surface, combining empirical data and theoretical analysis to better understand magnetic field distributions and their effects on spectral line formation.

Contribution

It introduces composite PDFs that account for randomness in magnetic field strength and orientation, enhancing modeling of solar surface magnetic fields.

Findings

Composite PDFs can mimic random magnetic fields at the solar surface.

Theoretical effects of various PDFs on Zeeman line formation are characterized.

Empirical PDFs from simulations and data inform the models.

Abstract

Numerical simulations of magneto-convection and analysis of solar magnetogram data provide empirical probability density functions (PDFs) for the line-of-sight component of the magnetic field. In this paper, we theoretically explore effects of several types of PDFs on polarized Zeeman line formation. We also propose composite PDFs to account for randomness in both field strength and orientation. Such PDFs can possibly mimic random fields at the solar surface.