Inferring the magnetic field vector in the quiet Sun. II. Interpreting results from the inversion of Stokes profiles

TL;DR

This study investigates the limitations of inferring magnetic field vectors in the quiet Sun from Stokes profile inversions, highlighting noise-induced overestimations of inclination and proposing selective inversion strategies.

Contribution

It extends previous analysis to correlated noise in Stokes $Q$ and $U$, and demonstrates the bias towards nearly vertical fields when inverting low signal-to-noise linear polarization data.

Findings

Overestimation of inclination occurs mainly for nearly vertical fields.

Inverting below-noise linear polarization signals yields random azimuth distributions.

Selective inversion of signals above noise improves accuracy but biases the sample.

Abstract

In a previous paper, we argued that the inversion of Stokes profiles applied to spectropolarimetric observations of the solar internetwork yield unrealistically large values of the inclination of the magnetic field vector ($\gamma$). This is because photon noise in Stokes $Q$ and $U$ are interpreted by the inversion code as valid signals, that leads to an overestimation of the transverse component $B_\perp$, thus the inclination $\gamma$. However, our study was based on the analysis of linear polarization signals that featured only uncorrelated noise. In this paper, we develop this idea further and study this effect in Stokes $Q$ and $U$ profiles that also show correlated noise. In addition, we extend our study to the three components of the magnetic field vector, as well as the magnetic filling factor $\alpha$. With this, we confirm the tendency to overestimate $\gamma$ when inverting linear polarization profiles that, although non-zero, are still below the noise level. We also establish that the overestimation occurs mainly for magnetic fields that are nearly vertical $\gamma \lesssim 20\deg$. This indicates that a reliable inference of the inclination of the magnetic field vector cannot be achieved by analyzing only Stokes $I$ and $V$. In addition, when inverting Stokes $Q$ and $U$ profiles below the noise, the inversion code retrieves a randomly uniform distribution of the azimuth of the magnetic field vector $\phi$. To avoid these problems, we propose only inverting Stokes profiles for which the linear polarization signals are sufficiently above the noise level. However, this approach is also biased because, in spite of allowing for a very accurate retrieval of the magnetic field vector from the selected Stokes profiles, it selects only profiles arising from highly inclined magnetic fields.