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

In a previous paper, we argued that the inversion of Stokes profiles applied to spectropolarimetric observations of the solar internet-work 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-perpendicular to, 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 less than or similar to 20 degrees. 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.