Inferring the magnetic field vector in the quiet Sun III. Disk variation of the Stokes profiles and isotropism of the magnetic field

Recent investigations of the magnetic field vector properties in the solar internetwork have provided diverging results. While some works found that the internetwork is mostly pervaded by horizontal magnetic fields, other works argued in favor of an isotropic distribution of the magnetic field vector. Motivated by these seemingly contradictory results and by the fact that most of these works have employed spectropolarimetric data at disk center only, we have revisited this problem employing high-quality data (noise level sigma approximate to 3 x 10(-4) in units of the quiet-Sun intensity) at different latitudes recorded with the Hinode/SP instrument. Instead of applying traditional inversion codes of the radiative transfer equation to retrieve the magnetic field vector at each spatial point on the solar surface and studying the resulting distribution of the magnetic field vector, we surmised a theoretical distribution function of the magnetic field vector and used it to obtain the theoretical histograms of the Stokes profiles. These histograms were then compared to the observed ones. Any mismatch between them was ascribed to the theoretical distribution of the magnetic field vector, which was subsequently modified to produce a better fit to the observed histograms. With this method we find that Stokes profiles with signals above 2 x 10(-3) (in units of the continuum intensity) cannot be explained by an isotropic distribution of the magnetic field vector. We also find that the differences between the histograms of the Stokes profiles observed at different latitudes cannot be explained in terms of line-of-sight effects. However, they can be explained by a distribution of the magnetic field vector that inherently varies with latitude. We note that these results are based on a series of assumptions that, although briefly discussed in this paper, need to be considered in more detail in the future.