Inferring the magnetic field vector in the quiet Sun I. Photon noise and selection criteria

In the past, spectropolarimetric data from Hinode/SP were employed to infer the distribution of the magnetic field vector in the quiet Sun. While some authors found predominantly horizontal magnetic fields, others favor an isotropic distribution. We investigate whether it is actually possible to accurately retrieve the magnetic field vector in regions with very low polarization signals ( e. g. internetwork), employing the FeI line pair at 6300 angstrom. We first perform inversions of the Stokes vector observed with Hinode/SP in the quiet Sun at disk center in order to confirm the distributions retrieved by other authors. We then carry out several Monte-Carlo simulations with synthetic data, with which we show that the observed distribution of the magnetic field vector can be explained in terms of purely vertical (gamma = 0 degrees) and weak fields ((B) over bar < 20 G), which are misinterpreted by the analysis technique ( Stokes inversion code) as being horizontal (gamma approximate to 90 degrees) and stronger ( <(K)over bar> approximate to 100 G), owing to the effect of the photon noise. This challenges the correctness of previous results, which presented the distributions for the magnetic field vector peaking at gamma = 90 degrees and (B) over bar = 100 G. We propose that an accurate determination of the magnetic field vector can be achieved by decreasing the photon noise to a point where most of the observed profiles posses Stokes Q or U profiles that are above the noise level. Unfortunately, for noise levels as low as 2.8 x 10(-4), only 30 % of the observed region with Hinode/SP have sufficiently strong Q or U signals, implying that the magnetic field vector remains unknown in the rest of the internetwork.