Analysis of unresolved photospheric magnetic field structure using Fe I 6301 and 6302 lines

Context. Early magnetographic observations indicated that the magnetic field in the solar photosphere has an unresolved small-scale structure. Near-infrared and optical data with extremely high spatial resolution show that these structures have scales of a few tens of kilometres, which are not resolved in the majority of solar observations. Aims. The goal of this study is to establish the effect of the unresolved photospheric magnetic field structure on Stokes profiles observed with relatively low spatial resolution. Ultimately, we aim to develop methods for fast estimation of the photospheric magnetic filling factor and line-of-sight gradient of the photospheric magnetic field, which can be applied to large observational data sets. Methods. We exploit 3D magnetohydrodynamic models of magneto-convection developed using the MURAM code. Corresponding profiles of Fe I 6301.5 and 6302.5 angstrom spectral lines are calculated using the NICOLE radiative transfer code. The resulting I and V Stokes [x,y,lambda] cubes with a reduced spatial resolution of 150 km are used to calculate magnetic field values as they would be obtained in observations with the Solar Optical Telescope (SOT) onboard Hinode or the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamic Observatory (SDO) mission. Results. Three different methods of magnetic filling factor estimation are considered: the magnetic line ratio method, the Stokes V width method, and a simple statistical method. We find that the statistical method and the Stokes V width method are sufficiently reliable for fast filling factor estimations. Furthermore, we find that the Stokes I +/- V bisector splitting gradient can be used for fast estimation of the line-of-sight gradient of the photospheric magnetic field.