Milne-Eddington inversion for unresolved magnetic structures in the quiet Sun photosphere

This paper is first devoted to present our method for modeling unresolved magnetic structures in the Milne-Eddington inversion of spectropolarimetric data. The related definitions and other approaches and different used inversion algorithms are recalled for comparison. In a second part, we apply our method to quiet Sun data outside active regions. We obtain the quiet Sun photospheric magnetic field as composed of unresolved opening and connected magnetic flux tubes, which form a loop carpet of field lines. We then analyze the spatial correlation, which we also observed for the magnetic field vector, in terms of flux tube diameter, distance, and field strength. We find that different observations with the Zurich imaging polarimeter and THEMIS polarimeter mounted on the THEMIS telescope give very close results, and we add results also very close derived from HINODE/Solar Optical Telescope/spectropolarimeter observations analyzed with the same method. We obtain a mean flux tube diameter of 30 km, a mean flux tube distance of 230 km, and a mean flux tube magnetic field of 1.3 kG.