On the StokesVAmplitude Ratio as an Indicator of the Field Strength in the Solar Internetwork

Abstract

The results of the determination of magnetic field strength from weak polarimetric signals in solar internetwork regions are contradictory. We investigate the origin of this contradiction with the help of MHD simulations. It is shown that the Stokes V amplitude ratio of the Fe I λλ15652-15648 lines is a good indicator of kG magnetic field concentrations, even for magnetic fields with a complex internal structure like those in MHD simulations. The Stokes V amplitude ratio of the Fe I λλ5247-5250 lines also shows a good correlation with magnetic field strength. However, in simulations with a flux level appropriate for the internetwork, it gives values corresponding to sub-kG fields. The reason is the rapid decrease of the field strength with height in kG magnetic field concentrations. These lines sample high regions of the atmosphere, where the field is already below kG levels. We also find that the Stokes V amplitude ratio of the Fe I λλ6301-6302 lines shows no correlation with the magnetic field strength. The reason lies in the large difference in the heights of formation of these two lines. The value of the magnetic field strength obtained from the Fe I λλ6301 and 6302 lines depends crucially on the treatment of gradients of the magnetic field, line-of-sight velocity, and temperature, even at a numerical spatial resolution of 20 km.