Determining the Magnetization of the Quiet Sun Photosphere from the Hanle Effect and Surface Dynamo Simulations

Abstract: The bulk of the quiet solar photosphere is thought to be significantly magnetized, due to the ubiquitous presence of a tangled magnetic field at subresolution scales with an average strength <B> ~ 100 G. This conclusion was reached through detailed three-dimensional (3D) radiative transfer modeling of the Hanle effect in the Sr I 4607 line, using the microturbulent field approximation and assuming that the shape of the probability density function of the magnetic field strength is exponential. Here we relax both approximations by modeling the observed scattering polarization in terms of the Hanle effect produced by the magnetic field of a 3D photospheric model resulting from a (state-of-the-art) magneto-convection simulation with surface dynamo action. We show that the scattering polarization amplitudes observed in the Sr I 4607 line can be explained only after enhancing the magnetic strength of the photospheric model by a sizable scaling factor, F=10, which implies <B> = 130 G in the upper photosphere. We argue also that in order to explain both the Hanle depolarization of the Sr I 4607 line and the Zeeman signals observed in Fe I lines we need to introduce a height-dependent scaling factor, such that the ensuing <B> = 160 G in the low photosphere and <B> = 130 G in the upper photosphere.