The Relationships of Sunspot Magnetic Field Strength with Sunspot Area, Umbral Area and Penumbra-Umbra Radius Ratio

Abstract

Stokes profile inversion is very important to get the information on the vector magnetic field. Because the magnetic fields cannot be directly observed, adopting Stokes spectrum analysis to obtain vector magnetic field has become the major technique recently. Therefore, by Stokes profile inversion, we obtained vector magnetic fields of two layers based on the numerical solution (DELO solution, ReEs et al., 1989) to the polarized radiative transfer equation. We analyze the relationships of sunspot magnetic field strength with sunspot area, umbral area and penumbra-umbra radius ratio. By statistical research, it is found that the field strengths of the upper layer and the lower one decrease with the increasing penumbra-umbra radius ratio, and that the logarithmic expression is able to fit well the relationship between the maximum field strength of the upper layer and the sunspot area. Furthermore, we verify the result obtained by Ringnes and Jensen (1961) about the relationship between the maximum magnetic field strength and the umbral area, and the result obtained by Antalová (1991) of the relationship between the field strength and the penumbra-umbra radius ratio.