Solar photosphere magnetization

Abstract: A recent review shows that observations performed with different telescopes, spectral lines, and interpretation methods all agree about a vertical magnetic field gradient in solar active regions on the order of 3 G/km, when a horizontal magnetic field gradient of only 0.3 G/km is found. This represents an inexplicable discrepancy with respect to the divB=0 law. The objective of this paper is to explain these observations through the law B=\mu_0(H+M) in magnetized media. Magnetization is due to plasma diamagnetism, which results from the spiral motion of free electrons or charges about the magnetic field. Their usual photospheric densities lead to very weak magnetization M, four orders of magnitude lower than H. It is then assumed that electrons escape from the solar interior, where their thermal velocity is much higher than the escape velocity, in spite of the effect of protons. They escape from lower layers in a quasi-static spreading, and accumulate in the photosphere. By evaluating the magnetic energy of an elementary atom embedded in the magnetized medium obeying the macroscopic law B=\mu_0(H+M), it is shown that the Zeeman Hamiltonian is due to the effect of H. Thus, what is measured is H. The decrease in density with height is responsible for non-zero divergence of M, which is compensated for by the divergence of H, in order to ensure divB=0. The behavior of the observed quantities is recovered. The problem of the divergence of the observed magnetic field in solar active regions finally reveals evidence of electron accumulation in the solar photosphere. This is not the case of the heavier protons, which remain in lower layers. An electric field would thus be present in the solar interior, but as the total charge remains negligible, no electric field or effect would result outside the star.