At the level in the photosphere where a sunspot's field is measured spectroscopically

PHYSICS · Subjective · Fermi University Physics · Astrophysics & Cosmology · Plasma Physics · Fluid and magnetohydrodynamic description

Stars from the Inside, Ch The Sun as a test: calibration, sound, neutrinos and a magnetised atmosphere

Problem

At the level in the photosphere where a sunspot's field is measured spectroscopically, the surrounding (field-free) gas pressure is Pe=1.4×104 PaP_e = 1.4\times10^{4}\,\mathrm{Pa}, while the gas pressure inside the umbra at that same level is Pi=4.0×103 PaP_i = 4.0\times10^{3}\,\mathrm{Pa}. Treating the umbral field as a vertical flux tube in magnetohydrostatic balance with negligible field-line tension, so that Pe=Pi+B2/2μ0P_e = P_i + B^2/2\mu_0, estimate the umbral field strength BB. Take μ0=4π×10−7 T m A−1\mu_0 = 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}}.

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