The magnetohydrodynamics of umbral flux tubes. I - Theoretical model

Astronomy and Astrophysics – Astrophysics

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Magnetohydrodynamics, Solar Magnetic Field, Sunspots, Umbras, Field Strength, Hydrodynamic Equations, Line Spectra, Mathematical Models, Photosphere, Solar Atmosphere

Scientific paper

The MHD consequences of thin vertical gas columns embedded in sunspot umbrae are investigated in order to elucidate the nature of umbral fine structure, specifically, umbral dots, from a theoretical perspective. Both these gas columns and the surrounding umbral stratification are permeated by a magnetic field, the field strength of the column being weaker than that of the ambient medium. The steady-state MHD equations are solved numerically in the thin flux tube approximation. The geometry of the flux tube, which in all cases is a rapidly converging column with increasing height in the atmosphere, is determined. At heights representing the observable layers of the umbra, the strengths of the magnetic fields inside and outside of the umbral flux tube approach a common value. It is shown that either high temperatures at the lower boundary of the umbral flux tubes or strong upflows are needed in order to produce bright continuum structures.

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