The geometrical height-scale and the pressure equilibrium in the sunspot umbra

Abstract

Spectra of spots very near to the solar limb (limb distance ≈ 8″) are used to determine the height difference between the levels of formation of the continuum and the line cores of 60 medium-strong Fraunhofer lines. For all lines (with Rowland Intensity < 10), this difference is < 1″ (= 725 km) and well correlated with the Rowland intensity. The line absorption coefficient is calculated for some lines with known oscillator strength. This gives a possibility to deduce a value for the scale height of the umbra, which is found to be about 100 km, thus being equal to the photospheric scale height. Pure hydrostatic equilibrium exists, therefore, in the umbra, and vertical magnetic forces are negligible. Other methods for determining the scale height are discussed for comparison.

The horizontal pressure equilibrium is discussed by taking into account the Wilson effect, and by neglecting dynamic terms (flow of matter). The magnetic field is confirmed to be force-free in higher layers (chromosphere). The pressure difference umbra-photosphere increases towards deeper layers, having a maximum at τ^* ∼- 1 which corresponds to about two times the magnetic pressure H ²/8π. If rotational symmetry of the field is assumed, this can be explained by a minimum radius of curvature of the field lines of 1/4 spot radius.