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Self-Consistent Models for Small Photospheric Flux Tubes

Published online by Cambridge University Press:  04 August 2017

W. Deinzer
Affiliation:
Universitäts-Sternwarte Göttingen, Federal Republic of Germany
G. Hensler
Affiliation:
Universitäts-Sternwarte Göttingen, Federal Republic of Germany
D. Schmitt
Affiliation:
Universitäts-Sternwarte Göttingen, Federal Republic of Germany
M. Schüssler
Affiliation:
Universitäts-Sternwarte Göttingen, Federal Republic of Germany
E. Weisshaar
Affiliation:
Universitäts-Sternwarte Göttingen, Federal Republic of Germany

Extract

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We give a short summary of some results of a numerical study of magnetic field concentrations in the solar photosphere and upper convection zone. We have developed a 2D time dependent code for the full MHD equations (momentum equation, equation of continuity, induction equation for infinite conductivity and energy equation) in slab geometry for a compressible medium. A Finite-Element-technique is used. Convective energy transport is described by the mixing-length formalism while the diffusion approximation is employed for radiation. We parametrize the inhibition of convective heat flow by the magnetic field and calculate the material functions (opacity, adiabatic temperature gradient, specific heat) self-consistently. Here we present a nearly static flux tube model with a magnetic flux of ∼ 1018 mx, a depth of 1000 km and a photospheric diameter of ∼ 300 km as the result of a dynamical calculation. The influx of heat within the flux tube at the bottom of the layer is reduced to 0.2 of the normal value. The mass distribution is a linear function of the flux function A: dm(A)/dA = const. Fig. 1 shows the model: Isodensities (a), fieldlines (b), isotherms (c) and lines of constant continuum optical depth (d) are given. The “Wilson depression” (height difference between τ = 1 within and outside the tube) is ∼ 150 km and the maximum horizontal temperature deficit is ∼ 3000 K. Field strengths as function of x for three different depths and as function of depth along the symmetry axis are shown in (e) and (f), respectively. Note the sharp edge of the tube.

Type
I. Magnetic Fields in Stellar Photospheres
Copyright
Copyright © Reidel 1983