EQUILIBRIUM STRUCTURE OF SOLAR MAGNETIC-FLUX TUBES - ENERGY-TRANSPORTWITH MULTISTREAM RADIATIVE-TRANSFER

We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magneto hydrostatic equations in the thin flux-tube approximation, allowing fo r energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opa city and local thermodynamic equilibrium. This constitutes a significa nt improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximat ion. Convection in the flux tube is treated using mixing-length theory , with an additional parameter alpha, characterizing the suppression o f convective energy transport in the tube by the strong magnetic held. The equations are solved using the method of partial linearization. W e present results for tubes with different values of the magnetic fiel d strength and radius at a fixed depth in the atmosphere. In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transpo rt operate simultaneously or in separate layers. A comparison of our r esults with semiempirical models shows that the temperature and intens ity contrast are in broad agreement. However, the field strengths of t he flux-tube models are somewhat lower than the values inferred from o bservations.