Abstract
Field configurations and temperature distributions of axially symmetric fluxtubes are determined on the basis of pressure equilibrium and energy balance of the tubes. The description concentrates on layers below ≈ 600 km above the photosphere; a magnetostatic field, and energy transport by a diffusion process are assumed. It is assumed also that the magnetic field of the tubes prevents convective flow across the field lines, so that only radiative energy exchange between the tube and the convection zone is present. A set of model tubes is presented ranging in size from facular points (150 km) to small pores (1000 km), for different values of the field amplitude and the asymptotic energy flux F 0 flowing along the tube from the deeper layers. Radial influx of heat into the tube at the photospheric level influences the temperature in the tube strongly for all these models. For a pore-like tube f 0 = 0.25 (similar to the flux from a spot umbra) seems appropriate (F 0 in units of the normal photospheric flux). If in the smallest fluxtubes F 0 is also 0.25, a comparison of the intensity contrast with observations of facular points indicates that the radius of tubes corresponding to facular points is 50–100 km. In the continuum the structure looks like a depression in the photosphere (similar to the Wilson depression of spots). The magnitude of this depression is ≈ 200 km for pores of 1000 km diameter and ≈ 100 km for facular points. The walls of the hole created by the depression contribute considerably to the contrast of structures observed near the solar limb. It is shown how this contribution may explain the centre to limb behaviour of facular contrast as seen in the continuum, and why the continuum CLV differs so strongly from that in line cores. Over the first 400 km above the photosphere the tube expands by a factor of ≈ 2 for all the tubes calculated.
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Spruit, H.C. Pressure equilibrium and energy balance of small photospheric fluxtubes. Sol Phys 50, 269–295 (1976). https://doi.org/10.1007/BF00155292
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DOI: https://doi.org/10.1007/BF00155292