A Stochastic Model of the Solar Atmosphere

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Abstract
We present a model for the lower solar atmosphere based on continuum observations of the Sun spanning the 2-1200 μm wavelength range. We have shown that the data, in particular the center-to-limb brightness profiles at 50-350 μm, cannot be accounted for by any model which is plane-parallel and homogeneous in the height range in which this radiation is formed. We accordingly set out to develop a two-component model as the natural generalization. Making use of a theory for radiation transfer in a stochastic multi-component atmosphere, we find that one can indeed obtain an inhomogeneous model which satisfies center-to-limb data over the 2-1200 μm range. This composite model is made up of hot "flux tubes" randomly embedded in a cool medium, the flux tubes expanding to occupy an increasing proportion of the atmosphere as we move up in height. The cool ambient component shows a monotonic decrease in temperature in the range defined by the data. The temperature in the hot component is constant at about 6500 K up to about 400 km and increases monotonically above that height. The center-to-limb observations demand that the gas in the interiors of the flux tubes be recessed downward with respect to a hydrostatic equilibrium distribution of density. This appears to constitute a chromospheric Wilson depression consistent with a magnetic field of about 120 G in the flux-tube interior at a height of about 600 km. The new model is shown to be consistent with other spectral measurements independent of those used to define it. It gives a very good fit to the 0.5 μm continuum intensities across the disk, and provides an excellent accounting for the disk-center brightness temperature in the center of the 3-2 R14 CO line at 4.667 μm. A boundary temperature of less than about 3000 K in the cold component is suggested from the limb-darkening data available for this line. In an appendix we mention a procedure for an analogous study based on the intensities of multiplet lines, which may hold promise for modeling over a wider range of heights that can be spanned by the IR data.