In *Plasma Dynamics and Diagnostics in the
Solar Transition Region and Corona
(Proceedings of the 8th SOHO Workshop)*
(eds. J.-C. Vial and B. Kaldeich-Schurmann)
ESA SP-446: Noordwijk (1999) 117-122.
## Heating the atmosphere above sunspots

D. Alexander,
N.E. Hurlburt

Lockheed Martin Solar and Astrophysics Laboratory,

3251 Hanover St., Palo Alto, CA 94304, USA

A.M.Rucklidge

Department of Applied Mathematics and Theoretical Physics,

University of Cambridge, Cambridge, CB3 9EW, UK

**Abstract.**
We present our results of a hybrid model of sunspots and their overlying
corona. The two-layer model considers both the nonlinear, compressible
magnetoconvection beneath the photosphere and potential, or linear force-free,
models of the coronal fields. Heating of the plasma along the field lines is
then treated using quasi-static and steady-state models with the heating rate
being specified by the dynamics of the magnetoconvection.
Two distinct magnetoconvection scenarios are considered. The first describes
magnetoconvection in a 2D axisymmetric geometry and considers the time
development of the overlying coronal field. The second describes a 3D
cylindrical geometry with a static coronal field configuration. Both scenarios
diverge from the standard practice of assuming constant temperature and
vertical magnetic field conditions at the top surface. Instead, a radiative
linear force-free field condition is adopted.

Extrapolation of the top surface boundary conditions results in a coronal field
configuration which is assumed to be filled with plasma heated to coronal
temperatures. The heating rate and thermodynamic behaviour of the plasma is
related to the sub-surface model by assuming that individual fluxtubes are
heated uniformly with the necessary energy being generated from the dissipation
of the Poynting flux entering the coronal volume. Radiation and conductive
losses are included.

The combination of a sunspot model, whereby the surface field is completely
specified, with a coronal heating model, in which the plasma parameters are
specified for a given energy input, allows us to explore a broad class of
heating paradigms.

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