Calculating the thermal structure of solar active regions in three dimensions

We describe a technique to obtain the temperature and density distribution in an active region for a specified plasma heating model. The technique can be applied in general to determine the magnetic field and thermal structure self-consistently. For simplicity, we illustrate the application of this technique in the limit of small plasma beta, in which the plasma dynamics decouples from that of the magnetic field, a good approximation in active regions, in which the magnetic field is strong. We select a particular active region, observed in 1996 August, to demonstrate the methodology. We apply the technique to a force-free magnetic field with a plasma heating model in which the volumetric coronal heating rate is directly proportional to the strength of the local magnetic field, and we compute the expected extreme-ultraviolet and soft X-ray emissions from the resulting thermal structure. We compare our solutions with one-dimensional loop models and analytic loop scaling laws. In the future, we plan to compare these emission images with those obtained by the SOHO EUV Imaging Telescope (EIT) and the Yohkoh Soft X-Ray Telescope (SXT) and to explore the relationship between coronal emission and various coronal heating models.