A Test for Coronal Magnetic Field Extrapolations

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Abstract
As models for the physical properties of the corona above solar active regions grow more sophisticated, we will require better means for testing them. In this paper we discuss and apply such a test to a magnetic field model for an active region. This test is based on the expectation that the temperatures at different points on a given magnetic field line should be well correlated because of the rapid transport of heat along field lines in the corona. We use radio observations of an active region to measure the temperatures on field lines as they cross two isogauss surfaces (at 430 and 750 G) in the corona. The field lines and isogauss surfaces are derived from a coronal magnetic field model obtained via a nonlinear force-free field extrapolation of a photospheric vector magnetogram; for comparison, we also investigate a potential-field extrapolation of the same magnetogram. In a region in which strongly sheared fields are present, the nonlinear force-free field model does indeed show a good correlation between the temperatures in the two surfaces at points on the same field line, while the potential-field model does not. This diagnostic acts both as a test of the magnetic field model as well as of the interpretation of the radio data, and we show how this test can also aid in understanding the radio data.