Three-Dimensional Solar Magnetic Field Extrapolation Using Analytical Magnetohydrostatic Equilibrium Solutions

Coronal magnetic field models have to rely on extrapolation methods using photospheric magnetograms as boundary conditions. In recent years, due to the increased resolution of observations and the need to resolve non-force free lower regions of the solar atmosphere, there have been increased efforts to use magnetohydrostatic (MHS) field models instead of force-free extrapolation methods. Although numerical methods to calculate MHS solutions can deal with non-linear problems and hence provide more accurate models, analytical three-dimensional MHS equilibria can also be used as a numerically relatively “cheap” complementary method.

We discuss an extrapolation method based on a family of analytical MHS equilibria that allows for a transition from a non-force-free region to a force-free region. The solution involves hypergeometric functions and while routines for the calculation of these are available, this can affect both the speed and the accuracy of the calculations. We have looked into the asymptotic behaviour of this solution to approximate it by exponential functions which improves the numerical efficiency. We present results with boundary conditions based on artificial magnetograms to test the method, and also the application of the model to observational data.