Stokes profile inversions in magneto-hydrostatic equilibrium

Inversion codes for the radiative transfer equation are tools that allow us to determine the temperature, magnetic field and plasma velocity in the solar atmosphere from spectro-polarimetric observations (i.e. Stokes vector) in spectral lines as a function of the optical depth.

To compare our new method we have determined the so-called Wilson depression (geometric height of location for optical depth unity through a sunspot). The colors show the height in km of the layer of optical depth equal unity. The the old hydrostatic approach (bottom panel), our new magneto-hydrostatic method (middle panel) are compared with the results from three-dimensional magnetohydrodynamic numerical simulations (top panel). As it can be seen the magneto-hydrostatic approach yields values for the Wilson depression, that are in much better agreement with the numerical simulations than the hydrostatic approach.

To convert from the optical depth to the geometrical height additional approximations are used, typically the assumption of hydrostatic equilibrium. However, hydrostatic equilibrium is not a good approximation in the presence of strong and inhomogeneous magnetic fields. This is the case for instance of Sunspots. We have developed a new method that employs instead the approximation of magneto-hydrostatic equilibrium that takes into account the effects of the magnetic pressure and tension forces.

To compare our new method we have determined the so-called Wilson depression (geometric height of location for optical depth unity through a sunspot) using the old hydrostatic approach (bottom panel), our new magneto-hydrostatic method (middle panel) and compare it with the results from three-dimensional magnetohydrodynamic numerical simulations (top panel). As it can be seen the magneto-hydrostatic approach yields values for the Wilson depression, that are in much better agreement with the numerical simulations than the hydrostatic approach.

Reference: Borrero, J.M.; Pastor Yabar, A.; Rempel, M.; Ruiz Cobo, B., "Combining magneto-hydrostatic constraints with Stokes profiles inversions. I. Role of boundary conditions", submitted to Astronomy & Astrophysics