A first step in reconstructing the solar corona self-consistently with a magnetohydrostatic model during solar activity minimum

Aims. We compute the distribution of the magnetic field and the plasma in the global corona with a self-consistent magnetohydrostatic (MHS) model.

Methods. Because direct measurements of the solar coronal magnetic field and plasma are extremely difficult and inaccurate, we use a modeling approach based on observational quantities, e. g. the measured photospheric magnetic field, to reconstruct the structure of the global solar corona. We take an analytic magnetohydrostatic model to extrapolate the magnetic field in the corona from photospheric magnetic field measurement. In the model, the electric current density can be decomposed into two components: one component is aligned with the magnetic field lines, whereas the other component flows in spherical shells. The second component of the current produces finite Lorentz forces that are balanced by the pressure gradient and the gravity force. We derive the 3D distribution of the magnetic field and plasma self-consistently in one model. The boundary conditions are given by a synoptic magnetogram on the inner boundary and by a source surface model at the outer boundary.

Results. The density in the model is higher in the equatorial plane than in the polar region. We compare the magnetic field distribution of our model with potential and force-free field models for the same boundary conditions and find that our model differs noticeably from both. We discuss how to apply the model and how to improve it.