http://arxiv.org/abs/1904.03149
We construct two classes of magnetohydrostatic (MHS) equilibria for an axisymmetric vertical flux tube spanning from the photosphere to the lower part of the transition region within a realistic stratified solar atmosphere subject to solar gravity. We assume a general quadratic expression of the magnetic flux function for the gas pressure and poloidal current and solve the Grad-Shafranov equation analytically. The solution is a combination of a homogeneous and a particular part where the former is separable by a Coulomb function in $r$ and exponential in $z$, while the particular part is an open configuration that has no $z$ dependence. We also present another open field solution by using a self-similar formulation with two different profile functions and incorporating stratified solar gravity to maintain the magnetohydrostatic equilibria, which is a modification of earlier self-similar models with a twist. We study the admitted parameter space that is consistent with the conditions in the solar atmosphere and derive magnetic and the thermodynamic structures inside the flux tube that are reasonably consistent with the photospheric magnetic bright points (MBPs) for both open and closed field Coulomb function and self-similar models as estimated from observations and simulations. The obtained open and closed field flux tube solutions can be used as the background conditions for the numerical simulations for the study of the wave propagation through the flux tubes. The solutions can also be used to construct realistic magnetic canopies.
S. Sen and A. Mangalam
Mon, 8 Apr 19
34/45
Comments: 34 pages; 21 figures with 29 sub-figures; 6 tables, Accepted in the Astrophysical Journal