A model of solar equilibrium: the hydrodynamic limit

Helioseismology has revealed the internal density and rotation profiles of the Sun. Yet, knowledge of its magnetic fields and meridional circulation is confined much closer to the surface, and latitudinal entropy gradients are below detectable limits. While numerical simulations can offer insight into the interior dynamics and help identify which ingredients are necessary to reproduce particular observations, some features of the Sun can be understood analytically from an equilibrium perspective. Examples of such features include: the 1D density profile arising from steady-state energy transport from the core to the surface, and the tilting of isorotation contours in the convection zone (CZ) due to baroclinic forcing. To help identify which features can be explained by equilibrium, we propose analyzing stationary axisymmetric ideal magnetohydrodynamic flows in the solar regime. By prescribing an appropriate entropy profile at the surface, we recover a rotation profile that reasonably matches observations in the bulk of the CZ. Additionally, by including the effects of poloidal flow, we reproduce a feature that is reminiscent of the near surface shear layer. However, no tachocline-like feature is seen in hydrodynamic equilibrium, suggesting the importance of either dynamics or magnetic fields in its description.