An 'analytic dynamical magnetosphere' formalism for X-ray and optical emission from slowly rotating magnetic massive stars

Slowly rotating magnetic massive stars develop 'dynamical magnetospheres' (DMs), characterized by trapping of stellar wind outflow in closed magnetic loops, shock heating from collision of the upflow from opposite loop footpoints, and subsequent gravitational infall of radiatively cooled material. In 2D and 3D magnetohydrodynamic (MHD) simulations, the interplay among these three components is spatially complex and temporally variable, making it difficult to derive observational signatures and discern their overall scaling trends. Within a simplified, steady-state analysis based on overall conservation principles, we present here an 'analytic dynamical magnetosphere' (ADM) model that provides explicit formulae for density, temperature, and flow speed in each of these three components - wind outflow, hot post-shock gas, and cooled inflow - as a function of colatitude and radius within the closed (presumed dipole) field lines of the magnetosphere. We compare these scalings with time-averaged results from MHD simulations, and provide initial examples of application of this ADM model for deriving two key observational diagnostics, namely hydrogen Hα emission line profiles from the cooled infall, and X-ray emission from the hot post-shock gas. We conclude with a discussion of key issues and advantages in applying this ADM formalism towards derivation of a broader set of observational diagnostics and scaling trends for massive stars with such dynamical magnetospheres.