An `Analytic Dynamical Magnetosphere' formalism for X-ray and optical emission from slowly rotating magnetic massive stars

TL;DR

This paper introduces an analytic model for the density, temperature, and flow within the dynamical magnetospheres of slowly rotating magnetic massive stars, simplifying complex MHD simulations to predict observational signatures.

Contribution

The paper presents a steady-state analytic formalism (ADM) that captures key physical properties of dynamical magnetospheres, enabling easier derivation of observational diagnostics.

Findings

The ADM model provides explicit formulas for density, temperature, and flow speed.

Comparison with MHD simulations shows good agreement with time-averaged results.

Initial applications demonstrate how to derive hydrogen line profiles and X-ray emission.

Abstract

Slowly rotating magnetic massive stars develop "dynamical magnetospheres" (DM's), 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 H-alpha 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 toward derivation of a broader set of observational diagnostics and scaling trends for massive stars with such dynamical magnetospheres.