Numerical Methods for Dynamically-Coupled Radiation in Atmospheric Outflows and Winds

In the study of astrophysical outflows, radiation can be a crucial component of the forces responsible for driving winds, but is often very difficult to include in analytic or numerical solutions without making substantial simplifying assumptions. In this dissertation I investigate several methods for solving radiative transfer more accurately in the context of numerical hydrodynamics simulations, highlighting two particular astrophysical contexts that demand the development of specialized methods; namely, (1.) the unique interactions of Lyman Alpha (hereafter Lyα) in the upper atmospheres of exoplanets and the impact of the resulting radiation forces, and (2.) radiation-driven winds from the surfaces of neutron stars (NS) during Type I X-ray bursts that exhibit photospheric radius expansion: a problem which necessitates careful inclusion of time-dependent, dynamically-coupled radiation forces. Chapter 2 explores the physics of resonant scattering using a semi-analytic approach, developing the equations necessary to implement physically self-consistent Lyα scattering methods in a numerical simulation. Two new additions to the solution of Lyα radiative transfer in spherical geometry are presented: (1) a correction to the treatment of the boundary condition for a steady source, and (2) a new solution of the time-dependent problem for an impulsive source. For the impulsive source, the time, spatial, and frequency dependence of the solution are expressed using an eigenfunction expansion in order to characterize the escape time distribution and emergent spectra of photons. The characterization of the escape-time distribution lays the groundwork for a Monte Carlo acceleration method that can sample photon escape properties from distributions rather than calculating every photon scattering, thereby reducing computational demand. Chapter 3 is a direct follow-up to this work in which a numerical radiation hydrodynamics solution is developed using the methods for handling resonance line radiation developed in Chapter 2. I focus specifically on the design and implementation of a Monte Carlo radiative transfer module for Athena++. As an example application of this powerful computational tool, I construct a simulated exoplanet atmosphere and include, piece by piece, the components of the radiation field that are coupled with the atomic hydrogen layer of the upper atmosphere. With the inclusion of each new piece of physics, tests are run to ensure convergence with the expected results for simple analytic limits. In the process of building and testing the modules necessary to implement this problem, I document several extensions to the Monte Carlo code’s capabilities implemented specifically for this application, including the ability for multiple populations of Monte Carlo photons to be evolved simultaneously, enabling each population to propagate through the domain with a unique frequency-dependent scattering or absorption opacity depending on how the photon was emitted. This is a crucial feature for the exoplanet atmosphere problem as the radiation field includes ionizing radiation from the star, the stellar Lyα line, and Lyα produced within the atmosphere by recombination. Using this module I have performed the first of several calculations modeling accurate radiation forces, heating, and cooling in the atmospheres of planets irradiated by strong EUV emission. Full-scale dynamically-coupled simulations will begin as soon as the completion of this dissertation. In Chapter 4, I explore numerical solutions to radiation-driven winds from the surfaces of neutron stars undergoing photospheric radius expansion during a Type I X-ray burst. I also utilize Athena++ to construct a numerical solution of the wind, but rather than using the Monte Carlo radiation transfer module as in Chapter 3, I instead use a direct solution of the radiative transfer equation along discrete angles. I have developed infrastructure for Athena++ that allows simulations to interpolate their boundary conditions from another powerful software, MESA, which has already been used to simulate radiation-driven winds from neutron stars using the diffusion approximation for optically-thick radiation. By leveraging these two powerful codes, I extend the existing wind models in MESA to include more realistic radiative transfer, progressing toward the most accurate time-dependent X-ray burst simulations to date.