The classical D-type expansion of spherical H II regions

TL;DR

This paper develops an improved analytical model for the expansion of spherical H II regions, accurately capturing late-time dynamics, pressure equilibrium, and oscillations, and aligning well with numerical results.

Contribution

It introduces a matched asymptotic equation that incorporates shell inertia and ambient temperature effects, surpassing previous models in accuracy.

Findings

The model accurately predicts the H II region radius at all times.

It captures late-time stalling and oscillations of the ionization front.

The solution works for both constant and varying radiation sources.

Abstract

Recent numerical and analytic work has highlighted some shortcomings in our understanding of the dynamics of H II region expansion, especially at late times, when the H II region approaches pressure equilibrium with the ambient medium. Here we reconsider the idealized case of a constant radiation source in a uniform and spherically symmetric ambient medium, with an isothermal equation of state. A thick-shell solution is developed which captures the stalling of the ionization front and the decay of the leading shock to a weak compression wave as it escapes to large radii. An acoustic approximation is introduced to capture the late-time damped oscillations of the H II region about the stagnation radius. Putting these together, a matched asymptotic equation is derived for the radius of the ionization front which accounts for both the inertia of the expanding shell and the finite temperature of the ambient medium. The solution to this equation is shown to agree very well with the numerical solution at all times, and is superior to all previously published solutions. The matched asymptotic solution can also accurately model the variation of H II region radius for a time-varying radiation source.