2018/05/23 by R. J. R. Williams, Robin J. R. Williams, Thomas G. Bisbas +2
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Astrophysics and Star Formation Studies #Asymptotic expansion #Classical mechanics #Equation of state #Inertia #Ionization #Isothermal process #Mathematical analysis #Mechanics #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #RADIUS #Shell (structure) #Shock (circulatory) #Shock wave #Spherical shell #Thermodynamics #astro-ph.GA
paper · pdf · doi:10.1093/mnras/sty1484
8 pages, 5 figures. Authors' original version, revised version with minor changes accepted for publication in MNRAS
arxiv created 2018/05/23 · openalex publication_date 2018/06/18 · arxiv updated 2018/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 that 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.