The classical D-type expansion of spherical H II regions
  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.
