Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...

that the I-front expands as an hour-glass shape above and below the disk,
and becomes more spherical at later times. Figure 3.8 compares the I-front
evolution with that predicted by the analytical Shu champagne flow solution
(Shu et al. 2002, see also Alvarez et al. 2006). Different analytical solutions
can be found for the evolution of gas under the propagation of an I-front into
a powerlaw density profile, which in our case is approximately ρ ∝ r −2 . The
ratio of the un-ionized gas temperature to that of the H ii region must also be
specified for the analytical solution, and in our case we choose a ratio of 20,000
K to 1000 K, or 0.05. The propagation of the I-front can then be described,
assuming D-type conditions and that the I-front closely follows the preceeding
shock, by a velocity of
while the size of the I-front is
vs = xscs, (3.15)
rs = xscst, (3.16)
where cs is the ionized gas soundspeed and xs is the position of the shock in
similarity coordinates, which for our case is xs = 2.54 (see panel b of Figure
3.8).
Multiple factors cause deviations from the analytical solution. For in-
stance, the density structure of the gas is not spherically symmetric. Further-
more, the initially close proximity of the ionization front to the sink causes
the gravity of the sink to have a non-negligible effect on the early H ii region
dynamics, a factor that is neglected in the analytical solution. However, this
effect loses importance as the H ii region grows well beyond the gravitational
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