Interpreting the Low Frequency Radio Spectra of Starburst Galaxies: A
  Pudding of Str\"omgren Spheres
  The low frequency radio emission of starburst galaxies is informative, but it
can be absorbed in several ways. Most importantly, starburst galaxies are home
to many H II regions, whose free-free absorption blocks low frequency radio
waves. These H II regions are discrete objects, but most multiwavelength models
of starbursts assume a uniform medium of ionized gas, if they include the
absorption at all. I calculate the effective absorption coefficient of H II
regions in starbursts, which is ultimately a cross section times the density of
H II regions. The cross sections are calculated by assuming that H II regions
are Str\"omgren spheres. The coefficient asymptotes to a constant value at low
frequencies, because H II regions partially cover the starburst, and are buried
part way into the starburst's synchrotron emitting material. Considering
Str\"omgren spheres around either OB stars or Super Star Clusters, I
demonstrate the method by fitting to the low frequency radio spectrum of M82. I
discuss implications of the results for synchrotron spectrum shape, H II region
pressure, and free-free emission as a star-formation rate indicator. However,
these results are preliminary, and could be affected by systematics. I argue
that there is no volume-filling warm ionized medium in starbursts, and that H
II regions may be the most important absorption process down to ~10 MHz. Future
data at low and high radio frequency will improve our knowledge of the ionized
gas.
