Interpreting the Low Frequency Radio Spectra of Starburst Galaxies: A Pudding of Str\"omgren Spheres

Abstract

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.