The Galactic HII Region Luminosity Function at Radio and Infrared
  Wavelengths
  The Galactic HII region luminosity function (LF) is an important metric for
understanding global star formation properties of the Milky Way, but only a few
studies have been done and all use relatively small numbers of HII regions. We
use a sample of 797 first Galactic quadrant HII regions compiled from the WISE
Catalog of Galactic HII Regions to examine the form of the LF at multiple
infrared and radio wavelengths. Our sample is statistically complete for all
regions powered by single stars of type O9.5V and earlier. We fit the LF at
each wavelength with single and double power laws. Averaging the results from
all wavelengths, the mean of the best-fit single power law index is
$\langle\alpha\rangle=-1.75\,\pm\,0.01$. The mean best-fit double power law
indices are $\langle\alpha_1\rangle=-1.40\,\pm\,0.03$ and
$\langle\alpha_2\rangle=-2.33\,\pm\,0.04$. We conclude that neither a single
nor a double power law is strongly favored over the other. The LFs show some
variation when we separate the HII region sample into subsets by heliocentric
distance, physical size, Galactocentric radius, and location relative to the
spiral arms, but blending individual HII regions into larger complexes does not
change the value of the power law indices of the best-fit LF models. The
consistency of the power law indices across multiple wavelengths suggests that
the LF is independent of wavelength. This implies that infrared and radio
tracers can be employed in place of H$\alpha$.
