  HII region heavy-element abundances throughout the Galactic disk provide
important constraints to theories of the formation and evolution of the Milky
Way. In LTE, radio recombination line (RRL) and free-free continuum emission
are accurate extinction-free tracers of the HII region electron temperature.
Since metals act as coolants in HII regions via the emission of collisionally
excited lines, the electron temperature is a proxy for metallicity. Shaver et
al. found a linear relationship between metallicity and electron temperature
with little scatter. Here, we use CLOUDY HII region simulations to (1)
investigate the accuracy of using RRLs to measure the electron temperature; and
(2) explore the metallicity-electron temperature relationship. We model 135 HII
regions with different ionizing radiation fields, densities, and metallicities.
We find that electron temperatures derived under the assumption of LTE are
about 20% systematically higher due to non-LTE effects, but overall LTE is a
good assumption for cm-wavelength RRLs. Our CLOUDY simulations are consistent
with the Shaver et al. metallicity-electron temperature relationship but there
is significant scatter since earlier spectral types or higher electron
densities yield higher electron temperatures. Using RRLs to derive electron
temperatures assuming LTE yields errors in the predicted metallicity as large
as 10%. We derive correction factors for Log(O/H) + 12 in each CLOUDY
simulation. For lower metallicities the correction factor depends primarily on
the spectral-type of the ionizing star and range from 0.95 to 1.10, whereas for
higher metallicities the correction factor depends on the density and is
between 0.97 and 1.05.
