We have detected the H92alpha radio recombination line from two dwarf starburst galaxies, NGC 5253 and He 2-10, using the Very Large Array. Both the line data as well as the radio continuum data are used to model the properties of the ionized gas in the centers of these galaxies. We consider a multi-density model for radio recombination lines and show why previous models, which were based on the assumption of gas at a single density, are valid in many situations. The models show that the ionized gas has a density of ~10^4 /cc in both galaxies, with an effective size of 2-10 pc and a total mass of about 10^4 Msun. The derived production rate of Lyman continuum photons is ~2.5 x 10^{52} /s in both the galaxies and the corresponding mass of stars (assuming a Salpeter IMF) is ~10^5 msun. The implied stellar density shows that the observed radio recombination lines arise from ionized gas around super star clusters (SSCs) in both galaxies (these SSCs have been recently detected through their radio continuum emission). The existence of ~10^4 Msun of ionized gas within a few parsecs of an SSC places strict constraints on dynamical models. Using simple arguments, the parameter space for a few possible models are derived. The well known radio-FIR correlation also holds for NGC 5253, although the radio emission from this galaxy is almost completely thermal. It is shown that NGC 5253 is strong evidence that the component of FIR emission from warm dust is correlated separately with the component of radio emission from thermal bremsstrahlung.
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