  We present new multi-frequency radio continuum imaging of the dwarf starburst
galaxy NGC 625 obtained with the Very Large Array. Data at 20, 6, and 3.6 cm
reveal global continuum emission dominated by free-free emission, with only
mild synchrotron components. Each of the major HII regions is detected; the
individual spectral indices are thermal for the youngest regions (showing
strongest H Alpha emission) and nonthermal for the oldest. We do not detect any
sources that appear to be associated with deeply embedded, dense, young
clusters, though we have discovered one low-luminosity, obscured source that
has no luminous optical counterpart and which resides in the region of highest
optical extinction. Since NGC 625 is a Wolf-Rayet galaxy with strong recent
star formation, these radio properties suggest that the youngest star formation
complexes have not yet evolved to the point where their thermal spectra are
significantly contaminated by synchrotron emission. The nonthermal components
are associated with regions of older star formation that have smaller ionized
gas components. These results imply a range of ages of the HII regions and
radio components that agrees with our previous resolved stellar population
analysis, where an extended burst of star formation has pervaded the disk of
NGC 625 over the last ~ 50 Myr. We compare the nature of radio continuum
emission in selected nearby dwarf starburst and Wolf-Rayet galaxies,
demonstrating that thermal radio continuum emission appears to be more common
in these systems than in typical HII galaxies with less recent star formation
and more evolved stellar clusters.

Astrophysics