We have acquired radio continuum data between 70,MHz and 48,GHz for a sample of 19 southern starburst galaxies at moderate redshifts ($0.067 < z < 0.227$) with the aim of separating synchrotron and free-free emission components. Using a Bayesian framework we find the radio continuum is rarely characterised well by a single power law, instead often exhibiting low frequency turnovers below 500,MHz, steepening at mid-to-high frequencies, and a flattening at high frequencies where free-free emission begins to dominate over the synchrotron emission. These higher order curvature components may be attributed to free-free absorption across multiple regions of star formation with varying optical depths. The decomposed synchrotron and free-free emission components in our sample of galaxies form strong correlations with the total-infrared bolometric luminosities. Finally, we find that without accounting for free-free absorption with turnovers between 90 to 500,MHz the radio-continuum at low frequency ($ u < 200$,MHz) could be overestimated by upwards of a factor of twelve if a simple power law extrapolation is used from higher frequencies. The mean synchrotron spectral index of our sample is constrained to be $alpha=-1.06$, which is steeper then the canonical value of $-0.8$ for normal galaxies. We suggest this may be caused by an intrinsically steeper cosmic ray distribution.
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