The physical relationship between the far-infrared and radio fluxes of star-forming galaxies has yet to be definitively determined. The favored interpretation, the "calorimeter model," requires that supernova generated cosmic-ray (CR) electrons cool rapidly via synchrotron radiation. However, this cooling should steepen their radio spectra beyond what is observed, and so enhanced ionization losses at low energies from high gas densities are also required. Further, evaluating the minimum energy magnetic field strength with the traditional scaling of the synchrotron flux may underestimate the true value in massive starbursts if their magnetic energy density is comparable to the hydrostatic pressure of their disks. Gamma-ray spectra of starburst galaxies, combined with radio data, provide a less ambiguous estimate of these physical properties in starburst nuclei. While the radio flux is most sensitive to the magnetic field, the GeV gamma-ray spectrum normalization depends primarily on gas density. To this end, spectra above 100?MeV were constructed for two nearby starburst galaxies, NGC?253 and M82, using Fermi data. Their nuclear radio and far-infrared spectra from the literature are compared to new models of the steady-state CR distributions expected from starburst galaxies. Models with high magnetic fields, favoring galaxy calorimetry, are overall better fits to the observations. These solutions also imply relatively high densities and CR ionization rates, consistent with molecular cloud studies.
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