The energy density of energetic protons, U_p, in several nearby starburst nuclei (SBNs) has been directly deduced from gamma-ray measurements of the radiative decay of neutral pions produced in interactions with ambient protons. Lack of sufficient se
nsitivity and spatial resolution makes this direct deduction unrealistic in the foreseeable future for even moderately distant SBNs. A more viable indirect method for determining U_p in star-forming galaxies is to use its theoretically based scaling to the energy density of energetic electrons, U_e, which can be directly deduced from radio synchrotron and possibly also nonthermal hard X-ray emission. In order to improve the quantitative basis and diagnostic power of this leptonic method we reformulate and clarify its main aspects. Doing so we obtain a basic expression for the ratio U_p/U_e in terms of the proton and electron masses and the power-law indices that characterize the particle spectral distributions in regions where the total particle energy density is at equipartition with that of the mean magnetic field. We also express the field strength and the particle energy density in the equipartition region in terms of the regions size, mean gas density, IR and radio fluxes, and distance from the observer, and determine values of U_p in a sample of nine nearby and local SBNs.
Cosmic-ray energy densities in central regions of starburst galaxies, as inferred from radio and gamma-ray measurements of, respectively, non-thermal synchrotron and neutral pion decay emission, are typically U_p = O(100)eV/cm3, i.e. typically at lea
st an order of magnitude larger than near the Galactic center and in other non-very-actively star-forming galaxies. We first show that these very different energy-density levels reflect a similar disparity in the respective supernova rates in the two environments, which is not unexpected given the supernova origin of (Galactic) energetic particles. As a consequence of this correspondence, we then demonstrate that there is partial quantitative evidence that the stellar initial mass function (IMF) in starburst nuclei has a low-mass truncation at ~2M_sun, as predicted by theoretical models of turbulent media, in contrast with the much smaller value of 0.1M_sun that characterizes the low-mass cutoff of the stellar IMF in `normal galactic environments.
