Estimates of relativistic electron and proton energy densities in starburst galactic nuclei from radio measurements

The energy density of energetic protons, U_p, in several nearby starburst nuclei (SBNs) has been directly deduced from γ-ray measurements of the radiative decay of π⁰ produced in interactions with ambient protons. Lack of sufficient sensitivity and spatial resolution makes this direct deduction unrealistic in the foreseeable future for even a moderately distant SBN. 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 region's 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.