The Physics of the FIR-Radio Correlation: I. Calorimetry, Conspiracy, and Implications

(Abridged) The far-infrared (FIR) and radio luminosities of star-forming galaxies are linearly correlated over a very wide range in star formation rate, from normal spirals like the Milky Way to the most intense starbursts. Using one-zone models of cosmic ray (CR) injection, cooling, and escape in star-forming galaxies, we attempt to reproduce the observed FIR-radio correlation over its entire span. We show that ~2% of the kinetic energy from supernova explosions must go into primary CR electrons and that ~10 - 20% must go into primary CR protons. Secondary electrons and positrons are likely comparable to or dominate primary electrons in dense starburst galaxies. We discuss the implications of our models for the magnetic field strengths of starbursts, the detectability of starbursts by Fermi, and cosmic ray feedback. Overall, our models indicate that both CR protons and electrons escape from low surface density galaxies, but lose most of their energy before escaping dense starbursts. The FIR-radio correlation is caused by a combination of the efficient cooling of CR electrons (calorimetry) in starbursts and a conspiracy of several factors. For lower surface density galaxies, the decreasing radio emission caused by CR escape is balanced by the decreasing FIR emission caused by the low effective UV dust opacity. In starbursts, bremsstrahlung, ionization, and Inverse Compton cooling decrease the radio emission, but they are countered by secondary electrons/positrons and the decreasing critical synchrotron frequency, which both increase the radio emission. Our conclusions hold for a broad range of variations on our fiducial model.