  Recent analyses of the gamma-ray spectrum from the ultra-luminous infrared
galaxy Arp 220 have revealed a discrepancy in the cosmic ray energy injection
rates derived from the gamma-rays versus the radio emission. While the observed
radio emission is consistent with the star formation rate inferred from
infrared observations, a significantly higher cosmic ray population is
necessary to accurately model the measured gamma-ray flux. To resolve this
discrepancy between the radio and gamma-ray observations, we find that we must
increase the cosmic ray energy injection rate and account for an infrared
optical depth greater than unity. Raising the energy injection rate naturally
raises the total gamma-ray flux but also raises the radio flux unless there is
also an increase in the energy loss rate for cosmic ray leptons. A optically
thick medium results in an increase in energy losses via inverse Compton for
cosmic ray leptons and preserves agreement with submillimeter, millimeter, and
infrared wavelength observations.
