The relationship between the velocity-integrated CO emission and the nonthermal radio continuum brightness in the disks of normal spiral galaxies is examined on a variety of length scales. On a global scale, the total CO intensity correlates strongly with the total radio continuum flux density for a sample of 31 galaxies. On scales of greater-than-or-similar-to 2 kpc in the disk of individual galaxies, we find that the ratio I(CO)/T20 remains fairly constant over the entire disk as well as from galaxy to galaxy. For the eight spirals in our sample, the disk-averaged values of I(CO)/T20 range 0.6-2.4, with the average over all eight galaxies being <I(CO)/T20> = 1.3 +/- 0.6. However, studies of giant molecular cloud complexes in the arms of nearby galaxies indicate that the relationship ceases to be constant on smaller (less-than-or-similar-to 1-2 kpc) scales, with the CO dominating the ratio. We conclude that what these various length scales actually trace are differences in the primary heating mechanism of the gas in the beam. The observed relationship between CO and nonthermal radio continuum emission can be explained by assuming that molecular gas in galactic disks is heated primarily by cosmic rays. We use the observed relationship to show that the brightness of synchrotron emission is proportional to n(cr)0.4-0.9 in galactic disks. Finally, we conclude that while in a general sense star formation is undoubtedly the primary source of energy that causes the relationship to exist, the details of the specific mechanism(s) at work are complicated by the very different scale heights and (small-scale) spatial distributions of the CO and nonthermal radio continuum emission.
