  We have studied the relationships between the radio continuum (RC) and CO
emission for a set of galaxies selected from the BIMA Survey of Nearby
Galaxies. We find that the global CO-RC correlation is as tight as the global
FIR-RC correlation for the 24 galaxies studied. Within 9 galaxies with ~6
arcsec CO and RC data available, the CO and RC emission is as tightly
correlated as its global value; the radially averaged correlation is nearly
linear, extends over four order of magnitude and holds down to the smallest
linear resolution of the observations, which is ~100 pc. We define qco as the
log of the ratio of the CO to RC flux as a way to characterize the CO-RC
correlation. Combining 6 arcsec pixel-by-pixel comparisons across all sources
yields an average small-scale correlation of qco = 1.1 +/- 0.28; that is, the
spatially resolved correlation has a dispersion that is less than a factor of
2. There are however systematic variations in the CO/RC ratio; the strongest
organized structures in qco tend to be found along spiral arms and on size
scales much larger than the resolution of the observations. We do not measure
any systematic trend in CO/RC ratio as a function of radius in galaxies. The
constancy of the CO/RC ratio stands in contrast to the previously measured
decrease in the FIR/RC ratio as a function of radius in galaxies. We suggest
that the excellent correlation between the CO, RC and FIR emission in galaxies
is a consequence of regulation by hydrostatic pressure; this model links all
three emissions without invoking an explicit dependence on a star formation
scenario.
