The Dense Gas Mass Fraction and the Relationship to Star Formation in
  M51
  Observations of 12CO J=1-0 and HCN J=1-0 emission from NGC 5194 (M51) made
with the 50~meter Large Millimeter Telescope and the SEQUOIA focal plane array
are presented. Using the HCN to CO ratio, we examine the dense gas mass
fraction over a range of environmental conditions within the galaxy. Within the
disk, the dense gas mass fraction varies along spiral arms but the average
value over all spiral arms is comparable to the mean value of interarm regions.
We suggest that the near constant dense gas mass fraction throughout the disk
arises from a population of density stratified, self gravitating molecular
clouds and the required density threshold to detect each spectral line. The
measured dense gas fraction significantly increases in the central bulge in
response to the effective pressure, P_e, from the weight from the stellar and
gas components. This pressure modifies the dynamical state of the molecular
cloud population and possibly, the HCN emitting regions, in the central bulge
from self-gravitating to diffuse configurations in which P_e is greater than
the gravitational energy density of individual clouds. Diffuse molecular clouds
comprise a significant fraction of the molecular gas mass in the central bulge,
which may account for the measured sublinear relationships between the surface
densities of the star formation rate and molecular and dense gas.
