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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.