  We present the first results from the EMPIRE survey, an IRAM large program
that is mapping tracers of high density molecular gas across the disks of nine
nearby star-forming galaxies. Here, we present new maps of the 3-mm transitions
of HCN, HCO+, and HNC across the whole disk of our pilot target, M51. As
expected, dense gas correlates with tracers of recent star formation, filling
the "luminosity gap" between Galactic cores and whole galaxies. In detail, we
show that both the fraction of gas that is dense, f_dense traced by HCN/CO, and
the rate at which dense gas forms stars, SFE_dense traced by IR/HCN, depend on
environment in the galaxy. The sense of the dependence is that high surface
density, high molecular gas fraction regions of the galaxy show high dense gas
fractions and low dense gas star formation efficiencies. This agrees with
recent results for individual pointings by Usero et al. 2015 but using unbiased
whole-galaxy maps. It also agrees qualitatively with the behavior observed
contrasting our own Solar Neighborhood with the central regions of the Milky
Way. The sense of the trends can be explained if the dense gas fraction tracks
interstellar pressure but star formation occurs only in regions of high density
contrast.
