Title: Dense Gas and Star Formation Rates in Galaxies Phil Solomon Astronomy Program SUNY Stony Brook Abstract: Results are presented on a large survey of HCN emission from 65 spiral galaxies. including normal spirals, luminous and ultraluminous galaxies. HCN emission is a tracer of dense molecular gas associated with star forming GMC cores, the sites of star formation. I analyze the relationship between the total far IR luminosity a tracer of the star formation rate, the HCN line luminosity a tracer of the mass of dense gas, and the CO luminosity a tracer of the total molecular content. There is a tight linear correlation between the HCN luminosity and the far IR luminosity over 3 orders of magnitude ( unlike the weaker and nonlinear IR-Co relation) The direct consequence of the linear relation is that the star formation law in terms of dense molecular gas has a power law index of 1.0. The global star formation rate in these galaxies is linearly proportional to the amount of dense gas in normal spirals luminous and ultraluminous galaxies, the most luminous objects in the local universe. This is strong evidence for star formation as the power source in ultraluminous galaxies. HCN emission is a molecular tracer directly related to star formation.