Regional Variations in the Dense Gas Heating and Cooling in M51 from Herschel Far-infrared Spectroscopy

We present Herschel PACS and SPIRE spectroscopy of the most important far-infrared cooling lines in M51, [C II](158 mu m), [N II](122 and 205 mu m), [OI](63 and 145 mu m), and [O III](88 mu m). We compare the observed flux of these lines with the predicted flux from a photon-dominated region model to determine characteristics of the cold gas such as density, temperature, and the far-ultraviolet (FUV) radiation field, G(0), resolving details on physical scales of roughly 600 pc. We find an average [C II]/F-TIR of 4 x 10(-3), in agreement with previous studies of other galaxies. A pixel-by-pixel analysis of four distinct regions of M51 shows a radially decreasing trend in both the FUV radiation field, G(0), and the hydrogen density, n, peaking in the nucleus of the galaxy, and then falling off out to the arm and interarm regions. We see for the first time that the FUV flux and gas density are similar in the differing environments of the arm and interarm regions, suggesting that the inherent physical properties of the molecular clouds in both regions are essentially the same.