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, [CII](158 \mu m), [NII](122 & 205 \mu m), [OI](63 and 145 \mu m) and [OIII](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 radiation field, G_0, resolving details on physical scales of roughly 600 pc. We find an average [CII]/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 far-ultraviolet (FUV) radiation field, G_0 and the hydrogen density, n, peaking in the nucleus of the galaxy, 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.