Insights into gas heating and cooling in the disc of NGC 891 from Herschel far-infrared spectroscopy

We present Herschel PACS and SPIRE spectroscopy of the most important far-infrared cooling lines in the nearby edge-on spiral galaxy, NGC 891: [CII] 158 $\mu$m, [NII] 122, 205 $\mu$m, [OI] 63, 145 $\mu$m, and [OIII] 88 $\mu$m. We find that the photoelectric heating efficiency of the gas, traced via the ([CII]+[OII]63)/$F_{\mathrm{TIR}}$ ratio, varies from a mean of 3.5$\times$10$^{-3}$ in the centre up to 8$\times$10$^{-3}$ at increasing radial and vertical distances in the disc. A decrease in ([CII]+[OII]63)/$F_{\mathrm{TIR}}$ but constant ([CII]+[OI]63)/$F_{\mathrm{PAH}}$ with increasing FIR colour suggests that polycyclic aromatic hydrocarbons (PAHs) may become important for gas heating in the central regions. We compare the observed flux of the FIR cooling lines and total IR emission with the predicted flux from a PDR model to determine the gas density, surface temperature and the strength of the incident far-ultraviolet (FUV) radiation field, $G_{0}$. Resolving details on physical scales of ~0.6 kpc, a pixel-by-pixel analysis reveals that the majority of the PDRs in NGC 891's disc have hydrogen densities of 1 < log ($n$/cm$^{-3}$) < 3.5 experiencing an incident FUV radiation field with strengths of 1.7 < log $G_0$ < 3. Although these values we derive for most of the disc are consistent with the gas properties found in PDRs in the spiral arms and inter-arm regions of M51, observed radial trends in $n$ and $G_0$ are shown to be sensitive to varying optical thickness in the lines, demonstrating the importance of accurately accounting for optical depth effects when interpreting observations of high inclination systems. With an empirical relationship between the MIPS 24 $\mu$m and [NII] 205 $\mu$m emission, we estimate an enhancement of the FUV radiation field strength in the far north-eastern side of the disc.