We present Herschel observations of the core of the Perseus cluster of galaxies. The brightest cluster galaxy, NGC 1275, is surrounded by a network of filaments previously imaged extensively in H{alpha} and CO. In this work, we report detections of FIR lines with Herschel. All but one of the lines are spatially extended, with the [CII] line emission extending up to 25 kpc from the core. There is spatial and kinematical correlation among [CII], H{alpha} and CO, which gives us confidence to model the different components of the gas with a common heating model. With the help of FIR continuum Herschel measurements, together with a suite of coeval radio, submm and infrared data, we performed a SED fitting of NGC 1275 using a model that contains contributions from dust emission as well as synchrotron AGN emission. The data indicate a low dust emissivity index, beta ~ 1, a total dust mass close to 10^7 solar mass, a cold dust component with temperature 38 pm 2 K and a warm dust component with temperature of 116 pm 9 K. The FIR-derived star formation rate (SFR) is 24 pm 1 solar mass per yr, in close agreement with the FUV-derived SFR. We investigated in detail the source of the Herschel FIR and H{alpha} emissions emerging from a core region 4 kpc in radius. Based on simulations conducted using the radiative transfer code, CLOUDY, a heating model comprising old and young stellar populations is sufficient to explain these observations. We have also detected [CII] in three well-studied regions of the filaments. We find a [OI]/[CII] ratio about 1 dex smaller than predicted by the otherwise functional Ferland (2009) model. The line ratio suggests that the lines are optically thick, as is typical of galactic PDRs, and implies that there is a large reservoir of cold atomic gas. [abridged]
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