The circumnuclear region of M31, consisting of multiphase interstellar medium, provides a close-up view of the interaction of the central supermassive black hole and surrounding materials. Far-infrared (FIR) line structure lines and their flux ratios can be used as diagnostics of physical properties of the neutral gas in this region. Here we present the first FIR spectroscopic mapping of the circumnuclear region of M31 in [C ii] 158 um, [O i] 63 um and [O iii] 88 um lines with the Herschel Space Observatory, covering a ~500 x 500 pc (2 x 2) field. Significant emissions of all three lines are detected along the so-called nuclear spiral across the central kpc of M31. The velocity field under a spatial resolution of ~50 pc of the three lines are in broad consistency and also consistent with previous CO(3-2) line observations in the central region. Combined with existing [C ii] and CO(3-2) observations of five other fields targeting on the disk, we derived the radial distribution of [C ii]/CO(3-2) flux ratio, and found that this ratio is higher in the center than the disk, indicating a low gas density and strong radiation field in the central region. We also found that the [C ii]/FIR ratio in the central region is 5.4 (+-0.8) x 10^-3, which exhibits an increasing trend with the galactocentric radius, suggesting an increasing contribution from old stellar population to dust heating towards the center.
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