  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.
