  NGC 1097 is a nearby SBb galaxy with a Seyfert nucleus and a bright starburst
ring. We study the physical properties of the interstellar medium (ISM) in the
ring using spatially resolved far-infrared spectral maps of the circumnuclear
starburst ring of NGC 1097, obtained with the PACS spectrometer on board the
Herschel Space Telescope. In particular, we map the important ISM cooling and
diagnostic emission lines of [OI] 63 $\mu$m, [OIII] 88 $\mu$m, [NII] 122
$\mu$m, [CII] 158 $\mu$m and [NII] 205 $\mu$m. We observe that in the [OI] 63
$\mu$m, [OIII] 88 $\mu$m, and [NII] 122 $\mu$m line maps, the emission is
enhanced in clumps along the NE part of the ring. We observe evidence of rapid
rotation in the circumnuclear ring, with a rotation velocity of ~220$ km
s$^{-1}$ (inclination uncorrected) measured in all lines. The [OI] 63
$\mu$m/[CII] 158 $\mu$m ratio varies smoothly throughout the central region,
and is enhanced on the northeastern part of the ring, which may indicate a
stronger radiation field. This enhancement coincides with peaks in the [OI] 63
$\mu$m and [OIII] 88 $\mu$m maps. Variations of the [NII] 122 $\mu$m/[NII] 205
$\mu$m ratio correspond to a range in the ionized gas density between 150 and
400 cm$^{-3}$.
