  The [CII] 158 micron line is one of the strongest emission lines observed in
star-forming galaxies, and has been empirically measured to correlate with the
star formation rate (SFR) globally and on ~kpc scales. However, due to the
multi-phase origins of [CII], one might expect this relation to break down at
small scales. We investigate the origins of [CII] emission by examining high
spatial resolution observations of [CII] in M31, with the Survey of Lines in
M31 (SLIM). We present five ~700x700 pc (3"x3") Fields mapping the [CII]
emission, Halpha emission, combined with ancillary infrared (IR) data. We
spatially separate star-forming regions from diffuse gas and dust emission on
~50 pc scales. We find that the [CII] - SFR correlation holds even at these
scales, although the relation typically has a flatter slope than found at
larger (~kpc) scales. While the Halpha emission in M31 is concentrated in the
SFR regions, we find that a significant amount (~20-90%) of the [CII] emission
comes from outside star-forming regions, and that the total IR (TIR) emission
has the highest diffuse fraction of all SFR tracers. We find a weak correlation
of the [CII]/TIR to dust color in each Field, and find a large scale trend of
increasing [CII]/TIR with galactocentric radius. The differences in the
relative diffuse fractions of [CII], Halpha and IR tracers are likely caused by
a combination of energetic photon leakage from HII regions and heating by the
diffuse radiation field arising from older (B-star) stellar populations.
However, we find that by averaging our measurements over ~kpc scales, these
effects are minimized, and the relation between [CII] and SFR found in other
nearby galaxy studies is retrieved.
