  We present a [CII] 158um map of the entire M51 (including M51b) grand--design
spiral galaxy observed with the FIFI-LS instrument on SOFIA. We compare the
[CII] emission with the total far--infrared (TIR) intensity and star formation
rate(SFR) surface density maps (derived using H_alpha and 24um emission) to
study the relationship between [CII] and the star formation activity in a
variety of environments within M51 on scales of 16" corresponding to ~660 pc.
We find that [CII] and the SFR surface density are well correlated in the
central, spiral arm, and inter-arm regions. The correlation is in good
agreement with that found for a larger sample of nearby galaxies at kpc scales.
We find that the SFR, and [CII] and TIR luminosities in M51 are dominated by
the extended emission in M51's disk. The companion galaxy M51b, however, shows
a deficit of [CII] emission compared with the TIR emission and SFR surface
density, with [CII] emission detected only in the S-W part of this galaxy. The
[CII] deficit is associated with an enhanced dust temperature in this galaxy.
We interpret the faint [CII] emission in M51b to be a result of suppressed star
formation in this galaxy, while the bright mid- and far-infrared emission,
which drive the TIR and SFR values, are powered by other mechanisms. A similar
but less pronounced effect is seen at the location of the black hole in M51's
center. The observed [CII] deficit in M51b suggests that this galaxy is a
valuable laboratory to study the origin of the apparent [CII] deficit observed
in ultra-luminous galaxies.
