The James Clerk Maxwell Telescope Nearby Galaxies Legacy Survey IX:
  $^{12}$CO $J=3\to2$ Observations of NGC 2976 and NGC 3351
  We present $^{12}$CO \textit{J=3$\rightarrow$2} maps of NGC 2976 and NGC 3351
obtained with the James Clerk Maxwell Telescope (JCMT), both early targets of
the JCMT Nearby Galaxy Legacy Survey (NGLS). We combine the present
observations with $^{12}$CO \textit{J=1$\rightarrow$0} data and find that the
computed $^{12}$CO \textit{J=3$\rightarrow$2} to $^{12}$CO
\textit{J=1$\rightarrow$0} line ratio ($R_{31}$) agrees with values measured in
other NGLS field galaxies. We compute the M$_{\rm{H_2}}$ value and find that it
is robust against the value of $R_{31}$ used. Using \textsc{Hi} data from the
The \textsc{Hi} Nearby Galaxy Survey (THINGS) survey, we find a tight
correlation between surface density of H$_2$ and star formation rate density
for NGC 3351 when $^{12}$CO \textit{J=3$\rightarrow$2} data are used. Finally,
we compare the $^{12}$CO \textit{J=3$\rightarrow$2} intensity with the PAH 8
$\mu$m surface brightness and find a good correlation in the high surface
brightness regions. We extend this study to include all 25 \textit{Spitzer}
Infrared Nearby Galaxies Survey (SINGS) galaxies within the NGLS sample and
find a tight correlation at large spatial scales. We suggest that both PAH 8
$\mu$m and $^{12}$CO \textit{J=3$\rightarrow$2} are likely to originate in
regions of active star formation.
