Dense Gas in the Outer Spiral Arm of M51
  There is a linear relation between the mass of dense gas, traced by the
HCN(1-0) luminosity, and the star formation rate (SFR), traced by the
far-infrared luminosity. Recent observations of galactic disks have shown some
systematic variations. In order to explore the SFR-dense gas link at high
resolution ($\sim 4"$, $\sim 150$ pc) in the outer disk of an external galaxy,
we have mapped a region about 5 kpc from the center along the northern spiral
arm of M51 in the HCN(1-0), HCO$^+$(1-0) and HNC(1-0) emission lines using the
Northern Extended Millimeter Array (NOEMA) interferometer. The HCN and HCO$^+$
lines were detected in 6 giant molecular associations (GMAs) while HNC emission
was only detected in the two brightest GMAs. One of the GMAs hosts a powerful
HII region and HCN is stronger than HCO$^+$ there. Comparing with observations
of GMAs in the disks of M31 and M33 at similar angular resolution ($\sim 100$
pc), we find that GMAs in the outer disk of M51 are brighter in both HCN and
HCO$^+$ lines by a factor of 3 on average. However, the $I_{HCN}/I_{CO}$ and
$I_{HCO^+}/I_{CO}$ ratios are similar to the ratios in nearby galactic disks
and the Galactic plane. Using the Herschel 70 $\mu$m data to trace the total IR
luminosity at the resolution of the GMAs, we find that both the
L$_{IR}$-L$_{HCN}$ and L$_{IR}$-L$_{HCO^+}$ relations in the outer disk GMAs
are consistent with the proportionality between the L$_{IR}$ and the dense gas
mass established globally in galaxies within the scatter. The IR/HCN and
IR/HCO$^+$ ratios of the GMAs vary by a factor of 3, probably depending on
whether massive stars are forming or not.
