CO Multi-line Imaging of Nearby Galaxies (COMING). III. Dynamical effect
  on molecular gas density and star formation in the barred spiral galaxy NGC
  4303
  We present the results of $^{12}$CO($J$=1-0) and $^{13}$CO($J$=1-0)
simultaneous mappings toward the nearby barred spiral galaxy NGC 4303 as a part
of the CO Multi-line Imaging of Nearby Galaxies (COMING) project. Barred spiral
galaxies often show lower star-formation efficiency (SFE) in their bar region
compared to the spiral arms. In this paper, we examine the relation between the
SFEs and the volume densities of molecular gas $n(\rm{H}_2)$ in the eight
different regions within the galactic disk with CO data combined with archival
far-ultraviolet and 24 $\mu$m data. We confirmed that SFE in the bar region is
lower by 39% than that in the spiral arms. Moreover, velocity-alignment
stacking analysis was performed for the spectra in the individual regions. The
integrated intensity ratios of $^{12}$CO to $^{13}$CO ($R_{12/13}$) range from
10 to 17 as the results of stacking. Fixing a kinetic temperature of molecular
gas, $n(\rm{H}_2)$ was derived from $R_{12/13}$ via non-local thermodynamic
equilibrium (non-LTE) analysis. The density $n(\rm{H}_2)$ in the bar is lower
by 31-37% than that in the arms and there is a rather tight positive
correlation between SFEs and $n(\rm{H}_2)$, with a correlation coefficient of
$\sim 0.8$. Furthermore, we found a dependence of $n(\rm{H}_2)$ on the velocity
dispersion of inter-molecular clouds ($\Delta V/ \sin i$). Specifically,
$n(\rm{H}_2)$ increases as $\Delta V/ \sin i$ increases when $\Delta V/ \sin i
< 100$ km s$^{-1}$. On the other hand, $n(\rm{H}_2)$ decreases as $\Delta V/
\sin i$ increases when $\Delta V/ \sin i > 100$ km s$^{-1}$. These relations
indicate that the variations of SFE could be caused by the volume densities of
molecular gas, and the volume densities could be governed by the dynamical
influence such as cloud-cloud collisions, shear and enhanced inner-cloud
turbulence.
