Coupling local to global star formation in spiral galaxies: the effect
  of differential rotation
  Star formation is one of the key factors that shapes galaxies. This process
is relatively well understood from both simulations and observations on a small
"local" scale of individual giant molecular clouds and also on a "global"
galaxy-wide scale (e.g. the Kennicutt-Schmidt law). However, there is still no
understanding on how to connect global to local star formation scales and
whether this connection is at all possible. Here we analyze spatially resolved
kinematics and the star formation rate density $\Sigma_{SFR}$ for a combined
sample of 17 nearby spiral galaxies obtained using our own optical observations
in H$\alpha$ for 9 galaxies and neutral hydrogen radio observations combined
with a multi-wavelength spectral energy distribution analysis for 8 galaxies
from the THINGS project. We show that the azimuthally averaged normalized star
formation rate density in spiral galaxies on a scale of a few hundred parsecs
is proportional to the kinetic energy of giant molecular cloud collisions due
to differential rotation of the galactic disc. This energy is calculated from
the rotation curve using the two Oort parameters A and B as $\log (\Sigma_{SFR}
/ SFR_{tot}) \propto \log[2 A^2+ 5 B^2]$. The total kinetic energy of collision
is defined by the shear velocity that is proportional to A and the rotational
energy of a cloud proportional to the vorticity B. Hence, shear does not act as
a stabilizing factor for the cloud collapse thus reducing star formation but
rather increases it by boosting the kinetic energy of collisions. This result
can be a tool through which one can predict a radial distribution of star
formation surface density using only a rotation curve.
