Pitch Angle of Galactic Spiral Arms
  One of the key parameters that characterize spiral arms in disk galaxies is a
pitch angle that measures the inclination of a spiral arm to the direction of
galactic rotation. The pitch angle differs from galaxy to galaxy, which
suggests that the rotation law of galactic disks determines it. In order to
investigate the relation between the pitch angle of spiral arms and the shear
rate of galactic differential rotation, we perform local $N$-body simulations
of pure stellar disks. We find that the pitch angle increases with the epicycle
frequency and decreases with the shear rate and obtain the fitting formula.
This dependence is explained by the swing amplification mechanism.
