A new method to estimate local pitch angles in spiral galaxies:
  Application to spiral arms and feathers in M81 and M51
  We examine $8\mu$m IRAC images of the grand design two-arm spiral galaxies
M81 and M51 using a new method whereby pitch angles are locally determined as a
function of scale and position, in contrast to traditional Fourier transform
spectral analyses which fit to average pitch angles for whole galaxies. The new
analysis is based on a correlation between pieces of a galaxy in circular
windows of $(\ln R, \theta)$ space and logarithmic spirals with various pitch
angles. The diameter of the windows is varied to study different scales. The
result is a best-fit pitch angle to the spiral structure as a function of
position and scale, or a distribution function of pitch angles as a function of
scale for a given galactic region or area. We apply the method to determine the
distribution of pitch angles in the arm and interarm regions of these two
galaxies. In the arms, the method reproduces the known pitch angles for the
main spirals on a large scale, but also shows higher pitch angles on smaller
scales resulting from dust feathers. For the interarms, there is a broad
distribution of pitch angles representing the continuation and evolution of the
spiral arm feathers as the flow moves into the interarm regions. Our method
shows a multiplicity of spiral structures on different scales, as expected from
gas flow processes in a gravitating, turbulent and shearing interstellar
medium. We also present results for M81 using classical 1D and 2D Fourier
transforms, together with a new correlation method, which shows good agreement
with conventional 2D Fourier transforms.
