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We examine $8\mu$m IRAC images of the grand design two-arm spiral galaxiesM81 and M51 using a new method whereby pitch angles are locally determined as afunction of scale and position, in contrast to traditional Fourier transformspectral analyses which fit to average pitch angles for whole galaxies. The newanalysis is based on a correlation between pieces of a galaxy in circularwindows of $(\ln R, \theta)$ space and logarithmic spirals with various pitchangles. The diameter of the windows is varied to study different scales. Theresult is a best-fit pitch angle to the spiral structure as a function ofposition and scale, or a distribution function of pitch angles as a function ofscale for a given galactic region or area. We apply the method to determine thedistribution of pitch angles in the arm and interarm regions of these twogalaxies. In the arms, the method reproduces the known pitch angles for themain spirals on a large scale, but also shows higher pitch angles on smallerscales resulting from dust feathers. For the interarms, there is a broaddistribution of pitch angles representing the continuation and evolution of thespiral arm feathers as the flow moves into the interarm regions. Our methodshows a multiplicity of spiral structures on different scales, as expected fromgas flow processes in a gravitating, turbulent and shearing interstellarmedium. We also present results for M81 using classical 1D and 2D Fouriertransforms, together with a new correlation method, which shows good agreementwith conventional 2D Fourier transforms.

A new method to estimate local pitch angles in spiral galaxies: Application to spiral arms and feathers in M81 and M51