2003ApJ...590..271E

The flocculent structure of star formation in galaxies has a Fourier transform power spectrum for azimuthal intensity scans with a power-law slope that increases systematically from about -1 at large scales to about -5/3 at small scales. This is the same pattern as in the power spectra for azimuthal scans of H I emission in the Large Magellanic Clouds and for flocculent dust clouds in galactic nuclei. The steep part also corresponds to the slope of about -3 for two-dimensional power spectra that have been observed in atomic and molecular gas surveys of the Milky Way and the Large and Small Magellanic Clouds. The power-law structure for star formation in galaxies arises in both flocculent and grand-design disks, which implies that star formation is the same in each and most likely related to turbulence. The characteristic scale that separates these two slopes corresponds to several tens of pixels or several hundred parsecs in most galaxies, which is comparable to the scale height, the inverse of the Jeans wavenumber, and the size of the largest star complexes. We suggest that the power spectrum of optical light is the result of turbulence and that the large-scale turbulent motions are generated by sheared gravitational instabilities that make flocculent spiral arms first and then cascade to form clouds and clusters on smaller scales. Stellar energy sources presumably contribute to this turbulence by driving smaller scale motions and by replacing the gravitational binding energy that is released during spiral arm collapse. The spiral wave mode in the image of M81 is removed by reconstructing the Fourier transforms without the lowest 10 wavenumbers. The result shows the underlying flocculent spirals and reverse-shear spirals of star formation that are normally overwhelmed by the density wave.