Hierarchical Star Formation in the Spiral Galaxy NGC 628

The distributions of size and luminosity for star-forming regions in the nearby spiral galaxy NGC 628 are studied over a wide range of scales using progressively blurred versions of an image from the Hubble Space Telescope Advanced Camera for Surveys. Four optical filters are considered for the central region, including Halpha. Two filters are used for an outer region. The features in each blurred image are counted and measured using SExtractor. The cumulative size distribution is found to be a power law in all passbands with a slope of about -1.5 over 1.8 orders of magnitudes. The luminosity distribution is approximately a power law too, with a slope of about -1 for logarithmic intervals of luminosity. The results suggest a scale-free nature for stellar aggregates in a galaxy disk. Fractal models of thin disks reproduce the projected size distribution and suggest a projected mass distribution slope of about -0.5 for these extended regions. This mass slope converts to the observed luminosity slope if we account for luminosity evolution and longer lifetimes in larger regions.