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 H alpha. 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 approximately - 1.5 over 1.8 orders of magnitude. The luminosity distribution is approximately a power law as well, with a slope of approximately - 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 approximately - 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.