The Fractal Distribution of HiiRegions in Disk Galaxies

It is known that the gas has a fractal structure in a wide range of spatial scales with a fractal dimension that seems to be a constant around Df = 2.7. It is expected that stars forming from this fractal medium exhibit similar fractal patterns. Here we address this issue by quantifying the degree to which star-forming events are clumped. We develop, test, and apply a precise and accurate technique to calculate the correlation dimension Dc of the distribution of HII regions in a sample of disk galaxies. We find that the determination of Dc is limited by the number of HII regions, since if there are < 100 regions available then a bias tending to underestimate the dimension is produced. The reliable results are distributed in the range 1.5 < Dc < 2.0 with an average value Dc = 1.81. This corresponds to a three-dimensional dimension of Df = 2.73, very similar to the value measured in the interstellar clouds. However, we get significant variations in the fractal dimension among galaxies, contrary to a universal picture sometimes claimed in literature. The fractal dimension exhibits a weak but significant correlation with the absolute magnitude and, to a lesser extent, with the galactic radius. The faintest galaxies tend to distribute their HII regions in more clustered (less uniform) patterns. The fractal dimension for the brightest HII regions within the same galaxy seems to be smaller than for the faintest ones suggesting some kind of evolutionary efffect, but the obtained correlation remains unchanged if only the brightest regions are taken into account.