Abstract
The fractal structure of star formation on large scales in disk galaxies is studied using the size distribution function of stellar aggregates in kiloparsec-scale star fields. Archival Hubble Space Telescope images of 10 galaxies are Gaussian-smoothed to define the aggregates, and a count of these aggregates versus smoothing scale gives the fractal dimension. Fractal and Poisson models confirm the procedure. The fractal dimension of star formation in all of the galaxies is ∼2.3. This is the same as the fractal dimension of interstellar gas in the Milky Way and nearby galaxies, suggesting that star formation is a passive tracer of gas structure defined by self-gravity and turbulence. Dense clusters such as the Pleiades form at the bottom of the hierarchy of structures, where the protostellar gas is densest. If most stars form in such clusters, then the fractal arises from the spatial distribution of their positions, giving dispersed star fields from continuous cluster disruption. Dense clusters should have an upper mass limit that increases with pressure, from ∼103 M⊙ in regions like the solar neighborhood to ∼106 M⊙ in starbursts.