A prescription for star formation feedback: the importance of multiple shell interactions

Abstract

The relation between the star formation rate and the kinetic energy increase in a region containing a large number of stellar sources is investigated as a possible prescription for star formation feedback in larger scale galaxy evolution simulations, and in connection with observed scaling relations for molecular clouds, extragalactic giant H ii regions and starburst galaxies. The kinetic energy increase is not simply proportional to the source input rate, but depends on the competition between stellar power input and dissipation caused by interactions between structures formed and driven by the star formation. A simple one-zone model is used to show that, in a steady state, the energy increase should be proportional to the two-thirds power of the stellar energy injection rate, with additional factors depending on the mean density of the region and the mean column density of the fragments. The scaling relation is tested using two-dimensional pressureless hydrodynamic simulations of wind-driven star formation, in which star formation occurs according to a threshold condition on the column density through a shell, and a large number of shells are present at any one time. The morphology of the simulations resembles an irregular network or web of dynamically interacting filaments. A set of 16 simulations, in which different parameters were varied, agrees remarkably well with the simple analytical prescription for the scaling relation. Converting from the wind power of massive stars to the Lyman continuum luminosity shows that the cluster wind model for giant H ii regions may still be viable.