A Prescription for Star Formation Feedback: The Importance of Multiple Shell Interactions

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 due to 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 mean column density of 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 simulations agree remarkably with the simple analytical prescription. Converting from wind power of massive stars to Lyman continuum luminosity shows that the cluster wind model for giant H II regions may still be viable.