  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 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 agree remarkably with the simple analytical
prescription for the scaling relation. 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.
