Three Dimensional Hydrodynamic Simulations of Multiphase Galactic Disks
  with Star Formation Feedback: I. Regulation of Star Formation Rates
  The energy and momentum feedback from young stars has a profound impact on
the interstellar medium (ISM), including heating and driving turbulence in the
neutral gas that fuels future star formation. Recent theory has argued that
this leads to a quasi-equilibrium self-regulated state, and for outer
atomic-dominated disks results in the surface density of star formation
$\Sigma_{SFR}$ varying approximately linearly with the weight of the ISM (or
midplane turbulent + thermal pressure). We use three-dimensional numerical
hydrodynamic simulations to test the theoretical predictions for thermal,
turbulent, and vertical dynamical equilibrium, and the implied functional
dependence of $\Sigma_{SFR}$ on local disk properties. Our models demonstrate
that all equilibria are established rapidly, and that the expected
proportionalities between mean thermal and turbulent pressures and
$\Sigma_{SFR}$ apply. For outer disk regions, this results in $\Sigma_{SFR}
\propto \Sigma \sqrt{\rho_{sd}}$, where $\Sigma$ is the total gas surface
density and $\rho_{sd}$ is the midplane density of the stellar disk (plus dark
matter). This scaling law arises because $\rho_{sd}$ sets the vertical
dynamical time in our models (and outer disk regions generally). The
coefficient in the star formation law varies inversely with the specific energy
and momentum yield from massive stars. We find proportions of warm and cold
atomic gas, turbulent-to-thermal pressure, and mean velocity dispersions that
are consistent with Solar-neighborhood and other outer-disk observations. This
study confirms the conclusions of a previous set of simulations, which
incorporated the same physics treatment but was restricted to radial-vertical
slices through the ISM.
