Self-Regulated Star Formation: From the Solar Neighborhood to
High-Redshift Disks

In disk galaxies ranging from our own Milky Way to high-redshift
systems, star formation takes place in very cold, dense cores, but
draws on a much larger reservoir of neutral atomic and molecular gas.
Recent surveys have spatially resolved both nearby galaxies and
high-redshift disks to establish increasingly precise empirical
correlations among gas, old stars, and the star formation rate (SFR).
Traditional single power law Kennicutt-Schmidt relations have been
refined to reveal three star-forming regimes for disks that extend
over more than six orders of magnitude in SFR.  In all regimes, gas
depletion timescales far exceed both global and local dynamical times.
To understand these empirical relations, it is necessary to consider
the physical state of the ISM, which is strongly coupled to recent
star formation through the feedback from massive stars -- including
copious UV radiation and powerful supernova blasts.  This energetic
feedback can lead to a state of self-regulated star formation.  Using
multiphase numerical simulations, we show that following the driving
and dissipation of turbulence in the warm/cold ISM, and resolving
scales down to pc in normal disks and 0.1 pc in starbursts, is
necessary to follow the detailed processes controlling SFRs.  The
equilibrium state can, however, also be captured with simple models in
which pressure powered by feedback balances gravitational confinement
of the warm/cold gas. Both numerical simulations and equilibrium
models are in remarkably good agreement with observations, and
demonstrate the importance of accurately modeling feedback in order to
understand galactic SFRs.