Regulation of star formation rates in multiphase galactic disks: Numerical tests of the thermal/dynamical equilibrium model

Chang Goo Kim, Woong Tae Kim, Eve Charis Ostriker

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130 Scopus citations


We use vertically resolved numerical hydrodynamic simulations to study star formation and the interstellar medium (ISM) in galactic disks. We focus on outer-disk regions where diffuse H I dominates, with gas surface densities Σ = 3-20 M pc-2 and star-plus-dark matter volume densities ρsd = 0.003-0.5 M pc -3. Star formation occurs in very dense, self-gravitating clouds that form by mergers of smaller cold cloudlets. Turbulence, driven by momentum feedback from supernova events, destroys bound clouds and puffs up the disk vertically. Time-dependent radiative heating (FUV from recent star formation) offsets gas cooling. We use our simulations to test a new theory for self-regulated star formation. Consistent with this theory, the disks evolve to a state of vertical dynamical equilibrium and thermal equilibrium with both warm and cold phases. The range of star formation surface densities and midplane thermal pressures is ΣSFR ∼ 10-4 to 10 -2 M kpc-2 yr-1 and P th/k B ∼ 102 to 104 cm -3 K. In agreement with observations, turbulent velocity dispersions are ∼7 km s-1 and the ratio of the total (effective) to thermal pressure is Ptot/P th ∼4-5, across this whole range (provided shielding is similar to the solar neighborhood). We show that ΣSFR is not well correlated with Σ alone, but rather with Σ√ρsd, because the vertical gravity from stars and dark matter dominates in outer disks. We also find that ΣSFR has a strong, nearly linear correlation with P tot, which itself is within ∼13% of the dynamical equilibrium estimate Ptot, DE. The quantitative relationships we find between ΣSFR and the turbulent and thermal pressures show that star formation is highly efficient for energy and momentum production, in contrast to the low efficiency of mass consumption. Star formation rates adjust until the ISM's energy and momentum losses are replenished by feedback within a dynamical time.

Original languageEnglish (US)
Article number25
JournalAstrophysical Journal
Issue number1
StatePublished - Dec 10 2011

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • galaxies: ISM
  • galaxies: kinematics and dynamics
  • galaxies: star formation
  • methods: numerical
  • turbulence


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