Nonlinear outcome of gravitational instability in disks with realistic cooling

Bryan M. Johnson, Charles F. Gammie

Research output: Contribution to journalArticlepeer-review


We consider the nonlinear outcome of gravitational instability in optically thick disks with a realistic cooling function. We use a numerical model that is local, razor thin, and unmagnetized. External illumination is ignored. Cooling is calculated from a one-zone model using analytic fits to low-temperature Rosseland mean opacities. The model has two parameters: the initial surface density Σ0 and the rotation frequency Ω. We survey the parameter space and find the following. (1) The disk fragments when «τc»Ω ∼ 1, where «τ c» is an effective cooling time defined as the average internal energy of the model divided by the average cooling rate. This is consistent with earlier results that used a simplified cooling function. (2) The initial cooling time τc0 for a uniform disk with Q = 1 can differ by orders of magnitude from «τc» in the nonlinear outcome. The difference is caused by sharp variations in the opacity with temperature. The condition τc0Ω ∼ 1 therefore does not necessarily indicate where fragmentation will occur. (3) The largest difference between «τc» and τc0 is near the opacity gap, where dust is absent and hydrogen is largely molecular. (4) In the limit of strong illumination the disk is isothermal; we find that an isothermal version of our model fragments for Q ≲ 1.4. Finally, we discuss some physical processes not included in our model and find that most are likely to make disks more susceptible to fragmentation. We conclude that disks with «τc»Ω ≲ 1 do not exist.

Original languageEnglish (US)
Pages (from-to)131-141
Number of pages11
JournalAstrophysical Journal
Issue number1 I
StatePublished - Nov 1 2003


  • Accretion, accretion disks
  • Galaxies: nuclei
  • Solar system: formation

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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