Year: 2003
Type: article
Abstract: 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 Σ 0 and the rotation frequency Ω. We survey the parameter space and find the following. (1) The disk fragments when ⟨⟨τ c ⟩⟩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 τ c 0 for a uniform disk with Q = 1 can differ by orders of magnitude from ⟨⟨τ c ⟩⟩ in the nonlinear outcome. The difference is caused by sharp variations in the opacity with temperature. The condition τ c 0 Ω ~ 1 therefore does not necessarily indicate where fragmentation will occur. (3) The largest difference between ⟨⟨τ c ⟩⟩ and τ c 0 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 ⟨⟨τ c ⟩⟩Ω ≲ 1 do not exist.
Source: The Astrophysical Journal
DOI: 10.1086/378392
Authors: Bryan M. Johnson, Charles F. Gammie
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2021248989