2001
DOI: 10.1086/320631
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Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks

Abstract: Thin, Keplerian accretion disks generically become gravitationally unstable at large radii. I investigate the nonlinear outcome of such instability in cool disks using razor-thin, local, numerical models. Cooling, characterized by a constant cooling time drives the instability. I show analytically that if the q c , disk can reach a steady state in which heating by dissipation of turbulence balances cooling, then the dimensionless angular momentum Ñux density Numerical experiments show a \ [(9/4)c(c [ 1))q c ]~… Show more

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Cited by 979 publications
(1,726 citation statements)
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References 49 publications
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“…Spiral structures start appearing at Q ∼ 1.7, while fragmentation occurs for Q ∼ 1 (Durisen et al 2007;Helled et al 2013). When this stage is reached, turbulence and shocks are expected to develop, providing a heating mechanism that may compensate for the cooling of the disk (Gammie 2001). We can therefore estimate the sound speed at the stage of fragmentation via…”
Section: Planet Formation Via Gravitational Instabilitiesmentioning
confidence: 99%
“…Spiral structures start appearing at Q ∼ 1.7, while fragmentation occurs for Q ∼ 1 (Durisen et al 2007;Helled et al 2013). When this stage is reached, turbulence and shocks are expected to develop, providing a heating mechanism that may compensate for the cooling of the disk (Gammie 2001). We can therefore estimate the sound speed at the stage of fragmentation via…”
Section: Planet Formation Via Gravitational Instabilitiesmentioning
confidence: 99%
“…M d is much smaller than the black hole mass so that the disk is not globally self-gravitating (i.e., in the radial direction; Shlosman & Begelman 1989) and will not gravitationally influence stellar dynamics in Sgr A * . The disk is locally (vertically) self-gravitating when -Bell 1965;Kolykhalov & Sunyaev 1980;Gammie 2001). We have…”
Section: Mass Of the Disk And Maximum Densitymentioning
confidence: 99%
“…Stamatellos et al 2007;Forgan et al 2009), or choosing a parametrized cooling law in order to mimic expected scaling relations (e.g. Gammie 2001). The former method was used by Bonnell & Rice (2008), but the accuracy of the Stamatellos et al (2007) scheme has recently been challenged by Wilkins & Clarke (2012).…”
Section: Coolingmentioning
confidence: 99%
“…Such simulations typically find that there is a critical value β crit ∼ 5 which marks the "fragmentation boundary". For slower cooling (β > β crit ), gravitational instability results in self-regulating spiral density waves which transport angular momentum through the disc, while faster cooling (β < β crit ) results in gravitational fragmentation into bound clumps (Gammie 2001 (Lodato & Clarke 2011;Paardekooper et al 2011;Rice et al 2012), but the exact origin of the lack of convergence in scale-free simulations of self-gravitating discs remains uncertain However, a parametrization where cooling depends only on position is not appropriate for our infalling cloud calculations, so we instead choose a parametrization where the cooling rate depends on the local gas density ρ. We choose a scaling such that…”
Section: Coolingmentioning
confidence: 99%