The effect of cooling on the global stability of self-gravitating protoplanetary discs

By W. Rice, Philip Armitage, Matthew R. Bate, Ian A. Bonnell. 2002

211 citations recorded by the source corpus.

Using a local model, Gammie has shown that accretion discs with cooling times tcool ≤ 3Ω−1 fragment into gravitationally bound objects, while those with cooling times tcool > 3Ω−1 evolve into a quasi-steady state. We use three-dimensional smoothed particle hydrodynamic simulations of protoplanetary accretion discs to test if the local results hold globally. We find that for disc masses appropriate for T Tauri discs, the fragmentation boundary still occurs at a cooling time close to tcool= 3Ω−1. For more massive discs, which are likely to be present at an earlier stage of the star formation process, fragmentation occurs for longer cooling times, but still within a factor of 2 of that predicted using a local model. These results have implications not only for planet formation in protoplanetary discs and star formation in active galactic nucleus discs, but also for the redistribution of angular momentum which could be driven by the presence of relatively massive objects within the accretion disc.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/400f1a7098da2318b57e0bd88edd08b3c03a7fb0

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Citations in the corpus

Dynamics of Protoplanetary Disks (2010, methodology): “Rice et al. (2003a), using Smooth Particle Hydrodynamics (SPH) simulations, found that for low-mass disks (roughly those for which Mdisk/M∗ ∼ 0.1, or less), the condition to avoid fragmentation could indeed be expressed via a minimum cooling time, given for γ = 5/3 by β ≈ 5.”
Flares in Long and Short Gamma-Ray Bursts: A Common Origin in a Hyperaccreting Accretion Disk (2005, background): “Fragmentation is inevitable if the local cooling time, tcool < tcrit ≈ 3Ω−1K , (4) in which case the maximum stress obtainable from gravitational instability (roughlyαmax ∼ 0.1) produces insufficient heating to offset cooling (Gammie 2001; Rice et al. 2003).”
The properties of brown dwarfs and low-mass hydrogen-burning stars formed by disc fragmentation (2008, background): “Both theory and simulations (Gammie 2001; Johnson & Gammie 2003; Rice et al. 2003, 2005; Mayer et al. 2004; Mejia et al. 2005; Stamatellos et al. 2007b) indicate that for disc fragmentation to occur, the cooling time must satisfy t COOL < C(γ) t ORB , 0.5 .”
Formation of Giant Planets (2004, background): “Numerical studies have established that fragmentation sensitively depends on the equation of state of the gas and on its cooling history (e.g., Rice et al. 2003), but also on the numerical treatment of the system, e.g., on the adopted geometry (two versus three dimensions, Young and Clarke 2015)…”
The physics of star formation (2003, background): “…outcome is less clear, but recent simulations that include a detailed treatment of radiative cooling show that even in a disk of modest mass, fragmentation can occur and lead to the formation of a smaller companion object such as a massive planet or small star (Boss 2001, 2002; Rice et al 2003).”
Investigating fragmentation conditions in self-gravitating accretion discs (2005, methodology): “2 S I M U L AT I O N R E S U LT S The simulations performed here are very similar to those of Rice et al. (2003a) and Lodato & Rice (2004, 2005).”
Nonlinear Outcome of Gravitational Instability in Disks with Realistic Cooling (2003, background): “Rice et al. (2003) consider a global three-dimensional SPH model with a cooling time that is a fixed multiple of 1ðrÞ.”
The Evolution of Gravitationally Unstable Protoplanetary Disks: Fragmentation and Possible Giant Planet Formation (2003, background): “Recent, lower resolution SPH simulations that solve for heating and cooling find that fragmentation can proceed when the cooling time is comparable to the disk orbital time (Rice et al. 2003), basically confirming previous simpler numerical and analytic calculations by Gammie (2001).”
Testing the locality of transport in self-gravitating accretion discs — II. The massive disc case (2003, background): “…spiral structure that we obtain (which would have been smeared out if significant particle interpenetration was indeed present), consistent with the results of previous simulations that used the standard SPH viscosity and higher values for the viscosity coefficients (Rice et al. 2003a,b).”
Formation and evolution of primordial protostellar systems (2012, background): “Again, this equation strictly applies only to infinitely thin discs, but has also been shown to predict the fragmentation of thick discs quite well (Rice et al. 2003).”
Global Models for the Evolution of Embedded, Accreting Protostellar Disks (2007, methodology): “As a result, the star will orbit the center of mass of the system, and this will produce a velocity offset of a few km s−1 between the stellar velocity and the zero velocity of the inner, Keplerian parts of the disk (Bertin & Lodato 1999; Rice et al. 2003; Krumholz et al. 2007a).”
The Burst Mode of Protostellar Accretion (2006, methodology): “Using either finite-difference (Boss 2003; Pickett et al. 2003; Mej́ia et al. 2005) or smoothed-particle hydrodynamics (Rice et al. 2003; Mayer et al. 2004) techniques, and either isothermal evolution or various recipes for heating, radiative cooling, and simplified radiative transfer, these…”
Characterizing the gravitational instability in cooling accretion discs (2008, background): “…enter within a given sink radius, and satisfy certain boundness conditions – see Bate et al. 1995) orbited by 500,000 SPH gas particles; a set up common to many other SPH simulations of such systems, (e.g. Lodato & Rice 2004, 2005; Rice et al. 2003; Clarke et al. 2007)but with increaesd resolution.”
Can Giant Planets Form by Direct Gravitational Instability? (2004, background): “Recent studies (Gammie 2001; Rice et al. 2003) have demonstrated that fragmentation is possible only provided that the cooling time of the disk tcool satisfies Ωtcool < ξ, (3) where ξ is a parameter of the order of unity; numerical simulations (Gammie 2001; Rice et al. 2003) suggest that ξ ≈ 3.”