Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks

By Charles F. Gammie. 2001

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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 τc, drives the instability. I show analytically that if the disk can reach a steady state in which heating by dissipation of turbulence balances cooling, then the dimensionless angular momentum flux density α = -1. Numerical experiments show that (1) if τc ≳ 3Ω-1 then the disk reaches a steady, gravitoturbulent state in which Q ~ 1 and cooling is balanced by heating due to dissipation of turbulence; (2) if τc ≲ 3Ω-1, then the disk fragments, possibly forming planets or stars; (3) in a steady, gravitoturbulent state, surface density structures have a characteristic physical scale ~64GΣ/Ω2 that is independent of the size of the computational domain.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/b945226d195bf6b53dfda3e273abfe34b337b177

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Citations in the corpus

Theory of Star Formation (2007, methodology): “However, similar simulations show that magnetic fields have a relatively small effect in slowing the rate of star formation if the gas is supercritical (Ostriker, Gammie, & Stone, 1999; Heitsch, Mac Low, & Klessen, 2001; Li et al., 2004; Vázquez-Semadeni et al., 2005; Vázquez-Semadeni, Kim, & Ball”
Fragmentation of massive protostellar discs (2006, methodology): “Extrapolating from Gammie (2001)’s two-dimensional simulations for a stiff equation of state, ML05 estimate Ṁmax = 0.89c 3 s/G for the case of a three-dimensional, γ = 5/3 disk.”
Global Models for the Evolution of Embedded, Accreting Protostellar Disks (2007, methodology): “Equally untested is the hypothesis that when fragmentation is strong enough, i.e., when Ṁin c3s/G so that Q 1 (Gammie 2001), accretion onto the central star will be choked off.”
THE TWO MODES OF GAS GIANT PLANET FORMATION (2009, methodology): “(1) When GIs are in a self-regulating phase, the effective Shakura & Sunyeaev (1973) α tends toward a few hundredths or less (e.g., Gammie 2001; Lodato & Rice 2004; Mejia et al. 2005; Boley et al. 2006), so the timescale for Σ and κ to change due to mass transport should be much larger than the…”
Planet-Disk Interaction and Orbital Evolution (2012, background): “The gas is able to cool in these regions on timescales less than about the local orbital period, allowing gravitationally unstable clumps to collapse to high densities (Gammie, 2001).”
Massive Black Hole Binary Evolution (2004, background): “Some of the mechanisms that remove angular momentum of interstellar gas and thus channel it into the neighborhood of SBHs include the torquing of gas flow by the rapidly-fluctuating potential of merging galaxies [144] and by nested stellar bars [199], angular momentum transport by hydrodynamical tur”
Investigating fragmentation conditions in self-gravitating accretion discs (2005, methodology): “However, as discussed in more detail in Gammie (2001), a mapping is possible between the 2D and the 3D adiabatic indices.”
Nonlinear Outcome of Gravitational Instability in Disks with Realistic Cooling (2003, methodology): “A naive application of the results of Gammie (2001) would suggest that fragmentation should occur for c0 d3.”
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).”
Three-phase Interstellar Medium in Galaxies Resolving Evolution with Star Formation and Supernova Feedback (TIGRESS): Algorithms, Fiducial Model, and Convergence (2016, methodology): “We solve Poisson’s equation (Equation (5)) using the FFT method with shearing-periodic boundary conditions in the horizontal directions (e.g., Gammie 2001) and vacuum boundary conditions in the vertical direction (Koyama & Ostriker 2009).”
THREE-DIMENSIONAL HYDRODYNAMIC SIMULATIONS OF MULTIPHASE GALACTIC DISKS WITH STAR FORMATION FEEDBACK. I. REGULATION OF STAR FORMATION RATES (2013, methodology): “In addition, we adopt a fast Fourier transform Poisson solver method with treatment of shearing horizontal coordinates as introduced by Gammie (2001) and with vacuum vertical boundary conditions as introduced by Koyama & Ostriker (2009a).”
Accelerated planetesimal growth in self-gravitating protoplanetary discs (2004, background): “Even if such small random velocities are possible, if objects are to grow via gravitational collapse, any increase in the random velocities has to be lost very rapidly (Gammie 2001; Rice et al. 2003a).”
Compaction and quenching of high-z galaxies in cosmological simulations: blue and red nuggets (2014, background): “Finally, intense gas inflow within the disc is naturally driven by VDI (Noguchi 1999; Gammie 2001; Dekel, Sari & Ceverino 2009; Krumholz & Burkert 2010; Burkert et al. 2010; Bournaud et al. 2011b; Forbes, Krumholz & Burkert 2012; Cacciato, Dekel & Genel 2012; Elmegreen, Zhang & Hunter 2012; Dekel…”
Particle Pileups and Planetesimal Formation (2003, background): “The term proportional to Pr dominates in active accretion disks that are rendered turbulent by, e.g., magnetorotational instability (Balbus & Hawley 1991) or gravitational instability (Gammie 2001).”
Formation of supermassive black holes by direct collapse in pre-galactic haloes (2006, background): “Although the cooling timescale of the gas is shorter than the dynamical time, and therefore violates the Gammie (2001) criterion for avoiding fragmentation, we do not expect fragmentation to deplete a large fraction of the inflow.”