The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks

By B. K. Pickett, A. C. Mejía, R. Durisen, P. Cassen, D. Berry, Robert Link. 2003

242 citations recorded by the source corpus.

We present a series of high-resolution, three-dimensional hydrodynamics simulations of a gravitationally unstable solar nebula model. The influences of both azimuthal grid resolution and the treatment of thermal processes on the origin and evolution of gravitational instabilities are investigated. In the first set of simulations, we vary the azimuthal resolution for a locally isothermal simulation, doubling and quadrupling the resolution used in a previous study; the largest number of grid points is (256, 256, 64) in cylindrical coordinates (r, φ, z). At this resolution, the disk breaks apart into a dozen short-lived condensations. Although our previous calculations underresolved the number and growth rate of clumps in the disk, the overall qualitative, but fundamental, conclusion remains: fragmentation under the locally isothermal condition in numerical simulations does not in itself lead to the survival of clumps to become gaseous giant protoplanets. Since local isothermality represents an extreme assumption about thermal processes in the disk, we also present several extended simulations in which heating from an artificial viscosity scheme and cooling from a simple volumetric cooling function are applied to two different models of the solar nebula. The models are differentiated primarily by disk temperature: a high-Q model generated directly by our self-consistent field equilibrium code and a low-Q model generated by cooling the high-Q model in a two-dimensional version of our hydrodynamics code. Here, "high-Q" and "low-Q" refer to the minimum values of the Toomre stability parameter Q in each disk, Qmin = 1.8 and 0.9, respectively. Previous simulations, by ourselves as well as others, have focused on initial states that are already gravitationally unstable, i.e., models similar to the low-Q model. This paper presents for the first time the numerical evolution of an essentially stable initial equilibrium state (the high-Q model) to a severely unstable one by cooling. The additional heating and cooling are applied to each model over the outer half of the disk or the entire disk. The models are subject to the rapid growth of a four-armed spiral instability; the subsequent evolution of the models depends on the thermal behavior of the disk. The cooling function tends to overwhelm the heating included in our artificial viscosity prescription, and as a result the spiral structure strengthens. The spiral disturbances transport mass at prodigious rates during the early nonlinear stages of development and significantly alter the disk's vertical surface. Although dense condensations of material can appear, their character depends on the extent of the volumetric cooling in the disk. In the simulation of the high-Q model with heating and cooling applied throughout the disk, thin, dense rings form at radii ranging from 1 to 3 AU and steadily increase in mass; later companion formation may occur in these rings as cooling drives them toward instability. When heating and cooling are applied only over the outer radial half of the disk, however, a succession of single condensations appears near 5 AU. Each clump has roughly the mass of Saturn, and some survive a complete orbit. Since the clumps form near the artificial boundary in the treatment of the disk gas physics, the production of a clump in this case is a numerical artifact. Nevertheless, radially abrupt transitions in disk gas characteristics, for example, in opacity, might mimic the artificial boundary effects in our simulations and favor the production of stable companions in actual protostellar and protoplanetary disks. The ultimate survival of condensations as eventual stellar or substellar companions to the central star is still largely an open question.

Subfields: Astronomy and Astrophysics

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Citations in the corpus

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…”
Pseudo-viscous modelling of self-gravitating discs and the formation of low mass ratio binaries (2009, result): “…is again consistent with a range of simulations of self-gravitating gas discs, which demonstrate such self-regulation (e.g. Lodato & Rice 2004, Boley et al 2006, Mayer et al 2007, Stamatellos et al 2007, Cossins et al 2009): the amplitude of spiral features self-adjusts so as to heat the disc…”
ON THE ROLE OF DISKS IN THE FORMATION OF STELLAR SYSTEMS: A NUMERICAL PARAMETER STUDY OF RAPID ACCRETION (2009, background): “…at various stages of evolution, however most involve isolated disks, without infall at large radii (Laughlin & Bodenheimer 1994; Laughlin & Rozyczka 1996; Rice et al. 2005; Lodato & Rice 2005; Fromang & Nelson 2006; Shetty & Ostriker 2006; Boley et al. 2006; Lodato et al. 2007; Cai et al. 2008).”
Planet-Disk Interaction and Orbital Evolution (2012, background): “In the gravito-turbulent state, the disk is in near-equilibrium with heating generated by spiral shocks balancing radiative cooling on average [although additional heat sources such as stellar radiation may also be important Cai et al. (2008); Zhu et al. (2012)].”
CHALLENGES IN FORMING PLANETS BY GRAVITATIONAL INSTABILITY: DISK IRRADIATION AND CLUMP MIGRATION, ACCRETION, AND TIDAL DESTRUCTION (2011, background): “S R ] 2 9 N ov 2 01 1 onto the disk as infall proceeds, and irradiation heating of the outer disk by the central star; the latter is known to weaken and/or suppress GI (Cai et al. 2008).”
NONSTEADY ACCRETION IN PROTOSTARS (2008, methodology): “Boley et al. (2006) performed a careful analysis of the torques in a three-dimensional model of a self-gravitating disk, including radiative transfer.”
THE FORMATION OF LOW-MASS BINARY STAR SYSTEMS VIA TURBULENT FRAGMENTATION (2010, background): “Previous analytic work (Matzner & Levin 2005), and numerical studies of isolated disks have suggested that disks around low-mass stars will be stable (Boley et al. 2007; Cai et al. 2008).”
THE TWO MODES OF GAS GIANT PLANET FORMATION (2009, background): “…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 local dynamical…”
The Evolution of Gravitationally Unstable Protoplanetary Disks: Fragmentation and Possible Giant Planet Formation (2003, background): “…in a protoplanetary disk are difficult to treat correctly because of both various numerical pitfalls that can arise in the simulations and the difficulty of accounting properly for all the cooling and heating mechanisms present in real protoplanetary disks (Pickett et al. 1998, 2000a, 2000b, 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 .”
THE EFFECTS OF RADIATIVE TRANSFER ON LOW-MASS STAR FORMATION (2009, background): “High-resolution radiationhydrodynamics simulations of low-mass disks including irradiation confirm that such disks, with properties similar to ours, are stable against fragmentation (Cai et al. 2008).”
Investigating fragmentation conditions in self-gravitating accretion discs (2005, methodology): “…that, for a self-gravitating accretion disc in thermal equilibrium, the dissipation arising from gravitational stresses agrees reasonably well with the expectations based on the standard viscous theory (Shakura & Sunyaev 1973; Pringle 1981) (see, however, Mejia et al. 2005 for a different result).”
PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS. II. EXTENSION TO FAINTER SOURCES (2010, background): “Typically those conditions are only met at large disk radii (Boley et al. 2006); such protoplanets must then migrate inward to reproduce the shorter period orbits observed in the Solar System and elsewhere.”