The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks. II. Extended Simulations with Varied Cooling Rates

Mejía, Annie C.; Durisen, R. H.; Pickett, Megan K.; Cai, Kai

doi:10.1086/426707

Cited by 146 publications

(227 citation statements)

References 73 publications

(128 reference statements)

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“…On the other hand, as already mentioned, the outcome of gravitational instabilities in discs strongly depends on the assumptions about the disc thermal behaviour. Simulations that employ a cooling time constant with radius seem to show significant global energy transport (Mejia et al 2004), in contrast to our results. Of course, both a constant cooling timescale and our choice are highly idealized assumptions, and further studies are needed to assess which of the two is more reasonable.…”

Section: Discussioncontrasting

confidence: 99%

“…In the case where M disc = 0.5M⋆ we observe the development of an initial transient m = 2 spiral structure, which induces a strong redistribution of matter and a steepening of the surface density profile, before the disc is eventually able to settle down as in the low disc mass case. Similar initial transients are also observed by Mejia et al (2004). We attribute it to an effect of the initial condition adopted.…”

Section: Discussionsupporting

confidence: 81%

“…This has been recognized in the analysis of isothermal simulations of massive discs (Laughlin & Bodenheimer 1994;Laughlin & Ròżyczka 1996) and subsequently analysed in a number of papers (Pickett et al 1998(Pickett et al , 2000Nelson et al 2000). However, only recently have simulations been performed which include a relatively more complex treatment of the thermal status of the disc (Rice et al 2003a;Pickett et al 2003;Mejia et al 2004). In a previous paper , hereafter Paper I), we have explored in detail the transport properties of self-gravitating, cooling discs, by performing some highresolution smoothed particle hydrodynamics (SPH) simulations.…”

Section: Introductionmentioning

confidence: 99%

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Testing the locality of transport in self-gravitating accretion discs

Lodato

Rice

2004

AIP Conference Proceedings

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In this paper, we extend our previous analysis of the transport properties induced by gravitational instabilities in cooling, gaseous accretion discs to the case where the disc mass is comparable to the central object. In order to do so, we have performed global, three-dimensional smoothed particle hydrodynamics simulations of massive discs. These new simulations show a much more complex temporal evolution with respect to the less massive case. Whereas in the low disc mass case a self-regulated, marginally stable state (characterized by an approximately constant radial profile of the stability parameter Q) is easily established, in the high disc mass case we observe the development of an initial transient and subsequent settling down in a self-regulated state in some simulations, or a series or recurrent spiral episodes, with low azimuthal wave number m, in others. Accretion in this last case can therefore be a highly variable process. On the other hand, we find that the secular evolution of the disc is relatively slow. In fact, the time-average of the stress induced by selfgravity results in accretion time-scales much longer than the dynamical timescale, in contrast with previous isothermal simulations of massive accretion discs. We have also compared the resulting stress tensor with the expectations based on a local theory of transport, finding no significant evidence for global wave energy transport.

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Section: Discussioncontrasting

confidence: 99%

Section: Discussionsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

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Testing the locality of transport in self-gravitating accretion discs

Lodato

Rice

2004

AIP Conference Proceedings

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“…Thermal processes play the primary role in regulating the amplitude and outcome of these instabilities (Pickett et al 1998(Pickett et al , 2000(Pickett et al , 2003Nelson et al 1998Nelson et al , 2000Mejía et al 2005). A disk's susceptibility to GIs can be parameterized by the Toomre Q-parameter (Toomre 1981); Q = c s κ/πGΣ, where c s is the sound speed, κ is the epicyclic frequency (∼ the rotation frequency Ω in a nearly Keplerian disk), and Σ is the disk surface mass density.…”

Section: Introductionmentioning

confidence: 99%

“…Numerous studies have shown that thermal physics controls GI amplitudes by a balance of heating and cooling (e.g., Tomley et al 1991Tomley et al , 1994Pickett et al 1998Pickett et al , 2000Pickett et al , 2003Gammie 2001;Boss 2002;Rice et al 2003;Mejía et al 2005;Boley et al 2006Boley et al , 2007aStamatellos & Whitworth 2008;Cossins et al 2009). Heating by GIs tends to increase c s , thus increasing Q.…”

Section: Introductionmentioning

confidence: 99%

Convergence Studies of Mass Transport in Disks With Gravitational Instabilities. I. The Constant Cooling Time Case

Michael

Steiman-Cameron

Durisen

et al. 2012

ApJ

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We conduct a convergence study of a protostellar disk, subject to a constant global cooling time and susceptible to gravitational instabilities (GIs), at a time when heating and cooling are roughly balanced. Our goal is to determine the gravitational torques produced by GIs, the level to which transport can be represented by a simple α-disk formulation, and to examine fragmentation criteria. Four simulations are conducted, identical except for the number of azimuthal computational grid points used. A Fourier decomposition of non-axisymmetric density structures in cos(mφ), sin(mφ) is performed to evaluate the amplitudes A m of these structures. The A m , gravitational torques, and the effective Shakura & Sunyaev α arising from gravitational stresses are determined for each resolution. We find nonzero A m for all m-values and that A m summed over all m is essentially independent of resolution. Because the number of measurable m-values is limited to half the number of azimuthal grid points, higher-resolution simulations have a larger fraction of their total amplitude in higher-order structures. These structures act more locally than lower-order structures. Therefore, as the resolution increases the total gravitational stress decreases as well, leading higher-resolution simulations to experience weaker average gravitational torques than lower-resolution simulations. The effective α also depends upon the magnitude of the stresses, thus α eff also decreases with increasing resolution. Our converged α eff is consistent with predictions from an analytic local theory for thin disks by Gammie, but only over many dynamic times when averaged over a substantial volume of the disk.

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Formation via Disk Instability

Mayer

2010

Formation and Evolution of Exoplanets

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In the disk instability model, giant planets form from direct collapse of the gas in the protoplanetary disk. The disk fragments into gravitationally bound clumps with sizes comparable to giant planets as a result of gravitational instability [1]. The idea that planets in the solar system could condense directly out of the nebula is one of the oldest in astrophysics since it dates back to Laplace in the eighteenth century. The concept was revived by Kuiper [2] and Cameron [3] in the context of the solar system. Since the discovery of extrasolar planets, the interest in disk instability has grown because fragmentation, when feasible, occurs quickly, naturally producing multiple giant planets [1, 4, 5] on a timescale comparable to the orbital time in the protoplanetary disk, that is, <100 years. A short formation timescale is attractive because the presence of protoplanetary disks becomes increasingly rare around stars older than a few million years [6], suggesting fairly short disk dissipation timescales.Gravitational instability requires high mass densities and low temperatures as it demands that the self-gravity of the gas, which drives the collapse, prevails over the stabilizing effect of thermal pressure. This translates into the requirement that, at some stage, the protoplanetary disk had to be very cold and massive. Furthermore, a protoplanetary disk revolving around its host star is in differential rotation. This causes shear, which also opposes the tendency toward collapse promoted by gravity. The competing effects of self-gravity, thermal pressure, and shear in the disk are nicely encapsulated in the Toomre Q parameter [7]:In Eq. (4.1), the gas surface density measures the importance of self-gravity, the sound speed c s is related to thermal pressure, and κ, the epicyclic frequency, determines the strength of the shear. The Toomre parameter can be derived via a local perturbative stability analysis of infinitesimally thin differentially rotating disks [8]. If Q < 1 then the gas is unstable to gravitational collapse, while if Q > 1 Formation and Evolution of Exoplanets. Edited by Rory Barnes

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The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks. II. Extended Simulations with Varied Cooling Rates

Cited by 146 publications

References 73 publications

Testing the locality of transport in self-gravitating accretion discs

Testing the locality of transport in self-gravitating accretion discs

Convergence Studies of Mass Transport in Disks With Gravitational Instabilities. I. The Constant Cooling Time Case

Formation via Disk Instability

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