Megan K. Pickett

THE THERMAL REGULATION OF GRAVITATIONAL INSTABILITIES IN PROTOPLANETARY DISKS. III. SIMULATIONS WITH RADIATIVE COOLING AND REALISTIC OPACITIES

This paper presents a fully three-dimensional radiative hydrodymanics simulation with realistic opacities for a gravitationally unstable 0.07 Mdisk around a 0.5 Mstar. We address the following aspects of disk evolution: the strengthofgravitationalinstabilitiesunderrealisticcooling,masstransportinthediskthatarisesfromGIs,comparisons betweenthegravitationalandReynoldsstressesmeasuredinthediskandthoseexpectedinan � -disk,andcomparisons between the SED derived for the disk and SEDs derived from observationally determined parameters. The mass transport in this disk is dominated by global modes, and the cooling times are too long to permit fragmentation for all radii. Moreover, our results suggest a plausible explanation for the FU Ori outburst phenomenon. Subject headingg accretion, accretion disks — convection — hydrodynamics — instabilities — solar system: formation

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

In order to investigate mass transport and planet formation through gravitational instabilities (GIs), we have extended our three-dimensional hydrodynamic simulations of protoplanetary disks from a previous paper. Our goal is to determine the asymptotic behavior of GIs and how it is affected by different constant cooling times. Initially, Rdisk = 40 AU, Mdisk = 0.07 M☉, M* = 0.5 M☉, and Qmin = 1.5. Sustained cooling, with tcool = 2 ORPs (outer rotation periods; 1 ORP ≈ 250 yr), drives the disk to instability in about 4 ORPs. This calculation is followed for 23.5 ORPs. After 12 ORPs, the disk settles into a quasi-steady state with sustained nonlinear instabilities, an average Q = 1.44 over the outer disk, a well-defined power law Σ(r), and a roughly steady ≈ 5 × 10-7 M☉ yr-1. The transport is driven by global low-order spiral modes. We restart the calculation at 11.2 ORPs with tcool = 1 and ORPs. The latter case is also run at high azimuthal resolution. We find that shorter cooling times lead to increased -values, denser and thinner spiral structures, and more violent dynamic behavior. The asymptotic total internal energy and the azimuthally averaged Q(r) are insensitive to tcool. Fragmentation occurs only in the high-resolution tcool = ORP case; however, none of the fragments survive for even a quarter of an orbit. Ringlike density enhancements appear and grow near the boundary between GI-active and GI-inactive regions. We discuss the possible implications of these rings for gas giant planet formation.

THE EFFECTS OF METALLICITY AND GRAIN SIZE ON GRAVITATIONAL INSTABILITIES IN PROTOPLANETARY DISKS

Observational studies show that the probability of finding gas giant planets around a star increases with the stars metallicity. Our latest simulations of disks undergoing gravitational instabilities (GIs) with realistic radiative cooling indicate that protoplanetary disks with lower metallicity generally cool faster and thus show stronger overall GI activity. More importantly, the global cooling times in our simulations are too long for disk fragmentation to occur, and the disks do not fragment into dense protoplanetary clumps. Our results suggest that direct gas giant planet formation via disk instabilities is unlikely to be the mechanism that produced most observed planets. Nevertheless, GIs may still play an important role in a hybrid scenario, compatible with the observed metallicity trend, where structure created by GIs accelerates planet formation by core accretion.

THE THERMAL REGULATION OF GRAVITATIONAL INSTABILITIES IN PROTOPLANETARY DISKS. IV. SIMULATIONS WITH ENVELOPE IRRADIATION

It is generally thought that protoplanetary disks embedded in envelopes are more massive and thus more suscep- tible to gravitational instabilities (GIs) than exposed disks. We present three-dimensional radiative hydrodynamic simulationsof protoplanetarydiskswiththepresenceof envelopeirradiation.Foradiskwitharadiusof 40AUanda mass of 0.07 Maround a young star of 0.5 M� , envelope irradiation tends to weaken and even suppress GIs as the irradiating flux is increased. The global mass transport induced by GIs is dominated by lower order modes, and irradiation preferentially suppresses higher order modes. As a result, gravitational torques and mass inflow rates are actually increased bymild irradiation. None of the simulations producedense clumps or rapid cooling byconvection, arguing against direct formation of giant planets by disk instability, at least in irradiated disks. However, dense gas rings andradial mass concentrationsare produced,and these mightbeconduciveto accelerated planetary coreforma- tion. Preliminary results from a simulation of a massive embedded disk with physical characteristics similar to one of thedisksintheembeddedsourceL1551IRS5indicatealongradiativecoolingtimeandnofragmentation.TheGIsin this disk are dominated by global two- and three-armed modes. Subject headingg accretion,accretiondisks — hydrodynamics — instabilities — planetarysystems:formation — planetary systems: protoplanetary disks

Giant Planet Formation by Disk Instability: A Comparison Simulation with an Improved Radiative Scheme

There has been disagreement about whether cooling in protoplanetary disks can be sufficiently fast to induce the formation of gas giant protoplanets via gravitational instabilities. Simulations by our own group and others indicate that this method of planet formation does not work for disks around young, low-mass stars inside several tens of AU, while simulations by other groups show fragmentation into protoplanetary clumps in this region. To allow direct comparison in hopes of isolating the cause of the differences, we here present a high-resolution three-dimensional hydrodynamics simulation of a protoplanetary disk, where the disk model, initial perturbation, and simulation conditions are essentially identical to those used in a recent set of simulations by Boss in 2007, hereafter B07. As in earlier papers by the same author, B07 purports to show that cooling is fast enough to produce protoplanetary clumps. Here, we evolve the same B07 disk using an improved version of one of our own radiative schemes and find that the disk does not fragment in our code but instead quickly settles into a state with only low amplitude nonaxisymmetric structure, which persists for at least several outer disk rotations. We see no rapid radiative or convective cooling. We conclude that the differences in results are due to different treatments of regions at and above the disk photosphere, and we explain at least one way in which the scheme in B07 may lead to artificially fast cooling.

The formation of fragments at corotation in isothermal protoplanetary disks

Numerical hydrodynamics simulations have established that disks which are evolved under the condition of local isothermality will fragment into small dense clumps due to gravitational instabilities when the Toomre stability parameter Q is sufficiently low. Because fragmentation through disk instability has been suggested as a gas giant planet formation mechanism, it is important to understand the physics underlying this process as thoroughly as possible. In this paper, we offer analytic arguments for why, at low Q, fragments are most likely to form first at the corotation radii of growing spiral modes, and we support these arguments with results from 3D hydrodynamics simulations.

Numerical Viscosity and the Survival of Gas Giant Protoplanets in Disk Simulations

We present three-dimensional hydrodynamic simulations of a gravitationally unstable protoplanetary disk model under the condition of local isothermality. Ordinarily, local isothermality precludes the need for an artificial viscosity (AV) scheme to mediate shocks. Without AV, the disk evolves violently, shredding into dense (although short-lived) clumps. When we introduce our AV treatment in the momentum equation, but without heating due to irreversible compression, our grid-based simulations begin to resemble smoothed particle hydrodynamics (SPH) calculations, where clumps are more likely to survive many orbits. In fact, the standard SPH viscosity appears comparable in strength to the AV that leads to clump longevity in our code. This sensitivity to one numerical parameter suggests extreme caution in interpreting simulations by any code in which long-lived gaseous protoplanetary bodies appear.

Erratum: “The Effects of Metallicity and Grain Size on Gravitational Instabilities in Protoplanetary Disks” (ApJ 636, L149 [2006])

We have found that the total cumulative radiative energy losses shown in Figure 2 of the above-mentioned Letter were computed for only half the disk. This caused the final global cooling times tcool in the eighth column of the original Table 1 to be too large by a factor of 2. Proper values of tcool are given in the revised Table 1 below. To be more consistent with what the Letter states, we now use instantaneous values for both the total internal energy and the final total net cooling rates to compute final tcool’s, instead of averaging the loss rates over an interval of time at the end of the calculations before dividing, as was done in the Letter. We also take this opportunity to make a few other inconsequential corrections to the fourth column of the table. In addition to the changes to Table 1, the approximate initial tcool relation in the fourth paragraph of § 3.2 becomes to within tens t ∼ Z/Z cool , of percent. Despite the corrections, our conclusions in the Letter remain unchanged. Most importantly, the final tcool’s vary with metallicity and are still too long for disk fragmentation to occur with our equation of state over the range of Z examined. We regret any inconvenience our errors may have caused.