Formation of Giant Planets by Fragmentation of Protoplanetary Disks (original) (raw)
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The Astrophysical Journal, 2004
We carry out a large set of very high resolution, three dimensional smoothed particle hydrodynamics (SPH) simulations describing the evolution of gravitationally unstable gaseous protoplanetary disks. We consider a broad range of initial disk parameters. Disk masses out to 20 AU range from 0.075 to 0.125 M ⊙ , roughly consistent with the high-end of the mass distribution inferred for disks around T Tauri stars.Minimum outer temperatures range from 30 to 100 K, as expected from studies of the early protosolar nebula and suggested by the modeling of protoplanetary disks spectra. The mass of the central star is also varied although it is usually assumed equal to that of the Sun. Overall the initial disks span minimum Q parameters between 0.8 and 2, with most models being around ∼ 1.4. The disks are evolved assuming either a locally isothermal equation of state or an adiabatic equation of state with varying γ. Heating by (artificial) viscosity and shocks is included when the adiabatic equation of state is used. When overdensities above a specific threshold appear as a result of gravitational instability in a locally isothermal calculation, the equation of state is switched to adiabatic to account for the increased optical depth. We show that when a disk has a minimum Q parameter less than 1.4 strong trailing spiral instabilities, typically three or four armed modes, form and grow until fragmentation occurs along the arms after about 5 mean disk orbital times. The resulting clumps contract quickly to densities several orders of magnitude higher than the initial disk density, and the densest of them survive even under adiabatic conditions. These clumps are stable to tidal disruption and merge quickly, leaving 2-3 protoplanets on fairly eccentric orbits (the mean eccentricity being around
A SEMI-ANALYTICAL DESCRIPTION FOR THE FORMATION AND GRAVITATIONAL EVOLUTION OF PROTOPLANETARY DISKS
The Astrophysical Journal, 2013
We investigate the formation process of self-gravitating protoplanetary disks in unmagnetized molecular clouds. The angular momentum is redistributed by the action of gravitational torques in the massive disk during its early formation. We develop a simplified one-dimensional accretion disk model that takes into account the infall of gas from the envelope onto the disk and the transfer of angular momentum in the disk with an effective viscosity. First we evaluate the gas accretion rate from the cloud core onto the disk by approximately estimating the effects of gas pressure and gravity acting on the cloud core. We formulate the effective viscosity as a function of the Toomre Q parameter that measures the local gravitational stability of the rotating thin disk. We use a function for viscosity that changes sensitively with Q when the disk is gravitationally unstable. We find a strong self-regulation mechanism in the disk evolution. During the formation stage of protoplanetary disks, the evolution of the surface density does not depend on the other details of the modeling of effective viscosity, such as the prefactor of the viscosity coefficient. Next, to verify our model, we compare the time evolution of the disk calculated with our formulation with that of three-dimensional hydrodynamical simulations. The structures of the resultant disks from the one-dimensional accretion disk model agree well with those of the three-dimensional simulations. Our model is a useful tool for the further modeling of chemistry, radiative transfer, and planet formation in protoplanetary disks.
The Astrophysical Journal, 2010
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 threedimensional 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 (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.
A revised condition for self-gravitational fragmentation of protoplanetary discs
Monthly Notices of the Royal Astronomical Society, 2016
Fragmentation of protoplanetary discs due to gravitational instabilities is a candidate of a formation mechanism of binary stars, brown dwarfs, and gaseous giant planets. The condition for the fragmentation has been thought that the disc cooling timescale is comparable to its dynamical timescale. However, some numerical simulations suggest that the fragmentation does not occur even if the cooling time is small enough, or the fragmentation can occur even when the cooling is inefficient. To reveal a realistic condition for fragmentation of selfgravitating discs, we perform two-dimensional numerical simulations that take into account the effect of the irradiation of the central star and radiation cooling of the disc, and precisely investigate the structure of the spiral arms formed in the protoplanetary discs. We show that the Toomre Q parameter in the spiral arms is an essential parameter for fragmentation. The spiral arms fragment only when Q < 0.6 in the spiral arms. We have further confirmed that this fragmentation condition observed in the numerical simulations can be obtained from the linear stability analysis for the self-gravitating spiral arms. These results indicate that the process of fragmentation of protoplanetary discs is divided into two stages: formation of the spiral arms in the discs; and fragmentation of the spiral arm. Our work reduces the condition for the fragmentation of the protoplanetary discs to the condition of the formation of the spiral arm that satisfies Q < 0.6.
The diverse lives of massive protoplanets in self-gravitating discs
Monthly Notices of the Royal Astronomical Society, 2018
Gas giant planets may form early-on during the evolution of protostellar discs, while these are relatively massive. We study how Jupiter-mass planet-seeds (termed protoplanets) evolve in massive, but gravitationally stable (Q > ∼ 1.5), discs using radiative hydrodynamic simulations. We find that the protoplanet initially migrates inwards rapidly, until it opens up a gap in the disc. Thereafter, it either continues to migrate inwards on a much longer timescale or starts migrating outwards. Outward migration occurs when the protoplanet resides within a gap with gravitationally unstable edges, as a high fraction of the accreted gas is high angular momentum gas from outside the protoplanet's orbit. The effect of radiative heating from the protoplanet is critical in determining the direction of the migration and the eccentricity of the protoplanet. Gap opening is facilitated by efficient cooling that may not be captured by the commonly used β-cooling approximation. The protoplanet initially accretes at a high rate (∼ 10 −3 M J yr −1), and its accretion luminosity could be a few tenths of the host star's luminosity, making the protoplanet easily observable (albeit only for a short time). Due to the high gas accretion rate, the protoplanet generally grows above the deuterium-burning mass-limit. Protoplanet radiative feedback reduces its mass growth so that its final mass is near the brown dwarf-planet boundary. The fate of a young planet-seed is diverse and could vary from a gas giant planet on a circular orbit at a few AU from the central star to a brown dwarf on an eccentric, wide orbit.
Rapid planetesimal formation in turbulent circumstellar disks
Nature, 2007
The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies 1 . How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem 2 : boulders stick together poorly 3 , and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas 4 . Gravitational collapse of the solid component has been suggested to overcome this barrier 1, 5, 6 . Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer 2, 7 , but turbulence must be present to explain observed gas accretion in protostellar discs 8 . Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas 9 , and these concentra-1 arXiv:0708.3890v1 [astro-ph]
Monthly Notices of the Royal Astronomical Society, 2013
We report the results of our three-dimensional radiation hydrodynamics simulation of collapsing unmagnetized molecular cloud cores. We investigate the formation and evolution of the circumstellar disk and the clumps formed by disk fragmentation. Our simulation shows that disk fragmentation occurs in the early phase of circumstellar disk evolution and many clumps form. The clump can be represented by a polytrope sphere of index n ∼ 3 and n 4 at central temperature T c 100 K and T c 100 K, respectively. We demonstrate, numerically and theoretically, that the maximum mass of the clump, beyond which it inevitably collapses, is ∼ 0.03 M ⊙ . The entropy of the clump increases during its evolution, implying that evolution is chiefly determined by mass accretion from the disk rather than by radiative cooling. Although most of the clumps rapidly migrate inward and finally fall onto the protostar, a few clumps remain in the disk. The central density and temperature of the surviving clump rapidly increase and the clump undergoes a second collapse within 1000 -2000 years after its formation. In our simulation, three second cores of masses 0.2 M ⊙ , 0.15 M ⊙ , and 0.06 M ⊙ formed. These are protostars or brown dwarfs rather than protoplanets. For the clumps to survive as planetary-mass objects, the rapid mass accretion should be prevented by some mechanisms.
PLANETESIMAL AND PROTOPLANET DYNAMICS IN A TURBULENT PROTOPLANETARY DISK: IDEAL UNSTRATIFIED DISKS
The Astrophysical Journal, 2009
The dynamics of planetesimals and planetary cores may be strongly influenced by density perturbations driven by magneto-rotational turbulence in their natal protoplanetary gas disks. Using the local shearing box approximation, we perform numerical simulations of planetesimals moving as massless particles in a turbulent, magnetized, unstratified gas disk. Our fiducial disk model shows turbulent accretion characterized by a Shakura-Sunyaev viscosity parameter of α ∼ 10 −2 , with root-mean-square density perturbations of ∼10%. We measure the statistical evolution of particle orbital properties in our simulations including mean radius, eccentricity, and velocity dispersion. We confirm random walk growth in time of all three properties, the first time that this has been done with direct orbital integration in a local model. We find that the growth rate increases with the box size used at least up to boxes of eight scale heights in horizontal size. However, even our largest boxes show velocity dispersions sufficiently low that collisional destruction of planetesimals should be unimportant in the inner disk throughout its lifetime. Our direct integrations agree with earlier torque measurements showing that type I migration dominates over diffusive migration by stochastic torques for most objects in the planetary core and terrestrial planet mass range. Diffusive migration remains important for objects in the mass range of kilometer-sized -2planetesimals. Discrepancies in the derived magnitude of turbulence between local and global simulations of magneto-rotationally unstable disks remains an open issue, with important consequences for planet formation scenarios.
Protostellar discs formed from turbulent cores
Monthly Notices of the Royal Astronomical Society, 2010
We investigate the collapse and fragmentation of low-mass, trans-sonically turbulent pre-stellar cores, using smoothed particle hydrodynamics simulations. The initial conditions are slightly supercritical Bonnor-Ebert spheres, all with the same density profile, the same mass (M O = 6.1 M) and the same radius (R O = 17 000 au), but having different initial turbulent velocity fields. 400 turbulent velocity fields have been generated, all scaled so that the mean Mach number is M = 1. Then, a subset of these (in total 11 setups), having a range of net angular momenta, j, has been evolved. The evolution of these turbulent cores is significantly different from the collapse of a rigidly rotating core. It is not strongly correlated with j. Instead, it is moderated by the formation of filamentary structures due to converging turbulent flows. A high fraction (9 out of 13, ∼69 per cent) of the individual protostars forming from turbulent cores are attended by resolved (R ≥ 10 au) protostellar accretion discs, but only a very small fraction (1 out of 9, ∼11 per cent) of these discs is sufficiently cool and extended to develop non-linear gravitational instabilities and fragment. Protostars with discs show two distinct growth modes. They initially grow by direct gravitational collapse, followed by subsequent disc accretion.
Arxiv preprint arXiv: …, 2010
We review the current theoretical understanding how growth from micrometer sized dust to massive giant planets occurs in disks around young stars. After introducing a number of observational constraints from the solar system, from observed protoplanetary disks, and from the extrasolar planets, we simplify the problem by dividing it into a number of discrete stages which are assumed to occur in a sequential way. In the first stage -the growth from dust to kilometer sized planetesimals -the aerodynamics of the bodies are of central importance. We discuss both a purely coagulative growth mode, as well as a gravoturbulent mode involving a gravitational instability of the dust. In the next stage, planetesimals grow to protoplanets of roughly 1000 km in size. Gravity is now the dominant force. The mass accretion can be strongly non-linear, leading to the detachment of a few big bodies from the remaining planetesimals. In the outer planetary system (outside a few AU), some of these bodies can become so massive that they eventually accrete a large gaseous envelope. This is the stage of giant planet formation, as understood within the core accretiongas capture paradigm. We also discuss the direct gravitational collapse model where giant planets are thought to form directly via a gravitational fragmentation of the gas disk. In the inner system, protoplanets collide in the last stage -probably after the dispersal of the gaseous disk -in giant impacts until the separations between the remaining terrestrial planets become large enough to allow long term stability. We finish the review with some selected questions.