The Evolution of Gravitationally Unstable Protoplanetary Disks: Fragmentation and Possible Giant Planet Formation (original) (raw)
Related papers
Formation of Giant Planets by Fragmentation of Protoplanetary Disks
Science, 2002
The evolution of gravitationally unstable protoplanetary gaseous disks has been studied using three dimensional smoothed particle hydrodynamics (SPH) simulations with unprecedented resolution. We have considered disks with initial masses and temperature profiles consistent with those inferred for the protosolar nebula and for other protoplanetary disks. We show that long-lasting, self-gravitating protoplanets arise after a few disk orbital times if cooling is efficient enough to maintain the temperature close to 50 K. The resulting bodies have masses and orbital eccentricities remarkably similar to those of observed extrasolar planets.
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.
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.
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.
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.
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]
Icarus, 1999
Recent studies indicate that the formation of jovian giant planets (probably Jupiter and possibly Saturn) may have preceded the formation of terrestrial planets because of the rapidity of the gascapture process of jovian planets and the stability of the terrestrial protoplanet system. In this paper, we investigate the stability and orbital evolution of medium-sized protoplanets in the terrestrial region under the perturbation by jovian giant planets, Jupiter and Saturn. In our numerical models of the terrestrial protoplanet system, typical masses of the protoplanets are about 0.1 to 0.2 Earth mass, and their spacings are varied from 4 to 20 mutual Hill radii. In initially low-eccentricity and low-inclination orbits, secular perturbation by jovian planets can enhance the eccentricities of terrestrial protoplanets and increase the probability of close encounters when the separation of the protoplanets is large. Due to the effect of the secular perturbation, the instability time scale of the terrestrial protoplanet system is limited to 10 6 years, at most 10 7 years, The time scale of instability also depends much on initial random velocity. Initially high random velocity of protoplanets also reduces the instability time scale two orders of magnitude or so compared with low random velocity and can accelerate the dynamical evolution of the systems.
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 migration and growth of protoplanets in protostellar discs
We investigate the gravitational interaction of a Jovian-mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions are investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Non-linear two-dimensional hydrodynamic simulations are employed using three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near-circular orbit after a characteristic viscous timescale of 10 4 initial orbital periods. This is found to be independent of whether the protoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion on to the central star. Maximally accreting protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is 5 Jupiter masses, if they originate in protoplanetary discs similar to the minimum-mass solar nebula. This is because of the reduced accretion rates obtained for planets of increasing mass. Assuming that some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc–protoplanet interactions during the late stages of giant planet formation.