Core instability models of giant planet accretion – II. Forming planetary systems

We develop a simple model for computing planetary formation based on the core instability model for the gas accretion and the oligarchic growth regime for the accretion of the solid core. In this model several planets can form simultaneously in the disc, a fact that has important implications especially for the changes in the dynamic of the planetesimals and the growth of the cores since we consider the collision between them as a source of potential growth. The type I and type II migration of the embryos and the migration of the planetesimals due to the interaction with the disc of gas are also taken into account. With this model we consider different initial conditions to generate a variety of planetary systems and analyse them statistically. We explore the effects of using different type I migration rates on the final number of planets formed per planetary system such as on the distribution of masses and semimajor axis of extrasolar planets, where we also analyse the implications of considering different gas accretion rates. A particularly interesting result is the generation of a larger population of habitable planets when the gas accretion rate and type I migration are slower.     

Methods for computing giant planet formation and evolution

We present a numerical code for computing all stages of the formation and evolution of giant planets in the framework of the core instability mechanism. This code is a non-trivial adaption of the stellar binary evolution code and is based on a standard Henyey technique. To investigate the performance of this code we applied it to the computation of the formation and evolution of a Jupiter mass object from a half Earth core mass to ages in excess of the age of the Universe.
We also present a new smoothed linear interpolation algorithm devised especially for the purpose of circumventing some problems found when some physical data (e.g. opacities, equation of state, etc.) are introduced into an implicit algorithm like the one employed in this work.     

Formation of gas giant planets: core accretion models with fragmentation and planetary envelope

We have calculated formation of gas giant planets based on the standard core accretion model including effects of fragmentation and planetary envelope. The accretion process is found to proceed as follows. As a result of runaway growth of planetesimals with initial radii of ∼10 km, planetary embryos with a mass of ∼10²⁷ g (∼ Mars mass) are found to form in ∼10⁵ years at Jupiter's position (5.2 AU), assuming a large enough value of the surface density of solid material (25 g/cm²) in the accretion disk at that distance. Strong gravitational perturbations between the runaway planetary embryos and the remaining planetesimals cause the random velocities of the planetesimals to become large enough for collisions between small planetesimals to lead to their catastrophic disruption. This produces a large number of fragments. At the same time, the planetary embryos have envelopes, that reduce energies of fragments by gas drag and capture them. The large radius of the envelope increases the collision rate between them, resulting in rapid growth of the planetary embryos. By the combined effects of fragmentation and planetary envelope, the largest planetary embryo with 21M_⊕ forms at 5.2 AU in 3.8×10⁶ years. The planetary embryo is massive enough to start a rapid gas accretion and forms a gas giant planet.     

Dynamical behaviour of planetesimals temporarily captured by a planet from heliocentric orbits: basic formulation and the case of low random velocity

Planetesimals encountering with a planet cannot be captured permanently unless energy dissipation is taken into account, but some of them can be temporarily captured in the vicinity of the planet for an extended period of time. Such a process would be important for the origin and dynamical evolution of irregular satellites, short-period comets, and Kuiper-belt binaries. In this paper, we describe the basic formulation for the study of temporary capture of planetesimals from heliocentric orbits using three-body orbital integration, such as the definition of the duration and rate of temporary capture, and present results in the case of low random velocity of planetesimals. In the case of planetesimals initially on circular orbits, we find that planetesimals undergo a close encounter with the planet before they become temporarily captured. When planetesimals are scattered by the planet into the vicinity of one of periodic orbits around the planet, the duration of temporary capture tends to be extended. Typically, these capture orbits are in the retrograde direction around the planet. We evaluate the rate of temporary capture of planetesimals, and find that the ratio of this rate to their collision rate on to the planet increases with increasing semimajor axis of the planet. Similar results are obtained for planetesimals with non-zero but small random velocities, as long as Kepler shear dominates the relative velocity between the planet and planetesimals. For larger initial random velocities of planetesimals, temporary capture in both prograde and retrograde directions with much longer duration becomes possible.     

Migration of giant planets in a time-dependent planetesimal accretion disc

In this paper we develop further the model for the migration of planets introduced in Del Popolo et al. We first model the protoplanetary nebula as a time-dependent accretion disc, and find self-similar solutions to the equations of the accretion disc that give us explicit formulae for the spatial structure and the temporal evolution of the nebula. These equations are then used to obtain the migration rate of the planet in the planetesimal disc, and to study how the migration rate depends on the disc mass, on its time evolution and on some values of the dimensionless viscosity parameter α . We find that planets that are embedded in planetesimal discs, having total mass of  10^-4-0.1 M_⊙  , can migrate inward a large distance for low values of α (e.g.,   α ≃10^-3-10^-2)  and/or large disc mass, and can survive only if the inner disc is truncated or because of tidal interaction with the star. Orbits with larger a are obtained for smaller values of the disc mass and/or for larger values of α . This model may explain several orbital features of the recently discovered giant planets orbiting nearby stars.     

Gap formation in a self-gravitating disk and the associated migration of the embedded giant planet

We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disk's self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of the disk's gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disk's selfgravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, ΣIand ΣII. When the surface density of the disk is lower than the first one, Σ0 ΣI, the effect of self-gravity suppresses the formation of a gap. When Σ0 ΣI, the self-gravity of the gas tends to benefit the gap formation process and enlarges the width/depth of the gap. According to our 1-D and2-D simulations, we estimate the first critical surface density to be ΣI≈ 0.8 MMSN.This effect increases until the surface density reaches the second critical value ΣII.When Σ0 ΣII, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5 MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disk's self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale correlates with the effective viscosity and can be up to 104yr.     

High-velocity dust collisions: forming planetesimals in a fragmentation cascade with final accretion

In laboratory experiments we determine the mass gain and loss in central collisions between centimetre- to decimetre-size SiO₂ dust targets and submillimetre- to centimetre-size SiO₂ dust projectiles of varying mass, size, shape and at different collision velocities up to ∼56.5 m s⁻¹. Dust projectiles much larger than 1 mm lead to a small amount of erosion of the target but decimetre targets do not break up. Collisions produce ejecta, which are smaller than the incoming projectile. Projectiles smaller than 1 mm are accreted by a target even at the highest collision velocities. This implies that net accretion of decimetre and larger bodies is possible. Independent of the original size of a considered projectile, after several collisions, all fragments will be of submillimetre size which might then be (re)accreted in the next collision with a larger body. The experimental data suggest that collisional growth through fragmentation and reaccretion is a viable mechanism to form planetesimals.     

Young Jupiters are faint: new models of the early evolution of giant planets

Here we show preliminary calculations of the cooling and contraction of a 2 M_J planet. These calculations, which are being extended to 1–10 M_J, differ from other published “cooling tracks” in that they include a core accretion‐gas capture formation scenario, the leading theory for the formation of gas giant planets.We find that the initial post‐accretionary intrinsic luminosity of the planet is ∼3 times less than previously published models which use arbitrary initial conditions. These differences last a few tens of millions of years. Young giant planets are intrinsically fainter than has been previously appreciated. We also discuss how uncertainties in atmospheric chemistry and the duration of the formation time of giant planets lead to challenges in deriving planetary physical properties from comparison with tabulated model values. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Episodic accretion in magnetically layered protoplanetary discs

We study protoplanetary disc evolution assuming that angular momentum transport is driven by gravitational instability at large radii, and magnetohydrodynamic (MHD) turbulence in the hot inner regions. At radii of the order of 1 au such discs develop a magnetically layered structure, with accretion occurring in an ionized surface layer overlying quiescent gas that is too cool to sustain MHD turbulence. We show that layered discs are subject to a limit cycle instability, in which accretion on to the protostar occurs in ∼10⁴-yr bursts with ̇ ∼10⁻⁵ M_⊙ yr⁻¹, separated by quiescent intervals lasting ∼10⁵ yr where ̇ ≈10⁻⁸ M_⊙ yr⁻¹. Such bursts could lead to repeated episodes of strong mass outflow in young stellar objects. The transition to this episodic mode of accretion occurs at an early epoch ( t ≪1 Myr), and the model therefore predicts that many young pre-main-sequence stars should have low rates of accretion through the inner disc. At ages of a few Myr, the discs are up to an order of magnitude more massive than the minimum-mass solar nebula, with most of the mass locked up in the quiescent layer of the disc at r ∼1 au. The predicted rate of low-mass planetary migration is reduced at the outer edge of the layered disc, which could lead to an enhanced probability of giant planet formation at radii of 1–3 au.