Circumstellar dust distribution in systems with two planets in resonance

We investigate via numerical modeling the effects of two planets locked in resonance, and migrating outward, on the dust distribution of the natal circumstellar disk. We aim to test whether the dust distribution exhibits peculiar features arising from the interplay among the gravitational perturbations of the planets in resonance, the evolution of the gas, and its influence on the dust grains' dynamics. We focus on the 3:2 and 2:1 resonance, where the trapping may be caused by the convergent migration of a Jupiter- and Saturn-mass planet, preceding the common gap formation and ensuing outward (or inward) migration. Models show that a common gap also forms in the dust component -- similarly to what a single, more massive planet would generate -- and that outward migration leads to a progressive widening of the dust gap and to a decoupling from the gas gap. As the system evolves, a significantly wider gap is observed in the dust distribution, which ceases to overlap with the gas gap in the inner disk regions. At the outer edge of the gas gap, outward migration of the planets produces an over-density of dust particles, which evolve differently in the 3:2 and 2:1 resonances. For the 3:2, the dust trap at the gap's outer edge is partly efficient and a significant fraction of the grains filters through the gap. For the 2:1 resonance, the trap is more efficient and very few grains cross the gap, while the vast majority accumulate at the outer edge of the gap.Comment: 16 pages, 12 figures. Accepted for publicatio

New Formation Models for the Kepler-36 System

Formation of the planets in the Kepler-36 system is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. The standard model is updated to include the dissolution of accreting rocky planetesimals in the gaseous envelope of the planet, leading to substantial enrichment of the envelope mass in heavy elements and a non-uniform composition with depth. For Kepler-36 c, models involving in situ formation and models involving orbital migration are considered. The results are compared with standard formation models. The calculations include the formation (accretion) phase, as well as the subsequent cooling phase, up to the age of Kepler-36 (7 Gyr). During the latter phase, mass loss induced by stellar XUV radiation is included. In all cases, the results fit the measured mass, 7.84 M$_\oplus$, and radius, 3.68 R$_\oplus$, of Kepler-36 c. Two parameters are varied to obtain these fits: the disk solid surface density at the formation location, and the "efficiency" factor in the XUV mass loss rate. The updated models are hotter and therefore less dense in the silicate portion of the planet and in the overlying layers of H/He, as compared with standard models. The lower densities mean that only about half as much H/He is needed to be accreted to fit the present-day mass and radius constraints. For Kepler-36 b, an updated in situ calculation shows that the entire H/He envelope is lost, early in the cooling phase, in agreement with observation.Comment: 21 pages, 18 figures, 1 table. Accepted for publication in The Astrophysical Journa

Recent Simulations of the Late Stages Growth of Jupiter

Presented by Lissauer et al. (2009, Icarus 199, 338) are used to test the model of capture of Jupiter's irregular satellites within proto-Jupiter's distended and thermally-supported envelope. We find such capture highly unlikely, since the envelope shrinks too slowly for a large number of moons to be retained, and many of those that would be retained would orbit closer to the planet than do the observed Jovian irregulars. Our calculations do not address (and therefore do not exclude) the possibility that the irregular satellites were captured as a result of gas drag within a circumjovian disk. Support for this research from NASA Outer Planets Research Program is gratefully acknowledged

Three-dimensional Disk-Planet Torques in a Locally Isothermal Disk

We determine an expression for the Type I planet migration torque involving a locally isothermal disk, with moderate turbulent viscosity (~0.0005 < alpha < ~0.05), based on three-dimensional nonlinear hydrodynamical simulations. The radial gradients (in a dimensionless logarithmic form) of density and temperature are assumed to be constant near the planet. We find that the torque is roughly equally sensitive to the surface density and temperature radial gradients. Both gradients contribute to inward migration when they are negative. Our results indicate that two-dimensional calculations with a smoothed planet potential, used to account for the effects of the third dimension, do not accurately determine the effects of density and temperature gradients on the three-dimensional torque. The results suggest that substantially slowing or stopping planet migration by means of changes in disk opacity or shadowing is difficult and appears unlikely for a disk that is locally isothermal. The scalings of the torque and torque density with planet mass and gas sound speed follow the expectations of linear theory. We also determine an improved formula for the torque density distribution that can be used in one-dimensional long-term evolution studies of planets embedded in locally isothermal disks. This formula can be also applied in the presence of mildly varying radial gradients and of planets that open gaps. We illustrate its use in the case of migrating super-Earths and determine some conditions sufficient for survival.Comment: 20 pages, 16 figures. To appear in The Astrophysical Journal. Updated with changes and corrections added in proo

Enhancement of the Accretion of Jupiters Core by a Voluminous Low-Mass Envelope

We present calculations of the early stages of the formation of Jupiter via core nucleated accretion and gas capture. The core begins as a seed body of about 350 kilometers in radius and orbits in a swarm of planetesimals whose initial radii range from 15 meters to 100 kilometers. We follow the evolution of the swarm by accounting for growth and fragmentation, viscous and gravitational stirring, and for drag-induced migration and velocity damping. Gas capture by the core substantially enhances the cross-section of the planet for accretion of small planetesimals. The dust opacity within the atmosphere surrounding the planetary core is computed self-consistently, accounting for coagulation and sedimentation of dust particles released in the envelope as passing planetesimals are ablated. The calculation is carried out at an orbital semi-major axis of 5.2 AU and an initial solids' surface density of 10/g/cm^2 at that distance. The results give a core mass of 7 Earth masses and an envelope mass of approximately 0.1 Earth mass after 500,000 years, at which point the envelope growth rate surpasses that of the core. The same calculation without the envelope gives a core mass of only 4 Earth masses

Outward Migration of Jupiter and Saturn in Evolved Gaseous Disks

The outward migration of a pair of resonant-orbit planets, driven by tidal interactions with a gas-dominated disk, is studied in the context of evolved solar nebula models. The planets' masses, M1 and M2, correspond to those of Jupiter and Saturn. Hydrodynamical calculations in two and three dimensions are used to quantify the migration rates and analyze the conditions under which the outward migration mechanism may operate. The planets are taken to be fully formed after 1e6 and before 3e6 years. The orbital evolution of the planets in an evolving disk is then calculated until the disk's gas is completely dissipated. Orbital locking in the 3:2 mean motion resonance may lead to outward migration under appropriate conditions of disk viscosity and temperature. However, resonance locking does not necessarily result in outward migration. This is the case, for example, if convergent migration leads to locking in the 2:1 mean motion resonance, as post-formation disk conditions seem to suggest. Accretion of gas on the planets may deactivate the outward migration mechanism by raising the mass ratio M2/M1 and/or by reducing the accretion rate toward the star, hence depleting the inner disk. For migrating planets locked in the 3:2 mean motion resonance, there are stalling radii that depend on disk viscosity and on stellar irradiation, when it determines the disk's thermal balance. Planets locked in the 3:2 orbital resonance that start moving outward from within 1-2 AU may reach beyond 5 AU only under favorable conditions. However, within the explored space of disk parameters, only a small fraction - less than a few per cent - of the models predict that the interior planet reaches beyond 4 AU.Comment: 24 pages, 22 figures. To appear in The Astrophysical Journal. Updated with corrections added in proo

Dust distribution around low-mass planets on converging orbits

Super-Earths can form at large orbital radii and migrate inward due to tidal interactions with the circumstellar disk. In this scenario, convergent migration may occur and lead to the formation of resonant pairs of planets. We explore the conditions under which convergent migration and resonance capture take place, and what dynamical consequences can be expected on the dust distribution surrounding the resonant pair. We combine hydrodynamic planet--disk interaction models with dust evolution calculations to investigate the signatures produced in the dust distribution by a pair of planets in mean-motion resonances. We find that convergent migration takes place when the outer planet is the more massive. However, convergent migration also depends on the local properties of the disk, and divergent migration may result as well. For similar disk parameters, the capture in low degree resonances (e.g., 2:1 or 3:2) is preferred close to the star where the resonance strength can more easily overcome the tidal torques exerted by the gaseous disk. Farther away from the star, convergent migration may result in capture in high degree resonances. The dust distribution shows potentially observable features typically when the planets are trapped in a 2:1 resonance. In other cases, with higher degree resonances (e.g., 5:4 or 6:5) dust features may not be sufficiently pronounced to be easily observable. The degree of resonance established by a pair of super-Earths may be indicative of the location in the disk where capture occurred. There can be significant differences in the dust distribution around a single super-Earth and a pair of super-Earths in resonance.Comment: Accepted for publication on Astronomy and Astrophysic