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Register a new userTidal Barrier and the Asymptotic Mass of Proto Gas-Giant Planets
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Extrasolar planets found with radial velocity surveys have masses ranging from several Earth to several Jupiter masses. While mass accretion onto protoplanetary cores in weak-line T-Tauri disks may eventually be quenched by a global depletion of gas, such a mechanism is unlikely to have stalled the growth of some known planetary systems which contain relatively low-mass and close-in planets along with more massive and longer period companions. Here, we suggest a potential solution for this conundrum. In general, supersonic infall of surrounding gas onto a protoplanet is only possible interior to both of its Bondi and Roche radii. At a critical mass, a protoplanets Bondi and Roche radii are equal to the disk thickness. Above this mass, the protoplanets tidal perturbation induces the formation of a gap. Although the disk gas may continue to diffuse into the gap, the azimuthal flux across the protoplanets Roche lobe is quenched. Using two different schemes, we present the results of numerical simulations and analysis to show that the accretion rate increases rapidly with the ratio of the protoplanets Roche to Bondi radii or equivalently to the disk thickness. In regions with low geometric aspect ratios, gas accretion is quenched with relatively low protoplanetary masses. This effect is important for determining the gas-giant planets mass function, the distribution of their masses within multiple planet systems around solar type stars, and for suppressing the emergence of gas-giants around low mass stars.
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After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues to diffuse onto horseshoe streamlines under effect of viscous dissipation, and meander in and out of the planets Hill sphere. Within the Hill sphere, the horseshoe streamlines intercept gas flow in circumplanetary disks. The host stars tidal perturbation induces a barrier across the converging streamlines interface. Viscous transfer of angular momentum across this tidal barrier determines the rate of mass diffusion from the horseshoe streamlines onto the circumplanetary disks, and eventually the accretion rate onto the protoplanets. We carry out a series of numerical simulations to test the influence of this tidal barrier on super thermal planets. In weakly viscous disks, protoplanets accretion rate steeply decreases with their masses above the thermal limit. As their growth timescale exceeds the gas depletion time scale, their masses reach asymptotic values comparable to that of Jupiter. In relatively thick and strongly viscous disks, protoplanets asymptotic masses exceed several times that of Jupiter. Two dimensional numerical simulations show that such massive protoplanets strongly excite the eccentricity of nearby horseshoe streamlines, destabilize orderly flow, substantially enhance the diffusion rate across the tidal barrier, and elevate their growth rate until their natal disk is severely depleted. In contrast, eccentric streamlines remain stable in three dimensional simulations. Based on the upper falloff in the observe mass distribution of known exoplanets, we suggest their natal disks had relatively low viscosity alpha sim 0.001, modest thickness H/R sim 0.03 to 0.05, and limited masses comparable to that of minimum mass solar nebula model.
The planets with a radius $<$ 4 $R$$_oplus$ observed by the Kepler mission exhibit a unique feature, and propose a challenge for current planetary formation models. The tidal effect between a planet and its host star plays an essential role in reconfiguring the final orbits of the short-period planets. In this work, based on various initial Rayleigh distributions of the orbital elements, the final semi-major axis distributions of the planets with a radius $<$ 4 $R_oplus$ after suffering tidal evolutions are investigated. Our simulations have qualitatively revealed some statistical properties: the semi-major axis and its peak value all increase with the increase of the initial semi-major axis and eccentricity. For the case that the initial mean semi-major axis is less than 0.1 au and the mean eccentricity is larger than 0.25, the results of numerical simulation are approximately consistent with the observation. In addition, the effects of other parameters, such as the tidal dissipation coefficient, stellar mass and planetary mass, etc., on the final semi-major axis distribution after tidal evolution are all relatively small. Based on the simulation results, we have tried to find some clues for the formation mechanism of low-mass planets. We speculate that these low-mass planets probably form in the far place of protoplanetary disk with a moderate eccentricity via the type I migration, and it is also possible to form in situ.
This paper presents a summary of four invited and twelve contributed presentations on asymptotic giant branch stars and red supergiants, given over the course of two afternoon splinter sessions at the 19th Cool Stars Workshop. It highlights both recent observations and recent theory, with some emphasis on high spatial resolution, over a wide range of wavelengths. Topics covered include 3D models, convection, binary interactions, mass loss, dust formation and magnetic fields.
Protoplanets are able to accrete primordial atmospheres when embedded in the gaseous protoplanetary disk. The formation and structure of the proto-atmosphere are subject to the planet--disk environment and orbital effects. Especially, when planets are on eccentric orbits, their relative velocities to the gas can exceed the sound speed. The planets generate atmosphere-stripping bow shocks. We investigate the proto-atmospheres on low-mass planets with eccentric orbits with radiation-hydrodynamics simulations. A 2D radiative model of the proto-atmosphere is established with tabulated opacities for the gas and dust. The solutions reveal large-scale gas recycling inside a bow shock structure. The atmospheres on eccentric planets are typically three to four orders of magnitude less massive than those of planets with circular orbits. Overall, however, a supersonic environment is favorable for planets to keep an early stable atmosphere, rather than harmful, due to the steady gas supply through the recycling flow. We also quantitatively explore how such atmospheres are affected by the relative velocity of the planet to the gas, the planet mass, and the background gas density. Our time-dependent simulations track the orbital evolution of the proto-atmosphere with the planet--disk parameters changing throughout the orbit. Atmospheric properties show oscillatory patterns as the planet travels on an eccentric orbit, with a lag in phase. To sum up, low-mass eccentric planets can retain small proto-atmospheres despite the stripping effects of bow shocks. The atmospheres are always connected to and interacting with the disk gas. These findings provide important insights into the impacts of migration and scattering on planetary proto-atmospheres.
Planets form in the discs of gas and dust that surround young stars. It is not known whether gas giant planets on wide orbits form the same way as Jupiter or by fragmentation of gravitationally unstable discs. Here we show that a giant planet, which has formed in the outer regions of a protostellar disc, initially migrates fast towards the central star (migration timescale ~10,000 yr) while accreting gas from the disc. However, in contrast with previous studies, we find that the planet eventually opens up a gap in the disc and the migration is essentially halted. At the same time, accretion-powered radiative feedback from the planet, significantly limits its mass growth, keeping it within the planetary mass regime (i.e. below the deuterium burning limit) at least for the initial stages of disc evolution. Giant planets may therefore be able to survive on wide orbits despite their initial fast inward migration, shaping the environment in which terrestrial planets that may harbour life form.
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