ABSTRACT
Ringed structures have been observed in a variety of protoplanetary discs. Among the processes that might be able to generate such features, the Secular Gravitational Instability (SGI) is a ...possible candidate. It has also been proposed that the SGI might lead to the formation of planetesimals during the non-linear phase of the instability. In this context, we employ two-fluid hydrodynamical simulations with self-gravity to study the non-axisymmetric, non-linear evolution of ringed perturbations that grow under the action of the SGI. We find that the non-linear evolution outcome of the SGI depends mainly on the initial linear growth rate. For SGI growth rates smaller than typically σ ${\lesssim}$ 10−4–10−5 Ω, dissipation resulting from dust feedback introduces a m = 1 spiral wave in the gas, even for Toomre gas stability parameters Qg > 2 for which non-axisymmetric instabilities appear in a purely gaseous disc. This one-armed spiral subsequently traps dust particles until a dust-to-gas ratio ϵ ∼ 1 is achieved. For higher linear growth rates, the dust ring is found to undergo gravitational collapse until the bump in the surface density profile becomes strong enough to trigger the formation of dusty vortices through the Rossby Wave Instability (RWI). Enhancements in dust density resulting from this process are found to scale with the linear growth rate, and can be such that the dust density is higher than the Roche density, leading to the formation of bound clumps. Fragmentation of axisymmetric rings produced by the SGI might therefore appear as a possible process for the formation of planetesimals.
Planetary embryos embedded in gaseous protoplanetary disks undergo Type I orbital migration. Migration can be inward or outward depending on the local disk properties but, in general, only planets ...more massive than several M⊕ can migrate outward. Here we propose that an embryo’s migration history determines whether it becomes a hot super-Earth or the core of a giant planet. Systems of hot super-Earths (or mini-Neptunes) form when embryos migrate inward and pile up at the inner edge of the disk. Giant planet cores form when inward-migrating embryos become massive enough to switch direction and migrate outward. We present simulations of this process using a modified N-body code, starting from a swarm of planetary embryos. Systems of hot super-Earths form in resonant chains with the innermost planet at or interior to the disk inner edge. Resonant chains are disrupted by late dynamical instabilities triggered by the dispersal of the gaseous disk. Giant planet cores migrate outward toward zero-torque zones, which move inward and eventually disappear as the disk disperses. Giant planet cores migrate inward with these zones and are stranded at ~1−5 AU. Our model reproduces several properties of the observed extra-solar planet populations. The frequency of giant planet cores increases strongly when the mass in solids is increased, consistent with the observed giant exoplanet – stellar metallicity correlation. The frequency of hot super-Earths is not a function of stellar metallicity, also in agreement with observations. Our simulations can reproduce the broad characteristics of the observed super-Earth population.
Reproducing Uranus and Neptune remains a challenge for simulations of solar system formation. The ice giants’ peculiar obliquities suggest that they both suffered giant collisions during their ...formation. Thus, there must have been an epoch of accretion dominated by collisions among large planetary embryos in the primordial outer solar system. We test this idea using N-body numerical simulations including the effects of a gaseous protoplanetary disk. One strong constraint is that the masses of the ice giants are very similar – the Neptune and Uranus mass ratio is ~1.18. We show that similar-sized ice giants do indeed form by collisions between planetary embryos beyond Saturn. The fraction of successful simulations varies depending on the initial number of planetary embryos in the system, their individual and total masses. Similar-sized ice giants are consistently reproduced in simulations starting with five to ten planetary embryos with initial masses of ~3–6 M⊕. We conclude that accretion from a population of planetary embryos is a plausible scenario for the origin of Uranus and Neptune.
ABSTRACT The orbital structure of the asteroid belt holds a record of the solar system's dynamical history. The current belt only contains ∼10−3 Earth masses yet the asteroids' orbits are dynamically ...excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter's orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth's orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter's and Saturn's early orbits were chaotic. Stochastic variations in the gas giants' orbits cause resonances to continually jump across the main belt and excite the asteroids' orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants' current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.
ABSTRACT
We examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble ...accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot{M}= 2\times 10^{-8}\, \mathrm{ M}_\odot$ yr−1 and pebble flux $\dot{M}_{\mathrm{ peb}}=170\, \mathrm{ M}_\oplus$ Myr−1, we find that embryo eccentricities attain values comparable to the disc aspect ratio. The planet radial excursion in the disc, however, causes the torque exerted by inflowing pebbles to cancel on average and migration to transition from outward to inward. This is found to arise because the magnitude of thermal torques decreases exponentially with increasing eccentricity, and we provide a fitting formula for the thermal torque attenuation as a function of eccentricity. As the disc evolves, the accretion luminosity becomes at some point too small to make the core eccentricity grow such that the solid component can exert a non-zero torque on the planet. This torque is positive and for gas accretion rates $\dot{M} \lesssim 5\times 10^{-9}$M⊙ yr−1 and pebble fluxes $\dot{M}_{\rm {peb}} \lesssim 120\, \mathrm{ M}_\oplus $ Myr−1, it is found to overcome the gas torque exerted on cores with mass $m_\mathrm{ p}\lesssim \, 1\,\mathrm{ {M}}_\oplus$, resulting in outward migration.
The formation of planets around binary stars may be more difficult than around single stars. In a close binary star (with a separation of less than a hundred astronomical units), theory predicts the ...presence of circumstellar disks around each star, and an outer circumbinary disk surrounding a gravitationally cleared inner cavity around the stars. Given that the inner disks are depleted by accretion onto the stars on timescales of a few thousand years, any replenishing material must be transferred from the outer reservoir to fuel planet formation (which occurs on timescales of about one million years). Gas flowing through disk cavities has been detected in single star systems. A circumbinary disk was discovered around the young low-mass binary system GG Tau A (ref. 7), which has recently been shown to be a hierarchical triple system. It has one large inner disk around the single star, GG Tau Aa, and shows small amounts of shocked hydrogen gas residing within the central cavity, but other than a single weak detection, the distribution of cold gas in this cavity or in any other binary or multiple star system has not hitherto been determined. Here we report imaging of gas fragments emitting radiation characteristic of carbon monoxide within the GG Tau A cavity. From the kinematics we conclude that the flow appears capable of sustaining the inner disk (around GG Tau Aa) beyond the accretion lifetime, leaving time for planet formation to occur there. These results show the complexity of planet formation around multiple stars and confirm the general picture predicted by numerical simulations.
Celotno besedilo
Dostopno za:
DOBA, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Observations of protoplanetary disks have revealed dust rings that are likely due to the presence of pressure bumps in the disk. Because these structures tend to trap drifting pebbles, it has been ...proposed that pressure bumps may play an important role in the planet formation process. In this paper, we investigate the orbital evolution of a 0.1 M ⊕ protoplanet embedded in a pressure bump using 2D hydrodynamical simulations of protoplanetary disks consisting of gas and pebbles. We examine the role of thermal forces generated by the pebble accretion-induced heat release, taking into account the feedback between the luminosity and the eccentricity. We also study the effect of the pebble-scattered flow on the planet’s orbital evolution. Due to the accumulation of pebbles at the pressure bump, the planet’s accretion luminosity is high enough to induce significant eccentricity growth through thermal forces. Accretion luminosity is also responsible for vortex formation at the planet’s position through baroclinic effects, which cause the planet to escape from the dust ring if dust feedback on the gas is neglected. Including the effect of the dust feedback leads to weaker vortices, which enable the planet to remain close to the pressure maximum on an eccentric orbit. Simulations in which the planet mass is allowed to increase as a consequence of pebble accretion result in the formation of giant planet cores with masses in the range of 5–20 M ⊕ over ~2 × 10 4 yr. This occurs for moderate values of the Stokes number, St ≈ 0.01, such that the pebble drift velocity is not too high and the dust ring mass not too small. Our results suggest that pressure bumps mays be preferred locations for the formation of giant planets, but this requires a moderate level of grain growth within the disk.
Abstract
‘Hot super-Earths’ (or ‘mini-Neptunes’) between one and four times Earth's size with period shorter than 100 d orbit 30–50 per cent of Sun-like stars. Their orbital configuration – measured ...as the period ratio distribution of adjacent planets in multiplanet systems – is a strong constraint for formation models. Here, we use N-body simulations with synthetic forces from an underlying evolving gaseous disc to model the formation and long-term dynamical evolution of super-Earth systems. While the gas disc is present, planetary embryos grow and migrate inward to form a resonant chain anchored at the inner edge of the disc. These resonant chains are far more compact than the observed super-Earth systems. Once the gas dissipates, resonant chains may become dynamically unstable. They undergo a phase of giant impacts that spreads the systems out. Disc turbulence has no measurable effect on the outcome. Our simulations match observations if a small fraction of resonant chains remain stable, while most super-Earths undergo a late dynamical instability. Our statistical analysis restricts the contribution of stable systems to less than 25 per cent. Our results also suggest that the large fraction of observed single-planet systems does not necessarily imply any dichotomy in the architecture of planetary systems. Finally, we use the low abundance of resonances in Kepler data to argue that, in reality, the survival of resonant chains happens likely only in ∼5 per cent of the cases. This leads to a mystery: in our simulations only 50–60 per cent of resonant chains became unstable, whereas at least 75 per cent (and probably 90–95 per cent) must be unstable to match observations.
The process of forming a circumbinary planet is thought to be intimately related to the structure of the nascent circumbinary disc. It has been shown that the structure of a circumbinary disc depends ...strongly on three-dimensional effects and on detailed modelling of the thermodynamics. Here, we employ three-dimensional hydrodynamical simulations, combined with a proper treatment of the thermal physics using the RADMC-3D radiation transport code, to examine the location of the snow line in circumbinary discs. The models have application to the circumbinary planets that have been discovered in recent years by the Kepler and TESS transit surveys. We find that the snow line is located in a narrow region of the circumbinary disc, close to the inner cavity that is carved out by the central binary, at typical orbital distances of ~ 1.5–2 au for the system parameters considered. In this region, previous work has shown that both grain growth and pebble accretion are likely to be inefficient because of the presence of hydrodynamical turbulence. Hence, in situ planet formation interior to the snow line is unlikely to occur and circumbinary planets should preferentially be icy, not rocky.
It is expected that a pressure bump can be formed at the inner edge of a dead-zone, and where vortices can develop through the Rossby Wave Instability (RWI). It has been suggested that self-gravity ...can significantly affect the evolution of such vortices. We present the results of 2D hydrodynamical simulations of the evolution of vortices forming at a pressure bump in self-gravitating discs with Toomre parameter in the range $4-30$. We consider isothermal plus non-isothermal disc models that employ either the classical $\beta$ prescription or a more realistic treatment for cooling. The main aim is to investigate whether the condensating effect of self-gravity can stabilize vortices in sufficiently massive discs. We confirm that in isothermal disc models with ${\cal Q} \gtrsim 15$, vortex decay occurs due to the vortex self-gravitational torque. For discs with $3\lesssim {\cal Q} \lesssim 7$, the vortex develops gravitational instabilities within its core and undergoes gravitational collapse, whereas more massive discs give rise to the formation of global eccentric modes. In non-isothermal discs with $\beta$ cooling, the vortex maintains a turbulent core prior to undergoing gravitational collapse for $\beta \lesssim 0.1$, whereas it decays if $\beta \ge 1$. In models that incorpore both self-gravity and a better treatment for cooling, however, a stable vortex is formed with aspect ratio $\chi \sim 3-4$. Our results indicate that self-gravity significantly impacts the evolution of vortices forming in protoplanetary discs, although the thermodynamical structure of the vortex is equally important for determining its long-term dynamics.
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