Ji-Lin Zhou

Post-oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems

In the sequential accretion model, planets form through the sedimentation of dust, cohesive collisions of planetesimals, and coagulation of protoplanetary embryos prior to the onset of efficient gas accretion. As progenitors of terrestrial planets and the cores of gas giant planets, embryos have comparable masses and are separated by the full width of their feeding zones after the oligarchic growth. Within this context, we investigate the orbit-crossing time (Tc) of protoplanetary systems with equal planetary masses and initial separation k0 scaled by their mutual Hill radii (EMS systems). In a gas-free environment, log [Tc/(1 yr)] A + B log (k0/2.3), where A and B are functions of the planetary masses and initial eccentricities. This power law is caused by a random-walk diffusion of velocity dispersion σ(t) in the EMS systems. The diffusion also leads to (1) a Rayleigh distribution of eccentricities with probability P(t) = (e/σ2) exp [-e2/(2σ2)] at time t and (2) an evolution of average eccentricity ∝t1/2. As evidence of this chaotic diffusion, the observed eccentricities of known extrasolar planets obey a Rayleigh distribution. In a gaseous environment, as embryos become well separated (with k0 6-12), their orbit-crossing tendency is suppressed by tidal drag, and their growth is stalled as their orbits are circularized. We evaluate the isolation masses of the embryos, which determine the probability of gas giant formation, as a function of the dust and gas surface densities.

Origin and ubiquity of short-period earth-like planets: Evidence for the sequential accretion theory of planet formation

The formation of gas giant planets is assumed to be preceded by the emergence of solid cores in the conventional sequential accretion paradigm. This hypothesis implies that the presence of Earth-like planets can be inferred from the detection of gas giants. A similar prediction cannot be made with the gravitational instability model, which assumes that gas giants formed from the collapse of gas fragments analogous to their host stars. We propose an observational test for the determination of the dominant planetary formation channel. Based on the sequential accretion model, we identify several potential avenues that may lead to the prolific formation of a population of close-in Earth-mass (M⊕) planets around stars with (1) short-period or (2) solitary eccentric giants and (3) systems that contain intermediate-period resonant giants. In contrast, these close-in Earths are not expected to form in systems where giants originated rapidly through gravitational instability. As a specific example, we suggest that sequential accretion processes led to the formation of the 7.5 M⊕ planet around GJ 876 and predict that it may have an atmosphere and envelope rich in O2 and liquid water. Assessments of the ubiquity of these planets will lead to (1) the detection of the first habitable terrestrial planets, (2) verification of the dominant mode of planet formation, (3) an estimate of the fraction of stars harboring Earth-like planets, and (4) modification of biomarker signatures.

PLANETESIMAL ACCRETION IN BINARY SYSTEMS: COULD PLANETS FORM AROUND α CENTAURI B?

Stellar perturbations affect planet formation in binary systems. Recent studies show that the planet-formation stage of mutual accretion of km-sized planetesimals is most sensitive to binary effects. In this paper, the condition for planetesimal accretion is investigated around α CenB, which is believed to be an ideal candidate for detection of an Earth-like planet in or near its habitable zone (0.5-0.9xa0AU). A simplified scaling method is developed to estimate the accretion timescale of the planetesimals embedded in a protoplanetary disk. Twenty-four cases with different binary inclinations (iB = 0, 01, 10, and 10°), gas densities (0.3, 1, and 3 times of the Minimum Mass of Solar Nebula, MMSN hereafter), and with and without gas depletion, are simulated. We find that (1) re-phasing of planetesimals orbits is independent of gas depletion in α CenB, and it is significantly reached at 1-2xa0AU, leading to accretion-favorable conditions after the first ~ 105 yr; (2) the planetesimal collision timescale at 1-2xa0AU is estimated as: TB col ~ (1 + 100iB ) × 103 yr, where 0° < iB < 10°; (3) disks with gas densities of 0.3-1.0 MMSN and inclinations of 1°-10° with respect to the binary orbit are found to be the favorable conditions in which planetesimals are likely to survive and grow up to planetary embryos; and (4) even for the accretion-favorable conditions, accretion is significantly less efficient as compared to the single-star case, and the time taken by accretion of km-sized planetesimals into planetary embryos or cores would be at least several times of TB col, which is probably longer than the timescale of gas depletion in such a close binary system. In other words, our results suggest that formation of Earth-like planets through accretion of km-sized planetesimals is possible in α CenB, while formation of gaseous giant planets is not favorable.

The Librating Companions in HD 37124, HD 12661, HD 82943, 47 Ursa Majoris, and GJ 876: Alignment or Antialignment?

We investigated the apsidal motion for the multiplanet systems. In the simulations, we found that the two planets of HD 37124, HD 12661, 47 UMa, and HD 82943 separately undergo apsidal alignment or antialignment. However, the companions of GJ 876 and v And are in apsidal lock only about 0degrees. Moreover, we obtained the criteria with Laplace-Lagrange secular theory to discern whether a pair of planets for a certain system are in libration or circulation.

Occurrence and Stability of Apsidal Resonance in Multiple Planetary Systems

With the help of the Laplace-Lagrange solution of the secular perturbation theory in a double-planet system, we study the occurrence and the stability of apsidal secular resonance between the two planets. The explicit criteria for predicting whether two planets are in apsidal resonance is derived, which shows that the occurrence of the apsidal resonance depends only on the mass ratio (m1/m2), semimajor axis ratio (a1/a2), initial eccentricity ratio (e10/e20), and the initial relative apsidal longitude (20 - 10) between the two planets. The probability of two planets falling in apsidal resonance is given in the initial element space. We verify the criteria with numerical integrations for the HD 12661 system and find they give good predictions except at the boundary of the criteria or when the planet eccentricities are too large. The nonlinear stability of the two planets in HD 12661 system are studied by calculating the Lyapunov exponents of their orbits in a general three-body model. We find that two planets in large-eccentricity orbits could be stable only when they are in aligned apsidal resonance. When the planets are migrated under the planet-disk interactions, for more than half of the studied cases, the configurations of the apsidal resonances are preserved. We find the two planets of the HD 12661 system could be in aligned resonance and thus more stable, provided they have Ω2 - Ω1 ≈ 180°. The applications of the criteria to the other multiple planetary systems are discussed.

Planetesimal Accretion onto Growing Proto-Gas Giant Planets

The solar and extrasolar gas giants appear to have diverse internal structure and metallicities. We examine a potential cause for these dispersions in the context of the conventional sequential accretion formation scenario. In principle, gas accretion onto cores with masses below several times that of the Earth is suppressed by the energy released from the bombardment of residual planetesimals. Due to their aerodynamical and tidal interaction with the nascent gas disk, planetesimals on eccentric orbits undergo slow orbital decay. We show that these planetesimals generally cannot pass through the mean motion resonances of the cores, and the suppression of planetesimal bombardment rate enables the cores to accrete gas with little interruption, thus shortening the timescale of gas giant formation. During growth from the cores to protoplanets, resonances overlap with each other, which strongly enhances the eccentricity excitation of the trapped planetesimals. Subsequent gas drag induces the planetesimals to migrate to the proximity of the protoplanets and collide with them. This process leads to the resumption and a surge of planetesimal bombardment during the advanced stage of the protoplanet growth. Intruder planetesimals with different masses can either be resolved in the envelope or reach the core of the protoplanets. This mechanism may account for the diversity of the core-envelope structure between Jupiter, Saturn, and the metallicity dispersion inferred from the transiting extrasolar planets. During the final formation stage of the proto-gas giants, gap opening in gas disk leads to the accumulation of planetesimals outside the feeding zone of the protoplanets. The surface density enhancement promotes the subsequent buildup of cores for secondary gas giant planets outside the orbit of the first-born protoplanets and the formation of eccentric multiple planet systems.

PLANETESIMAL ACCRETION IN BINARY SYSTEMS: ROLE OF THE COMPANION'S ORBITAL INCLINATION

Recent observations show that planets can reside in close binary systems with stellar separation of only ~20 AU. However, planet formation in such close binary systems is a challenge to current theory. One of the major theoretical problems occurs in the intermediate stage—planetesimals accretion into planetary embryos—during which the companions perturbations can stir up the relative velocities (▵V) of planetesimals and thus slow down or even cease their growth. Recent studies have shown that conditions could be even worse for accretion if the gas-disk evolution was included. However, all previous studies assumed a two-dimensional disk and a coplanar binary orbit. Extending previous studies by including a three-dimensional gas disk and an inclined binary orbit with small relative inclination of iB = 01-5°, we numerically investigate the conditions for planetesimal accretion at 1-2 AU, an extension of the habitable zone (~1-1.3 AU), around α Centauri A in this paper. Inclusion of the binary inclination leads to the following: (1) differential orbital phasing is realized in the three-dimensional space, and thus different-sized bodies are separated from each other, (2) total impact rate is lower, and impacts mainly occur between similar-sized bodies, (3) accretion is more favored, but the balance between accretion and erosion remains uncertain, and the possible accretion region extends up to 2 AU when assuming an optimistic Q* (critical specific energy that leads to catastrophic fragmentation), and (4) impact velocities (▵V) are significantly reduced but still much larger than their escape velocities, which infers that planetesimals grow by means of type II runaway mode. As a conclusion, the inclusion of a small binary inclination is a promising mechanism that favors accretion, opening a possibility that planet formation in close binary systems can go through the difficult stage of planetesimals accretion into planetary embryos.Currently, one of major problems concerning planet formation theory in close binary systems is, the strong perturbation from the companion star can increase relative velocities (

Predicting the Configuration of a Planetary System: KOI-152 Observed by Kepler

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Planetesimal Accretion in Binary Systems: The Effects of Gas Dissipation

) of planetesimals around the primary and thus hinder their growth. According to previous studies, while gas drag can reduce the

FROM DUST TO PLANETESIMAL: THE SNOWBALL PHASE ?

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