Model For Giant Planet Formation Research Articles

DIVERSITY OF EXTRASOLAR PLANETS AND DIVERSITY OF MOLECULAR CLOUD CORES. I. SEMIMAJOR AXES

We show that the diversity of extrasolar planetary systems may be related to the diversity of molecular cloud cores. In previous studies of planet formation, artificial initial conditions of protoplanetary disks or steady state disks, such as the minimum mass nebula model, have often been used so that the influence of cloud core properties on planet formation is not realized. To specifically and quantitatively demonstrate our point, we calculate the dependence of disk properties on cloud core properties and show that the boundary of the giant planet formation region in a disk is a function of cloud core properties with the conventional core accretion model of giant planet formation. The gravitational stability of a disk depends on the properties of its progenitor cloud core. We also compare our calculations with observations of extrasolar planets. From the observational data of cloud cores, our model could infer the range and most frequent values of observed semimajor axes of extrasolar planets. Our calculations suggest that planet formation at the snowline alone could not completely explain the semimajor axis distribution. If the current observations are not biased, our calculations indicate that the planet formation at the snowline is inefficient. We suggest that there will be more observed planets with semimajor axis 9 AU, even with a longer duration of observations, if the planet formation at the snowline is inefficient.

Giant planet formation with pebble accretion

In the core accretion model for giant planet formation, a solid core forms by coagulation of dust grains in a protoplanetary disk and then accretes gas from the disk when the core reaches a critical mass. Both stages must be completed in a few million years before the disk gas disperses. The slowest stage of this process may be oligarchic growth in which a giant-planet core grows by sweeping up smaller, asteroid-size planetesimals. Here, we describe new numerical simulations of oligarchic growth using a particle-in-a-box model. The simulations include several processes that can effect oligarchic growth: (i) planetesimal fragmentation due to mutual collisions, (ii) the modified capture rate of planetesimals due to a core’s atmosphere, (iii) drag with the disk gas during encounters with the core (so-called “pebble accretion”), (iv) modification of particle velocities by turbulence and drift caused by gas drag, (v) the presence of a population of mm-to-m size “pebbles” that represent the transition point between disruptive collisions between larger particles, and mergers between dust grains, and (vi) radial drift of small objects due to gas drag. Collisions between planetesimals rapidly generate a population of pebbles. The rate at which a core sweeps up pebbles is controlled by pebble accretion dynamics. Metre-size pebbles lose energy during an encounter with a core due to drag, and settle towards the core, greatly increasing the capture probability during a single encounter. Millimetre-size pebbles are tightly coupled to the gas and most are swept past the core during an encounter rather than being captured. Accretion efficiency per encounter increases with pebble size in this size range. However, radial drift rates also increase with size, so metre-size objects encounter a core on many fewer occasions than mm-size pebbles before they drift out of a region. The net result is that core growth rates vary weakly with pebble size, with the optimal diameter being about 10cm. The main effect of planetesimal size is to determine the rate of mutual collisions, fragment production and the formation of pebbles. 1-km-diameter planetesimals collide frequently and have low impact strengths, leading to a large surface density of pebbles and rapid core growth via pebble accretion. 100-km-diameter planetesimals produce fewer pebbles, and pebble accretion plays a minor role in this case. The strength of turbulence in the gas determines the scale height of pebbles in the disk, which affects the rate at which they are accreted. For an initial solid surface density of12g/cm2 at 5AU, with 10-cm diameter pebbles and a disk viscosity parameter α=10-4, a 10-Earth mass core can form in 3My for 1–10km diameter planetesimals. The growth of such a core requires longer than 3My if planetesimals are 100km in diameter.

Photophoresis boosts giant planet formation

In the core accretion model of giant planet formation, a solid protoplanetary core begins to accrete gas directly from the nebula when its mass reaches about 5 earth masses. The protoplanet has at most a few million years to reach runaway gas accretion, as young stars lose their gas disks after 10 million years at the latest. Yet gas accretion also brings small dust grains entrained in the gas into the planetary atmosphere. Dust accretion creates an optically thick protoplanetary atmosphere that cannot efficiently radiate away the kinetic energy deposited by incoming planetesimals. A dust-rich atmosphere severely slows down atmospheric cooling, contraction, and inflow of new gas, in contradiction to the observed timescales of planet formation. Here we show that photophoresis is a strong mechanism for pushing dust out of the planetary atmosphere due to the momentum exchange between gas and dust grains. The thermal radiation from the heated inner atmosphere and core is sufficient to levitate dust grains and to push them outward. Photophoresis can significantly accelerate the formation of giant planets.

MODELING THE FORMATION OF GIANT PLANET CORES. I. EVALUATING KEY PROCESSES

One of the most challenging problems we face in our understanding of planet formation is how Jupiter and Saturn could have formed before the the solar nebula dispersed. The most popular model of giant planet formation is the so-called 'core accretion' model. In this model a large planetary embryo formed first, mainly by two-body accretion. This is then followed by a period of inflow of nebular gas directly onto the growing planet. The core accretion model has an Achilles heel, namely the very first step. We have undertaken the most comprehensive study of this process to date. In this study we numerically integrate the orbits of a number of planetary embryos embedded in a swarm of planetesimals. In these experiments we have included: 1) aerodynamic gas drag, 2) collisional damping between planetesimals, 3) enhanced embryo cross-sections due to their atmospheres, 4) planetesimal fragmentation, and 5) planetesimal driven migration. We find that the gravitational interaction between the embryos and the planetesimals lead to the wholesale redistribution of material - regions are cleared of material and gaps open near the embryos. Indeed, in 90% of our simulations without fragmentation, the region near that embryos is cleared of planetesimals before much growth can occur. The remaining 10%, however, the embryos undergo a burst of outward migration that significantly increases growth. On timescales of ~100,000 years, the outer embryo can migrate ~6 AU and grow to roughly 30 Earth-masses. We also find that the inclusion of planetesimal fragmentation tends to inhibit growth.

Flux‐limited Diffusion Approximation Models of Giant Planet Formation by Disk Instability

Both core accretion and disk instability appear to be required as formation mechanisms in order to explain the entire range of giant planets found in extrasolar planetary systems. Disk instability is based on the formation of clumps in a marginally gravitationally unstable protoplanetary disk. These clumps can only be expected to contract and survive to become protoplanets if they are able to lose thermal energy through a combination of convection and radiative cooling. Here we present several new three-dimensional, radiative hydrodynamics models of self-gravitating protoplanetary disks, where radiative transfer is handled in the flux-limited diffusion approximation. We show that while the flux-limited models lead to higher midplane temperatures than in a diffusion approximation model without the flux limiter, the difference in temperatures does not appear to be sufficiently high to have any significant effect on the formation of self-gravitating clumps. Self-gravitating clumps form rapidly in the models both with and without the flux limiter. These models suggest that the reason for the different outcomes of numerical models of disk instability by different groups cannot be attributed solely to the handling of radiative transfer, but rather appears to be caused by a range of numerical effects and assumptions. Given the observational imperative to have disk instability form at least some extrasolar planets, these models imply that disk instability remains as a viable giant planet formation mechanism.

SpitzerObservations of NGC 2362: Primordial Disks at 5 Myr

We present results from a mid-infrared imaging survey of the ~5 Myr old cluster NGC 2362 carried out with the Infrared Array Camera (IRAC) on board the Spitzer Space Telescope. The archival mid-infrared data were merged with extant Hα emission data, optical and near-infrared photometry, and moderate-resolution optical spectroscopy to identify the remnant disk-bearing population of the cluster and to estimate the fraction of stars that still retain primordial circumstellar disks. The principal sample of 232 suspected cluster members with masses ranging from ~10 to 0.3 M_⊙ (B2-M5 spectral types) was drawn from known Hα emission stars, X-ray-detected stars from a single 100 ks archival Chandra observation, and established lithium-rich stars. A second sample of 153 stars over a similar mass range whose membership status was based on optical photometry alone was also examined. Measured fluxes in the optical and infrared passbands were fitted with synthetic, low-resolution spectra created using the NextGen atmospheric models, permitting the detection of infrared excesses relative to predicted stellar photospheric fluxes. Using the measured slope of the stellar spectral energy distribution through the four IRAC channels to characterize disk emission for the 195 out of 232 activity/lithium-selected stars and the 105 out of 153 photometric membership candidates having complete IRAC photometry, we derive an upper limit for the primordial, optically thick disk fraction of NGC 2362 of ~7% ± 2%, with another ~12% ± 3% of suspected members exhibiting infrared excesses indicative of weak or optically thin disk emission. The presence of circumstellar disks among candidate members of NGC 2362 is strongly mass-dependent, such that no stars more massive than ~1.2 M_⊙ exhibit significant infrared excess shortward of 8 μm. An upper limit for the fraction of stars hosting primordial, optically thick disks peaks near 10.7% ± 4% for stars with masses between 1.05 and 0.6 M_⊙, but the Spitzer IRAC survey is sensitivity-limited below ~0.3 M_⊙. From Hα emission-line strengths, an upper limit for the accretion fraction of the cluster is estimated at ~5%, with most suspected accretors associated with primordial, optically thick disks identified with Spitzer. The presence of primordial disk-bearing stars in NGC 2362, some of which are suspected of still experiencing gaseous accretion, may imply that even within dense cluster environments, sufficient numbers of inner disks survive to ages consistent with core accretion models of giant planet formation to account for the observed frequency of exoplanets within 5 AU of all FGKM-type stars.

Compositional constraints on giant planet formation

Using Ockham's razor as a guide, we have tried to find the simplest model for the formation of giant planets that can explain current observations of atmospheric composition. While this “top-down” approach is far from sufficient to define such models, it establishes a set of boundary conditions whose satisfaction is necessary. Using Jupiter as the prototype, we find that a simple model for giant planet formation that begins with a solar nebula of uniform composition and relies on accretion of low temperature icy planetesimals plus collapse of surrounding solar nebula gas supplies that satisfaction. We compare the resulting predictions of elemental abundances and isotope ratios in the atmospheres of the other giants with those from contrasting models and suggest some key measurements to make further progress.

Models of giant planet formation with migration and disc evolution

We present a new model of giant planet formation that extends the core-accretion model of Pollack etal (1996) to include migration, disc evolution and gap formation. We show that taking into account these effects can lead to a much more rapid formation of giant planets, making it compatible with the typical disc lifetimes inferred from observations of young circumstellar discs. This speed up is due to the fact that migration prevents the severe depletion of the feeding zone as observed in in situ calculations. Hence, the growing planet is never isolated and it can reach cross-over mass on a much shorter timescale. To illustrate the range of planets that can form in our model, we describe a set of simulations in which we have varied some of the initial parameters and compare the final masses and semi-major axes with those inferred from observed extra-solar planets.

Formation of Giant Planets– An Attempt in Matching Observational Constraints

We present models of giant planet formation, taking into account migration and disk viscous evolution. We show that migration can significantly reduce the formation timescale bringing it in good agreement with typical observed disk lifetimes. We then present a model that produces a planet whose current location, core mass and total mass are comparable with the one of Jupiter. For this model, we calculate the enrichments in volatiles and compare them with the one measured by the Galileo probe. We show that our models can reproduce both the measured atmosphere enrichments and the constraints derived by Guillot et al. (2004), if we assume the accretion of planetesimals with ices/rocks ratio equal to 4, and that a substantial amount of CO2 was present in vapor phase in the solar nebula, in agreement with ISM measurements.

Gravitational instability in binary protoplanetary discs: new constraints on giant planet formation

We use high-resolution three-dimensional smoothed particle hydrodynamic (SPH) simulations to study the evolution of self-gravitating binary protoplanetary discs. Heating by shocks and cooling is included. We consider different orbital separations and masses of the discs. Massive discs (M ∼0.1 M ○. ) that fragment in isolation as a result of gravitational instability develop only transient overdensities in binary systems with a separation of about 60 au. This is true even when the cooling time is significantly shorter than the orbital time because efficient heating owing to strong tidally induced spiral shocks dominates. The resulting temperatures, above 200 K, would vaporize water ice in the outer disc, posing a problem even for the other model of giant planet formation, core accretion. Light discs (M ∼ 0.01 M ○. ) do not fragment but remain cold because their low self-gravity inhibits strong shocks. Core accretion would not be hampered in them. At separations of about 120 au, tidally induced spiral shocks weaken significantly and fragmentation occurs similarly to isolated systems. If disc instability is the main formation mechanism for giant planets, ongoing surveys targeting binary systems should find considerably fewer planets in systems with separations below 100 au.

Models of Chemistry, Thermal Balance, and Infrared Spectra from Intermediate‐Aged Disks around G and K Stars

We model gas and dust emission from regions 0.3-20 AU from a central low-mass star in intermediate-aged (~107 yr) disks whose dust is fairly optically thin to stellar radiation. The models treat thermal balance and chemistry self-consistently and calculate the vertical density and temperature structure of the gas in a disk. The gas and dust temperatures are calculated separately. The models cover gas masses 10-3 to 1 MJ and dust masses 10-7 to 10-4 MJ and treat solar-type (G and K) stars. We focus on mid-infrared and far-infrared emission lines from various gas species such as the rotational lines of H2, OH, H2O, and CO molecules and the fine-structure lines of carbon, oxygen, sulfur, iron, and silicon atoms and ions. These lines and the dust continuum are observable by the Spitzer Space Telescope and future missions including SOFIA and the Herschel Space Observatory. We find that the [S I] 25.23 μm line is the strongest emission line for a wide range of disk and stellar parameters, followed by emission from [Si II] 34.8 μm, [Fe II] 26 μm, and [O I] 63 μm. [Fe I] 24 μm and rotational lines of OH and H2O are strong when gas masses are high (0.1 MJ). Emission from the rotational lines of H2 is more difficult to detect unless disk gas masses are substantial (0.1 MJ). For emission from H2 lines to be observable and yet for the dust to be optically thin in stellar light, the ratio of gas to small submillimeter-sized dust particle mass in the disk needs to be 1000, or at least an order of magnitude higher than that in the interstellar medium. This may be possible at intermediate stages in disk evolution, such as in the gas-gathering stage of the core accretion scenario for giant planet formation, in which most of the dust has coagulated into larger objects (1 mm) but the gas has not yet fully dispersed. Whereas the absolute fluxes observed in some lines such as [Fe I] 24 μm and H2 S(0) 28 μm primarily measure the gas mass in the disks, various line ratios diagnose the inner radius of the gas and the radial temperature and surface density distribution of the gas. Many lines become optically thick and/or suffer chemical or thermal effects such that the line luminosities do not increase appreciably with increasing gas mass. We predict that it may be difficult for the Spitzer Space Telescope to detect 1 MJ of gas in optically thin (in dust) disks at distances 150 pc. The models presented here will be useful in future infrared studies of the timescale for the dispersion of gas in a planet-forming disk and tests of core accretion models of giant planet formation.

Numerical models of giant planet formation with rotation

We present models of giant planet formation including the accretion and transport of angular momentum. The calculations are carried out in a one-dimensional quasispherical approximation, assuming hydrostatic equilibrium. The approximation of quasisphericity limits the calculations to relatively slowly rotating models. As in previous calculations without rotation (Bodenheimer and Pollack 1986), the so-called “core-accretion” model is adopted. Angular momentum transport is included for both radiative and convective zones. Convective regions are not forced to rotate uniformly at all times, but the angular momentum distribution in those regions is driven to uniform rotation, with transport coefficients based on mixing-length theory. Radiative regions whose angular momentum distributions are unstable according to the Goldreich-Schubert-Fricke criterion are driven to states of marginal stability, on timescales derived from linear theory and previous hydrodynamical modeling. The calculations are carried up to masses approximately equal to that of Saturn. Angular momentum transport is highly effective, producing models with a strong concentration of angular momentum in the outer convective zones that develop at envelope masses above 30 M +. Near the end of the calculation, gas accretion was turned off, and the models allowed to contract. The ratio of centrifugal force to gravity at the outer radius then rises high enough to validate the quasispherical approximation. At that point, mass is assumed to be shed to form a disk. We find that ∼1 M +, and ∼80% of the angular momentum, are lost to a disk. Such values of disk mass and angular momentum are amply sufficient for satellite system formation. As a result of the loss of angular momentum, however, the final planetary models have only one-third to one-half the present-day value of angular momentum of Saturn, indicating that yet larger amounts of angular momentum may have been present during formation.