Formation of planetary populations − II. Effects of initial disc size and radial dust drift (original) (raw)
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The Astrophysical Journal, 2008
In a further development of a deterministic planet formation model (Ida & Lin), we consider the effect of type I migration of protoplanetary embryos due to their tidal interaction with their nascent disks. During the early phase of protostellar disks, although embryos rapidly emerge in regions interior to the ice line, uninhibited type I migration leads to their efficient self-clearing. But embryos continue to form from residual planetesimals, repeatedly migrate inward, and provide a main channel of heavy-element accretion onto their host stars. During the advanced stages of disk evolution (a few Myr), the gas surface density declines to values comparable to or smaller than that of the minimum mass nebula model, and type I migration is no longer effective for Mars-mass embryos. Over wide ranges of initial disk surface densities and type I migration efficiencies, the surviving population of embryos interior to the ice line has a total mass of several M È. With this reservoir, there is an adequate inventory of residual embryos to subsequently assemble into rocky planets similar to those around the Sun. However, the onset of efficient gas accretion requires the emergence and retention of cores more massive than a few M È prior to the severe depletion of the disk gas. The formation probability of gas giant planets and hence the predicted mass and semimajor axis distributions of extrasolar gas giants are sensitively determined by the strength of type I migration. We suggest that the distributions consistent with observations can be reproduced only if the actual type I migration timescale is at least an order of magnitude longer than that deduced from linear theories.
Planet formation models: the interplay with the planetesimal disc
Astronomy & Astrophysics, 2012
Context. According to the sequential accretion model (or core-nucleated accretion model), giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. The most critical part of the model is the formation time of the core: to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. Aims. We calculate planetary formation models including a detailed description of the dynamics of the planetesimal disc, taking into account both gas drag and excitation of forming planets. Methods. We computed the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. Here we introduce a more realistic treatment for the evolution of planetesimals' relative velocities, which directly impact on the formation timescale. For this, we computed the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. Results. We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate-mass planets that have not yet started their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have masses either below 10 M ⊕ or above several Jupiter masses. Conclusions. To form giant planets before the dissipation of the disc, small planetesimals (∼0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate-mass planets. Other processes must therefore be at work to explain the population of extrasolar planets that are presently known.
Toward a Deterministic Model of Planetary Formation. IV. Effects of Type I Migration
The Astrophysical Journal, 2008
We address two outstanding issues in the sequential accretion scenario for gas giant planet formation, the retention of dust grains in the presence of gas drag and that of cores despite type I migration. The efficiency of these processes is determined by the disk structure. Theoretical models suggest that planets form in protostellar disk regions with an inactive neutral "dead zone" near the mid plane, sandwiched together by partially ionized surface layers where magnetorotational instability is active. Due to a transition in the abundance of dust grains, the active layer's thickness decreases abruptly near the ice line. Over a range of modest accretion rates (∼ 10 −9 − 10 −8 M ⊙ yr −1), the change in the angular momentum transfer rate leads to local surface density and pressure distribution maxima near the ice line. The azimuthal velocity becomes super-Keplerian and the grains accumulate in this transition zone. This barrier locally retains protoplanetary cores and enhances the heavy element surface density to the critical value needed to initiate efficient gas accretion. It leads to a preferred location and epoch of gas giant formation. We simulate and reproduce the observed frequency and mass-period distribution of gas giants around solar type stars without having to greatly reduce the type I migration strength. The mass function of the short-period planets can be utilized to calibrate the efficiency of type I migration and to extrapolate the fraction of stars with habitable terrestrial planets.
On the formation of terrestrial planets in hot-Jupiter systems
Astronomy & Astrophysics, 2007
"Context. There are numerous extrasolar giant planets which orbit close to their central stars. These “hot-Jupiters” probably formed in the outer, cooler regions of their protoplanetary disks, and migrated inward to ∼0.1 AU. Since these giant planets must have migrated through their inner systems at an early time, it is uncertain whether they could have formed or retained terrestrial planets. Aims. We present a series of calculations aimed at examining how an inner system of planetesimals/protoplanets, undergoing terrestrial planet formation, evolves under the influence of a giant planet undergoing inward type II migration through the region bounded between 5–0.1 AU. Methods. We have previously simulated the effect of gas giant planet migration on an inner system protoplanet/planetesimal disk using a N-body code which included gas drag and a prescribed migration rate. We update our calculations here with an improved model that incorporates a viscously evolving gas disk, annular gap and inner-cavity formation due to the gravitational field of the giant planet, and self-consistent evolution of the giant’s orbit. Results. We find that 60% of the solids disk survives by being scattered by the giant planet into external orbits. Planetesimals are scattered outward almost as efficiently as protoplanets, resulting in the regeneration of a solids disk where dynamical friction is strong and terrestrial planet formation is able to resume. A simulation that was extended for a few Myr after the migration of the giant planet halted at 0.1 AU, resulted in an apparently stable planet of ∼2 m⊕ forming in the habitable zone. Migration–induced mixing of volatile-rich material from beyond the “snowline” into the inner disk regions means that terrestrial planets that form there are likely to be water-rich. Conclusions. We predict that hot-Jupiter systems are likely to harbor water-abundant terrestrial planets in their habitable zones. These planets may be detected by future planet search missions."
The effect of type I migration on the formation of terrestrial planets in hot-Jupiter systems
Astronomy & Astrophysics, 2007
"Context. Our previous models of a giant planet migrating through an inner protoplanet/planetesimal disk find that the giant shepherds a portion of the material it encounters into interior orbits, whilst scattering the rest into external orbits. Scattering tends to dominate, leaving behind abundant material that can accrete into terrestrial planets. Aims. We add to the possible realism of our model by simulating type I migration forces which cause an inward drift, and strong eccentricity and inclination damping of protoplanetary bodies. This extra dissipation might be expected to enhance shepherding at the expense of scattering, possibly modifying our previous conclusions. Methods. We employ an N-body code that is linked to a viscous gas disk algorithm capable of simulating: gas accretion onto the central star; gap formation in the vicinity of the giant planet; type II migration of the giant planet; type I migration of protoplanets; and the effect of gas drag on planetesimals. We use the code to re-run three scenarios from a previous work where type I migration was not included. Results. The additional dissipation introduced by type I migration enhances the inward shepherding of material but does not severely reduce scattering. We find that >50% of the solids disk material still survives the migration in scattered exterior orbits: most of it well placed to complete terrestrial planet formation at <3 AU. The shepherded portion of the disk accretes into hot-Earths, which survive in interior orbits for the duration of our simulations. Conclusions. Water-rich terrestrial planets can form in the habitable zones of hot-Jupiter systems and hot-Earths and hot-Neptunes may also be present. These systems should be targets of future planet search missions."
The Astrophysical Journal, 2013
The rapid growth in the number of known exoplanets has revealed the existence of several distinct planetary populations in the observed mass-period diagram. Two of the most surprising are, (1) the concentration of gas giants around 1AU and (2) the accumulation of a large number of low-mass planets with tight orbits, also known as super-Earths and hot Neptunes. We have recently shown that protoplanetary disks have multiple planet traps that are characterized by orbital radii in the disks and halt rapid type I planetary migration. By coupling planet traps with the standard core accretion scenario, we showed that one can account for the positions of planets in the mass-period diagram. In this paper, we demonstrate quantitatively that most gas giants formed at planet traps tend to end up around 1 AU with most of these being contributed by dead zones and ice lines. In addition, we show that a large fraction of super-Earths and hot Neptunes are formed as "failed" cores of gas giants-this population being constituted by comparable contributions from dead zone and heat transition traps. Our results are based on the evolution of forming planets in an ensemble of disks where we vary only the lifetimes of disks as well as their mass accretion rates onto the host star. We show that a statistical treatment of the evolution of a large population of planetary cores initially caught in planet traps accounts for the existence of three distinct exoplantary populations-the hot Jupiters, the more massive planets at roughly orbital radii around 1 AU orbital, and the short period SuperEarths and hot Neptunes. There are very few evolutionary tracks that feed into the large orbital radii characteristic of the imaged Jovian planet and this is in accord with the result of recent surveys that find a paucity of Jovian planets beyond 10 AU. Finally, we find that low-mass planets in tight orbits become the dominant planetary population for low mass stars (M * ≤ 0.7M ⊙), in agreement with the previous studies which show that the formation of gas giants is preferred for massive stars.
Formation of Giant Planets– An Attempt in Matching Observational Constraints
Space Science Reviews, 2005
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 , if we assume the accretion of planetesimals with ices/rocks ratio equal to 4, and that a substantial amount of CO 2 was present in vapor phase in the solar nebula, in agreement with ISM measurements.
Formation of Earth‐like Planets During and After Giant Planet Migration
The Astrophysical Journal, 2007
Close-in giant planets are thought to have formed in the cold outer regions of planetary systems and migrated inward, passing through the orbital parameter space occupied by the terrestrial planets in our own Solar System. We present dynamical simulations of the effects of a migrating giant planet on a disk of protoplanetary material and the subsequent evolution of the planetary system. We numerically investigate the dynamics of post-migration planetary systems over 200 million years using models with a single migrating giant planet, one migrating and one non-migrating giant planet, and excluding the effects of a gas disk. Material that is shepherded in front of the migrating giant planet by moving mean motion resonances accretes into "hot Earths", but survival of these bodies is strongly dependent on dynamical damping. Furthermore, a significant amount of material scattered outward by the giant planet survives in highly excited orbits; the orbits of these scattered bodies are then damped by gas drag and dynamical friction over the remaining accretion time. In all simulations Earth-mass planets accrete on approximately 100 Myr timescales, often with orbits in the Habitable Zone. These planets range in mass and water content, with both quantities increasing with the presence of a gas disk and decreasing with the presence of an outer giant planet. We use scaling arguments and previous results to derive a simple recipe that constrains which giant planet systems are able to form and harbor Earth-like planets in the Habitable Zone, demonstrating that roughly one third of the known planetary systems are potentially habitable.
Accumulation and migration of the bodies from the zones of giant planets
Earth, Moon and Planets, 1987
Within the model of solid-body accumulation of planets (or their nuclei) the accumulation and migration of bodies from the feeding zones of the giant planets are investigated. The investigation is based on results of computer simulation of evolving disks which initially consisted of hundreds of particles moving about the Sun and coagulating under collisions. In some models the disks initially consisted of identical bodies. In other models they included also almost-formed planets. The computer simulation results as well as analytical investigations of the disk evolution depending on the number of particles in the disk allowed some estimates and conclusions on the accumulation process when the number of initial bodies was great (-106-lOI*). In this paper the characteristics of an initial protoplanetary circumsolar cloud, the body migration in the forming solar system, the planet orbit evolution, the formation of the beyond-Neptune belt and asteroid belts between the giant planet orbits are considered. The results obtained confirm many analytical estimates earlier made by V. S. Safronov and his colleagues.
N -Body Simulations of Terrestrial Planet Formation Under the Influence of a Hot Jupiter
The Astrophysical Journal, 2014
We investigate the formation of multiple-planet systems in the presence of a hot Jupiter using extended N -body simulations that are performed simultaneously with semi-analytic calculations. Our primary aims are to describe the planet formation process starting from planetesimals using highresolution simulations, and to examine the dependences of the architecture of planetary systems on input parameters (e.g., disk mass, disk viscosity). We observe that protoplanets that arise from oligarchic growth and undergo type I migration stop migrating when they join a chain of resonant planets outside the orbit of a hot Jupiter. The formation of a resonant chain is almost independent of our model parameters, and is thus a robust process. At the end of our simulations, several terrestrial planets remain at around 0.1 AU. The formed planets are not equal-mass; the largest planet constitutes more than 50 percent of the total mass in the close-in region, which is also less dependent on parameters. In the previous work of this paper (Ogihara et al. 2013), we have found a new physical mechanism of induced migration of the hot Jupiter, which is called a crowding-out. If the hot Jupiter opens up a wide gap in the disk (e.g., owing to low disk viscosity), crowding-out becomes less efficient and the hot Jupiter remains. We also discuss angular momentum transfer between the planets and disk.