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Register a new userToward a Deterministic Model of Planetary Formation IV: Effects of Type-I Migration
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In a further development of a deterministic planet-formation model (Ida & Lin 2004), we consider the effect of type-I migration of protoplanetary embryos due to their tidal interaction with their nascent disks. During the early embedded 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 at increasingly large radii, 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 an effective disruption mechanism for mars-mass embryos. Over wide ranges of initial disk surface densities and type-I migration efficiency, the surviving population of embryos interior to the ice line has a total mass several times that of the Earth. With this reservoir, there is an adequate inventory of residual embryos to subsequently assemble into rocky planets similar to those around the Sun. But, the onset of efficient gas accretion requires the emergence and retention of cores, more massive than a few M_earth, 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 observed fraction of solar-type stars with gas giant planets can be reproduced only if the actual type-I migration time scale is an order of magnitude longer than that deduced from linear theories.
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The ubiquity of planets and diversity of planetary systems reveal planet formation encompass many complex and competing processes. In this series of papers, we develop and upgrade a population synthesis model as a tool to identify the dominant physical effects and to calibrate the range of physical conditions. Recent planet searches leads to the discovery of many multiple-planet systems. Any theoretical models of their origins must take into account dynamical interaction between emerging protoplanets. Here, we introduce a prescription to approximate the close encounters between multiple planets. We apply this method to simulate the growth, migration, and dynamical interaction of planetary systems. Our models show that in relatively massive disks, several gas giants and rocky/icy planets emerge, migrate, and undergo dynamical instability. Secular perturbation between planets leads to orbital crossings, eccentricity excitation, and planetary ejection. In disks with modest masses, two or less gas giants form with multiple super-Earths. Orbital stability in these systems is generally maintained and they retain the kinematic structure after gas in their natal disks is depleted. These results reproduce the observed planetary mass-eccentricity and semimajor axis-eccentricity correlations. They also suggest that emerging gas giants can scatter residual cores to the outer disk regions. Subsequent in situ gas accretion onto these cores can lead to the formation of distant (> 30AU) gas giants with nearly circular orbits.
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 layers thickness decreases abruptly near the ice line. Over a range of modest accretion rates ($sim 10^{-9}-10^{-8} M_odot$ 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.
We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc. In the absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20% of the numerical simulations.
We investigate the tidal interaction between a low-mass planet and a self-gravitating protoplanetary disk, by means of two-dimensional hydrodynamic simulations. We first show that considering a planet freely migrating in a disk without self-gravity leads to a significant overestimate of the migration rate. The overestimate can reach a factor of two for a disk having three times the surface density of the minimum mass solar nebula. Unbiased drift rates may be obtained only by considering a planet and a disk orbiting within the same gravitational potential. In a second part, the disk self-gravity is taken into account. We confirm that the disk gravity enhances the differential Lindblad torque with respect to the situation where neither the planet nor the disk feels the disk gravity. This enhancement only depends on the Toomre parameter at the planet location. It is typically one order of magnitude smaller than the spurious one induced by assuming a planet migrating in a disk without self-gravity. We confirm that the torque enhancement due to the disk gravity can be entirely accounted for by a shift of Lindblad resonances, and can be reproduced by the use of an anisotropic pressure tensor. We do not find any significant impact of the disk gravity on the corotation torque.
Context. Giant planets open gaps in their protoplanetary and subsequently suffer so-called type II migration. Schematically, planets are thought to be tightly locked within their surrounding disks, and forced to follow the viscous advection of gas onto the central star. This fundamental principle however has recently been questioned, as migrating planets were shown to decouple from the gas radial drift. Aims. In this framework, we question whether the traditionally used linear scaling of migration rate of a giant planet with the disks viscosity still holds. Additionally, we assess the role of orbit-crossing material as part of the decoupling mechanism. Methods. We have performed 2D (r, {theta}) numerical simulations of point-mass planets embedded in locally isothermal {alpha}-disks in steady-state accretion, with various values of {alpha}. Arbitrary planetary accretion rates were used as a means to diminish or nullify orbit-crossing flows. Results. We confirm that the migration rate of a gap-opening planet is indeed proportional to the disks viscosity, but is not equal to the gas drift speed in the unperturbed disk. We show that the role of gap-crossing flows is in fact negligible. Conclusions. From these observations, we propose a new paradigm for type II migration : a giant planet feels a torque from the disk that promotes its migration, while the gap profile relative to the planet is restored on a viscous timescale, thus limiting the planet migration rate to be proportional to the disks viscosity. Hence, in disks with low viscosity in the planet region, type II migration should still be very slow. Key words. protoplanetary disks; planet-disk interactions; planets and satellites: formation
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