Shigeru Ida

Toward a Deterministic Model of Planetary Formation. I. A Desert in the Mass and Semimajor Axis Distributions of Extrasolar Planets

In an attempt to develop a deterministic theory for planet formation, we examine the accretion of cores of giant planets from planetesimals, gas accretion onto the cores, and their orbital migration. We adopt a working model for nascent protostellar disks with a wide variety of surface density distributions in order to explore the range of diversity among extrasolar planetary systems. We evaluate the cores mass growth rate c through runaway planetesimal accretion and oligarchic growth. The accretion rate of cores is estimated with a two-body approximation. In the inner regions of disks, the cores eccentricity is effectively damped by their tidal interaction with the ambient disk gas and their early growth is stalled by isolation. In the outer regions, the cores growth rate is much smaller. If some cores can acquire more mass than a critical value of several Earth masses during the persistence of the disk gas, they would be able to rapidly accrete gas and evolve into gas giant planets. The gas accretion process is initially regulated by the Kelvin-Helmholtz contraction of the planets gas envelope. Based on the assumption that the exponential decay of the disk gas mass occurs on the timescales ~106-107 yr and that the disk mass distribution is comparable to those inferred from the observations of circumstellar disks of T Tauri stars, we carry out simulations to predict the distributions of masses and semimajor axes of extrasolar planets. In disks as massive as the minimum-mass disk for the solar system, gas giants can form only slightly outside the ice boundary at a few AU. However, cores can rapidly grow above the critical mass inside the ice boundary in protostellar disks with 5 times more heavy elements than those of the minimum-mass disk. Thereafter, these massive cores accrete gas prior to its depletion and evolve into gas giants. The limited persistence of the disk gas and the decline in the stellar gravity prevent the formation of cores capable of efficient gas accretion outside 20-30 AU. Unimpeded dynamical accretion of gas is a runaway process that is terminated when the residual gas is depleted either globally or locally in the form of a gap in the vicinity of their orbits. Since planets masses grow rapidly from 10 to 100 M?, the gas giant planets rarely form with asymptotic masses in this intermediate range. Our model predicts a paucity of extrasolar planets with mass in the range 10-100 M? and semimajor axis less than 3 AU. We refer to this deficit as a planet desert. We also examine the dynamical evolution of protoplanets by considering the effect of orbital migration of giant planets due to their tidal interactions with the gas disks, after they have opened up gaps in the disks. The effect of migration is to sharpen the boundaries and to enhance the contrast of the planet desert. It also clarifies the separation between the three populations of rocky, gas giant, and ice giant planets. Based on our results, we suggest that the planets mass versus semimajor axes diagram can provide strong constraints on the dominant formation processes of planets analogous to the implications of the color-magnitude diagram on the paths of stellar evolution. We show that the mass and semimajor axis distributions generated in our simulations for the gas giants are consistent with those of the known extrasolar planets. Our results also indicate that a large fraction (90%-95%) of the planets that have migrated to within 0.05 AU must have perished. Future observations can determine the existence and the boundaries of the planet desert in this diagram, which can be used to extrapolate the ubiquity of rocky planets around nearby stars. Finally, the long-term dynamical interaction between planets of various masses can lead to both eccentricity excitation and scattering of planets to large semimajor axes. These effects are to be included in future models.

Formation of Protoplanet Systems and Diversity of Planetary Systems

We investigate the formation of protoplanet systems from planetesimal disks by global (N = 5000 and 10,000 and 0.5 AU 2. The growth timescale increases with a but decreases with Σ1. Based on the oligarchic growth model and the conventional Jovian planet formation scenario, we discuss the diversity of planetary systems. Jovian planets can form in the disk range where the contraction timescale of planetary atmosphere and the growth timescale of protoplanets (cores) are shorter than the lifetime of the gas disk. We find that for the disk lifetime ~108 yr, several Jovian planets would form from massive disks with Σ1 30 with Uranian planets outside the Jovian planets. Only terrestrial and Uranian planets would form from light disks with Σ1 3. Solar system-like planetary systems would form from medium disks with Σ1 10.

On the Origin of Massive Eccentric Planets

We propose a merger scenario for the newly discovered extrasolar planets around 70 Vir (Marcy & Butler) and HD 114762 (Latham, Stefanik, & Mazeh; Marcy & Butler). These planets have mass Mp sin i = 6.6 and 9MJ (where MJ is Jupiters mass and i is the orbital inclination), orbital semimajor axis a = 0.43 and 0.34 AU, and eccentricity e = 0.38 and 0.35, respectively. Our scenario is based on the conventional formation model of giant planets (gas accretion onto solid cores) and the long-term orbital stability theory of planetary systems. We suggest that in a relatively massive disk, several giant planets can be formed with Mp ~ 1-3MJ and a 1 AU. Under the persistence of the disk gas, the protogiant planet system is stable during its formation epoch (within 106-107 yr). But, after the depletion of the disk gas, mutual gravitational perturbation between the planets induces a gradual increase in their orbital eccentricities, until their orbits become unstable and begin to cross each other. We present numerical calculations of the orbital evolution leading to the orbit crossing stage. Our results indicate that the inner planets have a tendency to merge into a massive planet with relatively high e (0.2-0.9) and small a (0.5-1 AU). The orbital decay is a result of the gravitational perturbation by the outer planets and the dissipation of the colliding planets relative kinetic energy. Afterward, long-term perturbation would slightly reduce the merged bodys a, while it would keep its e high. The orbital properties of the merged body are consistent with those of the massive eccentric planets around 70 Vir and HD 114762. The onset timescale for orbit crossing within a planetary system is sensitively determined by the planets mass and separation, which may explain the diversity in the orbital properties among the newly discovered planetary systems.

Lunar accretion from an impact-generated disk

Although the mechanism by which the Moon was formed is currently unknown, several lines of evidence point to its accretion from a circumterrestrial disk of debris generated by a giant impact on the Earth. Theoretical simulations show that a single large moon can be produced from such a disk in less than a year, and establish a direct relationship between the size of the accreted moon and the initial configuration of the debris disk.

Investigation of the Physical Properties of Protoplanetary Disks around T Tauri Stars by a 1 Arcsecond Imaging Survey: Evolution and Diversity of the Disks in Their Accretion Stage*

We present the results of an imaging survey of protoplanetary disks around single T Tauri stars in Taurus. Thermal emission at 2 mm from dust in the disks has been imaged with a maximum spatial resolution of 1 by using the Nobeyama Millimeter Array. Disk images have been successfully obtained under almost uniform conditions for 13 T Tauri stars, two of which are thought to be embedded. We have derived the disk properties of outer radius, surface density distribution, mass, temperature distribution, and dust opacity coefficient, by analyzing both our images and the spectral energy distributions on the basis of two disk models: the usual power-law model and the standard model for viscous accretion disks. By examining correlations between the disk properties and disk clocks, we have found radial expansion of the disks with decreasing H? line luminosity, a measure of disk evolution. This expansion can be interpreted as radial expansion of accretion disks due to outward transport of angular momentum with evolution. The increasing rate of the disk radius suggests that the viscosity has weak dependence on radius r and ? ~ 0.01 for the ? parameterization of the viscosity. The power-law index p of the surface density distribution [?(r) = ?0(r/r0)-p] is 0-1 in most cases, which is smaller than 1.5 adopted in the Hayashi model for the origin of our solar system, while the surface density at 100 AU is 0.1-10 g cm-2, which is consistent with the extrapolated value in the Hayashi model. These facts may imply that in the disks of our sample it is very difficult to make planets like ours without redistribution of solids, if such low values for p hold even in the innermost regions.

Evidence for early stellar encounters in the orbital distribution of Edgeworth-Kuiper Belt objects

We have investigated effects of early stellar encounters on a protoplanetary disk (planetesimal disk) and found that they can explain the high eccentricities and inclinations observed in the outer part (

Orbital Migration of Neptune and Orbital Distribution of Trans-Neptunian Objects

>42

Orbital Evolution of Asteroids during Depletion of the Solar Nebula

AU) of the Edgeworth-Kuiper Belt (EKB). The proto-sun is considered as a member of a stellar aggregation that undergoes dissolution on a timescale

Protoplanetary Formation. I. Neptune

sim 10^8

Angular Momentum Transfer in a Protolunar Disk

yrs, such that a planetesimal disk experiences a flyby encounter at pericenter distance (