Radial migration of planetesimals

Planetesimals orbiting a protostar in a circumstellar disk are affected by gravitational interaction among themselves and by gas drag force due to disk gas. Within the Kyoto model of planetesimal accretion, the migration rate is interpreted as the inverse of the planetary formation time scale. Here, we study time scales of gravitational interaction and gas drag force and their influence on planetesimal migration in detail. Evaluating observations of 86 T Tauri stars (Beckwithet al., 1990), we find the mean radial temperature profile of circumstellar disks. The disk mass is taken to be 0.01M in accordance with minimum mass models and observed T Tauri disks. The time scale of gravitational interaction between planetesimals is studied analogously to Chandrasekhar's stellar dynamics. Hence, Chandrasekhar's coefficient , defined as the fraction between the mean separation of planetesimals and the impact parameter, plays an important role in determining the migration rate. We find ln to lie between 5 and 10 within the protosolar disk. Our result is that, at the stage of disk evolution considered here, gas drag force affects the radial migration of planetesimals by a few orders of magnitude more than gravitational interaction.Paper presented at the Conference on Planetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

Gap formation in the dust layer of 3D protoplanetary disks

We numerically model the evolution of dust in a protoplanetary disk using a two-phase (gas+dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a disk comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations: a small, minimum mass solar nebular (MMSN) disk and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the grain size and planetary mass to see how they effect the resulting disk structure. We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar, disk and planetary mass will have a different appearance depending on the grain size and that such differences will be detectable in the millimetre domain with ALMA. For low mass planets in our MMSN models, a gap can open in the dust disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region.     

Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: I. Effects of interaction with planetesimals and other protoplanets

We have performed N-body simulations on the stage of protoplanet formation from planetesimals, taking into account so-called “type-I migration,” and damping of orbital eccentricities and inclinations, as a result of tidal interaction with a gas disk without gap formation. One of the most serious problems in formation of terrestrial planets and jovian planet cores is that the migration time scale predicted by the linear theory is shorter than the disk lifetime (10⁶-10⁷ years). In this paper, we investigate retardation of type-I migration of a protoplanet due to a torque from a planetesimal disk in which a gap is opened up by the protoplanet, and torques from other protoplanets which are formed in inner and outer regions. In the first series of runs, we carried out N-body simulations of the planetesimal disk, which ranges from 0.9 to 1.1 AU, with a protoplanet seed in order to clarify how much retardation can be induced by the planetesimal disk and how long such retardation can last. We simulated six cases with different migration speeds. We found that in all of our simulations, a clear gap is not maintained for more than 10⁵ years in the planetesimal disk. For very fast migration, a gap cannot be created in the planetesimal disk. For migration slower than some critical speed, a gap does form. However, because of the growth of the surrounding planetesimals, gravitational perturbation of the planetesimals eventually becomes so strong that the planetesimals diffuse into the vicinity of the protoplanets, resulting in destruction of the gap. After the gap is destroyed, close encounters with the planetesimals rather accelerate the protoplanet migration. In this way, the migration cannot be retarded by the torque from the planetesimal disk, regardless of the migration speed. In the second series of runs, we simulated accretion of planetesimals in wide range of semimajor axis, 0.5 to 2-5 AU, starting with equal mass planetesimals without a protoplanet seed. Since formation of comparable-mass multiple protoplanets (“oligarchic growth”) is expected, the interactions with other protoplanets have a potential to alter the migration speed. However, inner protoplanets migrate before outer ones are formed, so that the migration and the accretion process of a runaway protoplanet are not affected by the other protoplanets placed inner and outer regions of its orbit. From the results of these two series of simulations, we conclude that the existence of planetesimals and multiple protoplanets do not affect type-I migration and therefore the migration shall proceed as the linear theory has suggested.     

Growth rate of a migrating protoplanet

We investigated the collision rate (i.e., the growth rate) of a migrating protoplanet with planetesimals. The collision rate strongly depends on the orbital elements of planetesimals (e.g., their eccentricities and inclinations). Thus we calculated the orbital evolutions of 2000 planetesimals in the vicinity of the migrating protoplanet and obtained the collision rate by counting the number of collisions with the protoplanet. For slow migration, the protoplanet makes a gap around its orbit in the planetesimals disk. On the other hand, for rapid migration, the protoplanet cannot shepherd planetesimals and keeps catching planetesimals. The obtained collision rate becomes larger with an increase in the migration speed. The comparison of the obtained collision rates with that of the previous work with no migration shows that the rapid migration of a protoplanet can enhance the collision rate by more than the factor 10. Using the obtained collision rate, we examined the growth of a migrating protoplanet. Our results suggest that, due to the enhancement of the collision rate, planets can be formed before they fall to the sun.     

The Tilt between Acretion Disk and Stellar Disk

The orientations of the accretion disk of active galactic nuclei (AGN) and the stellar disk of its host galaxy are both determined by the angular momentum of their forming gas, but on very different physical environments and spatial scales. Here we show the evidence that the orientation of the stellar disk is correlated with the accretion disk by comparing the inclinations of the stellar disks of a large sample of Type 2 AGNs selected from Sloan Digital Sky Survey (SDSS, York et al. 2000) to a control galaxy sample. Given that the Type 2 AGN fraction is in the range of 70–90 percent for low luminosity AGNs as a priori, we find that the mean tilt between the accretion disk and stellar disk is ~ 30 degrees (Shen et al. 2010).     

Radial diffusion rate of planetesimals due to gravitational encounters

We study the rate of radial diffusion of planetesimals due to mutual gravitational encounters under Hill’s approximations in the three-body problem. Planetesimals orbiting a central star radially migrate inward and outward as a result of mutual gravitational encounters and transfer angular momentum. We calculate the viscosity in a disk of equal-sized planetesimals due to their mutual gravitational encounters using three-body orbital integrations, and obtain a semianalytic expression that reproduces the numerical results. We find that the viscosity is independent of the velocity dispersion of planetesimals when the velocity dispersion is so small that Kepler shear dominates planetesimals’ relative velocities. On the other hand, in high-velocity cases where random velocities dominate the relative velocities, the viscosity is a decreasing function of the velocity dispersion, and is found to agree with previous estimates under the two-body approximation neglecting the solar gravity. We also calculate the rate of radial diffusion of planetesimals due to gravitational scattering by a massive protoplanet. Using these results, we discuss a condition for formation of nonuniform radial surface density distribution of planetesimals by gravitational perturbation of an embedded protoplanet.     

N-Body simulations of growth from 1 km planetesimals at 0.4 AU

We present N-body simulations of planetary accretion beginning with 1 km radius planetesimals in orbit about a 1 M_⊙ star at 0.4 AU. The initial disk of planetesimals contains too many bodies for any current N-body code to integrate; therefore, we model a sample patch of the disk. Although this greatly reduces the number of bodies, we still track in excess of 10⁵ particles. We consider three initial velocity distributions and monitor the growth of the planetesimals. The masses of some particles increase by more than a factor of 100. Additionally, the escape speed of the largest particle grows considerably faster than the velocity dispersion of the particles, suggesting impending runaway growth, although no particle grows large enough to detach itself from the power law size-frequency distribution. These results are in general agreement with previous statistical and analytical results. We compute rotation rates by assuming conservation of angular momentum around the center of mass at impact and that merged planetesimals relax to spherical shapes. At the end of our simulations, the majority of bodies that have undergone at least one merger are rotating faster than the breakup frequency. This implies that the assumption of completely inelastic collisions (perfect accretion), which is made in most simulations of planetary growth at sizes 1 km and above, is inappropriate. Our simulations reveal that, subsequent to the number of particles in the patch having been decreased by mergers to half its initial value, the presence of larger bodies in neighboring regions of the disk may limit the validity of simulations employing the patch approximation.     

Planetesimal formation by turbulent concentration

The formation of 1-1000 km diameter planetesimals from dust grains in a protoplanetary disk is a key step in planet formation. Conventional models for planetesimal formation involve pairwise sticking of dust grains, or the sedimentation of dust grains to a thin layer at the disk midplane followed by gravitational instability. Each of these mechanisms is likely to be frustrated if the disk is turbulent. Particles with stopping times comparable to the turnover time of the smallest eddies in a turbulent disk can become concentrated into dense clumps that may be the precursors of planetesimals. Such particles are roughly millimeter-sized for a typical protoplanetary disk. To survive to become planetesimals, clumps need to form in regions of low vorticity to avoid rotational breakup. In addition, clumps must have sufficient self gravity to avoid break up due to the ram pressure of the surrounding gas. Given these constraints, the rate of planetesimal formation can be estimated using a cascade model for the distribution of particle concentration and vorticity within eddies of various sizes in a turbulent disk. We estimate planetesimal formation rates and planetesimal diameters as a function of distance from a star for a range of protoplanetary disk parameters. For material with a solar composition, the dust-to-gas ratio is too low to allow efficient planetesimal formation, and most solid material will remain in small particles. Enhancement of the dust-to-gas ratio by 1-2 orders of magnitude, either vertically or radially, allows most solid material to be converted into planetesimals within the typical lifetime of a disk. Such dust-to-gas ratios may occur near the disk midplane as a result of vertical settling of short-lived clumps prior to clump breakup. Planetesimal formation rates are sensitive to the assumed size and rotational speed of the largest eddies in the disk, and formation rates increase substantially if the largest eddies rotate more slowly than the disk itself. Planetesimal formation becomes more efficient with increasing distance from the star unless the disk surface density profile has a slope of −1.5 or steeper as a function of distance. Planetesimal formation rates typically increase by an order-of-magnitude or more moving outward across the snow line for a solid surface density increase of a factor of 2. In all cases considered, the modal planetesimal size increases with roughly the square root of distance from the star. Typical modal diameters are 100 km and 400 km in the regions corresponding to the asteroid belt and Kuiper belt in the Solar System, respectively.     

The formation of a disk galaxy within a slowly growing dark halo

The formation of a disk galaxy within a slowly growing dark halo is simulated with a new chemo-dynamical model. The model describes the evolution of the stellar populations, the multi-phase ISM and all important interaction. I find, that the galaxy forms radially from inside-out and vertically from top-to-bottom. The derived stellar age distributions show that the inner halo is the oldest component, followed by the outer halo, the triaxial bulge, the halo-disk transition region and the disk. Despite the still idealized model, the final galaxy resembles present-day disk galaxies in many aspects. In particular, the stellar metallicity distribution in the halo of the model resembles the one of M31. The bulge in the model shows, at least two stellar subpopulations, an early collapse population and a population that formed later out of accreted disk mass. In the stellar metallicity distribution of the disk, I find a pronounced ‘G-dwarf problem’ which is the result of a pre-enrichment of the disk ISM with metal-rich gas from the bulge. This revised version was published online in September 2006 with corrections to the Cover Date.     

The role of sticky interstellar organic material in the formation of asteroids

Abstract— Collision experiments and measurements of viscoelastic properties were performed involving an interstellar organic material analogue to investigate the growth of organic grains in the protosolar nebula. The organic material was found to be stickiest at a radius of between 2.3 and 3.0 AU, with a maximum sticking velocity of 5 m s^?1 for millimeter‐size organic grains. This stickiness is considered to have resulted in the very rapid coagulation of organic grain aggregates and subsequent formation of planetesimals in the early stage of the turbulent accretion disk. The planetesimals formed in this region appear to be represent achondrite parent bodies. In contrast, the formation of planetesimals at <2.1 and >3.0 AU begins with the establishment of a passive disk because silicate and ice grains are not as sticky as organic grains.     

Envelope instability in giant planet formation

We compute the growth of isolated gaseous giant planets for several values of the density of the protoplanetary disk, several distances from the central star and two values for the (fixed) radii of accreted planetesimals. Calculations were performed in the frame of the core instability mechanism and the solids accretion rate adopted is that corresponding to the oligarchic growth regime. We find that for massive disks and/or for protoplanets far from the star and/or for large planetesimals, the planetary growth occurs smoothly. However, notably, there are some cases for which we find an envelope instability in which the planet exchanges gas with the surrounding protoplanetary nebula. The timescale of this instability shows that it is associated with the process of planetesimals accretion. The presence of this instability makes it more difficult the formation of gaseous giant planets.     

Against all odds? Forming the planet of the HD 196885 binary

HD 196885 Ab is the most ??extreme?? planet-in-a-binary discovered to date, whose orbit places it at the limit for orbital stability. The presence of a planet in such a highly perturbed region poses a clear challenge to planet-formation scenarios. We investigate this issue by focusing on the planet-formation stage that is arguably the most sensitive to binary perturbations: the mutual accretion of kilometre-sized planetesimals. To this effect we numerically estimate the impact velocities dv amongst a population of circumprimary planetesimals. We find that most of the circumprimary disc is strongly hostile to planetesimal accretion, especially the region around 2.6 AU (the planet??s location) where binary perturbations induce planetesimal-shattering dv of more than 1 kms^?1. Possible solutions to the paradox of having a planet in such accretion-hostile regions are (1) that initial planetesimals were very big, at least 250 km (2) that the binary had an initial orbit at least twice the present one, and was later compacted due to early stellar encounters (3) that planetesimals did not grow by mutual impacts but by sweeping of dust (the ??snowball?? growth mode identified by Xie et al., in Astrophys J 724:1153, 2010b), or (4) that HD 196885 Ab was formed not by core-accretion but by the concurrent disc instability mechanism. All of these 4 scenarios remain however highly conjectural.     

Effects of Planetary Migration on Natural Satellites of the Outer Planets

Numerous studies in the past few years have analyzed possible effects of planetary migration on the small bodies of the Solar System (mainly asteroids and KBOs), with the double aim of explaining certain dynamical structures in these systems, as well as placing limits on the magnitude of the radial migration of the planets. Here we undertake a similar aim, only this time concentrating on the dynamical stability of planetary satellites in a migration scenario. However, different from previous works, the strongest perturbations on satellite systems are not due to the secular variation of the semimajor axes of the planets, but from the planetesimals themselves. These perturbations result from close approaches between the planetesimals and satellites.We present results of several numerical simulations of the dynamical evolution of real and fictitious satellite systems around the outer planets, under the effects of multiple passages of a population of planetesimals representing the large-body component of a residual rocky disk. Assuming that this component dominated the total mass of the disk, our results show that the present systems of satellites of Uranus and Neptune do not seem to be compatible with a planetary migration larger than even one quarter that suggested by previous studies, unless these bodies were originated during the late stage of evaporation of the planetesimal disk. For larger variations of the semimajor axes of the planets, most of the satellites would either be ejected from the system or suffer mutual collisions due to excitation in their eccentricities. For the systems of Jupiter and Saturn, these perturbations are not so severe, and even large migrations do not introduce large instabilities.Nevertheless, even a small number of 1000-km planetesimals in the region may introduce significant excitation in the eccentricities and inclinations of satellites. Adequate values of this component may help explain the present dynamical distribution of distant satellites, including the highly peculiar orbit of Nereid.     

Oligarchic growth with migration and fragmentation

In the core-accretion model, giant-planet cores form by oligarchic growth from a population of planetesimals prior to the dispersal of the disk gas. Once a core reaches a critical mass of roughly 10 Earth masses, it begins to accrete a gaseous envelope, forming a giant planet. Collisions between planetesimals cause fragmentation. Planetesimal fragments are more easily captured by cores, speeding up growth, but fragments are also lost by radial drift, reducing the total solid mass in the disk. Interaction with the gas causes cores to undergo inward type-I migration. Migration allows a core to accrete planetesimals from a larger region, but migrating cores may be lost if they reach the star. Thus, migration and fragmentation have both a positive and a negative impact on core formation. Here we describe results of new simulations of oligarchic growth that include fragmentation and/or migration. In the absence of migration, cores grow until they reach their isolation mass, which increases with distance from the star, or until the disk gas disperses. Fragmentation increases the maximum core mass by increasing growth rates in the outer disk, allowing objects to reach their isolation mass during the disk lifetime. When migration is present, cores migrate inwards rapidly when they approach 1 Earth mass. Most migrating cores are lost. Migrating cores gain little extra mass since they are passing through regions that have been depleted by earlier generations of cores. For a disk viscosity parameter alpha=1e−3 and planetesimal radius = 10 km, the maximum core mass is roughly 4 and 0.5 Earth masses with/without fragmentation, respectively, with little dependence on the disk mass. Formation and survival of 10-Earth-mass cores, in the presence of migration, requires large alpha (1e−2) and a massive disk (0.1 solar masses). When alpha is large, type-I migration rates decrease rapidly with time, allowing large, late-forming cores to survive. The addition of a stochastic (random-walk) migration component makes little difference to the outcome, provided that stochastic migration affects only cores larger than 0.01 Earth masses. Stochastic migration becomes increasingly important if it also affects lower-mass objects.     

Evolution of the Galactic Halo and Disk

Correlations between stellar kinematics and chemical abundances are fossil evidence for evolutionary connections between Galactic structural components. Extensive stellar surveys show that the only tolerably clear distinction between galactic components appears in the distributions of specific angular momentum. Here the stellar metal-poor halo and the metal-rich bulge are indistinguishable from each other, as are the thick disk and the old disk. Each pair is very distinct from the other. This leads to an evolutionary model in which the metal-poor stellar halo evolves into the inner bulge, while the thick disk is a precursor to the thin disk. These evolutionary sequences are distinct. The galaxy is made of two discrete 'populations', one of low and one of high angular momentum. Some (minor?) complexity is added to this picture by the debris of late and continuing mergers, which will be especially important in the outer stellar halo.     

旋涡星系颜色梯度的研究进展

旋涡星系的颜色梯度反映了其星族构成沿径向的分布,包含了星系恒星形成历史的信息.因此,对旋涡星系颜色梯度的研究有助于理解星系的形成和演化过程.大部分旋涡星系存在负的颜色梯度,其主要原因是旋涡星系存在星族梯度.颜色梯度与星系的面亮度之间存在内禀的相关,表明质量面密度在星系的形成和演化过程中具有重要作用.     

Asteroids were born big

How big were the first planetesimals? We attempt to answer this question by conducting coagulation simulations in which the planetesimals grow by mutual collisions and form larger bodies and planetary embryos. The size frequency distribution (SFD) of the initial planetesimals is considered a free parameter in these simulations, and we search for the one that produces at the end objects with a SFD that is consistent with Asteroid belt constraints. We find that, if the initial planetesimals were small (e.g. km-sized), the final SFD fails to fulfill these constraints. In particular, reproducing the bump observed at diameter in the current SFD of the asteroids requires that the minimal size of the initial planetesimals was also ∼100 km. This supports the idea that planetesimals formed big, namely that the size of solids in the proto-planetary disk “jumped” from sub-meter scale to multi-kilometer scale, without passing through intermediate values. Moreover, we find evidence that the initial planetesimals had to have sizes ranging from 100 to several 100 km, probably even 1000 km, and that their SFD had to have a slope over this interval that was similar to the one characterizing the current asteroids in the same size range. This result sets a new constraint on planetesimal formation models and opens new perspectives for the investigation of the collisional evolution in the Asteroid and Kuiper belts as well as of the accretion of the cores of the giant planets.     

Accretion of jet streams and formation of asteroids

Our basic view on the formation of asteroids, stated in [1], is that the initial physical and chemical conditions in the asteroid region led to a slow growth of planetesimals in the region and a transfer of accretable matter to the Jupitor region, resulting in the planetesimals stopping at the “half-finished” stage, eventually forming only asteroids and not major planets. In this paper, using the conditions of the nebular disk obtained in that paper and the formula for gravitational instability and regarding the rings resulting from gravitational instability as “jet streams”, we apply the theory of accretion of jet streams to calculate the growth of the planetesimals and discuss the question of the transfer of accretable material, providing further confirmation of our basic view.     

MHD simulations of the long-term evolution of a dipolar magnetosphere surrounded by an accretion disk

The evolution of a stellar, initially dipole type magnetosphere interacting with an accretion disk is investigated using numerical ideal MHD simulations. The simulations follow several 1000 Keplerian periods of the inner disk (for animated movies see http://www.aip.de～cfendt).Our model prescribes a Keplerian disk around a rotating star as a fixed boundary condition. The initial magnetic field distribution remains frozen into the star and the disk. The mass flow rate into the corona is fixed for both components. The initial dipole type magnetic field develops into a spherically radial outflow pattern with two main components – a disk wind and a stellar wind – both evolving into a quasi-stationary final state. A neutral field line divides both components, along which small plasmoids are ejected in irregular time intervals. The half opening angle of the stellar wind cone varies from 30° to55° depending on the ratio of the mass flow rates of disk wind and stellar wind. The maximum speed of the outflow is about the Keplerian speed at the inner disk radius. An axial jet forms during the first decades of rotations. However, this feature does not survive on the very long time scale and a pressure driven low velocity flow along the axis evolves. Within a cone of 15° along the axis the formation of knots may be observed if the stellar wind is weak. With the chosen mass flow rates and field strength we see almost no indication for a flow self-collimation. This is due to the weak net poloidal electric current in the magnetosphere which is in difference to typical jet models.     

Globular Clusters and field stars in the Bulge

In this paper we discuss the characteristics of the stellar content of the galactic bulge excluding the stars within a few parsec from the galactic center. The bulge clusters and the field stars are comparedto the disk population. A scenario with a flattened bulge extending toabout 3–4 Kpc from the galactic center is presented. There is evidencefor an old bulge stellar population, decoupled from the disk. This revised version was published online in July 2006 with corrections to the Cover Date.