On the coorbital corotation torque in a viscous disk and its impact on planetary migration

We evaluate the coorbital corotation torque on a planet on a fixed circular orbit embedded in a viscous protoplanetary disk, for the case of a steady flow in the planet frame. This torque can be evaluated just from the flow properties at the separatrix between the librating (horseshoe) and circulating streamlines. A stationary solution is searched for the flow in the librating region. When used to evaluate the torque exerted by the circulating material of the outer and inner disk on the trapped material of the librating region, this solution leads to an expression of the coorbital corotation torque in agreement with previous estimates. An analytical expression is given for the corotation torque as a function of viscosity. Lastly, we show that additional terms in the torque expression can play a crucial role. In particular, they introduce a coupling with the disk density profile perturbation (the `dip' which surrounds the planet) and add to the corotation torque a small, positive fraction of the one-sided Lindblad torque. As a consequence, the migration could well be directed outwards in very thin disks (aspect ratio smaller than a few percent). This 2D analysis is especially relevant for mildly embedded protoplanets (sub-Saturn sized objects).Comment: 10 pages, 2 figure

The Lopsidedness of Present-Day Galaxies: Results from the Sloan Digital Sky Survey

Large-scale asymmetries in the stellar mass distribution in galaxies are believed to trace non-equilibrium situations in the luminous and/or dark matter component. These may arise in the aftermath of events like mergers, accretion, and tidal interactions. These events are key in the evolution of galaxies. In this paper we quantify the large-scale lopsidedness of light distributions in 25155 galaxies at z < 0.06 from the Sloan Digital Sky Survey Data Release 4 using the m = 1 azimuthal Fourier mode. We show that the lopsided distribution of light is primarily due to a corresponding lopsidedness in the stellar mass distribution. Observational effects, such as seeing, Poisson noise, and inclination, introduce only small errors in lopsidedness for the majority of this sample. We find that lopsidedness correlates strongly with other basic galaxy structural parameters: galaxies with low concentration, stellar mass, and stellar surface mass density tend to be lopsided, while galaxies with high concentration, mass, and density are not. We find that the strongest and most fundamental relationship between lopsidedness and the other structural parameters is with the surface mass density. We also find, in agreement with previous studies, that lopsidedness tends to increase with radius. Both these results may be understood as a consequence of several factors. The outer regions of galaxies and low-density galaxies are more susceptible to tidal perturbations, and they also have longer dynamical times (so lopsidedness will last longer). They are also more likely to be affected by any underlying asymmetries in the dark matter halo.Comment: 42 pages, 13 figures, 3 tables, accepted to Ap

Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations

Understanding the growth of the cores of giant planets is a difficult problem. Recently, Lambrechts and Johansen (2012; LJ12) proposed a new model in which the cores grow by the accretion of pebble-size objects, as the latter drift towards the star due to gas drag. Here, we investigate the dynamics of pebble-size objects in the vicinity of planetary embryos of 1 and 5 Earth masses and the resulting accretion rates. We use hydrodynamical simulations, in which the embryo influences the dynamics of the gas and the pebbles suffer gas drag according to the local gas density and velocities. The pebble dynamics in the vicinity of the planetary embryo is non-trivial, and it changes significantly with the pebble size. Nevertheless, the accretion rate of the embryo that we measure is within an order of magnitude of the rate estimated in LJ12 and tends to their value with increasing pebble-size. We conclude that the model by LJ12 has the potential to explain the rapid growth of giant planet cores. The actual accretion rates however, depend on the surface density of pebble size objects in the disk, which is unknown to date.Comment: In press in Astronomy and Astrophysic

Recent developments in planet migration theory

Planetary migration is the process by which a forming planet undergoes a drift of its semi-major axis caused by the tidal interaction with its parent protoplanetary disc. One of the key quantities to assess the migration of embedded planets is the tidal torque between the disc and planet, which has two components: the Lindblad torque and the corotation torque. We review the latest results on both torque components for planets on circular orbits, with a special emphasis on the various processes that give rise to additional, large components of the corotation torque, and those contributing to the saturation of this torque. These additional components of the corotation torque could help address the shortcomings that have recently been exposed by models of planet population syntheses. We also review recent results concerning the migration of giant planets that carve gaps in the disc (type II migration) and the migration of sub-giant planets that open partial gaps in massive discs (type III migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physic

On disc driven inward migration of resonantly coupled planets with application to the system around GJ876

We consider two protoplanets gravitationally interacting with each other and a protoplanetary disc. The two planets orbit interior to a tidally maintained disc cavity while the disc interaction indices inward migration. When the migration is slow enough, the more rapidly migrating outer protoplanet approaches and becomes locked in a 2:1 commensurability with the inner one. This is maintained in subsequent evolution. We study this evolution using a simple anaytic model, full hydrodynamic 2D simulations of the disc planet system and longer time N body integrations incorporating simple prescriptions for the effect of the disc on the planet orbits. The eccentricity of the protoplanets are found to be determined by the migration rate induced in the outer planet orbit by the external disc. We apply our results to the recently discovered resonant planets around GJ876. Simulation shows that a disc with parameters expected for protoplanetary discs causes trapping in the 2:1 commensurability when the planets orbit in an inner cavity and that eccentricities in the observed range may be obtained.Comment: 8 pages, 5 figures, submitted to A&A on 30/03/200

The Importance of Disk Structure in Stalling Type I Migration

As planets form they tidally interact with their natal disks. Though the tidal perturbation induced by Earth and super-Earth mass planets is generally too weak to significantly modify the structure of the disk, the interaction is potentially strong enough to cause the planets to undergo rapid type I migration. This physical process may provide a source of short-period super-Earths, though it may also pose a challenge to the emergence and retention of cores on long-period orbits with sufficient mass to evolve into gas giants. Previous numerical simulations have shown that the type I migration rate sensitively depends upon the circumstellar disk's properties, particularly the temperature and surface density gradients. Here, we derive these structure parameters for 1) a self-consistent viscous-disk model based on a constant \alpha-prescription, 2) an irradiated disk model that takes into account heating due to the absorption of stellar photons, and 3) a layered-accretion disk model with variable \alpha-parameter. We show that in the inner viscously-heated regions of typical protostellar disks, the horseshoe and corotation torques of super-Earths can exceed their differential Lindblad torque and cause them to undergo outward migration. However, the temperature profile due to passive stellar irradiation causes type I migration to be inwards throughout much of the disk. For disks in which there is outwards migration, we show that location and the mass range of the "planet traps" depends on some uncertain assumptions adopted for these disk models. Competing physical effects may lead to dispersion in super-Earths' mass-period distribution.Comment: 12 pages, Submitted to Ap

Double Bars, Inner Disks, and Nuclear Rings in Early-Type Disk Galaxies

We present results from an imaging survey of an unbiased sample of thirty-eight early-type (S0--Sa), low-inclination, optically barred galaxies in the field. Our goal was to find and characterize central stellar and gaseous structures: secondary bars, inner disks, and nuclear rings. Bars inside bars are surprisingly common: at least one quarter of the sample galaxies (possibly as many as 40%) are double-barred, with no preference for Hubble type or the strength of the primary bar. A typical secondary bar is ~12% of the size of its primary bar and 240--750 pc in radius. We see no significant effect of secondary bars on nuclear activity. We also find kiloparsec-scale inner disks in at least 20% of our sample, almost exclusively in S0 galaxies. These disks are on average 20% the size of their host bar, and show a wider range of relative sizes than do secondary bars. Nuclear rings are present in about a third of our sample. Most are dusty, sites of current or recent star formation, or both; such rings are preferentially found in Sa galaxies. Three S0 galaxies (15% of the S0's) appear to have purely stellar nuclear rings, with no evidence for dust or recent star formation. The fact that these central stellar structures are so common indicates that the inner regions of early-type barred galaxies typically contain dynamically cool and disklike structures. This is especially true for S0 galaxies, where secondary bars, inner disks, and/or stellar nuclear rings are present at least two thirds of the time. (abridged)Comment: LaTeX, 15 pages, 7 EPS figures; to appear in The Astronomical Journal (July 2002

Toward a Deterministic Model of Planetary Formation VI: Dynamical Interaction and Coagulation of Multiple Rocky Embryos and Super-Earth Systems around Solar Type Stars

Radial velocity and transit surveys indicate that solar-type stars bear super-Earths, with mass and period up to ~ 20 M_E and a few months, are more common than those with Jupiter-mass gas giants. In many cases, these super-Earths are members of multiple-planet systems in which their mutual dynamical interaction has influenced their formation and evolution. In this paper, we modify an existing numerical population synthesis scheme to take into account protoplanetary embryos' interaction with their evolving natal gaseous disk, as well as their close scatterings and resonant interaction with each other. We show that it is possible for a group of compact embryos to emerge interior to the ice line, grow, migrate, and congregate into closely-packed convoys which stall in the proximity of their host stars. After the disk-gas depletion, they undergo orbit crossing, close scattering, and giant impacts to form multiple rocky Earths or super-Earths in non-resonant orbits around ~ 0.1AU with moderate eccentricities of ~0.01-0.1. We suggest that most refractory super-Earths with period in the range of a few days to weeks may have formed through this process. These super-Earths differ from Neptune-like ice giants by their compact sizes and lack of a substantial gaseous envelope.Comment: 37 pages, 10 figures, accepted for publication in Ap

Type I planet migration in nearly laminar disks - long term behavior

We carry out 2-D high resolution numerical simulations of type I planet migration with different disk viscosities. We find that the planet migration is strongly dependent on disk viscosities. Two kinds of density wave damping mechanisms are discussed. Accordingly, the angular momentum transport can be either viscosity dominated or shock dominated, depending on the disk viscosities. The long term migration behavior is different as well. Influences of the Rossby vortex instability on planet migration are also discussed. In addition, we investigate very weak shock generation in inviscid disks by small mass planets and compare the results with prior analytic results.Comment: Accepted for publication in Ap

On the formation of hot Neptunes and super-Earths

The discovery of short-period Neptune-mass objects, now including the remarkable system HD69830 (Lovis et al. 2006) with three Neptune analogues, raises difficult questions about current formation models which may require a global treatment of the protoplanetary disc. Several formation scenarios have been proposed, where most combine the canonical oligarchic picture of core accretion with type I migration (e.g. Terquem & Papaloizou 2007) and planetary atmosphere physics (e.g. Alibert et al. 2006). To date, published studies have considered only a small number of progenitors at late times. This leaves unaddressed important questions about the global viability of the models. We seek to determine whether the most natural model -- namely, taking the canonical oligarchic picture of core accretion and introducing type I migration -- can succeed in forming objects of 10 Earth masses and more in the innermost parts of the disc. This problem is investigated using both traditional semianalytic methods for modelling oligarchic growth as well as a new parallel multi-zone N-body code designed specifically for treating planetary formation problems with large dynamic range (McNeil & Nelson 2009). We find that it is extremely difficult for oligarchic tidal migration models to reproduce the observed distribution. Even under many variations of the typical parameters, we form no objects of mass greater than 8 Earth masses. By comparison, it is relatively straightforward to form icy super-Earths. We conclude that either the initial conditions of the protoplanetary discs in short-period Neptune systems were substantially different from the standard disc models we used, or there is important physics yet to be understood.Comment: 19 pages, 18 figures. Final version accepted to MNRAS 30 September 200