A new model for the formation of Jovian planets is proposed. We consider planets forming at large distances from a protostar (>100 AU) through direct fragmentation of a gas cloud, by the same formation mechanism as wide stellar and brown dwarf binaries. We model the gravitational evolution of a system of these distant planets and a second population formed in a disk closer to the star. We compute the typical closest approach of these planets to the star (i.e., smallest pericenter) over the course of their evolution. When the planets reach a pericenter within a gaseous disk surroundig the star, dynamical friction from this disk slows down the planet at each plunge, causing its orbit to be gradually circularized and made coplanar with the disk. After the disk dissipates, a large fraction of these planets may be left at orbits small enough to be detected in present radial velocity surveys. A brief analytic derivation of the rate of orbital energy dissipation during these disk crossings is presented. Observational tests of this model are discussed.
We present a numerical study of rapid, so called type III migration for Jupitersized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy t…
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 prescripti…
In isothermal disks the migration of protoplanets is directed inward. For small planetary masses the standard type-I migration rates are so fast that this may result in an unrealistic loss of planets into the stars. We investigate the planet-disk interaction in non-isothermal disks and analyze the magnitude and direction of migration for an extended range of planet masses. We have performed detailed two-dimensional numerical simulations of embedded planets including heating/cooling effects as well as radiative diffusion for realistic opacities. In radiative disks, small planets with M_planet <…
We calculate the linear torque exerted by a planet on a circular orbit on a disc containing a toroidal magnetic field. All fluid perturbations are singular at the so--called magnetic resonances, where the Doppler shifted frequency of the perturbation matches that of a slow MHD wave propagating along the field line. These lie on both sides of the corotation radius. Waves propagate outside the Lindblad resonances, and also in a restricted region around the magnetic resonances. The magnetic resonances contribute to a significant global torque which, like the Lindblad torque, is negative (positive…
Giant planets in circumstellar disks can migrate inward from their initial (formation) positions. Radial migration is caused by inward torques between the planet and the disk; by outward torques between the planet and the spinning star; and by outward torques due to Roche lobe overflow and consequent mass loss from the planet. We present self-consistent numerical considerations of the problem of migrating giant planets. Summing torques on planets for various physical parameters, we find that Jupiter-mass planets can stably arrive and survive at small heliocentric distances, thus reproducing ob…
This series of papers investigates the early stages of planet formation by modeling the evolution of the gas and solid content of protostellar disks from the early T Tauri phase until complete dispersal of the gas. In this first paper, I present a new set of simplified equations modeling the growth and migration of various species of grains in a gaseous protostellar disk evolving as a result of the combined effects of viscous accretion and photo-evaporation from the central star. Using the assumption that the grain size distribution function always maintains a power-law structure approximating…
The growth of Jovian mass planets during migration in their protoplanetary disks is one of the most important problems that needs to be solved in light of observations of the exosolar planets. Studies of the migration of planets in standard gas disk models routinely show that migration is too fast to form Jovian planets, and that such migrating planetary cores generally plunge into the central stars in less than a Myr. In previous work, we have shown that a poorly ionized, less viscous region in a protoplanetary disk called a dead zone slows down the migration of fixed-mass planets. In this pa…
Aims: We investigate the effect of including a proper energy balance on the interaction of a low-mass planet with a protoplanetary disk. Methods: We use a three-dimensional version of the RODEO method to perform hydrodynamical simulations including the energy equation. Radiation is included in the flux-limited diffusion approach. Results: The sign of the torque depends sensitively on the ability of the disk to radiate away the energy generated in the immediate surroundings of the planet. In the case of high opacity, corresponding to the dense inner regions of protoplanetary disks, migration is…
We investigate the gravitational interaction of a Jovian mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions have been investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Nonlinear hydrodynamic simulations are employed using three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches t…
(Abridged) We consider models of gas giant planets forming in protoplanetary disks consisting of solid cores with gaseous envelopes in contact with their critical Hill spheres while accreting gas from the surrounding disk.We suppose the luminosity derives from gas accretion alone.We label such models as type A and follow their evolution which may occur on a time scale similar to the protostellar disk lifetime until rapid gas accretion. We consider another set of models, we label type B, with a free surface, powered by gravitational contraction, while accreting through a disk.We find these mode…
In the core-accretion model, gas-giant planets form solid cores which then accrete gaseous envelopes. Tidal interactions with disk gas cause a core to undergo inward type-I migration in 10^4 to 10^5 years. Cores must form faster than this to survive. Giant planets clear a gap in the disk and undergo inward type-II migration in <10^6 years if observed disk accretion rates apply to the disk as a whole. Type-II migration times exceed typical disk lifetimes if viscous accretion occurs mainly in the surface layers of disks. Low turbulent viscosities near the midplane may allow planetesimals to form…
We investigate resonant capture of small bodies by planets that migrate inwards, using analytic arguments and three-body integrations. If the orbits of the planet and the small body are initially circular and coplanar, the small body is captured when it crosses the 2:1 resonance with the planet. As the orbit shrinks it becomes more eccentric, until by the time its semimajor axis has shrunk by a factor of four, its eccentricity reaches nearly unity (1-e<<10^{-4}). In typical planetary systems, bodies in this high-eccentricity phase are likely to be consumed by the central star. If they can avoi…
We show that the dearth of brown dwarfs in short-period orbits around Solar-mass stars - the brown dwarf desert - can be understood as a consequence of inward migration within an evolving protoplanetary disc. Brown dwarf secondaries forming at the same time as the primary star have masses which are comparable to the initial mass of the protoplanetary disc. Subsequent disc evolution leads to inward migration, and destruction of the brown dwarf, via merger with the star. This is in contrast with massive planets, which avoid this fate by forming at a later epoch when the disc is close to being di…
We present a numerical model for the evolution of a protostellar disc that has formed self-consistently from the collapse of a molecular cloud core. The global evolution of the disc is followed for several million years after its formation. The capture of a wide range of spatial and temporal scales is made possible by use of the thin-disc approximation. We focus on the role of gravitational torques in transporting mass inward and angular momentum outward during different evolutionary phases of a protostellar disc with disc-to-star mass ratio of order 0.1. In the early phase, when the infall of…
The discovery of close orbiting extrasolar giant planets led to extensive studies of disk planet interactions and the forms of migration that can result as a means of accounting for their location. Early work established the type I and type II migration regimes for low mass embedded planets and high mass gap forming planets respectively. While providing an attractive means of accounting for close orbiting planets intially formed at several AU, inward migration times for objects in the earth mass range were found to be disturbingly short, making the survival of giant planet cores an issue. Rece…
This paper investigates the influence of magneto-centrifugally driven or simply magnetic winds of rapidly-rotating, strongly-magnetized T Tauri stars in causing the inward or outward migration of close-in giant planets. The azimuthal ram pressure of the magnetized wind acting on the planet tends to increase the planet's angular momentum and cause outward migration if the star's rotation period $P_*$ is less than the planet's orbital period $P_p$. In the opposite case, $P_* > P_p$, the planet migrates inward. Thus, planets orbiting at distances larger (smaller) than $0.06 {\rm AU}(P_*/5{\rm d})…
Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of $10^{-4}-0.01 M_{\odot}$, can migrate inward a large distance and can survive only if the inner disc is truncated or because of tidal interaction with the star. In this case the semi-major axis, a, of the planetary orbit is less than 0.1 AU. Orbits with larger $a$ are obtained for sm…
Protoplanet eccentricities of e >~ H/r can slow or reverse migration, but previous 2D studies have shown that gravitational scattering cannot maintain significant planet eccentricities against disc-induced damping. We simulate the evolution of low-mass protoplanetary swarms in three dimensions. The aim is to examine both protoplanet survival rates and the dynamical structure of the resulting planetary systems, and to compare them with 2D simulations. We present results from a 3D hydrodynamic simulation of eight protoplanets embedded in a protoplanetary disc. We also present a suite of simulati…
We present analytic and numerical results which illustrate the effects of Jupiter's accretion of nebular gas and the planet's radial migration on its Trojan companions. Initially, we approximate the system by the planar circular restricted three-body problem and assume small Trojan libration amplitudes. Employing an adiabatic invariant calculation, we show that Jupiter's thirty-fold growth from a $10 M_\oplus$ core to its present mass causes the libration amplitudes of Trojan asteroids to shrink by a factor of about 2.5 to $\sim 40%$ of their original size. The calculation also shows that Jupi…
Using 2D MHD numerical simulations performed with two different finite difference Eulerian codes, we analyze the effect that a toroidal magnetic field has on low mass planet migration in nonturbulent protoplanetary discs. The presence of the magnetic field modifies the waves that can propagate in the disc. In agreement with a recent linear analysis (Terquem 2003), we find that two magnetic resonances develop on both sides of the planet orbit, which contribute to a significant global torque. In order to measure the torque exerted by the disc on the planet, we perform simulations in which the la…
We report an analytical expression for the locations of Lindblad resonances induced by a perturbing protoplanet, including the effect of disk gravity. Inner, outer and differential torques are found to be enhanced compared to situations where a keplerian velocity field for the dynamics of both the disk and the planet is assumed. Inward migration is strongly accelerated when the disk gravity is only accounted for in the planet orbital motion. The addition of disk self-gravity slows down the planet drift but not enough to stop it.
The processes of planet formation and migration depend intimately on the interaction between planetesimals and the gaseous disks in which they form. The formation of gaps in the disk can severely limit the mass of the planet and its migration toward the protostar. We investigate the process of gap formation through magnetohydrodynamic simulations in which internal stress arises self-consistently from turbulence generated by the magnetorotational instability. The simulations investigate three different planetary masses and two disk temperatures to bracket the tidal (thermal) and viscous gap ope…
Motivated by recent observations which detect an outer boundary for starless cores, and evidence for time-dependent mass accretion in the Class 0 and Class I protostellar phases, we reexamine the case of spherical isothermal collapse in the case of a finite mass reservoir. The presence of a core boundary results in the generation of an inward propagating rarefaction wave. This steepens the gas density profile from r^{-2} to r^{-3} or steeper. After a protostar forms, the mass accretion rate \dot{M} evolves through three distinct phases: (1) an early phase of decline in \dot{M}, which is a non-…
We calculate global $m=1$ modes with low pattern speed corresponding to introducing a finite eccentricity into a protoplanetary disc. We consider disc models which are either isolated or contain one or two protoplanets orbiting in an inner cavity. Global modes that are strongly coupled to inner protoplanets are found to have disc orbits which tend to have apsidal lines antialigned with respect to those of the inner protoplanets. Other modes corresponding to free disc modes may be global over a large range of length scales and accordingly be long lived. We consider the motion of a protoplanet i…
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 shephe…
We present a numerical study of rapid, so called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of outward migration, and study in detail its evolution and physics, concentrating on the structure of the co-rotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. We find that the outward directed type III migration can b…
The formation of resonant planets pairs in exoplanetary systems involves planetary migration inside the protoplanetary disc : an inwards migrating outer planet captures in Mean Motion Resonance an inner planet. During the migration of the resonant pair of planets, the eccentricities are expected to rise excessively, if no damping mechanism is applied on the inner planet. We express the required damping action to match the observations, and we show that the inner disk can play this role. This result applies for instance to the system GJ 876 : we reproduce the observed orbital elements through a…
Substantial orbital migration of massive planets may occur in most extrasolar planetary systems. Since migration is likely to occur after a significant fraction of the dust has been locked up into planetesimals, ubiquitous migration could reduce the probability of forming terrestrial planets at radii of the order of 1 au. Using a simple time dependent model for the evolution of gas and solids in the disk, I show that replenishment of solid material in the inner disk, following the inward passage of a giant planet, is generally inefficient. Unless the timescale for diffusion of dust is much sho…
This paper examines how type I planet migration is affected by the presence of turbulent density fluctuations in the circumstellar disk. For type I migration, the planet does not clear a gap in the disk and its secular motion is driven by torques generated by the wakes it creates in the surrounding disk fluid. MHD turbulence creates additional density perturbations that gravitationally interact with the planet and can dominate the torques produced by the migration mechanism itself. This paper shows that conventional type I migration can be readily overwhelmed by turbulent perturbations and hen…
Close-in giant planets (e.g. ``Hot Jupiters'') are thought to form far from their host stars and migrate inward, through the terrestrial planet zone, via torques with a massive gaseous disk. Here we simulate terrestrial planet growth during and after giant planet migration. Several-Earth mass planets also form interior to the migrating Jovian planet, analogous to recently-discovered ``Hot Earths''. Very water-rich, Earth-mass planets form from surviving material outside the giant planet's orbit, often in the Habitable Zone and with low orbital eccentricities. More than a third of the known sys…
We study the radial migration of dust particles in accreting protostellar disks analogous to the primordial solar nebula. This study takes account of the two dimensional (radial and normal) structure of the disk gas, including the effects of the variation in the gas velocity as a function of distance from the midplane. It is shown that the dust component of disks accretes slower than the gas component. At high altitude from the disk midplane, the gas rotates faster than particles because of the inward pressure gradient force, and its drag force causes particles to move outward in the radial di…
We present new numerical simulations in the thin-disk approximation which characterize the burst mode of protostellar accretion. The burst mode begins upon the formation of a centrifugally balanced disk around a newly formed protostar. It is comprised of prolonged quiescent periods of low accretion rate (typically $\la 10^{-7} \Msun$ yr$^{-1}$) which are punctuated by intense bursts of accretion (typically $\ga 10^{-4} \Msun$ yr$^{-1}$, with duration $\la 100$ yr) during which most of the protostellar mass is accumulated. The accretion bursts are associated with the formation of dense protoste…
Observations of the dust and gas around embedded stellar clusters reveal some of the processes involved in their formation and evolution. Large scale mass infall with rates dM/dt=4e-4 solar masses/year is found to be disrupted on small scales by protostellar outflows. Observations of the size and velocity dispersion of clusters suggest that protostellar migration from their birthplace begins at very early times and is a potentially useful evolutionary indicator.
More than 30 extra-solar Jupiter-like planets have shorter periods than the planet Mercury. It is generally accepted that they formed further out, and migrated inwards. In order to be driven by tidal torques from the gaseous disc, the disc exterior to the planet had to contain about a planetary mass. The fact that the planets stopped migrating means that their outer disc was removed. We suggest that the outer disc was accreted by the planet. In this scenario, the endgame is a race. The planet survives if it accretes its outer disc before being accreted by the star. The winner is determined sol…
One dimensional, convective, vertical structure models and one dimensional, time dependent, radial diffusion models are combined to create a self-consistent picture in which FU~Orionis outbursts occur in young stellar objects (YSOs) as the result of a large scale, self-regulated, thermal ionization instability in the surrounding protostellar accretion disk. By fitting the results of time dependent disk models to observed time scales of FU~Orionis events, we estimate the magnitude of the effeciency of the effective viscous stress in the inner disk (r < 1 AU) to be, in accordance with the ad hoc…
If supermassive black holes (BHs) are generically present in galaxy centers, and if galaxies are built up through hierarchical merging, BH binaries are at least temporary features of most galactic bulges. Observations suggest, however, that binary BHs are rare, pointing towards a binary lifetime far shorter than the Hubble time. We show that, regardless of the detailed mechanism, all stellar-dynamical processes are insufficient to reduce significantly the orbital separation once orbital velocities in the binary exceed the virial velocity of the system. We propose that a massive gas disk surrou…
In the standard model of gas giant planet formation, a large solid core (~ 10 times the Earth's mass) forms first, then accretes its massive envelope (100 or more Earth masses) of gas. However, inward planet migration due to gravitational interaction with the proto-stellar gas disk poses a difficulty in this model. Core-sized bodies undergo rapid "Type I" migration; for typical parameters their migration timescale is much shorter than their accretion timescale. How, then, do growing cores avoid spiraling into the central star before they ever get the chance to become gas giants? Here, we prese…
We present bispectrum speckle interferometry of the massive protostellar object IRAS 23151+5912 in the near-infrared K' band. The reconstructed image shows the diffuse nebulosity north-east of two point-like sources in unprecedented detail. The comparison of our near-infrared image with mm continuum and CO molecular line maps shows that the brighter of the two point sources lies near the center of the mm peak, indicating that it is a high-mass protostar. The nebulosity coincides with the blue-shifted molecular outflow component. The most prominent feature in the nebulosity is a bow-shock-like …
We report on the results of novel global high-resolution three-dimensional simulations of disk-planet interaction which incorporate simultaneously realistic radiation physics and the self-gravity of the gas, as well as allowing the planet to move. We find that thermodynamics and radiative physics have a remarkable effect on both migration and accretion of Jupiter mass planets. In simulations with radiative transfer adopting flux-limited diffusion, inward migration can be decreased by about 30% relative to the isothermal case, while in adiabatic runs migration nearly shuts off after a few tens …
In the current paper, we further develop the model for the migration of planets introduced in Del Popolo et al. (2001) and extended to time-dependent accretion discs in Del Popolo and Eksi (2002). We use a method developed by Stepinski and Valageas (1996, 1997), that is able to simultaneously follow the evolution of gas and solid particles for up to $10^7 {\rm yr}$. The disc model is coupled to the migration model introduced in Del Popolo et al. (2001) in order to obtain the migration rate of the planet in the planetesimal disc. We find that in the case of discs having total mass of $10^{-3}-0…
Motivated by recent observations that show starless molecular cloud cores exhibit subsonic inward velocities, we revisit the collapse problem for polytropic gaseous spheres. In particular, we provide a generalized treatment of protostellar collapse in the spherical limit and find semi-analytic (self-similar) solutions, corresponding numerical solutions, and purely analytic calculations of the mass infall rates (the three approaches are in good agreement). This study focuses on collapse solutions that exhibit nonzero inward velocities at large radii, as observed in molecular cloud cores, and ex…
We investigate the role of non-isothermality in gravitational collapse and protostellar accretion by explicitly including the effects of molecular radiative cooling, gas-dust energy transfer, and cosmic ray heating in models of spherical hydrodynamic collapse. Isothermal models have previously shown an initial decline in the mass accretion rate \dot{M}, due to a gradient of infall speed that develops in the prestellar phase. Our results show that: (1) in the idealized limit of optically thin cooling, a positive temperature gradient is present in the prestellar phase which effectively cancels o…
In this paper, we further develop the model for the migration of planets introduced in Del Popolo et al. (2001). We first model the protoplanetary nebula as a time-dependent accretion disc and find self-similar solutions to the equations of the accretion disc that give to us explicit formulas for the spatial structure and the temporal evolution of the nebula. These equations are then used to obtain the migration rate of the planet in the planetesimal disc and to study how the migration rate depends on the disc mass, on its time evolution and on some values of the dimensionless viscosity parame…
The final masses of Jovian planets are attained when the tidal torques that they exert on their surrounding protostellar disks are sufficient to open gaps in the face of disk viscosity, thereby shutting off any further accretion. In sufficiently well-ionized disks, the predominant form of disk viscosity originates from the Magneto-Rotational Instability (MRI) that drives hydromagnetic disk turbulence. In the region of sufficiently low ionization rate -- the so-called dead zone -- turbulence is damped and we show that lower mass planets will be formed. We considered three ionization sources (X-…
The exo-solar planet HD 80606b has a highly eccentric (e=0.93) and tight (a=0.47 AU) orbit. We study how it might arrive at such an orbit and how it has avoided being tidally circularized until now. The presence of a stellar companion to the host star suggests the possibility that the Kozai mechanism and tidal dissipation combined to draw the planet inward well after it formed: Kozai oscillations produce periods of extreme eccentricity in the planet orbit, and the tidal dissipation that occurs during these periods of small pericentre distances leads to gradual orbital decay. We call this migra…
