Observations of extrasolar planets reveal that planets can be found in close binary systems, where the semi-major axis of the binary orbit is less than 20 AU. The existence of these planets challenges planet formation theory, because the strong gravitational perturbations due to the companion increase encounter velocities between planetesimals and make it difficult for them to grow through accreting collisions. We study planetesimal encounter velocities in binary systems, where the planetesimals are embedded in a circumprimary gas disc that is allowed to evolve under influence of the gravitational perturbations of the companion star. We find that the encounter velocities between planetesimals of different size strongly depend on the gas disc eccentricity. In all cases studied, inclusion of the full gas dynamics increases the encounter velocity compared to the case of a static, circular gas disc. Full numerical parameter exploration is still impossible, but we derive analytical formulae to estimate encounter velocities between bodies of different sizes given the gas disc eccentricity. The gas dynamical evolution of a protoplanetary disc in a binary system tends to make planetesimal accretion even more difficult than in a static, axisymmetric gas disc.
We have investigated the planetesimal accretion rate onto giant planets that are growing through gas accretion, using numerical simulations and analytical arguments. We derived the condition for gap opening in the planetesimal disk, which is determined by a competition between the expansion of the planet's Hill radius due to the planet growth and the damping of planetesimal eccentricity due to gas drag. We also derived the semi-analytical formula for the planetesimal accretion rate as a function of ratios of the rates of the Hill radius expansion, the damping, and planetesimal scattering by th…
The solar and extra solar gas giants appear to have diverse internal structure and metallicities. We examine a potential cause for these dispersions in the context of the conventional sequential accretion formation scenario. In principle, gas accretion onto cores with masses below several times that of the Earth is suppressed by the energy released from the bombardment of residual planetesimals. We show that these planetesimals generally cannot pass through the mean motion resonances of the cores, and the suppression of planetesimal bombardment rate enables the cores to accrete gas with little…
We study the migration and resonant capture of planetesimals in a planetary system consisting of a gaseous disc analogous to the primordial solar nebula and a Neptune-like planet. Using a simple treatment of the drag force we find that planetesimals are mainly trapped in the 3:2 and 2:1 resonances and that the resonant populations are correlated with the gaseous drag strength in a sense that the 3:2 resonant population increases with the stronger gaseous drag, but the 2:1 resonant population does not. Since planetesimals can lead to the formation of larger bodies similar to asteroids and Kuipe…
We study to which extent planetesimal accretion is affected by the perturbing presence of a compagnon star. We concentrate on one crucial parameter: the distribution of encounter velocities within the planetesimal swarm. We numerically explore the evolution of this parameter taking into account the secular perturbations of the binary and friction due to the very likely presence of gas in the disk. $<Δv>$ maps are derived, for planetesimals of different sizes, for a total of 120 binary configurations (eccentricity eb and separation ab). We identify for each case 3 different accreting behaviours…
Currently, one of major problems concerning planet formation theory in close binary systems is, the strong perturbation from the companion star can increase relative velocities ($\triangle V$) of planetesimals around the primary and thus hinder their growth. According to previous studies, while gas drag can reduce the $\triangle V$ between bodies of the same sizes by forcing orbital alignment to planetesimals, it increases the $\triangle V$ among bodies of different sizes. In this paper, focusing on the $γ$ Cephei binary system, we propose a mechanism that can overcome this difficulty. We show…
In this paper we consider the evolution of small planetesimals in marginally stable, self-gravitating protoplanetary discs. The drag force between the disc gas and the embedded planetesimals generally causes the planetesimals to drift inwards through the disc at a rate that depends on the particle size. In a marginally stable, self-gravitating disc, however, the planetesimals are significantly influenced by the non-axisymmetric spiral structures resulting from the growth of the gravitational instability. For small particles, that are strongly coupled to the disc gas, and for large particles, t…
We numerically investigate the possibility of planetesimal accretion in circumbinary disks, under the coupled influence of both stars' secular perturbations and friction due to the gaseous component of the protoplanetary disk. We focus on one crucial parameter: the distribution of encounter velocities between planetesimals in the 0.5 to 100km size range. An extended range of binary systems with differing orbital parameters is explored. The resulting encounter velocities are compared to the threshold velocities below which the net outcome of a collision is accumulation into a larger body instea…
More than half of stars reside in binary or multiple star systems and many planets have been found in binary systems. From theoretical point of view, however, whether or not the planetary formation proceeds in a binary system is a very complex problem, because secular perturbation from the companion star can easily stir up the eccentricity of the planetesimals and cause high-velocity, destructive collisions between planetesimals. Early stage of planetary formation process in binary systems has been studied by restricted three-body approach with gas drag and it is commonly accepted that accreti…
Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. (1986), heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as $\sim R_H/2$. At first, the net angula…
I review the processes that shape the evolution of protoplanetary discs around young, solar-mass stars. I first discuss observations of protoplanetary discs, and note in particular the constraints these observations place on models of disc evolution. The processes that affect the evolution of gas discs are then discussed, with the focus in particular on viscous accretion and photoevaporation, and recent models which combine the two. I then discuss the dynamics and growth of dust grains in discs, considering models of grain growth, the gas-grain interaction and planetesimal formation, and revie…
Proposed mechanisms for the formation of km-sized solid planetesimals face long-standing difficulties. Robust sticking mechanisms that would produce planetesimals by coagulation alone remain elusive. The gravitational collapse of smaller solids into planetesimals is opposed by stirring from turbulent gas. This proceeding describes recent works showing that "particle feedback," the back-reaction of drag forces on the gas in protoplanetary disks, promotes particle clumping as seeds for gravitational collapse. The idealized streaming instability demonstrates the basic ability of feedback to gener…
We investigate the formation of planetesimals via the gravitational instability of solids that have settled to the midplane of a circumstellar disk. Vertical shear between the gas and a subdisk of solids induces turbulent mixing which inhibits gravitational instability. Working in the limit of small, well-coupled particles, we find that the mixing becomes ineffective when the surface density ratio of solids to gas exceeds a critical value. Solids in excess of this precipitation limit can undergo midplane gravitational instability and form planetesimals. However, this saturation effect typicall…
Numerical simulations of planetesimal accretion in circumprimary and circumbinary orbits are described. The secular perturbations by the com- panion star and gas drag are included in our models. We derive limits on the parameters of the binary system for which accretion and then planetary forma- tion are possible. In the circumbinary case we also outline the radial distance from the baricenter of the stars beyond which accumulation always occurs. Hy- drodynamical simulations are also presented to validate our N-body approach based on the axisymmetric approximation for the gas of the disk.
In the current paper, we further improved the model for the migration of planets introduced in Del Popolo et al. (2001) and extended to time-dependent planetesimal accretion disks in Del Popolo and Eksi (2002). In the current study, the assumption of Del Popolo and Eksi (2002), that the surface density in planetesimals is proportional to that of gas, is released. In order to obtain the evolution of planetesimal density, we use a method developed in Stepinski and Valageas (1997) which is able to simultaneously follow the evolution of gas and solid particles for up to 10^7 yrs. Then, the disk mo…
We analyze the stability of dust layer in protoplanetary disk to understand the effect of the relative motion between gas and dust. The previous analyses not including the effect of relative motion between gas and dust show that the shear-induced turbulence may prevent the dust grains from settling sufficiently to be gravitationally unstable. We determine the growth rate of Kelvin-Helmholtz instability in wide range of parameter space, and propose a possible path toward the planetesimal formation through the gravitational instability. We expect the density of dust layer becomes $ρ_\mathrm{d}/ρ…
In this paper, we further develop the model for the migration of planets introduced in Del Popolo, Gambera and Ercan, and extended to time-dependent planetesimal accretion disks in Del Popolo and Eksi. More precisely, the assumption of Del Popolo and Eksi that the surface density in planetesimals is proportional to that of gas is released. Indeed, the evolution of the radial distribution of solids is governed by many processes: gas-solid coupling, coagulation, sedimentation, evaporation/condensation, so that the distribution of planetesimals emerging from a turbulent disk does not necessarily …
The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin…
We explore the dynamics of small planetesimals coexisting with massive protoplanetary cores in a gaseous nebula. Gas drag strongly affects the motion of small bodies leading to the decay of their eccentricities and inclinations, which are excited by the gravity of protoplanetary cores. Drag acting on larger ($\gtrsim 1$ km), high velocity planetesimals causes a mere reduction of their average random velocity. By contrast, drag qualitatively changes the dynamics of smaller ($\lesssim 0.1-1$ km), low velocity objects: (1) small planetesimals sediment towards the midplane of the nebula forming ve…
We explore the effect of magnetorotational turbulence on the dynamics and concentrations of boulders in local box simulations of a sub-Keplerian protoplanetary disc. The solids are treated as particles each with an independent space coordinate and velocity. We find that the turbulence has two effects on the solids. 1) Meter and decameter bodies are strongly concentrated, locally up to a factor 100 times the average dust density, whereas decimeter bodies only experience a moderate density increase. The concentrations are located in large scale radial gas density enhancements that arise from a c…
Formation of terrestrial planets by agglomeration of planetesimals in protoplanetary disks sensitively depends on the velocity evolution of planetesimals. We describe a novel semi-analytical approach to the treatment of planetesimal dynamics incorporating the gravitational scattering by massive protoplanetary bodies. Using this method we confirm that planets grow very slowly in the outer Solar System if gravitational scattering is the only process determining planetesimal velocities, making it hard for giant planets to acquire their massive gaseous envelopes within less than 10 Myr. We put for…
An unsolved issue in the standard core accretion model for gaseous planet formation is how kilometre-sized planetesimals form from, initially, micron-sized dust grains. Solid growth beyond metre sizes can be difficult both because the sticking efficiency becomes very small, and because these particles should rapidly migrate into the central star. We consider here how metre-sized particles evolve in self-gravitating accretion discs using simulations in which the gravitational influence of the solid particles is also included. Metre-sized particles become strongly concentrated in the spiral stru…
We investigate classical planetesimal accretion in a binary star system of separation ab<50AU by numerical simulations, with particular focus on the region at a distance of 1 AU from the primary. The planetesimals orbit the primary, are perturbed by the companion and are in addition subjected to a gas drag force. We concentrate on the problem of relative velocities dv among planetesimals of different sizes. For various stellar mass ratios and binary orbital parameters we determine regions where dv exceed planetesimal escape velocities v_esc (thus preventing runaway accretion) or even the thres…
We numerically explore planet formation around alpha Cen A by focusing on the crucial planetesimals-to-embryos phase. Our code computes the relative velocity distribution, and thus the accretion vs. fragmentation trend, of planetesimal populations having any given size distribution. This is a critical aspect of planet formation in binaries since the pericenter alignment of planetesimal orbits due to the gravitational perturbations of the companion star and to gas friction strongly depends on size. We find that, for the nominal case of a MMSN gas disc, the region beyond 0.5AU from the primary i…
The first challenge in the formation of both terrestrial planets and the cores of gas giants is the retention of grains in protoplanetary disks. In most regions of these disks, gas attains sub-Keplerian speeds as a consequence of a negative pressure gradient. Hydrodynamic drag leads to orbital decay and depletion of the solid material in the disk, with characteristic timescales as short as only a few hundred years for meter-sized objects at 1 AU. In this paper, we suggest a particle retention mechanism which promotes the accumulation of grains and the formation of planetesimals near the water …
We present the first observations of the circumstellar (CS) disk system 51 Ophiuchi with the Far Ultraviolet Spectroscopic Explorer. We detect several absorption lines arising from the unusual metastable atomic species NI (2D), NI (2P), and SII (2D). These levels lie 1.8 - 3.6 eV above the ground level and have radiative decay lifetimes of 2 days or less, indicating that the lines arise from warm CS gas. The high S/N FUSE spectra, obtained six days apart, also show time-variable absorption features arising from NI, NII, OI (1D), and FeIII, which are redshifted with respect to the stellar veloc…
