We study the conditions for collisions between planetesimals to be accretional or disruptive in turbulent disks, through analytical arguments based on fluid dynamical simulations and orbital integrations. In turbulent disks, the velocity dispersion of planetesimals is pumped up by random gravitational perturbations from density fluctuations of the disk gas. When the velocity dispersion is larger than the planetesimals' surface escape velocity, collisions between planetesimals do not result in accretion, and may even lead to their destruction. In disks with a surface density equal to that of the ``minimum mass solar nebula'' and with nominal MRI turbulence, we find that accretion proceeds only for planetesimals with sizes above $\sim 300$ km at 1AU and $\sim 1000$ km at 5AU. We find that accretion is facilitated in disks with smaller masses. However, at 5AU and for nominal turbulence strength, km-sized planetesimals are in a highly erosive regime even for a disk mass as small as a fraction of the mass of Jupiter. The existence of giant planets implies that either turbulence was weaker than calculated by standard MRI models or some mechanism was capable of producing Ceres-mass planetesimals in very short timescales. In any case, our results show that in the presence of turbulence planetesimal accretion is most difficult in massive disks and at large orbital distances.
The formation of planetesimals in protoplanetary disks due to collisional sticking of smaller dust aggregates has to face at least two severe obstacles, namely the rapid loss of material due to radial inward drift and particle fragmentation due to destructive collisions. We present a scenario to circumvent these two hurdles. Our dust evolution model involves two main mechanisms. First, we consider a disk with a dead zone. In an almost laminar region close to the midplane, the relative velocities of the turbulent particles are comparatively small, which decreases the probability of destructive …
We show that small solids in low mass, turbulent protoplanetary disks collect into self-gravitating rings. Growth is faster than disk lifetimes and radial drift times for moderately strong turbulence, characterized by dimensionless diffusivities, $α_g < 10^{-6} -- 10^{-3}$ when particles are mm-sized. This range reflects a strong dependance on disk models. Growth is faster for higher particle surface densities. Lower gas densities and larger solids also give faster growth, as long as aerodynamic coupling is tight. In simple power law models, growth is slowest around ~0.3 AU, where drag couplin…
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…
This pedagogical review covers an unsolved problem in the theory of protoplanetary disks: the growth of dust grains into planetesimals, solids at least a kilometer in size. I summarize timescale constraints imposed on planetesimal formation by circumstellar disk observations, analysis of meteorites, and aerodynamic radial migration. The infall of ~meter-sized solids in a hundred years is the most stringent constraint. I review proposed mechanisms for planetesimal formation. Collisional coagulation models are informed by laboratory studies of microgravity collisions. The gravitational collapse …
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…
The debate over whether kilometer-sized solids, or planetesimals, assemble by collision-induced chemical sticking or by gravity-driven unstable modes remains unsettled. In light of recent work showing that gravitational growth can occur despite turbulent stirring, we critically evaluate the collisional hypothesis. Impact speeds in protoplanetary disks reach 50 m/s in a laminar disk and may be larger in turbulent disks. We consider the role of elastic and plastic deformations, restructuring of "rubble piles," and sticky organic matter. Coagulation is possible for dust grains with large surface …
Solid particles in protoplanetary disks that are sufficiently super-solar in metallicity overcome turbulence generated by vertical shear to gravitationally condense into planetesimals. Super-solar metallicities result if solid particles pile up as they migrate starward as a result of aerodynamic drag. Previous analyses of aerodynamic drift rates that account for mean flow differences between gas and particles yield particle pile-ups. We improve on these studies not only by accounting for the collective inertia of solids relative to that of gas, but also by including the transport of angular mo…
(Abridged).We present the results of MHD simulations of low mass protoplanets interacting with turbulent disks. We calculate the orbital evolution of `planetesimals' and protoplanets with masses in the range 0 < m_p < 30 M_Earth. Planetesimals and protoplanets undergo stochastic migration due to interaction with turbulent density fluctuations. Over run times of ~ 150 planet orbits, stochastic migration dominates over type I migration for many models. Fourier analysis of the torques experienced by planets indicates that the torque fluctuations contain components with significant power whose tim…
The interaction of a shock with a cloud has been extensively studied in the literature, where the effects of magnetic fields, radiative cooling and thermal conduction have been considered. However, the formation of fully developed turbulence has often been prevented by the artificial viscosity inherent in hydrodynamical simulations, and a uniform post-shock flow has been assumed in all previous single-cloud studies. In reality, the flow behind the shock is also likely to be turbulent, with non-uniform density, pressure and velocity structure created as the shock sweeps over inhomogenities upst…
It is difficult to imagine a planet formation model that does not at some stage include a gravitationally unstable disc. Initially unstable gas-dust discs may form planets directly, but the high surface density required has motivated the alternative that gravitational instability occurs in a dust sub-layer only after grains have grown large enough by electrostatic sticking. Although such growth up to the instability stage is efficient for laminar discs, concern has mounted as to whether realistic disc turbulence catastrophically increases the settling time, thereby requiring additional process…
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 analyze the gravitational collapse of solids subject to gas drag in a protoplanetary disk. We also study the stirring of solids by turbulent fluctuations to determine the velocity dispersion and thickness of the midplane particle layer. The usual thresholds for determining gravitational instability in disks, Toomre's criterion and/or the Roche density, do not apply. Dissipation of angular momentum allows instability at longer wavelengths, lower densities, and higher velocity dispersions than without drag. Small solids will slowly leak into axisymmetric rings since initial collapse occurs ov…
This document contains refereed supplementary information for the paper ``Rapid planetesimal formation in turbulent circumstellar discs''. It contains 15 sections (\S1.1 -- \S1.15) that address a number of subjects related to the main paper. We describe in detail the Poisson solver used to find the self-potential of the solid particles, including a linear and a non-linear test problem (\S1.3). Dissipative collisions remove energy from the motion of the particles by collisional cooling (\S1.4), an effect that allows gravitational collapse to occur in somewhat less massive discs (\S1.7). A resol…
To treat the problem of growing protoplanetary disc solids across the meter barrier, we consider a very simplified two-component coagulation-fragmentation model that consists of macroscopic boulders and smaller dust grains, the latter being the result of catastrophic collisions between the boulders. Boulders in turn increase their radii by sweeping up the dust fragments. An analytical solution to the dynamical equations predicts that growth by coagulation-fragmentation can be efficient and allow agglomeration of 10-meter-sized objects within the time-scale of the radial drift. These results ar…
We argue that massive stars are the dominant sources of energy for the turbulent motions within giant molecular clouds, and that the primary agent of feedback is the expansion of H II regions within the cloud volume. This conclusion is suggested by the low efficiency of star formation and corroborated by dynamical models of H II regions. We evaluate the turbulent energy input rate in clouds more massive than one third of a million solar masses, for which gravity does not significantly affect the expansion of H II regions. Such clouds achieve a balance between the decay of turbulent energy and …
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…
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…
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 …
We have studied dust evolution in a quiescent or turbulent protoplanetary disk by numerically solving coagulation equation for settling dust particles, using the minimum mass solar nebular model. As a result, if we assume an ideally quiescent disk, the dust particles settle toward the disk midplane to form a gravitationally unstable layer within 2x10^3 - 4x10^4 yr at 1 - 30 AU, which is in good agreement with an analytic calculation by Nakagawa, Sekiya, & Hayashi (1986) although they did not take into account the particle size distribution explicitly. In an opposite extreme case of a globally …
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…
The number of stars that are known to have debris disks is greater than that of stars known to harbour planets. These disks are detected because dust is created in the destruction of planetesimals in the disks much in the same way that dust is produced in the asteroid belt and Kuiper belt in the solar system. For the nearest stars the structure of their debris disks can be directly imaged, showing a wide variety of both axisymmetric and asymmetric structures. A successful interpretation of these images requires a knowledge of the dynamics of small bodies in planetary systems, since this allows…
The effect of smooth cloud boundaries on the interaction of steady planar shock waves with interstellar clouds is studied using a high-resolution local AMR technique with a second-order accurate axisymmetric Godunov hydrodynamic scheme. A 3D calculation is also done to confirm the results of the 2D ones. We consider an initially spherical cloud whose density distribution is flat near the cloud center and has a power-law profile in the cloud envelope. When an incident shock is transmitted into a smooth cloud, velocity gradients in the cloud envelope steepen the smooth density profile at the ups…
Two dimensional hydrodynamical disks are nonlinearly unstable to the formation of vortices. Once formed, these vortices essentially survive forever. What happens in three dimensions? We show with pseudospectral simulations that in 3D a vortex in a short box forms and survives just as in 2D. But a vortex in a tall box is unstable and is destroyed. In our simulation, the unstable vortex decays into a transient turbulent-like state that transports angular momentum outward at a nearly constant rate for hundreds of orbital times. The 3D instability that destroys vortices is a generalization of the …
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…
Terrestrial planets form in a series of dynamical steps from the solid component of circumstellar disks. First, km-sized planetesimals form likely via a combination of sticky collisions, turbulent concentration of solids, and gravitational collapse from micron-sized dust grains in the thin disk midplane. Second, planetesimals coalesce to form Moon- to Mars-sized protoplanets, also called "planetary embryos". Finally, full-sized terrestrial planets accrete from protoplanets and planetesimals. This final stage of accretion lasts about 10-100 Myr and is strongly affected by gravitational perturba…
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})…
