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Register a new userThe fate of planetesimals in turbulent disks with dead zones. II. Limits on the viability of runaway accretion
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A critical phase in the standard model for planet formation is the runaway growth phase. During runaway growth bodies in the 0.1--100 km size range (planetesimals) quickly produce a number of much larger seeds. The runaway growth phase is essential for planet formation as the emergent planetary embryos can accrete the leftover planetesimals at large gravitational focusing factors. However, torques resulting from turbulence-induced density fluctuations may violate the criterion for the onset of runaway growth, which is that the magnitude of the planetesimals random (eccentric) motions are less than their escape velocity. This condition represents a more stringent constraint than the condition that planetesimals survive their mutual collisions. To investigate the effects of MRI turbulence on the viability of the runaway growth scenario, we apply our semi-analytical recipes of Paper I, which we augment by a coagulation/fragmentation model for the dust component. We find that the surface area-equivalent abundance of 0.1 micron particles is reduced by factors 10^2--10^3, which tends to render the dust irrelevant to the turbulence. We express the turbulent activity in the midplane regions in terms of a size s_run above which planetesimals will experience runaway growth. We find that s_run is mainly determined by the strength of the vertical net field that threads the disks and the disk radius. At disk radii beyond 5 AU, s_run becomes larger than ~100 km and the collision times among these bodies longer than the duration of the nebula phase. Our findings imply that the classical, planetesimal-dominated, model for planet formation is not viable in the outer regions of a turbulent disk.
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Low mass, self-gravitating accretion disks admit quasi-steady,`gravito-turbulent states in which cooling balances turbulent viscous heating. However, numerical simulations show that gravito-turbulence cannot be sustained beyond dynamical timescales when the cooling rate or corresponding turbulent viscosity is too large. The result is disk fragmentation. We motivate and quantify an interpretation of disk fragmentation as the inability to maintain gravito-turbulence due to formal secondary instabilities driven by: 1) cooling, which reduces pressure support; and/or 2) viscosity, which reduces rotational support. We analyze the axisymmetric gravitational stability of viscous, non-adiabatic accretion disks with internal heating, external irradiation, and cooling in the shearing box approximation. We consider parameterized cooling functions in 2D and 3D disks, as well as radiative diffusion in 3D. We show that generally there is no critical cooling rate/viscosity below which the disk is formally stable, although interesting limits appear for unstable modes with lengthscales on the order of the disk thickness. We apply this new linear theory to protoplanetary disks subject to gravito-turbulence modeled as an effective viscosity, and cooling regulated by dust opacity. We find that viscosity renders the disk beyond $sim 60$AU dynamically unstable on radial lengthscales a few times the local disk thickness. This is coincident with the empirical condition for disk fragmentation based on a maximum sustainable stress. We suggest turbulent stresses can play an active role in realistic disk fragmentation by removing rotational stabilization against self-gravity, and that the observed transition in behavior from gravito-turbulent to fragmenting may reflect instability of the gravito-turbulent state itself.
Many massive objects have been found in the outer region of the Solar system. How they were formed and evolved has not been well understood, although there have been intensive studies on accretion process of terrestrial planets. One of the mysteries is the existence of binary planetesimals with near-equal mass components and highly eccentric orbits. These binary planetesimals are quite different from the satellites observed in the asteroid belt region. The ratio of the Hill radius to the physical radius of the planetesimals is much larger for the outer region of the disk, compared to the inner region of the disk. The Hill radius increases with the semi major axis. Therefore, planetesimals in the outer region can form close and eccentric binaries, while those in the inner region would simply collide. In this paper, we carried out $N$-body simulations in different regions of the disk and studied if binaries form in the outer region of the disk. We found that large planetesimals tend to form binaries. A significant fraction of large planetesimals are components of the binaries. Planetesimals that become the components of binaries eventually collide with a third body, through three-body encounters. Thus, the existence of binaries can enhance the growth rate of planetesimals in the Trans-Neptunian Object (TNO) region.
The presence of rings and gaps in protoplanetary discs are often ascribed to planet-disc interactions, where dust and pebbles are trapped at the edges of planetary induced gas gaps. Recent work has shown that these are likely sites for planetesimal formation via the streaming instability. Given the large amount of planetesimals that potentially form at gap edges, we address the question of their fate and ability to radially transport solids in protoplanetary discs. We perform a series of N-body simulations of planetesimal orbits, taking into account the effect of gas drag and mass loss via ablation. We consider two planetary systems: one akin to the young Solar System, and another one inspired by HL Tau. In both systems, the close proximity to the gap-opening planets results in large orbital excitations, causing the planetesimals to leave their birth locations and spread out across the disc soon after formation. Planetesimals that end up on eccentric orbits interior of 10au experience efficient ablation, and lose all mass before they reach the innermost disc region. In our nominal Solar System simulation with $dot{M}_0=10^{-7}, M_{odot}, textrm{yr}^{-1}$ and $alpha=10^{-2}$, we find that 70% of the initial planetesimal mass has been ablated after 500kyr. The ablation rate in HL Tau is lower, and only 11% of the initial planetesimal mass has been ablated after 1Myr. The ablated material consist of a mixture of solid grains and vaporized ices, where a large fraction of the vaporized ices re-condense to form solid ice. Assuming that the solids grow to pebbles in the disc midplane, this results in a pebble flux of $sim 10-100,M_{oplus}textrm{Myr}^{-1}$ through the inner disc. Our results demonstrate that scattered planetesimals can carry a significant flux of solids past planetary-induced gaps in young and massive protoplanetary discs.
When an accretion disk falls prey to the runaway instability, a large portion of its mass is devoured by the black hole within a few dynamical times. Despite decades of effort, it is still unclear under what conditions such an instability can occur. The technically most advanced relativistic simulations to date were unable to find a clear sign for the onset of the instability. In this work, we present three-dimensional relativistic hydrodynamics simulations of accretion disks around black holes in dynamical space-time. We focus on the configurations that are expected to be particularly prone to the development of this instability. We demonstrate, for the first time, that the fully self-consistent general relativistic evolution does indeed produce a runaway instability.
We calculate the chemical evolution of protoplanetary disks considering radial viscous accretion, vertical turbulent mixing and vertical disk winds. We study the effects on the disk chemical structure when different models for the formation of molecular hydrogen on dust grains are adopted. Our gas-phase chemistry is extracted from the UMIST Database for Astrochemistry (Rate06) to which we have added detailed gas-grain interactions. We use our chemical model results to generate synthetic near- and mid-infrared LTE line emission spectra and compare these with recent Spitzer observations. Our results show that if H2 formation on warm grains is taken into consideration, the H2O and OH abundances in the disk surface increase significantly. We find the radial accretion flow strongly influences the molecular abundances, with those in the cold midplane layers particularly affected. On the other hand, we show that diffusive turbulent mixing affects the disk chemistry in the warm molecular layers, influencing the line emission from the disk and subsequently improving agreement with observations. We find that NH3, CH3OH, C2H2 and sulphur-containing species are greatly enhanced by the inclusion of turbulent mixing. We demonstrate that disk winds potentially affect the disk chemistry and the resulting molecular line emission in a similar manner to that found when mixing is included.
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