The streaming instability is a promising mechanism to drive the formation of planetesimals in protoplanetary disks. To trigger this process, it has been argued that sedimentation of solids onto the ...mid-plane needs to be efficient, and therefore that a quiescent gaseous environment is required. It is often suggested that dead-zone or disk-wind structure created by non-ideal magnetohydrodynamical (MHD) effects meets this requirement. However, simulations have shown that the mid-plane of a dead zone is not completely quiescent. In order to examine the concentration of solids in such an environment, we use the local-shearing-box approximation to simulate a particle-gas system with an Ohmic dead zone including mutual drag force between the gas and the solids. We systematically compare the evolution of the system with ideal or non-ideal MHD, with or without backreaction drag force from particles on gas, and with varying solid abundances. Similar to previous investigations of dead-zone dynamics, we find that particles of dimensionless stopping time do not sediment appreciably more than those in ideal magnetorotational turbulence, resulting in a vertical scale height an order of magnitude larger than in a laminar disk. Contrary to the expectation that this should curb the formation of planetesimals, we nevertheless find that strong clumping of solids still occurs in the dead zone when solid abundances are similar to the critical value for a laminar environment. This can be explained by the weak radial diffusion of particles near the mid-plane. The results imply that the sedimentation of particles to the mid-plane is not a necessary criterion for the formation of planetesimals by the streaming instability.
A recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals,
may not be as efficient as previously thought. Under some disc ...conditions, the growth time-scale of the instability can be longer
than the disc lifetime when multiple dust species are considered. To further explore this finding, we use both linear analysis and
direct numerical simulations with gas fluid and dust particles tomutually validate and study the unstablemodes of the instability in
more detail.We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution
Ts, min, Ts, max and the total solid-to-gas mass ratio ε and introduce a third dimension with the slope q of the size distribution.
We find that the fast-growth regime and the slow-growth regime are distinctly separated in the ε–Ts, max space, while this boundary
is not appreciably sensitive to q or Ts, min.With a wide range of dust sizes present in the disc (e.g. Ts, min 10−3), the growth rate
in the slow-growth regime decreases as more dust species are considered.With a narrow range of dust sizes (e.g. Ts, max/Ts, min =
5), on the other hand, the growth rate in most of the ε–Ts, max space is converged with increasing dust species, but the fast and the
slow growth regimes remain clearly separated. Moreover, it is not necessary that the largest dust species dominate the growth of
the unstable modes, and the smaller dust species can affect the growth rate in a complicated way. In any case, we find that the
fast-growth regime is bounded by ε 1 or Ts, max 1, which may represent the favourable conditions for planetesimal formation.
The streaming instability is a mechanism to concentrate solid particles into overdense filaments that undergo gravitational collapse and form planetesimals. However, it remains unclear how the ...initial mass function of these planetesimals depends on the box dimensions of numerical simulations. To resolve this, we perform simulations of planetesimal formation with the largest box dimensions to date, allowing planetesimals to form simultaneously in multiple filaments that can only emerge within such large simulation boxes. In our simulations, planetesimals with sizes between 80 km and several hundred kilometers form. We find that a power law with a rather shallow exponential cutoff at the high-mass end represents the cumulative birth mass function better than an integrated power law. The steepness of the exponential cutoff is largely independent of box dimensions and resolution, while the exponent of the power law is not constrained at the resolutions we employ. Moreover, we find that the characteristic mass scale of the exponential cutoff correlates with the mass budget in each filament. Together with previous studies of high-resolution simulations with small box domains, our results therefore imply that the cumulative birth mass function of planetesimals is consistent with an exponentially tapered power law with a power-law exponent of approximately −1.6 and a steepness of the exponential cutoff in the range of 0.3–0.4.
Abstract
Giant planets have been discovered at large separations from the central star. Moreover, a striking number of young circumstellar disks have gas and/or dust gaps at large orbital ...separations, potentially driven by embedded planetary objects. To form massive planets at large orbital separations through core accretion within the disk lifetime, however, an early solid body to seed pebble and gas accretion is desirable. Young protoplanetary disks are likely self-gravitating, and these gravitoturbulent disks may efficiently concentrate solid material at the midplane driven by spiral waves. We run 3D local hydrodynamical simulations of gravitoturbulent disks with Lagrangian dust particles to determine whether particle and gas self-gravity can lead to the formation of dense solid bodies, seeding later planet formation. When self-gravity between dust particles is included, solids of size St = 0.1–1 concentrate within the gravitoturbulent spiral features and collapse under their own self-gravity into dense clumps up to several
M
⊕
in mass at wide orbits. Simulations with dust that drift most efficiently, St = 1, form the most massive clouds of particles, while simulations with smaller dust particles, St = 0.1, have clumps with masses an order of magnitude lower. When the effect of dust backreaction onto the gas is included, dust clumps become smaller by a factor of a few but more numerous. The existence of large solid bodies at an early stage of the disk can accelerate the planet formation process, particularly at wide orbital separations, and potentially explain planets distant from the central stars and young protoplanetary disks with substructures.
The radial drift and diffusion of dust particles in protoplanetary disks affect both the opacity and temperature of such disks, as well as the location and timing of planetesimal formation. In this ...paper, we present results of numerical simulations of particle-gas dynamics in protoplanetary disks that include dust grains with various size distributions. We have considered three scenarios in terms of particle size ranges, one where the Stokes number τs = 10−1−100, one where τs = 10−4−10−1, and finally one where τs = 10−3−100. Moreover, we considered both discrete and continuous distributions in particle size. In accordance with previous works we find in our multispecies simulations that different particle sizes interact via the gas and as a result their dynamics changes compared to the single-species case. The larger species trigger the streaming instability and create turbulence that drives the diffusion of the solid materials. We measured the radial equilibrium velocity of the system and find that the radial drift velocity of the large particles is reduced in the multispecies simulations and that the small particle species move on average outwards. We also varied the steepness of the size distribution, such that the exponent of the solid number density distribution, dN∕da ∝ a−q, is either q = 3 or q = 4. Overall, we find that the steepness of the size distribution and the discrete versus continuous approach have little impact on the results. The level of diffusion and drift rates are mainly dictated by the range of particle sizes. We measured the scale height of the particles and observe that small grains are stirred up well above the sedimented midplane layer where the large particles reside. Our measured diffusion and drift parameters can be used in coagulation models for planet formation as well as to understand relative mixing of the components of primitive meteorites (matrix, chondrules and CAIs) prior to inclusion in their parent bodies.
The streaming instability is a fundamental process that can drive dust–gas dynamics and ultimately planetesimal formation inprotoplanetary discs. As a linear instability, it has been shown that its ...growth with a distribution of dust sizes can be classifiedinto two distinct regimes, fast- and slow-growth, depending on the dust-size distribution and the total dust-to-gas density ratio . Using numerical simulations of an unstratified disc, we bring three cases in different regimes into non-linear saturation. Wefind that the saturation states of the two fast-growth cases are similar to its single-species counterparts. The one with maximumdimensionless stopping timeτs,max=0.1 and =2 drives turbulent vertical dust–gas vortices, while the other withτs,max=2and =0.2 leads to radial traffic jams and filamentary structures of dust particles. The dust density distribution for the former isflat in low densities, while the one for the latter has a low-end cut-off. By contrast, the one slow-growth case results in a virtuallyquiescent state. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particlesmoving towards dense regions while small particles remain in the diffuse regions, and the mean radial drift of each dust speciesis appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived frommultiwavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latteralong with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary discs.
Abstract
We investigate the utility of deep learning for modeling the clustering of particles that are aerodynamically coupled to turbulent fluids. Using a Lagrangian particle module within the ...Athena++ hydrodynamics code, we simulate the dynamics of particles in the Epstein drag regime within a periodic domain of isotropic forced hydrodynamic turbulence. This setup is an idealized model relevant to the collisional growth of micron- to millimeter-sized dust particles in early-stage planet formation. The simulation data are used to train a U-Net deep-learning model to predict gridded three-dimensional representations of the particle density and velocity fields, given as input the corresponding fluid fields. The trained model qualitatively captures the filamentary structure of clustered particles in a highly nonlinear regime. We assess model fidelity by calculating metrics of the density field (the radial distribution function) and of the velocity field (the relative velocity and the relative radial velocity between particles). Although trained only on the spatial fields, the model predicts these statistical quantities with errors that are typically <10%. Our results suggest that, given appropriately expanded training data, deep learning could complement direct numerical simulations in predicting particle clustering within turbulent flows.
ABSTRACT Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in ...observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff-particularly because of small particles and/or strong local solid concentration-that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.
Abstract
Pebble accretion is recognized as a significant accelerator of planet formation. Yet only formulae for single-sized (monodisperse) distribution have been derived in the literature. These can ...lead to significant underestimates for Bondi accretion, for which the best accreted pebble size may not be the one that dominates the mass distribution. We derive in this paper the polydisperse theory of pebble accretion. We consider a power-law distribution in pebble radius, and we find the resulting surface and volume number density distribution functions. We derive also the exact monodisperse analytical pebble accretion rate for which 3D accretion and 2D accretion are limits. In addition, we find analytical solutions to the polydisperse 2D Hill and 3D Bondi limits. We integrate the polydisperse pebble accretion numerically for the MRN distribution, finding a slight decrease (by an exact factor 3/7) in the Hill regime compared to the monodisperse case. In contrast, in the Bondi regime, we find accretion rates 1–2 orders of magnitude higher compared to monodisperse, also extending the onset of pebble accretion to 1–2 orders of magnitude lower in mass. We find megayear timescales, within the disk lifetime, for Bondi accretion on top of planetary seeds of masses 10
−6
to 10
−4
M
⊕
, over a significant range of the parameter space. This mass range overlaps with the high-mass end of the planetesimal initial mass function, and thus pebble accretion is possible directly following formation by streaming instability. This alleviates the need for mutual planetesimal collisions as a major contribution to planetary growth.
Observations show that radial metallicity gradients in disk galaxies are relatively shallow, if not flat, especially at large galactocentric distances and for galaxies in the high-redshift universe. ...Given that star formation and metal production are centrally concentrated, this requires a mechanism to redistribute metals. However, the nature of this mechanism is poorly understood, let alone quantified. To address this problem, we conduct magnetohydrodynamical simulations of a local shearing sheet of a thin, thermally unstable, gaseous disk driven by a background stellar spiral potential, including metals modeled as passive scalar fields. Contrary to what a simple a prescription for the gas disk would suggest, we find that turbulence driven by thermal instability is very efficient at mixing metals, regardless of the presence or absence of stellar spiral potentials or magnetic fields. The timescale for homogenizing randomly distributed metals is comparable to or less than the local orbital time in the disk. This implies that turbulent mixing of metals is a significant process in the history of chemical evolution of disk galaxies.
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