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Abstract The streaming instability (SI) is a leading mechanism for concentrating solid particles into regions dense enough to form planetesimals. Its efficiency in clumping particles depends primarily on the dimensionless stopping time (τ_s, a proxy for particle size) and dust-to-gas surface density ratio (Z). Previous simulations identified a criticalZ(Z_crit) above which strong clumping occurs, where particle densities exceed the Hill density (thus satisfying a condition for gravitational collapse), over a wide range ofτ_s. These works found that, forτ_s≤ 0.01,Z_critwas above the interstellar medium value (∼0.01). In this work, we reexamine the clumping threshold using 2D axisymmetric, stratified simulations at high resolution and with relatively large (compared to many previous simulations) domain sizes. Our main results are as follows: First, whenτ_s = 0.01, strong clumping occurs even atZ ≲ 0.01, lower thanZ_critfound in all previous studies. Consequently, we revise a previously published fit to theZ_critcurve to account for this updatedZ_crit. Second, higher resolution results in a thicker dust layer, which may result from other instabilities manifesting, such as the vertically shearing SI. Third, despite this thicker layer, higher resolution can lead to strong clumping even with a lower midplane dust-to-gas density ratios (which results from the thicker particle layer) so long asZ ≳ Z_crit. Our results demonstrate the efficiency of the SI in clumping small particles atZ ∼ 0.01, which is a significant refinement of the conditions for planetesimal formation by the SI. 

Abstract The Rossby wave instability (RWI) is the fundamental nonaxisymmetric radial shear instability in disks. The RWI can facilitate disk accretion, set the shape of planetary gaps, and produce large vortices. It arises from density and/or temperature features, such as radial gaps, bumps, or steps. A general, sufficient condition to trigger the RWI is lacking, which we address by studying the linear RWI in a suite of simplified models, including incompressible and compressible shearing sheets and global, cylindrical disks. We focus on enthalpy amplitude and width as the fundamental properties of disk features with various shapes. We find analytic results for the RWI boundary and growth rates across a wide parameter space, in some cases with exact derivations and in others as a description of numerical results. Features wider than a scale height generally become unstable about halfway to Rayleigh instability, i.e., when the squared epicyclic frequency is about half the Keplerian value, reinforcing our previous finding. RWI growth rates approximately scale as enthalpy amplitude to the 1/3 power, with a weak dependence on width, across much of the parameter space. Global disk curvature affects wide planetary gaps, making the outer gap edge more susceptible to the RWI. Our simplified models are barotropic and height integrated, but the main results should carry over to more complex and realistic scenarios. 

Abstract A high-resolution fourth-order Padé scheme is used to simulate locally isothermal 3D disk turbulence driven by the vertical shear instability (VSI) using 268.4 M points. In the early nonlinear period of axisymmetric VSI, angular momentum transport by vertical jets creates correlatedN-shaped radial profiles of perturbation vertical and azimuthal velocity. This implies dominance of positive perturbation vertical vorticity layers and a recently discovered angular momentum staircase with respect to radius (r). These features are present in 3D in a weaker form. The 3D flow consists of vertically and azimuthally coherent turbulent shear layers containing small vortices with all three vorticity components active. Previously observed large persistent vortices in the interior of the domain driven by the Rossby wave instability are absent. We speculate that this is due to a weaker angular momentum staircase in 3D in the present simulations compared to a previous simulation. The turbulent viscosity parameterα(r) increases linearly withr. At intermediate resolution, the value ofα(r) at midradius is close to that of a previous simulation. The specific kinetic energy spectrum with respect to radial wavenumber has a power-law region with exponent −1.84, close to the value −2 expected for shear layers. The spectrum with respect to azimuthal wavenumber has a −5/3 region and lacks a −5 region reported in an earlier study. Finally, it is found that axisymmetric VSI has artifacts at late times, including a very strong angular momentum staircase, which in 3D is present weakly in the disk’s upper layers. 

Abstract Given the important role turbulence plays in the settling and growth of dust grains in protoplanetary disks, it is crucial that we determine whether these disks are turbulent and to what extent. Protoplanetary disks are weakly ionized near the midplane, which has led to a paradigm in which largely laminar magnetic field structures prevail deeper in the disk, with angular momentum being transported via magnetically launched winds. Yet, there has been little exploration of the precise behavior of the gas within the bulk of the disk. We carry out 3D, local shearing box simulations that include all three low-ionization effects (ohmic diffusion, ambipolar diffusion, and the Hall effect) to probe the nature of magnetically driven gas dynamics 1–30 au from the central star. We find that gas turbulence can persist with a generous yet physically motivated ionization prescription (order unity Elsässer numbers). The gas velocity fluctuations range from 0.03 to 0.09 of the sound speedc_sat the disk midplane to ∼c_snear the disk surface, and are dependent on the initial magnetic field strength. However, the turbulent velocities do not appear to be strongly dependent on the field polarity, and thus appear to be insensitive to the Hall effect. The midplane turbulence has the potential to drive dust grains to collision velocities exceeding their fragmentation limit, and likely reduces the efficacy of particle clumping in the midplane, though it remains to be seen if this level of turbulence persists in disks with lower ionization levels. 

Abstract Disk vortices, seen in numerical simulations of protoplanetary disks and found observationally in Atacama Large Millimeter/submillimeter Array and Very Large Array images of these objects, are promising sites for planet formation given their pebble trapping abilities. Previous works have shown a strong concentration of pebbles in vortices, but gravitational collapse has only been shown in low-resolution, two-dimensional, global models. In this Letter, we aim to study the pebble concentration and gravitational collapse of pebble clouds in vortices via high-resolution, three-dimensional, local models. We performed simulations of the dynamics of gas and solids in a local shearing box where the gas is subject to convective overstability, generating a persistent giant vortex. We find that the vortex produces objects of Moon and Mars mass, with a mass function of power-law $d\ln N/d\ln M=-1.6\pm 0.3$. The protoplanets grow rapidly, doubling in mass in about five orbits, following pebble accretion rates. The mass range and mass doubling rate are in broad agreement with previous low-resolution global models. We conclude that Mars-mass planetary embryos are the natural outcome of planet formation inside the disk vortices seen in millimeter and radio images of protoplanetary disks. 

Abstract The streaming instability (SI) is a leading candidate for planetesimal formation, which can concentrate solids through two-way aerodynamic interactions with the gas. The resulting concentrations can become sufficiently dense to collapse under particle self-gravity, forming planetesimals. Previous studies have carried out large parameter surveys to establish the critical particle to gas surface density ratio (Z), above which SI-induced concentration triggers planetesimal formation. The thresholdZdepends on the dimensionless stopping time (τ_s, a proxy for dust size). However, these studies neglected both particle self-gravity and external turbulence. Here, we perform 3D stratified shearing box simulations with both particle self-gravity and turbulent forcing, which we characterize via a turbulent diffusion parameter,α_D. We find that forced turbulence, at amplitudes plausibly present in some protoplanetary disks, can increase the thresholdZby up to an order of magnitude. For example, forτ_s= 0.01, planetesimal formation occurs whenZ≳ 0.06, ≳0.1, and ≳0.2 atα_D= 10⁻⁴, 10^−3.5, and 10⁻³, respectively. We provide a single fit to the criticalZrequired for the SI to work as a function ofα_Dandτ_s(although limited to the rangeτ_s= 0.01–0.1). Our simulations also show that planetesimal formation requires a mid-plane particle-to-gas density ratio that exceeds unity, with the critical value being largely insensitive toα_D. Finally, we provide an estimation of particle scale height that accounts for both particle feedback and external turbulence. 

ABSTRACT The streaming instability, a promising mechanism to drive planetesimal formation in dusty protoplanetary discs, relies on aerodynamic drag naturally induced by the background radial pressure gradient. This gradient should vary in discs, but its effect on the streaming instability has not been sufficiently explored. For this purpose, we use numerical simulations of an unstratified disc to study the non-linear saturation of the streaming instability with mono-disperse dust particles and survey a wide range of gradients for two distinct combinations of the particle stopping time and the dust-to-gas mass ratio. As the gradient increases, we find most kinematic and morphological properties increase but not always in linear proportion. The density distributions of tightly coupled particles are insensitive to the gradient whereas marginally coupled particles tend to concentrate by more than an order of magnitude as the gradient decreases. Moreover, dust–gas vortices for tightly coupled particles shrink as the gradient decreases, and we note higher resolutions are required to trigger the instability in this case. In addition, we find various properties at saturation that depend on the gradient may be observable and may help reconstruct models of observed discs dominated by streaming turbulence. In general, increased dust diffusion from stronger gradients can lower the concentration of dust filaments and can explain the higher solid abundances needed to trigger strong particle clumping and the reduced planetesimal formation efficiency previously found in vertically stratified simulations. 

Abstract Kuiper Belt objects (KBOs) show an unexpected trend, whereby large bodies have increasingly higher densities, up to five times greater than their smaller counterparts. Current explanations for this trend assume formation at constant composition, with the increasing density resulting from gravitational compaction. However, this scenario poses a timing problem to avoid early melting by decay of²⁶Al. We aim to explain the density trend in the context of streaming instability and pebble accretion. Small pebbles experience lofting into the atmosphere of the disk, being exposed to UV and partially losing their ice via desorption. Conversely, larger pebbles are shielded and remain icier. We use a shearing box model including gas and solids, the latter split into ices and silicate pebbles. Self-gravity is included, allowing dense clumps to collapse into planetesimals. We find that the streaming instability leads to the formation of mostly icy planetesimals, albeit with an unexpected trend that the lighter ones are more silicate-rich than the heavier ones. We feed the resulting planetesimals into a pebble accretion integrator with a continuous size distribution, finding that they undergo drastic changes in composition as they preferentially accrete silicate pebbles. The density and masses of large KBOs are best reproduced if they form between 15 and 22 au. Our solution avoids the timing problem because the first planetesimals are primarily icy and²⁶Al is mostly incorporated in the slow phase of silicate pebble accretion. Our results lend further credibility to the streaming instability and pebble accretion as formation and growth mechanisms. 

Abstract In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, Ω_L, is the local Keplerian frequency Ω_K. In terms of the standard dimensionless Shakura–Sunyaevαparameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by $\sqrt{\alpha }H$and $\sqrt{\alpha }c$, in whichHandcare the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where Ω_L≥ Ω_Kand show that, under these conditions, the characteristic length and velocity scales are respectively $\sqrt{\alpha /R\prime }H$and $\sqrt{\alpha R\prime }c$, where $R\prime \equiv {\mathrm{\Omega }}_L/{\mathrm{\Omega }}_K$is twice the Rossby number. It follows that $\alpha =\tilde{\alpha }/R\prime$, where $\sqrt{\tilde{\alpha }}c$is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For $R\prime >1$, the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation. 

Abstract High-resolution submillimeter observations of protoplanetary disks with ALMA have revealed that dust rings are common in large, bright disks. The leading explanation for these structures is dust trapping in a local gas pressure maximum, caused by an embedded planet or other dynamical process. Independent of origin, such dust traps should be stable for many orbits to collect significant dust. However, ringlike perturbations in gas disks are also known to trigger the Rossby wave instability (RWI). We investigate whether axisymmetric pressure bumps can simultaneously trap dust and remain stable to the RWI. The answer depends on the thermodynamic properties of pressure bumps. For isothermal bumps, dust traps are RWI stable for widths from ∼1 to several gas scale heights. Adiabatic dust traps are stable over a smaller range of widths. For temperature bumps with no surface density component, however, all dust traps tend to be unstable. Smaller values of disk aspect ratio allow stable dust trapping at lower bump amplitudes and over a larger range of widths. We also report a new approximate criterion for RWI. Instability occurs when the radial oscillation frequency is ≲75% of the Keplerian frequency, which differs from the well-known Lovelace necessary (but not sufficient) criterion for instability. Our results can guide ALMA observations of molecular gas by constraining the resolution and sensitivity needed to identify the pressure bumps thought to be responsible for dust rings.