Cooling-induced Vortex Decay in Keplerian Disks

Vortices are readily produced by hydrodynamical instabilities, such as the Rossby wave instability, in protoplanetary disks. However, large-scale asymmetries indicative of dust-trapping vortices are uncommon in submillimeter continuum observations. One possible explanation is that vortices have short lifetimes. In this paper, we explore how radiative cooling can lead to vortex decay. Elliptical vortices in Keplerian disks go through adiabatic heating and cooling cycles. Radiative cooling modifies these cycles and generates baroclinicity that changes the potential vorticity of the vortex. We show that the net effect is typically a spin down, or decay, of the vortex for a subadiabatic radial stratification. We perform a series of two-dimensional shearing box simulations, varying the gas cooling (or relaxation) time, t cool, and initial vortex strength. We measure the vortex decay half-life, t half, and find that it can be roughly predicted by the timescale ratio t cool/t turn, where t turn is the vortex turnaround time. Decay is slow in both the isothermal (t cool ≪ t turn) and adiabatic (t cool ≫ t turn) limits; it is fastest when t cool ∼ 0.1 t turn, where t half is as short as ∼300 orbits. At tens of astronomical units where disk rings are typically found, t turn is likely much longer than t cool, potentially placing vortices in the fast decay regime.

Dust trapping around Lagrangian points in protoplanetary disks

Aims. Trojans are defined as objects that share the orbit of a planet at the stable Lagrangian points L4 and L5. In the Solar System, these bodies show a broad size distribution ranging from micrometer (μm) to centimeter (cm) particles (Trojan dust) and up to kilometer (km) rocks (Trojan asteroids). It has also been theorized that earth-like Trojans may be formed in extra-solar systems. The Trojan formation mechanism is still under debate, especially theories involving the effects of dissipative forces from a viscous gaseous environment. Methods. We perform hydro-simulations to follow the evolution of a protoplanetary disk with an embedded 1–10 Jupiter-mass planet. On top of the gaseous disk, we set a distribution of μm–cm dust particles interacting with the gas. This allows us to follow dust dynamics as solids get trapped around the Lagrangian points of the planet. Results. We show that large vortices generated at the Lagrangian points are responsible for dust accumulation, where the leading Lagrangian point L4 traps a larger amount of submillimeter (submm) particles than the trailing L5, which traps mostly mm–cm particles. However, the total bulk mass, with typical values of ~Mmoon, is more significant in L5 than in L4, in contrast to what is observed in the current Solar System a few gigayears later. Furthermore, the migration of the planet does not seem to affect the reported asymmetry between L4 and L5. Conclusions. The main initial mass reservoir for Trojan dust lies in the same co-orbital path of the planet, while dust migrating from the outer region (due to drag) contributes very little to its final mass, imposing strong mass constraints for the in situ formation scenario of Trojan planets.

The evolution of large cavities and disc eccentricity in circumbinary discs

ABSTRACT We study the mutual evolution of the orbital properties of high-mass ratio, circular, co-planar binaries and their surrounding discs, using 3D Smoothed Particle Hydrodynamics simulations. We investigate the evolution of binary and disc eccentricity, cavity structure, and the formation of orbiting azimuthal overdense features in the disc. Even with circular initial conditions, all discs with mass ratios q > 0.05 develop eccentricity. We find that disc eccentricity grows abruptly after a relatively long time-scale (∼400–700 binary orbits), and is associated with a very small increase in the binary eccentricity. When disc eccentricity grows, the cavity semimajor axis reaches values $a_{\rm cav}\approx 3.5\, a_{\rm bin}$. We also find that the disc eccentricity correlates linearly with the cavity size. Viscosity and orbit crossing appear to be responsible for halting the disc eccentricity growth – eccentricity at the cavity edge in the range ecav ∼ 0.05–0.35. Our analysis shows that the current theoretical framework cannot fully explain the origin of these evolutionary features when the binary is almost circular (ebin ≲ 0.01); we speculate about alternative explanations. As previously observed, we find that the disc develops an azimuthal overdense feature in Keplerian motion at the edge of the cavity. A low-contrast overdensity still co-moves with the flow after 2000 binary orbits; such an overdensity can in principle cause significant dust trapping, with important consequences for protoplanetary disc observations.

Dynamical signatures of Rossby vortices in cavity-hosting disks

Context. Planets are formed amidst young circumstellar disks of gas and dust. The latter is traced by thermal radiation, where strong asymmetric clumps have been observed in a handful of cases. These dust traps could be key to understanding the early stages of planet formation, when solids grow from micron-size to planetesimals. Aims. Vortices are among the few known asymmetric dust trapping scenarios. The present work aims to predict their characteristics in a complementary observable. Namely, line-of-sight velocities are well suited to trace the presence of a vortex. Moreover, the dynamics of disks is subject to recent developments. Methods. Two-dimensional hydro simulations were performed in which a vortex forms at the edge of a gas-depleted region. We derived idealized line-of-sight velocity maps, varying disk temperature and orientation relative to the observer. The signal of interest, as a small perturbation to the dominant axisymmetric component in velocity, may be isolated in observational data using a proxy for the dominant quasi-Keplerian velocity. We propose that the velocity curve on the observational major axis be such a proxy. Results. Applying our method to the disk around HD 142527 as a study case, we predict that line-of-sight velocities are barely detectable by currently available facilities, depending on disk temperature. We show that corresponding spirals patterns can also be detected with similar spectral resolutions, which will help to test against alternative explanations.

The observational impact of dust trapping in self-gravitating discs

ABSTRACT We present a 3D semi-analytical model of self-gravitating discs, and include a prescription for dust trapping in the disc spiral arms. Using Monte Carlo radiative transfer, we produce synthetic ALMA (Atacama Large Millimeter/submillimeter Array) observations of these discs. In doing so, we demonstrate that our model is capable of producing observational predictions, and able to model real image data of potentially self-gravitating discs. For a disc to generate spiral structure that would be observable with ALMA requires that the disc’s dust mass budget is dominated by millimetre- and centimetre-sized grains. Discs in which grains have grown to the grain fragmentation threshold may satisfy this criterion; thus, we predict that signatures of gravitational instability may be detectable in discs of lower mass than has previously been suggested. For example, we find that discs with disc-to-star mass ratios as low as 0.10 are capable of driving observable spiral arms. Substructure becomes challenging to detect in discs where no grain growth has occurred or in which grain growth has proceeded well beyond the grain fragmentation threshold. We demonstrate how we can use our model to retrieve information about dust trapping and grain growth through multiwavelength observations of discs, and using estimates of the opacity spectral index. Applying our disc model to the Elias 27, WaOph 6, and IM Lup systems, we find gravitational instability to be a plausible explanation for the observed substructure in all three discs, if sufficient grain growth has indeed occurred.

A dusty origin for the correlation between protoplanetary disc accretion rates and dust masses

ABSTRACT Recent observations have uncovered a correlation between the accretion rates (measured from the UV continuum excess) of protoplanetary discs and their masses inferred from observations of the submm continuum. While viscous evolution models predict such a correlation, the predicted values are in tension with data obtained from the Lupus and Upper Scorpius star-forming regions; for example, they underpredict the scatter in accretion rates, particularly in older regions. Here, we argue that since the submm observations trace the discs’ dust, by explicitly modelling the dust grain growth, evolution, and emission, we can better understand the correlation. We show that for turbulent viscosities with α ≲ 10−3, the depletion of dust from the disc due to radial drift means we can reproduce the range of masses and accretion rates seen in the Lupus and Upper Sco data sets. One consequence of this model is that the upper locus of accretion rates at a given dust mass does not evolve with the age of the region. Moreover, we find that internal photoevaporation is necessary to produce the lowest accretion rates observed. In order to replicate the correct dust masses at the time of disc dispersal, we favour relatively low photoevaporation rates ≲ 10−9 M⊙ yr−1 for most sources but cannot discriminate between EUV or X-ray-driven winds. A limited number of sources, particularly in Lupus, are shown to have higher masses than predicted by our models which may be evidence for variations in the properties of the dust or dust trapping induced in substructures.

Migrating low-mass planets in inviscid dusty protoplanetary discs

ABSTRACT Disc-driven planet migration is integral to the formation of planetary systems. In standard, gas-dominated protoplanetary discs, low-mass planets or planetary cores undergo rapid inwards migration and are lost to the central star. However, several recent studies indicate that the solid component in protoplanetary discs can have a significant dynamical effect on disc–planet interaction, especially when the solid-to-gas mass ratio approaches unity or larger and the dust-on-gas drag forces become significant. As there are several ways to raise the solid abundance in protoplanetary discs, for example through disc winds and dust trapping in pressure bumps, it is important to understand how planets migrate through a dusty environment. To this end, we study planet migration in dust-rich discs via a systematic set of high-resolution, two-dimensional numerical simulations. We show that the inwards migration of low-mass planets can be slowed down by dusty dynamical corotation torques. We also identify a new regime of stochastic migration applicable to discs with dust-to-gas mass ratios of ≳0.3 and particle Stokes numbers ≳0.03. In these cases, disc–planet interaction leads to the continuous development of small-scale, intense dust vortices that scatter the planet, which can potentially halt or even reverse the inwards planet migration. We briefly discuss the observational implications of our results and highlight directions for future work.

Theoretical and experimental study on the effective area of water film and dust removal efficiency

We investigate the capture process of dust flow through a vibrating wire, water fog, and a water film to address the problem of excessively high exhaust dust concentrations in mine exhaust shafts according to the theory of liquid-solid flow and capillary film formation. Functional expressions of the thickness and height of dust-trapping water film are derived by using Young-Laplace equations and Navier-Stokes equations, respectively. The theoretical relationship between the effective water film area and dedusting efficiency on a vibrating wire is obtained.The dedusting efficiency of a resonant chord grid is measured experimentally.The results show that wire spacing plays a decisive role in water film formation.The instantaneous effective water film area of the vibrating wire grid is proportional to the dedusting efficiency. When the diameter distance ratio of the resonance chord grid was 1.14 with the dedusting wind speed controlled at 3 m/s and a spray pressure of 0.7 MPa. The total dust control efficiency can reach > 92%.