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The streaming instability (SI) is currently the leading candidate for triggering planetesimal formation in protoplanetary disks. Recently, a novel variation, the `azimuthal-drift' streaming instability (AdSI), was discovered in disks exhibiting laminar gas accretion. Unlike the classical SI, the AdSI does not require pressure gradients and can concentrate dust even at low abundances. We extend previous simulations of the AdSI to explore the impact of dust abundance, accretion flow strength, pressure gradients, and grain size. For a dimensionless accretion flow strength $\alpha_{\mathrm{M}}=0.1$ and particle Stokes number $\operatorname{St}=0.1$, we find the AdSI produces dust filaments for initial dust-to-gas ratios as low as $\epsilon=0.01$. For $\epsilon\gtrsim 1$, maximum dust-to-gas ratios of order 100 are attained, which can be expected to undergo gravitational collapse. Furthermore, even in systems dominated by the classical SI, an accretion flow drives filament formation, without which the disk remains in a state of small-scale turbulence. Our results suggest that an underlying accretion flow facilitates dust concentration and may thus promote planetesimal formation., Comment: 16 pages, 16 figures, Accepted by ApJ

We investigate the formation of dust traffic jams in polar-aligning circumbinary discs. In our first paper, we found as the circumbinary disc evolves towards a polar configuration perpendicular to the binary orbital plane, the differential precession between the gas and dust components leads to multiple dust traffic jams. These dust traffic jams evolve to form a coherent dust ring. In part two, we use 3D smoothed particle hydrodynamical simulations of gas and dust to model an initially highly misaligned circumbinary disc around the 99 Herculis (99 Her) binary system. Our results reveal that the formation of these dust rings is observed across various disc parameters, including the disc aspect ratio, viscosity, surface density power law index, and temperature power law index. The dust traffic jams are long-lived and persist even when the disc is fully aligned polar. The midplane dust-to-gas ratio within the rings can surpass unity, which may be a favourable environment for planetesimal formation. Using 2D inviscid shearing box calculations with parameters from our 3D simulations, we find streaming instability modes with significant growth rates. The streaming instability growth timescale is less than the tilt oscillation timescale during the alignment process. Therefore, the dust ring will survive once the gas disc aligns polar, suggesting that the streaming instability may aid in forming polar planets around 99 Her., Comment: 13 pages, 11 figures, Accepted for publication in MNRAS

Rings and gaps are routinely observed in the dust continuum emission of protoplanetary discs (PPDs). How they form and evolve remains debated. Previous studies have demonstrated the possibility of spontaneous gas rings and gaps formation in wind-launching disks. Here, we show that such gas substructures are unstable to the Rossby Wave Instability (RWI) through numerical simulations. Specifically, shorter wavelength azimuthal modes develop earlier, and longer wavelength ones dominate later, forming elongated (arc-like) anti-cyclonic vortices in the rings and (strongly magnetized) cyclonic vortices in the gaps that persist until the end of the simulation. Highly elongated vortices with aspect ratios of 10 or more are found to decay with time in our non-ideal MHD simulation, in contrast with the hydro case. This difference could be caused by magnetically induced motions, particularly strong meridional circulations with large values of the azimuthal component of the vorticity, which may be incompatible with the columnar structure preferred by vortices. The cyclonic and anti-cyclonic RWI vortices saturate at moderate levels, modifying but not destroying the rings and gaps in the radial gas distribution of the disk. In particular, they do not shut off the poloidal magnetic flux accumulation in low-density regions and the characteristic meridional flow patterns that are crucial to the ring and gap formation in wind-launching disks. Nevertheless, the RWI and their associated vortices open up the possibility of producing non-axisymmetric dust features observed in a small fraction of protoplanetary disks through non-ideal MHD, although detailed dust treatment is needed to explore this possibility., Comment: Accepted by MNRAS. 18 pages, 16 figures

Rossby wave instability (RWI) is considered the underlying mechanism to crescent-shaped azimuthal asymmetries, discovered in (sub-)millimeter dust continuum of many protoplanetary disks. Previous works on linear theory were conducted in the hydrodynamic limit. Nevertheless, protoplanetary disks are likely magnetized and weakly ionized. We examine the influence of magnetic fields and non-ideal magnetohydrodynamic (MHD) effects - namely, Ohmic resistivity, Hall drift, and ambipolar diffusion - on the RWI unstable modes. We perform radially global linear analyses, employing constant azimuthal ($B_\phi$) or vertical ($B_z$) background magnetic fields. It is found that, in the ideal MHD regime, magnetism can either enhance or diminish RWI growth. Strong non-ideal MHD effects cause RWI growth rates to recover hydrodynamic results. The sign of Hall Els\"{a}sser number subtly complicates the results, and vertical wavenumbers generically diminish growth rates., Comment: 13 pages, 4 figures, submitted to MNRAS

Recent analyses of mm-wavelength protoplanetary disk observations have revealed several emission excesses on the previously identified dust rings, referred to as dust shoulders. The prevalence of dust shoulders suggests that they trace a common but unclear mechanism. In this work, we combine 3D, multifluid hydrodynamic simulations with radiative transfer calculations to explain the formation of dust shoulders. We find that the ring-shoulder pairs can result from the 3D planet-disk interactions with massive, gap-opening planets. The key driver is the dust filtration effect at the local pressure maximum due to planet-driven outward gas flows. Our work provides a possible explanation for the outer dust shoulders in recent super-resolution analyses of ALMA observations. It also provides insights into the formation of the inner dust shoulder in the PDS 70 disk and highlights the role of 3D effects in planet-disk interaction studies., Comment: accepted to ApJ

We investigate the formation of dust traffic jams in polar-aligning circumbinary discs. We use 3D smoothed particle hydrodynamical simulations of both gas and dust to model an initially highly misaligned circumbinary disc around an eccentric binary. As the circumbinary disc evolves to a polar configuration (perpendicular to the binary orbital plane), the difference in the precession between the gas and dust produces dust traffic jams, which become dense dust rings. We find the formation of dust rings exists for different Stokes number, binary eccentricity, and initial disc tilt. Dust rings are only produced while the circumbinary disc is misaligned to the binary orbital plane. When the disc becomes polar aligned, the dust rings are still present and long-lived. Once these dust rings are formed, they drift inward. The drift timescale depends on the Stokes number. The lower the Stokes number, the faster the dust ring drifts near the inner edge of the disc. The dust rings will have an increased midplane dust-to-go ratio, which may be a favourable environment for the steaming instability to operate., Comment: Accepted for publication in MNRAS, 19 pages, 17 figures

Protoplanetary disks are prone to several hydrodynamic instabilities. One candidate, Convective Overstability (COS), can drive radial semi-convection that may influence dust dynamics and planetesimal formation. However, the COS has primarily been studied in local models. This paper investigates the COS near the mid-plane of radially global disk models. We first conduct a global linear stability analysis, which shows that linear COS modes exist only radially inward of their Lindblad resonance (LR). The fastest-growing modes have LRs near the inner radial domain boundary with effective radial wavelengths that can be a substantial fraction of the disk radius. We then perform axisymmetric global simulations and find that the COS's nonlinear saturation is similar to previous incompressible shearing box simulations. In particular, we observe the onset of persistent zonal and elevator flows for sufficiently steep radial entropy gradients. In full 3D, non-axisymmetric global simulations, we find the COS produces large-scale, long-lived vortices, which induce outward radial transport of angular momentum via the excitation of spiral density waves. The corresponding $\alpha$-viscosity values of order $10^{-3}$ agree well with those found in previous 3D compressible shearing box simulations. However, in global disks, significant modifications to their radial structure are found, including the formation of pressure bumps. Interestingly, the COS typically generates an outward radial mass transport, i.e. decretion. We briefly discuss the possible implications of our results for planetesimal formation and for interpreting dust rings and asymmetries observed in protoplanetary disks., Comment: 30 pages, 24 figures

Recent studies have shown that the large-scale gas dynamics of protoplanetary disks (PPDs) are controlled by non-ideal magneto-hydrodynamics (MHD), but how this influences dust dynamics is not fully understood. To this end, we investigate the stability of dusty, magnetized disks subject to the Hall effect, which applies to planet-forming regions of PPDs. We find a novel Background Drift Hall Instability (BDHI) that may facilitate planetesimal formation in Hall-effected disk regions. Through a combination of linear analysis and nonlinear simulations, we demonstrate the viability and characteristics of BDHI. We find it can potentially dominate over the classical streaming instability (SI) and standard MHD instabilities at low dust-to-gas ratios and weak magnetic fields. We also identify magnetized versions of the classic SI, but these are usually subdominant. We highlight the complex interplay between magnetic fields and dust-gas dynamics in PPDs, underscoring the need to consider non-ideal MHD like the Hall effect in the broader narrative of planet formation., Comment: 23 pages, 12 figures, accepted by ApJ. Welcome any comments and suggestions!

We report the finding of a new, local diffusion instability in a protoplanetary disk, which can operate in a dust fluid, subject to mass diffusion, shear viscosity, and dust-gas drag, provided diffusivity, viscosity, or both decrease sufficiently rapidly with increasing dust surface mass density. We devise a vertically averaged, axisymmetric hydrodynamic model to describe a dense, mid-plane dust layer in a protoplanetary disk. The gas is modeled as a passive component, imposing an effective, diffusion-dependent pressure, mass diffusivity, and viscosity onto the otherwise collisionless dust fluid, via turbulence excited by the gas alone, or dust and gas in combination. In particular, we argue that such conditions are met when the dust-gas mixture generates small-scale turbulence through the streaming instability, as supported by recent measurements of dust mass diffusion slopes in simulations. We hypothesize that the newly discovered instability may be the origin of filamentary features, almost ubiquitously found in simulations of the streaming instability. In addition, our model allows for growing oscillatory modes, which operate in a similar fashion as the axisymmetric viscous overstability in dense planetary rings. However, it remains speculative if the required conditions for such modes can be met in protoplanetary disks., Comment: Updated ArXiv Version with the contents of in press erratum, 22 pages, 13 figures

The traditional paradigm of viscosity-dominated evolution of protoplanetary discs has been recently challenged by magnetized disc winds. However, distinguishing wind-driven and turbulence-driven accretion through observations has been difficult. In this study, we present a novel approach to identifying their separate contribution to angular momentum transport by studying the gap and ring morphology of planet-forming discs in the ALMA continuum. We model the gap-opening process of planets in discs with both viscous evolution and wind-driven accretion by 2D multi-fluid hydrodynamical simulations. Our results show that gap-opening planets in wind-driven accreting discs generate characteristic substructures that differ from those in purely viscous discs. Specifically, we demonstrate that discs, where wind-driven accretion dominates the production of substructures, exhibit significant asymmetries. Based on the diverse outputs of mock images in the ALMA continuum, we roughly divide the planet-induced features into four regimes (moderate-viscosity dominated, moderate-wind dominated, strong-wind dominated, inviscid). The classification of these regimes sets up a potential method to constrain the strength of magnetized disc wind and viscosity based on the observed gap and ring morphology. We discuss the asymmetry feature in our mock images and its potential manifestation in ALMA observations., Comment: 11 pages, 6 figures, accepted by MNRAS. Welcome any comments and suggestions!

Protoplanetary discs (PPDs) can host a number of instabilities that may partake directly or indirectly in the process of planetesimal formation. These include the Vertical Shear Instability (VSI), Convective Overstability (COS), Streaming Instability (SI), and Dust Settling Instability (DSI), to name a few. Notably, the VSI and COS have mostly been studied in purely gaseous discs, while the SI and DSI have only been analyzed in isothermal discs. How these instabilities operate under more general conditions is therefore unclear. To this end, we devise a local model of a PPD describing a non-isothermal gas interacting with a single species of dust via drag forces. Using this, we find that dust drag sets minimum length scales below which the VSI and COS are suppressed. Similarly, we find that the SI can be suppressed on sufficiently small scales by the gas' radial buoyancy if it cools on roughly a dynamical timescale. We show that the DSI can be effectively stabilized by vertical buoyancy, except at special radial and vertical length scales. We also find novel instabilities unique to a dusty, non-isothermal gas. These result in a dusty analog of the COS that operates in slowly cooled discs, and a dusty version of the VSI that is strongly enhanced by dust settling. We briefly discuss the possible implications of our results on planetesimal formation., Comment: 40 pages, 26 figures

Past computational studies of planet-induced vortices have shown that the dust asymmetries associated with these vortices can be long-lived enough that they should be much more common in mm/sub-mm observations of protoplanetary discs, even though they are quite rare. Observed asymmetries also have a range of azimuthal extents from compact to elongated even though computational studies have shown planet-induced vortices should be preferentially elongated. In this study, we use 2-D and 3-D hydrodynamic simulations to test whether those dust asymmetries should really be so long-lived or so elongated. With higher resolution (29 cells radially per scale height) than our previous work, we find that vortices can be more compact by developing compact cores when higher-mass planets cause them to re-form, or if they are seeded by tiny compact vortices from the vertical shear instability (VSI), but not through dust feedback in 3-D as was previously expected in general. Any case with a compact vortex or core(s) also has a longer lifetime. Even elongated vortices can have longer lifetimes with higher-mass planets or if the associated planet is allowed to migrate, the latter of which can cause the dust asymmetry to stop decaying as the planet migrates away from the vortex. These longer dust asymmetry lifetimes are even more inconsistent with observations, perhaps suggesting that discs still have an intermediate amount of effective viscosity., Comment: 24 pages, 21 figures; Published in MNRAS

As one of the most commonly observed disk substructures, dust rings from high-resolution disk surveys appear to have different radial widths. Recent observations on PDS 70 and AB Aur reveal not only planets in the disk, but also the accompanying wide dust rings. We use three-dimensional dust-and-gas disk simulations to study whether gap-opening planets are responsible for the large ring width in disk observations. We find that gap-opening planets can widen rings of dust trapped at the pressure bump via planetary perturbations, even with the mid-plane dust-to-gas ratio approaching order unity and with the dust back-reaction accounted for. We show that the planet-related widening effect of dust rings can be quantified using diffusion-advection theory, and provide a generalized criterion for an equilibrated dust ring width in three-dimensional disk models. We also suggest that the ring width can be estimated using the gas turbulent viscosity $\alpha_{\rm turb}$, but with cautions about the Schmidt number greater than order unity., Comment: 17 pages, 6+3 figures, 2 tables, accepted in ApJ

The streaming instability (SI) is one of the most promising candidates for triggering planetesimal formation by producing dense dust clumps that undergo gravitational collapse. Understanding how the SI operates in realistic protoplanetary disks (PPDs) is therefore crucial to assess the efficiency of planetesimal formation. Modern models of PPDs show that large-scale magnetic torques or winds can drive laminar gas accretion near the disk midplane. In a previous study, we identified a new linear dust-gas instability, the azimuthal drift SI (AdSI), applicable to such accreting disks and is powered by the relative azimuthal motion between dust and gas that results from the gas being torqued. In this work, we present the first nonlinear simulations of the AdSI. We show that it can destabilize an accreting, dusty disk even in the absence of a global radial pressure gradient, which is unlike the classic SI. We find the AdSI drives turbulence and the formation of vertically-extended dust filaments that undergo merging. In dust-rich disks, merged AdSI filaments reach maximum dust-to-gas ratios exceeding 100. Moreover, we find that even in dust-poor disks the AdSI can increase local dust densities by two orders of magnitude. We discuss the possible role of the AdSI in planetesimal formation, especially in regions of an accreting PPD with vanishing radial pressure gradients., Comment: Accepted by ApJ

C-type shocks are believed to be ubiquitous in turbulent molecular clouds thanks to ambipolar diffusion. We investigate whether the drag instability in 1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can appear in non-ideal magnetohydrodynamic simulations. Two C-shock models (with narrow and broad steady-state shock widths) are considered to represent the typical environment of star-forming clouds. The ionization-recombination equilibrium is adopted for the one-fluid approach. In the 1D simulation, the inflow gas is continuously perturbed by a sinusoidal density fluctuation with a constant frequency. The perturbations clearly grow after entering the C-shock region until they start being damped at the transition to the postshock region. We show that the profiles of a predominant Fourier mode extracted locally from the simulated growing perturbation match those of the growing mode derived from the linear analysis. Moreover, the local growth rate and wave frequency derived from the predominant mode generally agree with those from the linear theory. Therefore, we confirm the presence of the drag instability in simulated 1D isothermal C-shocks. We also explore the nonlinear behavior of the instability by imposing larger-amplitude perturbations to the simulation. We find that the drag instability is subject to wave steepening, leading to saturated perturbation growth. Issues concerning local analysis, nonlinear effects, one-fluid approach, and astrophysical applications are discussed., Comment: 19 pages, 10 figures

Planet induced sub-structures, like annular gaps, observed in dust emission from protoplanetary disks provide a unique probe to characterize unseen young planets. While deep learning based model has an edge in characterizing the planet's properties over traditional methods, like customized simulations and empirical relations, it lacks in its ability to quantify the uncertainty associated with its predictions. In this paper, we introduce a Bayesian deep learning network "DPNNet-Bayesian" that can predict planet mass from disk gaps and provides uncertainties associated with the prediction. A unique feature of our approach is that it can distinguish between the uncertainty associated with the deep learning architecture and uncertainty inherent in the input data due to measurement noise. The model is trained on a data set generated from disk-planet simulations using the \textsc{fargo3d} hydrodynamics code with a newly implemented fixed grain size module and improved initial conditions. The Bayesian framework enables estimating a gauge/confidence interval over the validity of the prediction when applied to unknown observations. As a proof-of-concept, we apply DPNNet-Bayesian to dust gaps observed in HL Tau. The network predicts masses of $ 86.0 \pm 5.5 M_{\Earth} $, $ 43.8 \pm 3.3 M_{\Earth} $, and $ 92.2 \pm 5.1 M_{\Earth} $ respectively, which are comparable to other studies based on specialized simulations., Comment: 14 pages, 6 figures, submitted to ApJ

We investigate the evolution of dust and gas in the vicinity of local pressure enhancements (pressure bumps) in a protoplanetary disc (PPD) with turbulence due to the Vertical Shear Instability (VSI). We perform global 2D axisymmetric and 3D simulations of dust and gas for a range of values for Z (ratio of dust-to-gas (d/g) surface mass densities or metallicity), particle Stokes numbers tau, and pressure bump amplitude A. Dust feedback onto the gas is included. For the first time we demonstrate in global 3D simulations the collection of dust in long-lived vortices induced by the VSI. Without a pressure bump and for Z~0.01 and tau~0.01 we find that such vortices reach d/g density ratios slightly below unity in the discs mid-plane, while for Z>0.05 long-lived vortices are largely absent. In presence of a pressure bump, for Z~0.01 & tau~0.01 a dusty vortex forms reaching d/g ratios of a few times unity, such that the SI is expected to develop, before it eventually shears out into a turbulent dust ring. For Z~0.03 this occurs for tau~0.005, with a weaker, more short-lived vortex, while for larger tau only a turbulent dust ring forms. For Z>0.03 we find that the dust ring becomes increasingly axisymmetric for increasing tau and d/g ratios reach ~1 for tau>0.005. Furthermore, the disc's vertical mass flow profile is strongly affected by dust for Z>0.03, such that gas is transported inward near the mid-plane and outward at larger heights, i.e. the reversed situation compared to simulations with zero or small amounts of dust. Viscous $\alpha$-values drop moderately as 0.001-0.0001 for increasing Z=0-0.05. Our results suggest that the VSI can play an active role in planetesimal formation through the formation of vortices for plausible values of Z and tau. Also it may provide a natural explanation for the presence/absence of asymmetries of observed dust rings in PPDs, depending on the value of Z.

The streaming instability is one of the most promising pathways to the formation of planetesimals from pebbles. Understanding how this instability operates under realistic conditions expected in protoplanetary disks is therefore crucial to assess the efficiency of planet formation. Contemporary models of protoplanetary disks show that magnetic fields are key to driving gas accretion through large-scale, laminar magnetic stresses. However, the effect of such magnetic fields on the streaming instability has not been examined in detail. To this end, we study the stability of dusty, magnetized gas in a protoplanetary disk. We find the streaming instability can be enhanced by passive magnetic torques and even persist in the absence of a global radial pressure gradient. In this case, instability is attributed to the azimuthal drift between dust and gas, unlike the classical streaming instability, which is driven by radial drift. This suggests that the streaming instability can remain effective inside dust-trapping pressure bumps in accreting disks. When a live vertical field is considered, we find the magneto-rotational instability can be damped by dust feedback, while the classic streaming instability can be stabilized by magnetic perturbations. We also find that Alfv\'en waves can be destabilized by dust-gas drift, but this instability requires nearly ideal conditions. We discuss the possible implications of these results for dust dynamics and planetesimal formation in protoplanetary disks., Comment: Accepted by ApJ

The observed sub-structures, like annular gaps, in dust emissions from protoplanetary disk, are often interpreted as signatures of embedded planets. Fitting a model of planetary gaps to these observed features using customized simulations or empirical relations can reveal the characteristics of the hidden planets. However, customized fitting is often impractical owing to the increasing sample size and the complexity of disk-planet interaction. In this paper we introduce the architecture of DPNNet-2.0, second in the series after DPNNet \citep{aud20}, designed using a Convolutional Neural Network ( CNN, here specifically ResNet50) for predicting exoplanet masses directly from simulated images of protoplanetary disks hosting a single planet. DPNNet-2.0 additionally consists of a multi-input framework that uses both a CNN and multi-layer perceptron (a class of artificial neural network) for processing image and disk parameters simultaneously. This enables DPNNet-2.0 to be trained using images directly, with the added option of considering disk parameters (disk viscosities, disk temperatures, disk surface density profiles, dust abundances, and particle Stokes numbers) generated from disk-planet hydrodynamic simulations as inputs. This work provides the required framework and is the first step towards the use of computer vision (implementing CNN) to directly extract mass of an exoplanet from planetary gaps observed in dust-surface density maps by telescopes such as the Atacama Large (sub-)Millimeter Array., Comment: 15 pages, 10 figures, to appear in ApJ

The vertical shear instability (VSI) is a robust phenomenon in irradiated protoplanetary disks (PPDs). While there is extensive literature on the VSI in the hydrodynamic limit, PPDs are expected to be magnetized and their extremely low ionization fractions imply that non-ideal magneto-hydrodynamic (MHD) effects should be properly considered. To this end, we present linear analyses of the VSI in magnetized disks with Ohmic resistivity. We primarily consider toroidal magnetic fields, which are likely to dominate the field geometry in PPDs. We perform vertically global and radially local analyses to capture characteristic VSI modes with extended vertical structures. To focus on the effect of magnetism, we use a locally isothermal equation of state. We find that magnetism provides a stabilizing effect to dampen the VSI, with surface modes, rather than body modes, being the first to vanish with increasing magnetization. Subdued VSI modes can be revived by Ohmic resistivity, where sufficient magnetic diffusion overcome magnetic stabilization, and hydrodynamic results are recovered. We also briefly consider poloidal fields to account for the magnetorotational instability (MRI), which may develop towards surface layers in the outer parts of PPDs. The MRI grows efficiently at small radial wavenumbers, in contrast to the VSI. When resistivity is considered, we find the VSI dominates over the MRI for Ohmic Els\"{a}sser numbers $\lesssim 0.09$ at plasma beta parameter $\beta_Z \sim 10^4$., Comment: 17 pages, 11 figures, accepted for publication in MNRAS

Recent ALMA observations have found many protoplanetary discs with rings that can be explained by gap-opening planets less massive than Jupiter. Meanwhile, recent studies have suggested that protoplanetary discs should have low levels of turbulence. Past computational work on low-viscosity discs has hinted that these two developments might not be self-consistent because even low-mass planets can be accompanied by vortices instead of conventional double rings. We investigate this potential discrepancy by conducting hydrodynamic simulations of growing planetary cores in discs with various aspect ratios ($H/r=0.04$, 0.06, 0.08) and viscosities ($1.5 \times 10^{-5} \lesssim \alpha \lesssim 3 \times 10^{-4}$), having these cores accrete their gas mass directly from the disc. With $\alpha < 10^{-4}$, we find that sub-Saturn-mass planets in discs with $H/r \le 0.06$ are more likely to be accompanied by dust asymmetries compared to Jupiter-mass planets because they can trigger several generations of vortices in succession. We also find that vortices with $H/r = 0.08$ survive $>6000$ planet orbits regardless of the planet mass or disc mass because they are less affected by the planet's spiral waves. We connect our results to observations and find that the outward migration of vortices with $H/r \ge 0.08$ may be able to explain the cavity in Oph IRS 48 or the two clumps in MWC 758. Lastly, we show that the lack of observed asymmetries in the disc population in Taurus is unexpected given the long asymmetry lifetimes in our low viscosity simulations ($\alpha \sim 2 \times 10^{-5}$), a discrepancy we suggest is due to these discs having higher viscosities., Comment: 24 pages, 20 figures, 2 tables; Accepted to MNRAS

Dust gaps and rings appear ubiquitous in bright protoplanetary disks. Disk-planet interaction with dust-trapping at the edges of planet-induced gaps is one plausible explanation. However, the sharpness of some observed dust rings indicate that sub-mm-sized dust grains have settled to a thin layer in some systems. We test whether or not such dust around gas gaps opened by planets can remain settled by performing three-dimensional, dust-plus-gas simulations of protoplanetary disks with an embedded planet. We find planets massive enough to open gas gaps stir small, sub-mm-sized dust grains to high disk elevations at the gap edges, where the dust scale-height can reach ~70% of the gas scale-height. We attribute this dust 'puff-up' to the planet-induced meridional gas flows previously identified by Fung & Chiang and others. We thus emphasize the importance of explicit 3D simulations to obtain the vertical distribution of sub-mm-sized grains around gas gaps opened by massive planets. We caution that the gas-gap-opening planet interpretation of well-defined dust rings is only self-consistent with large grains exceeding mm in size., Comment: 15 pages, 7+2 figures, accepted in ApJ

Under the right conditions, the streaming instability between imperfectly coupled dust and gas is a powerful mechanism for planetesimal formation as it can concentrate dust grains to the point of gravitational collapse. In its simplest form, the streaming instability can be captured by analyzing the linear stability of unstratified disk models, which represent the midplane of protoplanetary disks. We extend such studies by carrying out vertically-global linear stability analyses of dust layers in protoplanetary disks. We find the dominant form of instability in stratified dust layers is one driven by the vertical gradient in the rotation velocity of the dust-gas mixture, but also requires partial dust-gas coupling. These vertically-shearing streaming instabilities grow on orbital timescales and occur on radial length scales $\sim10^{-3}H_\mathrm{g}$, where $H_\mathrm{g}$ is the local pressure scale height. The classic streaming instability, associated with the relative radial drift between dust and gas, occur on radial length scales $\sim10^{-2}H_\mathrm{g}$, but have much smaller growth rates than vertically-shearing streaming instabilities. Including gas viscosity is strongly stabilizing and leads to vertically-elongated disturbances. We briefly discuss the potential effects of vertically-shearing streaming instabilities on planetesimal formation., Comment: Accepted by ApJ; project source codes are hosted at https://github.com/minkailin/stratsi; for a lay summary, see https://minkailin.wixsite.com/minkailin/post/streaming-instabilities-in-stratified-protoplanetary-disks

Observations of bright protoplanetary disks often show annular gaps in their dust emission. One interpretation of these gaps is disk-planet interaction. If so, fitting models of planetary gaps to observed protoplanetary disk gaps can reveal the presence of hidden planets. However, future surveys are expected to produce an ever-increasing number of protoplanetary disks with gaps. In this case, performing a customized fitting for each target becomes impractical owing to the complexity of disk-planet interaction. To this end, we introduce DPNNet (Disk Planet Neural Network), an efficient model of planetary gaps by exploiting the power of machine learning. We train a deep neural network with a large number of dusty disk-planet hydrodynamic simulations across a range of planet masses, disk temperatures, disk viscosities, disk surface density profiles, particle Stokes numbers, and dust abundances. The network can then be deployed to extract the planet mass for a given gap morphology. In this work, first in a series, we focus on the basic concepts of our machine learning framework. We demonstrate its utility by applying it to the dust gaps observed in the protoplanetary disk around HL Tau at $10$ au, $30$ au, and $80$ au. Our network predict planet masses of $80 \, M_{\rm Earth}$, $63 \, M_{\rm Earth}$, and $70 \, M_{\rm Earth}$, respectively, which are comparable to other studies based on specialized simulations. We discuss the key advantages of our DPNNet in its flexibility to incorporate new physics, any number of parameters and predictions, and its potential to ultimately replace hydrodynamical simulations for disk observers and modelers., Comment: 16 Pages, 8 Figures, to appear in ApJ

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 $\gtrsim 0.3$ and particle Stokes numbers $\gtrsim 0.03$. 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., Comment: Accepted by MNRAS

The streaming instability is a popular candidate for planetesimal formation by concentrating dust particles to trigger gravitational collapse. However, its robustness against physical conditions expected in protoplanetary disks is unclear. In particular, particle stirring by turbulence may impede the instability. To quantify this effect, we develop the linear theory of the streaming instability with external turbulence modelled by gas viscosity and particle diffusion. We find the streaming instability is sensitive to turbulence, with growth rates becoming negligible for alpha-viscosity parameters $\alpha \gtrsim \mathrm{St} ^{1.5}$, where $\mathrm{St}$ is the particle Stokes number. We explore the effect of non-linear drag laws, which may be applicable to porous dust particles, and find growth rates are modestly reduced. We also find that gas compressibility increase growth rates by reducing the effect of diffusion. We then apply linear theory to global models of viscous protoplanetary disks. For minimum-mass Solar nebula disk models, we find the streaming instability only grows within disk lifetimes beyond $\sim 10$s of AU, even for cm-sized particles and weak turbulence ($\alpha\sim 10^{-4}$). Our results suggest it is rather difficult to trigger the streaming instability in non-laminar protoplanetary disks, especially for small particles., Comment: Accepted by ApJ, see https://minkailin.wixsite.com/minkailin/post/making-planets-in-turbulent-disks-is-not-so-easy for a lay summary

In the innermost regions of protoplanerary discs, the solid-to-gas ratio can be increased considerably by a number of processes, including photoevaporative and particle drift. MHD disc models also suggest the existence of a dead-zone at $R\lesssim 10$ AU, where the regions close to the midplane remain laminar. In this context, we use two-fluid hydrodynamical simulations to study the interaction between a low-mass planet ($\sim 1.7 \;{\rm M_\oplus}$) on a fixed orbit and an inviscid pebble-rich disc with solid-to-gas ratio $\epsilon\ge 0.5$. For pebbles with Stokes numbers St=0.1, 0.5, multiple dusty vortices are formed through the Rossby Wave Instability at the planet separatrix. Effects due to gas drag then lead to a strong enhancement in the solid-to-gas ratio, which can increase by a factor of $\sim 10^3$ for marginally coupled particles with St=0.5. As in streaming instabilities, pebble clumps reorganize into filaments that may plausibly collapse to form planetesimals. When the planet is allowed to migrate in a MMSN disc, the vortex instability is delayed due to migration but sets in once inward migration stops due a strong positive pebble torque. Again, particle filaments evolving in a gap are formed in the disc while the planet undergoes an episode of outward migration. Our results suggest that vortex instabilities triggered by low-mass planets could play an important role in forming planetesimals in pebble-rich, inviscid discs, and may significantly modify the migration of low-mass planets. They also imply that planetary dust gaps may not necessarily contain planets if these migrated away., Comment: Accepted in MNRAS

Enhancing the local dust-to-gas ratio in protoplanetary discs is a necessary first step to planetesimal formation. In laminar discs, dust settling is an efficient mechanism to raise the dust-to-gas ratio at the disc midplane. However, turbulence, if present, can stir and lift dust particles, which ultimately hinders planetesimal formation. In this work, we study dust settling in protoplanetary discs with hydrodynamic turbulence sustained by the vertical shear instability. We perform axisymmetric numerical simulations to investigate the effect of turbulence, particle size, and solid abundance or metallicity on dust settling. We highlight the positive role of drag forces exerted onto the gas by the dust for settling to overcome the vertical shear instability. In typical disc models we find particles with a Stokes number $\sim 10^{-3}$ can sediment to $\lesssim 10\%$ of the gas scale-height, provided that $\Sigma_\mathrm{d}/\Sigma_\mathrm{g}\gtrsim 0.02$-$0.05$, where $\Sigma_\mathrm{d,g}$ are the surface densities in dust and gas, respectively. This coincides with the metallicity condition for small particles to undergo clumping via the streaming instability. Super-solar metallicities, at least locally, are thus required for a self-consistent picture of planetesimal formation. Our results also imply that dust rings observed in protoplanetary discs should have smaller scale-heights than dust gaps, provided that the metallicity contrast between rings and gaps exceed the corresponding contrast in gas density., Comment: Accepted by MNRAS; see https://minkailin.wixsite.com/minkailin/blog/dust-settling-in-turbulent-discs for a summary

Gap-opening planets can generate dust-trapping vortices that may explain some of the latest discoveries of high-contrast crescent-shaped dust asymmetries in transition discs. While planet-induced vortices were previously thought to have concentrated shapes, recent computational work has shown that these features naturally become much more elongated in the gas when simulations account for the relatively long timescale over which planets accrete their mass. In this work, we conduct two-fluid hydrodynamical simulations of vortices induced by slowly-growing Jupiter-mass planets in discs with very low viscosity ($\alpha = 3 \times 10^{-5}$). We simulate the dust dynamics for four particle sizes spanning 0.3 mm to 1 cm in order to produce synthetic ALMA images. In our simulations, we find that an elongated vortex still traps dust, but not directly at its center. With a flatter pressure bump and disruptions from the planet's overlapping spiral density waves, the dust instead circulates around the vortex. This motion (1) typically carries the peak off-center, (2) spreads the dust out over a wider azimuthal extent $\geq 180^{\circ}$, (3) skews the azimuthal profile towards the front of the vortex, and (4) can also create double peaks in newly-formed vortices. In particular, we expect that the most defining observational signature, a peak offset of more than $30^{\circ}$, should be detectable $>30\%$ of the time in observations with a beam diameter of at most the planet's separation from its star., Comment: Accepted to MNRAS. 13 pages, 8 figures. Movies available at: https://lavinia.as.arizona.edu/~mhammer/vortex_signatures.html

Large-scale, dust-trapping vortices may account for observations of asymmetric protoplanetary discs. Disc vortices are also potential sites for accelerated planetesimal formation by concentrating dust grains. However, in 3D discs vortices are subject to destructive `elliptic instabilities', which reduces their viability as dust traps. The survival of vortices in 3D accretion discs is thus an important issue to address. In this work, we perform shearing box simulations to show that disc self-gravity enhances the survival of 3D vortices, even when self-gravity is weak in the classic sense (e.g. with a Toomre $Q\simeq5$). We find a 3D, self-gravitating vortex can grow on secular timescales in spite of the elliptic instability. The vortex aspect-ratio decreases as it strengthens, which feeds the elliptic instability. The result is a 3D vortex with a turbulent core that persists for $\sim 10^{3}$ orbits. We find when gravitational and hydrodynamic stresses become comparable, the vortex may undergo episodic bursts, which we interpret as interaction between elliptic and gravitational instabilities. We estimate the distribution of dust particles in self-gravitating, turbulent vortices. Our results suggest large-scale vortices in protoplanetary discs are more easily observed at large radii., Comment: Accepted by MNRAS; full resolution article at https://docs.wixstatic.com/ugd/f3eb2c_500e5bc1e9354ba295e7b954b8f5247e.pdf

It is expected that a pressure bump can be formed at the inner edge of a dead-zone, and where vortices can develop through the Rossby Wave Instability (RWI). It has been suggested that self-gravity can significantly affect the evolution of such vortices. We present the results of 2D hydrodynamical simulations of the evolution of vortices forming at a pressure bump in self-gravitating discs with Toomre parameter in the range $4-30$. We consider isothermal plus non-isothermal disc models that employ either the classical $\beta$ prescription or a more realistic treatment for cooling. The main aim is to investigate whether the condensating effect of self-gravity can stabilize vortices in sufficiently massive discs. We confirm that in isothermal disc models with ${\cal Q} \gtrsim 15$, vortex decay occurs due to the vortex self-gravitational torque. For discs with $3\lesssim {\cal Q} \lesssim 7$, the vortex develops gravitational instabilities within its core and undergoes gravitational collapse, whereas more massive discs give rise to the formation of global eccentric modes. In non-isothermal discs with $\beta$ cooling, the vortex maintains a turbulent core prior to undergoing gravitational collapse for $\beta \lesssim 0.1$, whereas it decays if $\beta \ge 1$. In models that incorpore both self-gravity and a better treatment for cooling, however, a stable vortex is formed with aspect ratio $\chi \sim 3-4$. Our results indicate that self-gravity significantly impacts the evolution of vortices forming in protoplanetary discs, although the thermodynamical structure of the vortex is equally important for determining its long-term dynamics., Comment: Accepted in MNRAS

Protoplanets may be born into dust-rich environments if planetesimals formed through streaming or gravitational instabilities, or if the protoplanetary disc is undergoing mass loss due to disc winds or photoevaporation. Motivated by this possibility, we explore the interaction between low mass planets and dusty protoplanetary discs with focus on disc-planet torques. We implement Lin & Youdin's newly developed, purely hydrodynamic model of dusty gas into the PLUTO code to simulate dusty protoplanetary discs with an embedded planet. We find that for imperfectly coupled dust and high metallicity, e.g. Stokes number $10^{-3}$ and dust-to-gas ratio $\Sigma_\mathrm{d}/\Sigma_\mathrm{g}=0.5$ , a `bubble' develops inside the planet's co-orbital region, which introduces unsteadiness in the flow. The resulting disc-planet torques sustain large amplitude oscillations that persists well beyond that in simulations with perfectly coupled dust or low dust-loading, where co-rotation torques are always damped. We show that the desaturation of the co-rotation torques by finite-sized particles is related to potential vorticity generation from the misalignment of dust and gas densities. We briefly discuss possible implications for the orbital evolution of protoplanets in dust-rich discs. We also demonstrate Lin & Youdin's dust-free framework reproduces previous results pertaining to dusty protoplanetary discs, including dust-trapping by pressure bumps, dust settling, and the streaming instability., Comment: Accepted by MNRAS

Small solids embedded in gaseous protoplanetary disks are subject to strong dust-gas friction. Consequently, tightly-coupled dust particles almost follow the gas flow. This near conservation of dust-to-gas ratio along streamlines is analogous to the near conservation of entropy along flows of (dust-free) gas with weak heating and cooling. We develop this thermodynamic analogy into a framework to study dusty gas dynamics in protoplanetary disks. We show that an isothermal dusty gas behaves like an adiabatic pure gas; and that finite dust-gas coupling may be regarded as an effective heating/cooling. We exploit this correspondence to deduce that 1) perfectly coupled, thin dust layers cannot cause axisymmetric instabilities; 2) radial dust edges are unstable if the dust is vertically well-mixed; 3) the streaming instability necessarily involves a gas pressure response that lags behind dust density; 4) dust-loading introduces buoyancy forces that generally stabilizes the vertical shear instability associated with global radial temperature gradients. We also discuss dusty analogs of other hydrodynamic processes (e.g. Rossby wave instability, convective overstability, and zombie vortices), and how to simulate dusty protoplanetary disks with minor tweaks to existing codes for pure gas dynamics., Comment: accepted by ApJ, extended discussions

The presence of a giant planet in a low-viscosity disc can create a gap edge in the disc's radial density profile sharp enough to excite the Rossby Wave Instability. This instability may evolve into dust-trapping vortices that might explain the "banana-shaped" features in recently observed asymmetric transition discs with inner cavities. Previous hydrodynamical simulations of planet-induced vortices have neglected the timescale of hundreds to thousands of orbits to grow a massive planet to Jupiter-size. In this work, we study the effect of a giant planet's runaway growth timescale on the lifetime and characteristics of the resulting vortex. For two different planet masses (1 and 5 Jupiter masses) and two different disc viscosities ($\alpha$=3$\times 10^{-4}$ and 3$\times10^{-5}$), we compare the vortices induced by planets with several different growth timescales between 10 and 4000 planet orbits. In general, we find that slowly-growing planets create significantly weaker vortices with lifetimes and surface densities reduced by more than $50\%$. For the higher disc viscosity, the longest growth timescales in our study inhibit vortex formation altogether. Additionally, slowly-growing planets produce vortices that are up to twice as elongated, with azimuthal extents well above $180^{\circ}$ in some cases. These unique, elongated vortices likely create a distinct signature in the dust observations that differentiates them from the more concentrated vortices that correspond to planets with faster growth timescales. Lastly, we find that the low viscosities necessary for vortex formation likely prevent planets from growing quickly enough to trigger the instability in self-consistent models., Comment: 12 pages, 7 figures, Accepted by MNRAS

We quantify the thermodynamic requirement for the Vertical Shear Instability and evaluate its relevance to realistic protoplanetary disks as a potential route to hydrodynamic turbulence., Comment: IAUS 314 proceedings, main paper arXiv:1505.02163

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., Comment: Accepted by ApJ; a talk is available at https://lavinia.as.arizona.edu/~minkailin/docs/LK16.pdf

The vertical shear instability (VSI) offers a potential hydrodynamic mechanism for angular momentum transport in protoplanetary disks (PPDs). The VSI is driven by a weak vertical gradient in the disk's orbital motion, but must overcome vertical buoyancy, a strongly stabilizing influence in cold disks, where heating is dominated by external irradiation. Rapid radiative cooling reduces the effective buoyancy and allows the VSI to operate. We quantify the cooling timescale $t_c$ needed for efficient VSI growth, through a linear analysis of the VSI with cooling in vertically global, radially local disk models. We find the VSI is most vigorous for rapid cooling with $t_c<\Omega_\mathrm{K}^{-1}h|q|/(\gamma -1)$ in terms of the Keplerian orbital frequency, $\Omega_\mathrm{K}$; the disk's aspect-ratio, $h\ll1$; the radial power-law temperature gradient, $q$; and the adiabatic index, $\gamma$. For longer $t_c$, the VSI is much less effective because growth slows and shifts to smaller length scales, which are more prone to viscous or turbulent decay. We apply our results to PPD models where $t_c$ is determined by the opacity of dust grains. We find that the VSI is most effective at intermediate radii, from $\sim5$AU to $\sim50$AU with a characteristic growth time of $\sim30$ local orbital periods. Growth is suppressed by long cooling times both in the opaque inner disk and the optically thin outer disk. Reducing the dust opacity by a factor of 10 increases cooling times enough to quench the VSI at all disk radii. Thus the formation of solid protoplanets, a sink for dust grains, can impede the VSI., Comment: Accepted by ApJ; minor changes from previous version; a poster is available at http://lavinia.as.arizona.edu/~minkailin/docs/iaus314.pdf

We describe a new mechanism that leads to the destabilisation of non-axisymmetric waves in astrophysical discs with an imposed radial temperature gradient. This might apply, for example, to the outer parts of protoplanetary discs. We use linear density wave theory to show that non-axisymmetric perturbations generally do not conserve their angular momentum in the presence of a forced temperature gradient. This implies an exchange of angular momentum between linear perturbations and the background disc. In particular, when the disturbance is a low-frequency trailing wave and the disc temperature decreases outwards, this interaction is unstable and leads to the growth of the wave. We demonstrate this phenomenon through numerical hydrodynamic simulations of locally isothermal discs in 2D using the FARGO code and in 3D with the ZEUS-MP and PLUTO codes. We consider radially structured discs with a self-gravitating region which remains stable in the absence of a temperature gradient. However, when a temperature gradient is imposed we observe exponential growth of a one-armed spiral mode (azimuthal wavenumber $m=1$) with co-rotation radius outside the bulk of the spiral arm, resulting in a nearly-stationary one-armed spiral pattern. The development of this one-armed spiral does not require the movement of the central star, as found in previous studies. Because destabilisation by a forced temperature gradient does not explicitly require disc self-gravity, we suggest this mechanism may also affect low-frequency one-armed oscillations in non-self-gravitating discs., Comment: 15 pages, accepted by MNRAS

Several observations of transition discs show lopsided dust-distributions. A potential explanation is the formation of a large-scale vortex acting as a dust-trap at the edge of a gap opened by a giant planet. Numerical models of gap-edge vortices have thus far employed locally isothermal discs, but the theory of this vortex-forming or `Rossby wave' instability was originally developed for adiabatic discs. We generalise the study of planetary gap stability to non-isothermal discs using customised numerical simulations of disc-planet systems where the planet opens an unstable gap. We include in the energy equation a simple cooling function with cooling timescale $t_c=\beta\Omega_k^{-1}$, where $\Omega_k$ is the Keplerian frequency, and examine the effect of $\beta$ on the stability of gap edges and vortex lifetimes. We find increasing $\beta$ lowers the growth rate of non-axisymmetric perturbations, and the dominant azimuthal wavenumber $m$ decreases. We find a quasi-steady state consisting of one large-scale, over-dense vortex circulating the outer gap edge, typically lasting $O(10^3)$ orbits. Vortex lifetimes were found to generally increase with cooling times up to an optimal value, beyond which vortex lifetimes decrease. This non-monotonic dependence is qualitatively consistent with recent studies using strictly isothermal discs that vary the disc aspect ratio., Comment: 12 pages, 13 figures, 1 table, accepted by MNRAS

Magneto-rotational instability (MRI) and gravitational instability (GI) are the two principle routes to turbulent angular momentum transport in accretion disks. Protoplanetary disks may develop both. This paper aims to reinvigorate interest in the study of magnetized massive protoplanetary disks, starting from the basic issue of stability. The local linear stability of a self-gravitating, uniformly magnetized, differentially rotating, three-dimensional stratified disk subject to axisymmetric perturbations is calculated numerically. The formulation includes resistivity. It is found that the reduction in the disk thickness by self-gravity can decrease MRI growth rates; the MRI becomes global in the vertical direction, and MRI modes with small radial length scales are stabilized. The maximum vertical field strength that permits the MRI in a strongly self-gravitating polytropic disk with polytropic index $\Gamma=1$ is estimated to be $B_{z,\mathrm{max}} \simeq c_{s0}\Omega\sqrt{\mu_0/16\pi G} $, where $c_{s0}$ is the midplane sound speed and $\Omega$ is the angular velocity. In massive disks with layered resistivity, the MRI is not well-localized to regions where the Elsasser number exceeds unity. For MRI modes with radial length scales on the order of the disk thickness, self-gravity can enhance density perturbations, an effect that becomes significant in the presence of a strong toroidal field, and which depends on the symmetry of the underlying MRI mode. In gravitationally unstable disks where GI and MRI growth rates are comparable, the character of unstable modes can transition smoothly between MRI and GI. Implications for non-linear simulations are discussed briefly., Comment: Accepted by ApJ; project source code available at https://github.com/minkailin/sgmri

Gap formation by giant planets in self-gravitating disks may lead to a gravitational edge instability (GEI). We demonstrate this GEI with global 3D and 2D self-gravitating disk-planet simulations using the ZEUS, PLUTO and FARGO hydrodynamic codes. High resolution 2D simulations show that an unstable outer gap edge can lead to outwards orbital migration. Our results have important implications for theories of giant planet formation in massive disks., Comment: Published in the proceedings of IAUS 299. Associated paper is arXiv:1306.2514. Poster can be found at http://cita.utoronto.ca/~mklin924/IAUposter.pdf

Vortex formation through the Rossby wave instability (RWI) in protoplanetary discs has been invoked to play a role in planet formation theory, and suggested to explain the observation of large dust asymmetries in several transitional discs. However, whether or not vortex formation operates in layered accretion discs, i.e. models of protoplanetary discs including dead zones near the disc midplane --- regions that are magnetically inactive and the effective viscosity greatly reduced --- has not been verified. As a first step toward testing the robustness of vortex formation in layered discs, we present non-linear hydrodynamical simulations of global 3D protoplanetary discs with an imposed kinematic viscosity that increases away from the disc midplane. Two sets of numerical experiments are performed: (i) non-axisymmetric instability of artificial radial density bumps in viscous discs; (ii) vortex-formation at planetary gap edges in layered discs. Experiment (i) shows that the linear instability is largely unaffected by viscosity and remains dynamical. The disc-planet simulations also show the initial development of vortices at gap edges, but in layered discs the vortices are transient structures which disappear well into the non-linear regime. We suggest that the long term survival of columnar vortices, such as those formed via the RWI, requires low effective viscosity throughout the vertical extent of the disc, so such vortices do not persist in layered discs., Comment: 14 pages, accepted by MNRAS

The Atacama Large Millimeter Array (ALMA) has been returning images of transitional disks in which large asymmetries are seen in the distribution of mm-sized dust in the outer disk. The explanation in vogue borrows from the vortex literature by suggesting that these asymmetries are the result of dust trapping in giant vortices, excited via Rossby wave instability (RWI) at planetary gap edges. Due to the drag force, dust trapped in vortices will accumulate in the center, and diffusion is needed to maintain a steady state over the lifetime of the disk. While previous work derived semi-analytical models of the process, in this paper we provide analytical steady-state solutions. Exact solutions exist for certain vortex models. The solution is determined by the vortex rotation profile, the gas scale height, the vortex aspect ratio, and the ratio of dust diffusion to gas-dust friction. In principle, all these quantities can be derived from observations, which would give validation of the model, also giving constrains on the strength of the turbulence inside the vortex core. Based on our solution, we derive quantities such as the gas-dust contrast, the trapped dust mass, and the dust contrast at the same orbital location. We apply our model to the recently imaged Oph IRS 48 system, finding values within the range of the observational uncertainties., Comment: 11 pages, 3 figures, accepted by ApJ

It has been suggested that long-period giant planets, such as HD 95086b and HR 8799bcde, may have formed through gravitational instability of protoplanetary discs. However, self-gravitating disc-satellite interaction can lead to the formation of a gravitationally unstable gap. Such an instability significantly affects the orbital migration of gap-opening perturbers in massive discs. We use 2D hydrodynamical simulations to examine the role of planet mass on the gravitational stability of gaps and its impact on orbital migration. We consider giant planets with planet-to-star mass ratio q=0.0003 to q=0.003, in a self-gravitating disc with disc-to-star mass ratio M_d/M_*=0.08, aspect ratio h=0.05, and Keplerian Toomre parameter Q = 1.5 at 2.5 times the planet's initial orbital radius. Fixed-orbit simulations show that all planet masses we consider open gravitationally unstable gaps, but the instability is stronger and develops sooner with increasing planet mass. The disc-on-planet torques typically become more positive with increasing planet mass. In freely-migrating simulations, we observe faster outward migration with increasing planet mass, but only for planet masses capable of opening unstable gaps early on. For q=0.0003, the planet undergoes rapid inward type III migration before it can open a gap. For q=0.0013 we find it is possible to balance the tendency for inward migration by the positive torques due to an unstable gap, but only for a few 10's of orbital periods. We find the unstable outer gap edge can trigger outward type III migration, sending the planet to twice its initial orbital radius on dynamical timescales. This triggered type III migration may be a way of bringing giant planets to large orbital distances. On the other hand, our results also imply gap-opening is not a sufficient condition for the in situ formation of giant planets on wide orbits through disc fragmentation., Comment: 13 pages, 15 figures, accepted by MNRAS. Audio/video commentary available at http://youtu.be/5VCt2NdKFeg

Numerical simulations are presented to study the stability of gaps opened by giant planets in 3D self-gravitating disks. In weakly self-gravitating disks, a few vortices develop at the gap edge and merge on orbital time-scales. The result is one large but weak vortex with Rossby number -0.01. In moderately self-gravitating disks, more vortices develop and their merging is resisted on dynamical time-scales. Self-gravity can sustain multi-vortex configurations, with Rossby number -0.2 to -0.1, over a time-scale of order 100 orbits. Self-gravity also enhances the vortex vertical density stratification, even in disks with initial Toomre parameter of order 10. However, vortex formation is suppressed in strongly self-gravitating disks and replaced by a global spiral instability associated with the gap edge which develops during gap formation., Comment: Proceeding for `Instabilities and Structures in Proto-Planetary Disks' workshop. Includes additional results analysis of Lin (2012, arXiv:1205.4034) and an additional simulation. Talk pdf available at http://cita.utoronto.ca/~mklin924/talks.html

The linear Rossby wave instability (RWI) in global, 3D polytropic discs is revisited with a much simpler numerical method than that previously employed by the author. The governing partial differential equation is solved with finite differences in the radial direction and spectral collocation in the vertical direction. RWI modes are calculated subject to different upper disc boundary conditions. These include free surface, solid boundaries and variable vertical domain size. Boundary conditions that oppose vertical motion increase the instability growth rate by a few per cent. The magnitude of vertical flow throughout the fluid column can be affected but the overall flow pattern is qualitatively unchanged. Numerical results support the notion that the RWI is intrinsically two dimensional. This implies that inconsistent upper disc boundary conditions, such as vanishing enthalpy perturbation, may inhibit the RWI in 3D., Comment: 5 pages, published in MNRAS; this article precedes arXiv:1209.0470 and details the numerical scheme employed therein

Astrophysical disks with localized radial structure, such as protoplanetary disks containing dead zones or gaps due to disk-planet interaction, may be subject to the non-axisymmetric Rossby wave instability (RWI) that lead to vortex-formation. The linear instability has recently been demonstrated in three-dimensional (3D) barotropic disks. It is the purpose of this study to generalize the 3D linear problem to include an energy equation, thereby accounting for baroclinity in three-dimensions. Linear stability calculations are presented for radially structured, vertically stratified, geometrically-thin disks with non-uniform entropy distribution in both directions. Polytropic equilibria are considered but adiabatic perturbations assumed. The unperturbed disk has a localized radial density bump making it susceptible to the RWI. The linearized fluid equations are solved numerically as a partial differential equation eigenvalue problem. Emphasis on the ease of method implementation is given. It is found that when the polytropic index is fixed and adiabatic index increased, non-uniform entropy has negligible effect on the RWI growth rate, but pressure and density perturbation magnitudes near a pressure enhancement increases away from the midplane. The associated meridional flow is also qualitatively changed from homentropic calculations. Meridional vortical motion is identified in the nonhomentropic linear solution, as well as in a nonlinear global hydrodynamic simulation of the RWI in an initially isothermal disk evolved adiabatically. Numerical results suggest buoyancy forces play an important role in the internal flow of Rossby vortices., Comment: 16 pages, accepted by ApJ, substantial re-writes for improved clarity, extended results analysis

Numerical simulations of global three-dimensional (3D), self-gravitating discs with a gap opened by an embedded planet are presented. The simulations are customised to examine planetary gap stability. Previous results, obtained by Lin & Papaloizou from two-dimensional (2D) disc models, are reproduced in 3D. These include (i) the development of vortices associated with local vortensity minima at gap edges and their merging on dynamical timescales in weakly self-gravitating discs, (ii) the increased number of vortices as the strength of self-gravity is increased and their resisted merging, and (iii) suppression of the vortex instability and development of global spiral arms associated with local vortensity maxima in massive discs. The vertical structure of these disturbances are examined. In terms of the relative density perturbation, the vortex disturbance has weak vertical dependence when self-gravity is neglected. Vortices become more vertically stratified with increasing self-gravity. This effect is seen even when the unperturbed region around the planet's orbital radius has a Toomre stability parameter ~10. The spiral modes display significant vertical structure at the gap edge, with the midplane density enhancement being several times larger than that near the upper disc boundary. However, for both instabilities the vertical Mach number is typically a few per cent,and on average vertical motions near the gap edge do not dominate horizontal motions., Comment: 15 pages, 19 figures, accepted by MNRAS, updated acknowledgments

Protoplanetary discs may become dynamically unstable due to structure induced by an embedded giant planet. In this thesis, I discuss the stability of such systems and explore the consequence of instability on planetary migration. I begin with non-self-gravitating, low viscosity discs and show that giant planets induce shocks inside its co-orbital region, leading to a profile unstable to vortex formation around a potential vorticity minimum. This instability is commonly known as the vortex or Rossby wave instability. Vortex-planet interaction lead to episodic phases of migration, which can be understood in the framework of type III migration. I then examine the effect of disc self-gravity on gap stability. The linear theory of the Rossby wave instability is extended to include disc gravity, which shows that self-gravity is effective at stabilising the vortex instability at small azimuthal wavenumber. This is consistent with the observation that more vortices develop with increasing disc mass in hydrodynamic simulations. Vortices in self-gravitating discs also resist merging, and is most simply understood as pair-vortices undergoing mutual horsehoe turns upon encounter. I show that in sufficiently massive discs vortex modes are suppressed. Instead, global spiral instabilities develop which are associated with a potential vorticity maximum at the gap edge. These edge modes can be physically understood as a result of unstable interaction between the gap edge and the exterior disc through gravity. I show the spiral arms can provide a positive torque on the planet, leading to fast migration outwards. I confirm the above results, obtained from razor-thin disc models, persist in three-dimensions., Comment: PhD thesis (Cambridge), defended on October 20, 2011. Contents of Ch.2 to 5 have been partly published in MNRAS. Resolution of figures have been lowered