arXiv subjects

Min-Kai Lin

Publications and source records attributed to Min-Kai Lin.

At least 55 records · Page 3Linked to original sources

arXiv2020

A Machine Learning model to infer planet masses from gaps observed in 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.

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arXiv2020

Migrating Low-Mass Planets in Inviscid Dusty Protoplanetary Discs

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.

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arXiv2020

How efficient is the streaming instability in viscous protoplanetary disks?

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 $α\gtrsim \mathrm{St} ^{1.5}$, 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 ($α\sim 10^{-4}$). Our results suggest it is rather difficult to trigger the streaming instability in non-laminar protoplanetary disks, especially for small particles.

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arXiv2019

Vortex instabilities triggered by low-mass planets in pebble-rich, inviscid protoplanetary discs

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 $ε\ge 0.5$. 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.

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arXiv2019

Dust settling against hydrodynamic turbulence in protoplanetary discs

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 $Σ_\mathrm{d}/Σ_\mathrm{g}\gtrsim 0.02$-$0.05$, where $Σ_\mathrm{d,g}$ 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.

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arXiv2018

Observational diagnostics of elongated planet-induced vortices with realistic planet formation timescales

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 ($α= 3 \times 10^{-5}$). 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.

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arXiv2018

On the evolution of vortices in massive protoplanetary discs

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 $β$ 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 $β$ cooling, the vortex maintains a turbulent core prior to undergoing gravitational collapse for $β\lesssim 0.1$, whereas it decays if $β\ge 1$. In models that incorpore both self-gravity and a better treatment for cooling, however, a stable vortex is formed with aspect ratio $χ\sim 3-4$. 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.

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arXiv2018

Vortex survival in 3D self-gravitating accretion discs

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.

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arXiv2018

Dusty disc-planet interaction with dust-free simulations

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 $Σ_\mathrm{d}/Σ_\mathrm{g}=0.5$ , 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.

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arXiv2017

A thermodynamic view of dusty protoplanetary disks

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.

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arXiv2017

Slowly-growing gap-opening planets trigger weaker vortices

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 ($α$=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.

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arXiv2016

On the gravitational stability of gravito-turbulent accretion disks

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.

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arXiv2016

Vertical shear instability in the solar nebula

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.

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arXiv2015

Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks

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 $t_c<Ω_\mathrm{K}^{-1}h|q|/(γ-1)$ in terms of the Keplerian orbital frequency, $Ω_\mathrm{K}$; the disk's aspect-ratio, $h\ll1$; the radial power-law temperature gradient, $q$; and the adiabatic index, $γ$. 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.

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arXiv2015

Gap formation and stability in non-isothermal protoplanetary discs

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 $t_c=βΩ_k^{-1}$, where $Ω_k$ is the Keplerian frequency, and examine the effect of $β$ on the stability of gap edges and vortex lifetimes. We find increasing $β$ 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.

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arXiv2015

One-armed spirals in locally isothermal, radially structured self-gravitating discs

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.

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arXiv2014

Linear stability of magnetized massive protoplanetary disks

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 $Γ=1$ is estimated to be $B_{z,\mathrm{max}} \simeq c_{s0}Ω\sqrt{μ_0/16πG} $, where $c_{s0}$ is the midplane sound speed and $Ω$ 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.

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arXiv2014

Gravitational instability of planetary gaps and its effect on orbital migration

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.

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