arXiv subjects

Chao-Chin Yang

Publications and source records attributed to Chao-Chin Yang.

At least 37 records · Page 2Linked to original sources

arXiv2023

Exciting spiral arms in protoplanetary discs from flybys

Spiral arms are observed in numerous protoplanetary discs. These spiral arms can be excited by companions, either on bound or unbound orbits. We simulate a scenario where an unbound perturber, i.e. a flyby, excites spiral arms during a periastron passage. We run three-dimensional hydrodynamical simulations of a parabolic flyby encountering a gaseous protoplanetary disc. The perturber mass ranges from $10\, \rm M_J$ to $1\, \rm M_{\odot}$. The perturber excites a two-armed spiral structure, with a more prominent spiral feature for higher mass perturbers. The two arms evolve over time, eventually winding up, consistent with previous works. We focus on analysing the pattern speed and pitch angle of these spirals during the whole process. The initial pattern speed of the two arms are close to the angular velocity of the perturber at periastron, and then it decreases over time. The pitch angle also decreases over time as the spiral winds up. The spirals disappear after several local orbital times. An inclined prograde orbit flyby induces similar disc substructures as a coplanar flyby. A solar-mass flyby event causes increased eccentricity growth in the protoplanetary disc, leading to an eccentric disc structure which dampens over time. The spirals' morphology and the disc eccentricity can be used to search for potential unbound stars or planets around discs where a flyby is suspected. Future disc observations at high resolution and dedicated surveys will help to constrain the frequency of such stellar encounters in nearby star-forming regions.

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arXiv2023

An Analytical Theory for the Growth from Planetesimals to Planets by Polydisperse Pebble Accretion

Pebble accretion is recognized as a significant accelerator of planet formation. Yet, only formulae for single-sized (monodisperse) distribution have been derived in the literature. These can lead to significant underestimates for Bondi accretion, for which the best accreted pebble size may not be the one that dominates the mass distribution. We derive in this paper the polydisperse theory of pebble accretion. We consider a power-law distribution in pebble radius, and we find the resulting surface and volume number density distribution functions. We derive also the exact monodisperse analytical pebble accretion rate for which 3D and 2D accretion are limits. In addition, we find analytical solutions to the polydisperse 2D Hill and 3D Bondi limits. We integrate the polydisperse pebble accretion numerically for the MRN distribution, finding a slight decrease (by an exact factor 3/7) in the Hill regime compared to the monodisperse case. In contrast, in the Bondi regime, we find 1-2 orders of magnitude higher accretion rates compared to monodisperse, also extending the onset of pebble accretion to 1-2 order of magnitude lower in mass. We find Myr-timescales, within the disk lifetime, for Bondi accretion on top of planetary seeds of masses $10^{-6}-10^{-4} M_\oplus$, over a significant range of the parameter space. This mass range overlaps with the high mass end of the planetesimal initial mass function, and thus pebble accretion is possible directly following formation by streaming instability. This alleviates the need for mutual planetesimal collisions as a major contribution to planetary growth.

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arXiv2022

Formation of Dust Rings and Gaps in Non-ideal MHD Disks Through Meridional Gas Flows

Rings and gaps are commonly observed in the dust continuum emission of young stellar disks. Previous studies have shown that substructures naturally develop in the weakly ionized gas of magnetized, non-ideal MHD disks. The gas rings are expected to trap large mm/cm-sized grains through pressure gradient-induced radial dust-gas drift. Using 2D (axisymmetric) MHD simulations that include ambipolar diffusion and dust grains of three representative sizes (1~mm, 3.3~mm, and 1~cm), we show that the grains indeed tend to drift radially relative to the gas towards the centers of the gas rings, at speeds much higher than in a smooth disk because of steeper pressure gradients. However, their spatial distribution is primarily controlled by meridional gas motions, which are typically much faster than the dust-gas drift. In particular, the grains that have settled near the midplane are carried rapidly inwards by a fast accretion stream to the inner edges of the gas rings, where they are lifted up by the gas flows diverted away from the midplane by a strong poloidal magnetic field. The flow pattern in our simulation provides an attractive explanation for the meridional flows recently inferred in HD 163296 and other disks, including both "collapsing" regions where the gas near the disk surface converges towards the midplane and a disk wind. Our study highlights the prevalence of the potentially observable meridional flows associated with the gas substructure formation in non-ideal MHD disks and their crucial role in generating rings and gaps in dust.

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arXiv2022

Direct Formation of Planetary Embryos in Self-Gravitating Disks

Giant planets have been discovered at large separations from the central star. Moreover, a striking number of young circumstellar disks have gas and/or dust gaps at large orbital separations, potentially driven by embedded planetary objects. To form massive planets at large orbital separations through core accretion within disk lifetime, however, an early solid body to seed pebble and gas accretion is desirable. Young protoplanetary disks are likely self-gravitating, and these gravitoturbulent disks may efficiently concentrate solid material at the midplane driven by spiral waves. We run 3D local hydrodynamical simulations of gravitoturbulent disks with Lagrangian dust particles to determine whether particle and gas self-gravity can lead to the formation of dense solid bodies, seeding later planet formation. When self-gravity between dust particles is included, solids of size $\mathrm{St} = 0.1$ to $1$ concentrate within the gravitoturbulent spiral features and collapse under their own self-gravity into dense clumps up to several $M_{\oplus}$ in mass at wide orbits. Simulations with dust that drift most efficiently, $\mathrm{St}=1$, form the most massive clouds of particles, while simulations with smaller dust particles, $\mathrm{St}=0.1$, have clumps with masses an order of magnitude lower. When the effect of dust backreaction onto the gas is included, dust clumps become smaller by a factor of a few but more numerous. The existence of large solid bodies at an early stage of the disk can accelerate the planet formation process, particularly at wide orbital separations, and potentially explain planets distant from the central stars and young protoplanetary disks with substructures.

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arXiv2021

Streaming Instability with Multiple Dust Species: II. Turbulence and Dust-Gas Dynamics at Nonlinear Saturation

The streaming instability is a fundamental process that can drive dust-gas dynamics and ultimately planetesimal formation in protoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classified into two distinct regimes, fast- and slow-growth, depending on the dust-size distribution and the total dust-to-gas density ratio $ε$. Using numerical simulations of an unstratified disc, we bring three cases in different regimes into nonlinear saturation. We find that the saturation states of the two fast-growth cases are similar to its single-species counterparts. The one with maximum dimensionless stopping time $τ_\mathrm{s,max}=0.1$ and $ε=2$ drives turbulent vertical dust-gas vortices, while the other with $τ_\mathrm{s,max}=2$ and $ε=0.2$ leads to radial traffic jams and filamentary structures of dust particles. The dust density distribution for the former is flat in low densities, while the one for the latter has a low-end cutoff. By contrast, the one slow-growth case results in a virtually quiescent state. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particles moving towards dense regions while small particles remain in the diffuse regions, and the mean radial drift of each dust species is appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived from multi-wavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latter along with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary discs.

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arXiv2021

Kozai-Lidov oscillations triggered by a tilt instability of detached circumplanetary discs

Circumplanetary discs can be linearly unstable to the growth of disc tilt in the tidal potential of the star-planet system. We use three-dimensional hydrodynamical simulations to characterize the disc conditions needed for instability, together with its long term evolution. Tilt growth occurs for disc aspect ratios, evaluated near the disc outer edge, of $H/r\gtrsim 0.05$, with a weak dependence on viscosity in the wave-like regime of warp propagation. Lower mass giant planets are more likely to have circumplanetary discs that satisfy the conditions for instability. We show that the tilt instability can excite the inclination to above the threshold where the circumplanetary disc becomes unstable to Kozai--Lidov (KL) oscillations. Dissipation in the Kozai--Lidov unstable regime caps further tilt growth, but the disc experiences large oscillations in both inclination and eccentricity. Planetary accretion occurs in episodic accretion events. We discuss implications of the joint tilt--KL instability for the detectability of circumplanetary discs, for the obliquity evolution of forming giant planets, and for the formation of satellite systems.

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arXiv2020

Streaming Instability with Multiple Dust Species: I. Favourable Conditions for the Linear Growth

Recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the growth timescale of the instability can be longer than the disc lifetime when multiple dust species are considered. To further explore this finding, we use both linear analysis and direct numerical simulations with gas fluid and dust particles to mutually validate and study the unstable modes of the instability in more detail. We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution $[T_{s,min}, T_{s,max}]$ and the total solid-to-gas mass ratio $\varepsilon$ and introduce a third dimension with the slope $q$ of the size distribution. We find that the fast-growth regime and the slow-growth regime are distinctly separated in the $\varepsilon$-$T_{s,max}$ space, while this boundary is not appreciably sensitive to $q$ or $T_{s,min}$. With a wide range of dust sizes present in the disc (e.g. $T_{s,min}\lesssim10^{-3}$), the growth rate in the slow-growth regime decreases as more dust species are considered. With a narrow range of dust sizes (e.g. $T_{s,max}/T_{s,min}=5$), on the other hand, the growth rate in most of the $\varepsilon$-$T_{s,max}$ space is converged with increasing dust species, but the fast and the slow growth regimes remain clearly separated. Moreover, it is not necessary that the largest dust species dominate the growth of the unstable modes, and the smaller dust species can affect the growth rate in a complicated way. In any case, we find that the fast-growth regime is bounded by $\varepsilon\gtrsim 1$ or $T_{s,max}\gtrsim 1$, which may represent the favourable conditions for planetesimal formation.

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arXiv2020

The evolution of a circumplanetary disc with a dead zone

We investigate whether the regular Galilean satellites could have formed in the dead zone of a circumplanetary disc. A dead zone is a region of weak turbulence in which the magnetorotational instability (MRI) is suppressed, potentially an ideal environment for satellite formation. With the grid-based hydrodynamic code, FARGO3D, we examine the evolution of a circumplanetary disc model with a dead zone. Material accumulates in the dead zone of the disc leading to a higher total mass and but a similar temperature profile compared to a fully turbulent disc model. The tidal torque increases the rate of mass transport through the dead zone leading to a steady state disc with a dead zone that does not undergo accretion outbursts. We explore a range of disc, dead zone and mass inflow parameters and find that the maximum mass of the disc is around 0.001 MJ . Since the total solid mass of such a disc is much lower, we find that there is not sufficient material in the disc for in situ formation of the Galilean satellites and that external supplement is required.

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arXiv2020

Formation of the polar debris disc around 99 Herculis

We investigate the formation mechanism for the observed nearly polar aligned (perpendicular to the binary orbital plane) debris ring around the eccentric orbit binary 99 Herculis. An initially inclined nonpolar debris ring or disc will not remain flat and will not evolve to a polar configuration, due to the effects of differential nodal precession that alter its flat structure. However, a gas disc with embedded well coupled solids around the eccentric binary may evolve to a polar configuration as a result of pressure forces that maintain the disc flatness and as a result of viscous dissipation that allows the disc to increase its tilt. Once the gas disc disperses, the debris disc is in a polar aligned state in which there is little precession. We use three-dimensional hydrodynamical simulations, linear theory, and particle dynamics to study the evolution of a misaligned circumbinary gas disc and explore the effects of the initial disc tilt, mass, and size. We find that for a wide range of parameter space, the polar alignment timescale is shorter than the lifetime of the gas disc. Using the observed level of alignment of 3 deg. from polar, we place an upper limit on the mass of the gas disc of about 0.014 M_sun at the time of gas dispersal. We conclude that the polar debris disc around 99 Her can be explained as the result of an initially moderately inclined gas disc with embedded solids. Such a disc may provide an environment for the formation of polar planets.

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arXiv2019

Morphological signatures induced by dust back reaction in discs with an embedded planet

Recent observations have revealed a gallery of substructures in the dust component of nearby protoplanetary discs, including rings, gaps, spiral arms, and lopsided concentrations. One interpretation of these substructures is the existence of embedded planets. Not until recently, however, most of the modelling effort to interpret these observations ignored the dust back reaction to the gas. In this work, we conduct local-shearing-sheet simulations for an isothermal, inviscid, non-self-gravitating, razor-thin dusty disc with a planet on a fixed circular orbit. We systematically examine the parameter space spanned by planet mass ($0.1M_\text{th} \le M_\text{p} \le 1M_\text{th}$, where $M_\text{th}$ is the thermal mass), dimensionless stopping time ($10^{-3} \le τ_\text{s} \le 1$), and solid abundance ($0 < Z \le 1$). We find that when the dust particles are tightly coupled to the gas ($τ_\text{s} < 0.1$), the spiral arms are less open and the gap driven by the planet becomes deeper with increasing $Z$, consistent with a reduced speed of sound in the approximation of a single dust-gas mixture. By contrast, when the dust particles are marginally coupled ($0.1 \lesssim τ_\text{s} \lesssim 1$), the spiral structure is insensitive to $Z$ and the gap structure in the gas can become significantly skewed and unidentifiable. When the latter occurs, the pressure maximum radially outside of the planet is weakened or even extinguished, and hence dust filtration by a low-mass ($M_\text{p} < M_\text{th}$) planet could be reduced or eliminated. Finally, we find that the gap edges where the dust particles are accumulated as well as the lopsided large-scale vortices driven by a massive planet, if any, are unstable, and they are broken into numerous small-scale dust-gas vortices.

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arXiv2018

Diffusion and Concentration of Solids in the Dead Zone of a Protoplanetary Disk

The streaming instability is a promising mechanism to drive the formation of planetesimals in protoplanetary disks. To trigger this process, it has been argued that sedimentation of solids onto the mid-plane needs to be efficient and therefore that a quiescent gaseous environment is required. It is often suggested that dead-zone or disk-wind structure created by non-ideal magnetohydrodynamical (MHD) effects meets this requirement. However, simulations have shown that the midplane of a dead zone is not completely quiescent. In order to examine the concentration of solids in such an environment, we use the local-shearing-box approximation to simulate a particle-gas system with an Ohmic dead zone including mutual drag force between the gas and the solids. We systematically compare the evolution of the system with ideal or non-ideal MHD, with or without back-reaction drag force from particles on gas, and with varying solid abundances. Similar to previous investigations of dead zone dynamics, we find that particles of dimensionless stopping time $τ_s=0.1$ do not sediment appreciably more than those in ideal magneto-rotational turbulence, resulting in a vertical scale height an order of magnitude larger than in a laminar disk. Contrary to the expectation that this should curb the formation of planetesimals, we nevertheless find that strong clumping of solids still occurs in the dead zone when solid abundances are similar to the critical value for a laminar environment. This can be explained by the weak radial diffusion of particles near the mid-plane. The results imply that the sedimentation of particles to the mid-plane is not a necessary criterion for the formation of planetesimals by the streaming instability.

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arXiv2018

Streaming Instability of Multiple Particle Species in Protoplanetary Disks

The radial drift and diffusion of dust particles in protoplanetary disks affect both the opacity and temperature of such disks as well as the location and timing of planetesimal formation. In this paper, we present results of numerical simulations of particle-gas dynamics in protoplanetary disks that include dust grains with various size distributions. We consider three scenarios in terms of particle size ranges, one where the Stokes number $τ_{\rm{s}} = 10^{-1} - 10^0$, one where $τ_{\rm{s}} = 10^{-4} - 10^{-1}$ and finally one where $τ_{\rm{s}} = 10^{-3} - 10^{0}$. Moreover, we consider both discrete and continuous distributions in particle size. In accordance with previous works we find in our multi-species simulations that different particle sizes interact via the gas and as a result their dynamics changes compared to the single-species case. The larger species trigger the streaming instability and create turbulence that drives the diffusion of the solid materials. We measure the radial equilibrium velocity of the system and find that the radial drift velocity of the large particles is reduced in the multi-species simulations and that the small particle species move on average outwards. We also vary the steepness of the size distribution, such that the exponent of the solid number density distribution, $\rm{d}\it{N}/\rm{d}\it{a} \propto \it{a^{-q}}$, is either $q = 3$ or $q = 4$. We measure the scale height of the particles and observe that small grains are stirred up well above the sedimented midplane layer where the large particles reside. Our measured diffusion and drift parameters can be used in coagulation models for planet formation as well as to understand relative mixing of the components of primitive meteorites (matrix, chondrules and CAIs) prior to inclusion in their parent bodies.

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arXiv2017

Concentrating small particles in protoplanetary disks through the streaming instability

Laboratory experiments indicate that direct growth of silicate grains via mutual collisions can only produce particles up to roughly millimeters in size. On the other hand, recent simulations of the streaming instability have shown that mm/cm-sized particles require an excessively high metallicity for dense filaments to emerge. Using a numerical algorithm for stiff mutual drag force, we perform simulations of small particles with significantly higher resolutions and longer simulation times than in previous investigations. We find that particles of dimensionless stopping time $τ_\mathrm{s} = 10^{-2}$ and $10^{-3}$ -- representing mm- and cm-sized particles interior of the water ice line -- concentrate themselves via the streaming instability at a solid abundance of a few percent. We thus revise a previously published critical solid abundance curve for the regime of $τ_\mathrm{s} \ll 1$. The solid density in the concentrated regions reaches values higher than the Roche density, indicating that direct collapse of particles down to mm sizes into planetesimals is possible. Our results hence bridge the gap in particle size between direct dust growth limited by bouncing and the streaming instability.

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arXiv2016

Initial mass function of planetesimals formed by the streaming instability

The streaming instability is a mechanism to concentrate solid particles into overdense filaments that undergo gravitational collapse and form planetesimals. However, it remains unclear how the initial mass function of these planetesimals depends on the box dimensions of numerical simulations. To resolve this, we perform simulations of planetesimal formation with the largest box dimensions to date, allowing planetesimals to form simultaneously in multiple filaments that can only emerge within such large simulation boxes. In our simulations, planetesimals with sizes between 80 km and several hundred kilometers form. We find that a power law with a rather shallow exponential cutoff at the high-mass end represents the cumulative birth mass function better than an integrated power law. The steepness of the exponential cutoff is largely independent of box dimensions and resolution, while the exponent of the power law is not constrained at the resolutions we employ. Moreover, we find that the characteristic mass scale of the exponential cutoff correlates with the mass budget in each filament. Together with previous studies of high-resolution simulations with small box domains, our results therefore imply that the cumulative birth mass function of planetesimals is consistent with an exponentially tapered power law with a power-law exponent of approximately -1.6 and a steepness of the exponential cutoff in the range of 0.3-0.4.

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arXiv2016

Integration of Particle-Gas Systems with Stiff Mutual Drag Interaction

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff, particularly because of small particles and/or strong local solid concentration, that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can for example be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.

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arXiv2014

On the Feeding Zone of Planetesimal Formation by the Streaming Instability

The streaming instability is a promising mechanism to overcome the barriers in direct dust growth and lead to the formation of planetesimals. Most previous studies of the streaming instability, however, were focused on a local region of a protoplanetary disk with a limited simulation domain such that only one filamentary concentration of solids has been observed. The characteristic separation between filaments is therefore not known. To address this, we conduct the largest-scale simulations of the streaming instability to date, with computational domains up to 1.6 gas scale heights both horizontally and vertically. The large dynamical range allows the effect of vertical gas stratification to become prominent. We observe more frequent merging and splitting of filaments in simulation boxes of high vertical extent. We find multiple filamentary concentrations of solids with an average separation of about 0.2 local gas scale heights, much higher than the most unstable wavelength from linear stability analysis. This measures the characteristic separation of planetesimal forming events driven by the streaming instability and thus the initial feeding zone of planetesimals.

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arXiv2014

Temperature Fluctuations driven by Magnetorotational Instability in Protoplanetary Disks

The magnetorotational instability (MRI) drives magnetized turbulence in sufficiently ionized regions of protoplanetary disks, leading to mass accretion. The dissipation of the potential energy associated with this accretion determines the thermal structure of accreting regions. Until recently, the heating from the turbulence has only been treated in an azimuthally averaged sense, neglecting local fluctuations. However, magnetized turbulence dissipates its energy intermittently in current sheet structures. We study this intermittent energy dissipation using high resolution numerical models including a treatment of radiative thermal diffusion in an optically thick regime. Our models predict that these turbulent current sheets drive order unity temperature variations even where the MRI is damped strongly by Ohmic resistivity. This implies that the current sheet structures where energy dissipation occurs must be well resolved to correctly capture the flow structure in numerical models. Higher resolutions are required to resolve energy dissipation than to resolve the magnetic field strength or accretion stresses. The temperature variations are large enough to have major consequences for mineral formation in disks, including melting chondrules, remelting calcium-aluminum rich inclusions, and annealing silicates; and may drive hysteresis: current sheets in MRI active regions could be significantly more conductive than the remainder of the disk.

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arXiv2013

Hydrodynamical Simulations of the Barred Spiral Galaxy NGC 1097

NGC 1097 is a nearby barred spiral galaxy believed to be interacting with the elliptical galaxy NGC 1097A located to its northwest. It hosts a Seyfert 1 nucleus surrounded by a circumnuclear starburst ring. Two straight dust lanes connected to the ring extend almost continuously out to the bar. The other ends of the dust lanes attach to two main spiral arms. To provide a physical understanding of its structural and kinematical properties, two-dimensional hydrodynamical simulations have been carried out. Numerical calculations reveal that many features of the gas morphology and kinematics can be reproduced provided that the gas flow is governed by a gravitational potential associated with a slowly rotating strong bar. By including the self-gravity of the gas disk in our calculation, we have found the starburst ring to be gravitationally unstable which is consistent with the observation in \citet{hsieh11}. Our simulations show that the gas inflow rate is 0.17 M$_\sun$ yr$^{-1}$ into the region within the starburst ring even after its formation, leading to the coexistence of both a nuclear ring and a circumnuclear disk.

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