arXiv subjects

Rixin Li

Publications and source records attributed to Rixin Li.

34 records · Page 2Linked to original sources

arXiv2024

Hydrodynamical Evolution of Black-Hole Binaries Embedded in AGN Discs: III. The Effects of Viscosity

Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs offer a distinct dynamical channel to produce black hole mergers detected in gravitational waves by LIGO/Virgo. To understand their orbital evolution through interactions with the disc gas, we perform a suite of 2D high-resolution, local shearing box, viscous hydrodynamical simulations of equal-mass binaries. We find that viscosity not only smooths the flow structure around prograde circular binaries, but also greatly raises their accretion rates. The torque associated with accretion may be overwhelmingly positive and dominate over the gravitational torque at a high accretion rate. However, the accreted angular momentum per unit mass decreases with increasing viscosity, making it easier to shrink the binary orbit. In addition, retrograde binaries still experience rapid orbital decay, and prograde eccentric binaries still experience eccentricity damping. Our numerical experiments further show that prograde binaries are more likely to be hardened if the physical sizes of the accretors are sufficiently small such that the accretion rate is reduced. The dependency of the binary accretion rate on the accretor size can be weaken through boosted accretion either due to a high viscosity or a more isothermal-like equation of state (EOS). Our results widen the explored parameter space for the hydrodynamics of embedded BBHs and demonstrate that their orbital evolution in AGN discs is a complex, multifaceted problem.

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arXiv2023

Streaming Instability and Turbulence: Conditions for Planetesimal Formation

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

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arXiv2023

Planetesimal Initial Mass Functions following Diffusion Regulated Gravitational Collapse

The initial mass function (IMF) of planetesimals is of key importance for understanding the initial stages of planet formation, yet theoretical predictions so far have been insufficient in explaining the variety of IMFs found in simulations. Here, we connect diffusion-tidal-shear limited planetesimal formation within the framework of a Toomre-like instability in the particle mid-plane of a protoplanetary disk to an analytic prediction for the planetesimal IMF. The shape of the IMF is set by the stability parameter $Q_\mathrm{p}$, which in turn depends on the particle Stokes number, the Toomre $Q$ value of the gas, the local dust concentration and the local diffusivity. We compare our prediction to high-resolution numerical simulations of the streaming instability and planetesimal formation via gravitational collapse. We find that our IMF prediction agrees with numerical results, and is consistent with both the `planetesimals are born big' paradigm and the power law description commonly found in simulations.

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arXiv2022

Hydrodynamical Evolution of Black-Hole Binaries Embedded in AGN Discs

Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs are possible progenitors of black-hole mergers detected in gravitational waves by LIGO/VIRGO. To better understand the hydrodynamical evolution of BBHs interacting with the disc gas, we perform a suite of high-resolution 2D simulations of binaries in local disc (shearing-box) models, considering various binary mass ratios, eccentricities and background disc properties. We use the $γ$-law equation of state and adopt a robust post-processing treatment to evaluate the mass accretion rate, torque and energy transfer rate on the binary to determine its long-term orbital evolution. We find that circular comparable-mass binaries contract, with an orbital decay rate of a few times the mass doubling rate. Eccentric binaries always experience eccentricity damping. Prograde binaries with higher eccentricities or smaller mass ratios generally have slower orbital decay rates, with some extreme cases exhibiting orbital expansion. The averaged binary mass accretion rate depends on the physical size of the accretor. The accretion flows are highly variable, and the dominant variability frequency is the apparent binary orbital frequency (in the rotating frame around the central massive BH) for circular binaries but gradually shifts to the radial epicyclic frequency as the binary eccentricity increases. Our findings demonstrate that the dynamics of BBHs embedded in AGN discs is quite different from that of isolated binaries in their own circumbinary discs. Furthermore, our results suggest that the hardening timescales of the binaries are much shorter than their migration timescales in the disc, for all reasonable binary and disc parameters.

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arXiv2022

Hydrodynamical Evolution of Black-Hole Binaries Embedded in AGN Discs: II. Dependence on Equation of State, Binary Mass, and Separation Scales

Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs offer a promising dynamical channel to produce black-hole mergers that are detectable by LIGO/Virgo. Modeling the interactions between the disc gas and the embedded BBHs is crucial to understand their orbital evolution. Using a suite of 2D high-resolution simulations of prograde equal-mass circular binaries in local disc models, we systematically study how their hydrodynamical evolution depends on the equation of state (EOS; including the $γ$-law and isothermal EOS) and on the binary mass and separation scales (relative to the supermassive BH mass and the Hill radius, respectively). We find that binaries accrete slower and contract in orbit if the EOS is far from isothermal such that the surrounding gas is diffuse, hot, and turbulent. The typical orbital decay rate is of the order of a few times the mass doubling rate. For a fixed EOS, the accretion flows are denser, hotter, and more turbulent around more massive or tighter binaries. The torque associated with accretion is often comparable to the gravitational torque, so both torques are essential in determining the long-term binary orbital evolution. We carry out additional simulations with non-accreting binaries and find that their orbital evolution can be stochastic and is sensitive to the gravitational softening length, and the secular orbital evolution can be very different from those of accreting binaries. Our results indicate that stellar-mass BBHs may be hardened efficiently under ideal conditions, namely less massive and wider binaries embedded in discs with a non-isothermal EOS.

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arXiv2021

Dust Accumulation near the Magnetospheric Truncation of Protoplanetary Discs around T Tauri Stars

The prevalence of short-period super-Earths that are independent of host metallicity challenges the theoretical construction of their origin. We propose that dust trapping in the global pressure bump induced by magnetospheric truncation in evolved protoplanetary discs (PPDs) around T Tauri stars offers a promising formation mechanism for super-Earths, where the host metallicity is already established. To better understand this planet forming scenario, we construct a toy inner disc model and focus on the evolution of dust trapped in the bump, taking into account the supply from drifting pebbles and loss due to funnel flows. We develop an implicit coagulation-fragmentation code, $\mathtt{Rubble}$, and perform a suite of simulations to evolve the local dust size distributions. Our study for the first time considers dust feedback effect on turbulent diffusion in this kind of model. We report that efficient dust growth and significant accumulation of dust mass is possible in less turbulent disc with sturdier solids and with faster external supply, laying out a solid foundation for further growth towards planetesimals and planetary embryos. We further find that, depending on the dominant process, solid mass may predominantly accumulate in cm-sized grains or particles in runaway growth, indicating different ways of forming planetesimals. Furthermore, these various outcomes show different efficiencies in saving dust from funnel flows, suggesting that they may be distinguishable by constraining the opacity of funnel flows. Also, these diverse dust behaviours may help explain the observed dipper stars and rapidly varying shadows in PPDs.

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arXiv2021

Thresholds for Particle Clumping by the Streaming Instability

The streaming instability (SI) is a mechanism to aerodynamically concentrate solids in protoplanetary disks and trigger the formation of planetesimals. The SI produces strong particle clumping if the ratio of solid to gas surface density -- an effective metallicity -- exceeds a critical value. This critical value depends on particle sizes and disk conditions such as radial drift-inducing pressure gradients and levels of turbulence. To quantify these thresholds, we perform a suite of vertically-stratified SI simulations over a range of dust sizes and metallicities. We find a critical metallicity as low as 0.4% for the optimum particle sizes and standard radial pressure gradients (normalized value of $Π= 0.05$). This sub-Solar metallicity is lower than previous results due to improved numerical methods and computational effort. We discover a sharp increase in the critical metallicity for small solids, when the dimensionless stopping time (Stokes number) is $\leq 0.01$. We provide simple fits to the size-dependent SI clumping threshold, including generalizations to different disk models and levels of turbulence. We also find that linear, unstratified SI growth rates are a surprisingly poor predictor of particle clumping in non-linear, stratified simulations, especially when the finite resolution of simulations is considered. Our results widen the parameter space for the SI to trigger planetesimal formation.

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arXiv2021

Protoplanetary Disk Rings as Sites for Planetesimal Formation

Axisymmetric dust rings are a ubiquitous feature of young protoplanetary disks. These rings are likely caused by pressure bumps in the gas profile; a small bump can induce a traffic jam-like pattern in the dust density, while a large bump may halt radial dust drift entirely. The resulting increase in dust concentration may trigger planetesimal formation by the streaming instability (SI), as the SI itself requires some initial concentration. Here we present the first 3D simulations of planetesimal formation in the presence of a pressure bump modeled specifically after those observed by ALMA. In particular, we place a pressure bump at the center of a large 3D shearing box, along with an initial solid-to-gas ratio of $Z = 0.01$, and we include both particle back-reaction and particle self-gravity. We consider both mm-sized and cm-sized particles separately. For simulations with cm-sized particles, we find that even a small pressure bump leads to the formation of planetesimals via the streaming instability; a pressure bump does {\it not} need to fully halt radial particle drift for the SI to become efficient. Furthermore, pure gravitational collapse via concentration in pressure bumps (such as would occur at sufficiently high concentrations and without the streaming instability) is not responsible for planetesimal formation. For mm-sized particles, we find tentative evidence that planetesimal formation does not occur. This result, if it holds up at higher resolution and for a broader range of parameters, could put strong constraints on where in protoplanetary disks planetesimals can form. Ultimately, however, our results suggest that for cm-sized particles, planetesimal formation in pressure bumps is an extremely robust process.

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arXiv2020

Binary Planetesimal Formation from Gravitationally Collapsing Pebble Clouds

Planetesimals are compact astrophysical objects roughly 1-1000 km in size, massive enough to be held together by gravity. They can grow by accreting material to become full-size planets. Planetesimals themselves are thought to form by complex physical processes from small grains in protoplanetary disks. The streaming instability (SI) model states that mm/cm-size particles (pebbles) are aerodynamically collected into self-gravitating clouds which then directly collapse into planetesimals. Here we analyze ATHENA simulations of the SI to characterize the initial properties (e.g., rotation) of pebble clouds. Their gravitational collapse is followed with the PKDGRAV N-body code, which has been modified to realistically account for pebble collisions. We find that pebble clouds rapidly collapse into short-lived disk structures from which planetesimals form. The planetesimal properties depend on the cloud's scaled angular momentum, l=L/(M R_H^2 Omega, where L and M are the angular momentum and mass, R_H is the Hill radius, and Omega is the orbital frequency. Low-l pebble clouds produce tight (or contact) binaries and single planetesimals. Compact high-l clouds give birth to binary planetesimals with attributes that closely resemble the equal-size binaries found in the Kuiper belt. Significantly, the SI-triggered gravitational collapse can explain the angular momentum distribution of known equal-size binaries -- a result pending verification from studies with improved resolution. About 10% of collapse simulations produce hierarchical systems with two or more large moons. These systems should be found in the Kuiper belt when observations reach the threshold sensitivity.

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arXiv2020

Turbulence Regulates the Rate of Planetesimal Formation via Gravitational Collapse

We study how the interaction between the streaming instability and intrinsic gas-phase turbulence affects planetesimal formation via gravitational collapse in protoplanetary disks. Turbulence impedes the formation of particle clumps by acting as an effective turbulent diffusivity, but it can also promote planetesimal formation by concentrating solids, for example in zonal flows. We quantify the effect of turbulent diffusivity using numerical simulations of the streaming instability in small local domains, forced with velocity perturbations that establish approximately Kolmogorov-like turbulence. We find that planetesimal formation is suppressed by turbulence once velocity fluctuations exceed $\langle δv^2 \rangle \simeq 10^{-3.5} - 10^{-3} c_s^2$. Turbulence whose strength is just below the threshold reduces the rate at which solids are bound into clumps. Our results suggest that the well-established turbulent thickening of the mid-plane solid layer is the primary mechanism by which turbulence influences planetesimal formation and that planetesimal formation requires a mid-plane solid-to-gas ratio $ε\gtrsim 0.5$. We also quantify the initial planetesimal mass function using a new clump-tracking method to determine each planetesimal mass shortly after collapse. For models in which planetesimals form, we show that the mass function is well-described by a broken power law, whose parameters are robust to the inclusion and strength of imposed turbulence. Turbulence in protoplanetary disks is likely to substantially exceed the threshold for planetesimal formation at radii where temperatures $T \gtrsim 10^3 \ {\rm K}$ lead to thermal ionization. Planetesimal formation may therefore be unviable in the inner disk out to 2-3 times the dust sublimation radius.

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arXiv2020

Demographics of Planetesimals Formed by the Streaming Instability

The streaming instability (SI) is a mechanism to aerodynamically concentrate solids in protoplanetary disks and facilitate the formation of planetesimals. Recent numerical modeling efforts have demonstrated the increasing complexity of the initial mass distribution of planetesimals. To better constrain this distribution, we conduct SI simulations including the self-gravity with hitherto the highest resolution. To subsequently identify all of the self-bound clumps, we develop a new clump-finding tool, PLanetesimal ANalyzer (\texttt{PLAN}). We then apply a maximum likelihood estimator to fit a suite of parameterized models with different levels of complexity to the simulated mass distribution. To determine which models are best-fitting and statistically robust, we apply three model selection criteria with different complexity penalties. We find that the initial mass distribution of clumps is not universal regarding both the functional forms and parameter values. Our model selection criteria prefer models different from those previously considered in the literature. Fits to multi-segment power law models break to a steeper distribution above masses close to 100 km collapsed planetesimals, similar to observed Kuiper Belt size distributions. We find evidence for a turnover in the low mass end of the planetesimal mass distribution in our high resolution run. Such a turnover is expected for gravitational collapse, but had not previously been reported.

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arXiv2019

The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. II. The Effect of the Radial Gas Pressure Gradient

The streaming instability concentrates solid particles in protoplanetary disks, leading to gravitational collapse into planetesimals. Despite its key role in producing particle clumping and determining critical length scales in the instability's linear regime, the influence of the disk's radial pressure gradient on planetesimal properties has not been examined in detail. Here, we use streaming instability simulations that include particle self-gravity to study how the planetesimal initial mass function depends on the radial pressure gradient. Fitting our results to a power-law, ${\rm d}N / {\rm d}M_p \propto M_p^{-p}$, we find a single value $p \approx 1.6$ describes simulations in which the pressure gradient varies by $\gtrsim 2$. An exponentially truncated power-law provides a significantly better fit, with a low mass slope of $p^\prime \approx 1.3$ that weakly depends on the pressure gradient. The characteristic truncation mass is found to be $\sim M_G = 4 π^5 G^2 Σ_p^3 / Ω^4$. We exclude the cubic dependence of the characteristic mass with pressure gradient suggested by linear considerations, finding instead a linear scaling. These results strengthen the case for a streaming-derived initial mass function that depends at most weakly on the aerodynamic properties of the disk and participating solids. A simulation initialized with zero pressure gradient---which is {\em not} subject to the streaming instability---also yields a top-heavy mass function but with modest evidence for a different shape. We discuss the consistency of the theoretically predicted mass function with observations of Kuiper Belt planetesimals, and describe implications for models of early stage planet formation..

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arXiv2019

Trans-Neptunian Binaries as Evidence for Planetesimal Formation by the Streaming Instability

A critical step toward the emergence of planets in a protoplanetary disk consists in accretion of planetesimals, bodies 1-1000 km in size, from smaller disk constituents. This process is poorly understood partly because we lack good observational constraints on the complex physical processes that contribute to planetesimal formation. In the outer solar system, the best place to look for clues is the Kuiper belt, where icy planetesimals survived to this day. Here we report evidence that Kuiper belt planetesimals formed by the streaming instability, a process in which aerodynamically concentrated clumps of pebbles gravitationally collapse into 100-km-class bodies. Gravitational collapse was previously suggested to explain the ubiquity of equal-size binaries in the Kuiper belt. We analyze new hydrodynamical simulations of the streaming instability to determine the model expectations for the spatial orientation of binary orbits. The predicted broad inclination distribution with 80% of prograde binary orbits matches the observations of trans-Neptunian binaries. The formation models which imply predominantly retrograde binary orbits can be ruled out. Given its applicability over a broad range of protoplanetary disk conditions, it is expected that the streaming instability seeded planetesimal formation also elsewhere in the solar system, and beyond.

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arXiv2018

On the Numerical Robustness of the Streaming Instability: Particle Concentration and Gas Dynamics in Protoplanetary Disks

The Streaming Instability (SI) is a mechanism to concentrate solids in protoplanetary disks. Nonlinear particle clumping from the SI can trigger gravitational collapse into planetesimals. To better understand the numerical robustness of the SI, we perform a suite of vertically-stratified 3D simulations with fixed physical parameters known to produce strong clumping. We vary the numerical implementation, namely the computational domain size and the vertical boundary conditions (vBCs), comparing newly-implemented outflow vBCs to the previously-used periodic and reflecting vBCs. We find strong particle clumping by the SI is mostly independent of the vBCs. However, peak particle densities are higher in larger simulation domains due to a larger particle mass reservoir. We report SI-triggered zonal flows, i.e., azimuthally-banded radial variations of gas pressure. These structures have low amplitudes, insufficient to halt particle radial drift, confirming that particle trapping in gas pressure maxima is not the mechanism of the SI. We find that outflow vBCs produce artificially large gas outflow rates at vertical boundaries. However, the outflow vBCs reduce artificial reflections at vertical boundaries, allowing more particle sedimentation, and showing less temporal variation and better convergence with box size. The radial spacing of dense particle filaments is $\sim0.15$ gas scale heights ($H$) for all vBCs, which sets the feeding zone for planetesimal growth in self-gravitating simulations. Our results validate the use of the outflow vBCs in SI simulations, even with vertical boundaries close ($\leq 0.4H$) to the disk midplane. Overall, our study demonstrates the numerical robustness of nonlinear particle clumping by the SI.

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arXiv2017

Evidence for universality in the initial planetesimal mass function

Planetesimals may form from the gravitational collapse of dense particle clumps initiated by the streaming instability. We use simulations of aerodynamically coupled gas-particle mixtures to investigate whether the properties of planetesimals formed in this way depend upon the sizes of the particles that participate in the instability. Based on three high resolution simulations that span a range of dimensionless stopping time $6 \times 10^{-3} \leq τ\leq 2$ no statistically significant differences in the initial planetesimal mass function are found. The mass functions are fit by a power-law, ${\rm d}N / {\rm d}M_p \propto M_p^{-p}$, with $p=1.5-1.7$ and errors of $Δp \approx 0.1$. Comparing the particle density fields prior to collapse, we find that the high wavenumber power spectra are similarly indistinguishable, though the large-scale geometry of structures induced via the streaming instability is significantly different between all three cases. We interpret the results as evidence for a near-universal slope to the mass function, arising from the small-scale structure of streaming-induced turbulence.

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arXiv2016

The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. I. The Role of Self-Gravity

We study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over-densities generated via the streaming instability. To carry out these studies, we implement and test a particle-mesh self-gravity module for the Athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self-gravitating solid particles. Upon employment of our algorithm to planetesimal formation simulations, we find that (when a direct comparison is possible) the Athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques. In particular, the gravitational collapse of streaming-initiated clumps leads to an initial planetesimal mass function that is well-represented by a power-law, dN/dM ~ M^{-p}, with p = 1.6 +/- 0.1, which equates to a differential size distribution dN/dR ~ R^{-q}, with q = 2.8 +/- 0.1. We find no significant trends with resolution from a convergence study of up to 512^3 grid zones and Npar = 1.5x10^8 particles. Likewise, the power-law slope appears indifferent to changes in the relative strength of self-gravity and tidal shear, and to the time when (for reasons of numerical economy) self-gravity is turned on, though the strength of these claims is limited by small number statistics. For a typically assumed radial distribution of minimum mass solar nebula solids (assumed here to have dimensionless stopping time τ= 0.3), our results support the hypothesis that bodies on the scale of large asteroids or Kuiper Belt Objects could have formed as the high-mass tail of a primordial planetesimal population.

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