arXiv subjects

Andrew N. Youdin

Publications and source records attributed to Andrew N. Youdin.

At least 37 records · Page 2Linked to original sources

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

Dust Settling Instability in Protoplanetary Discs

The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the midplane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the midplane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the midplane. This work presents a range of linear calculations and non-linear simulations, performed with FARGO3D, to assess conditions for DSI growth. We expand on previous linear analyses by including particle size distributions and performing a detailed study of the amount of background turbulence needed to stabilize the DSI. When including binned size distributions, the DSI often produces converged growth rates with fewer bins than the standard SI. With background turbulence, we find that the most favorable conditions for DSI growth are weak turbulence, characterized by $α\lesssim 10^{-6}$ with intermediate-sized grains that settle from one gas scale-height. These conditions could arise during a sudden decrease in disc turbulence following an accretion outburst. Ignoring background turbulence, we performed a parameter survey of local 2D DSI simulations. Particle clumping was either weak or occurred slower than particles settle. Clumping was reduced by a factor of two in a comparison 3D simulation. Overall, our results strongly disfavor the hypothesis that the DSI significantly promotes planetesimal formation. Non-linear simulations of the DSI with different numerical methods could support or challenge these findings.

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arXiv2020

Superparticle Method for Simulating Collisions

For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated to represent a collectively large collisional cross section of real particles. Here we develop a superparticle-based method that replicates the kinetic energy loss during real-world collisions, implement it in an $N$-body code and test it. The tests provide interesting insights into dynamics of self gravitating collisional systems. They show how particle systems evolve over several free fall timescales to form central concentrations and equilibrated outer shells. The superparticle method can be extended to account for the accretional growth of objects during inelastic mergers.

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arXiv2019

Astro2020 APC White Paper: Theoretical Astrophysics 2020-2030

The past two decades have seen a tremendous investment in observational facilities that promise to reveal new and unprecedented discoveries about the universe. In comparison, the investment in theoretical work is completely dwarfed, even though theory plays a crucial role in the interpretation of these observations, predicting new types of phenomena, and informing observing strategies. In this white paper, we argue that in order to reach the promised critical breakthroughs in astrophysics over the next decade and well beyond, the national agencies must take a serious approach to investment in theoretical astrophysics research. We discuss the role of theory in shaping our understanding of the universe, and then we provide a multi-level strategy, from the grassroots to the national, to address the current underinvestment in theory relative to observational work.

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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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arXiv2018

Witnessing Planetary Systems in the Making with the Next Generation Very Large Array

The discovery of thousands of exoplanets over the last couple of decades has shown that the birth of planets is a very efficient process in nature. Theories invoke a multitude of mechanisms to describe the assembly of planets in the disks around pre-main-sequence stars, but observational constraints have been sparse on account of insufficient sensitivity and resolution. Understanding how planets form and interact with their parental disk is crucial also to illuminate the main characteristics of a large portion of the full population of planets that is inaccessible to current and near-future observations. This White Paper describes some of the main issues for our current understanding of the formation and evolution of planets, and the critical contribution expected in this field by the Next Generation Very Large Array.

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arXiv2018

Inside-Out Planet Formation. IV. Pebble Evolution and Planet Formation Timescales

Systems with tightly-packed inner planets (STIPs) are very common. Chatterjee & Tan proposed Inside-Out Planet Formation (IOPF), an in situ formation theory, to explain these planets. IOPF involves sequential planet formation from pebble-rich rings that are fed from the outer disk and trapped at the pressure maximum associated with the dead zone inner boundary (DZIB). Planet masses are set by their ability to open a gap and cause the DZIB to retreat outwards. We present models for the disk density and temperature structures that are relevant to the conditions of IOPF. For a wide range of DZIB conditions, we evaluate the gap opening masses of planets in these disks that are expected to lead to truncation of pebble accretion onto the forming planet. We then consider the evolution of dust and pebbles in the disk, estimating that pebbles typically grow to sizes of a few cm during their radial drift from several tens of AU to the inner, $\lesssim1\:$AU-scale disk. A large fraction of the accretion flux of solids is expected to be in such pebbles. This allows us to estimate the timescales for individual planet formation and entire planetary system formation in the IOPF scenario. We find that to produce realistic STIPs within reasonable timescales similar to disk lifetimes requires disk accretion rates of $\sim10^{-9}\:M_\odot\:{\rm yr}^{-1}$ and relatively low viscosity conditions in the DZIB region, i.e., Shakura-Sunyaev parameter of $α\sim10^{-4}$.

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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

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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arXiv2017

Structure and Evolution of Internally Heated Hot Jupiters

Hot Jupiters receive strong stellar irradiation, producing equilibrium temperatures of $1000 - 2500 \ \mathrm{Kelvin}$. Incoming irradiation directly heats just their thin outer layer, down to pressures of $\sim 0.1 \ \mathrm{bars}$. In standard irradiated evolution models of hot Jupiters, predicted transit radii are too small. Previous studies have shown that deeper heating -- at a small fraction of the heating rate from irradiation -- can explain observed radii. Here we present a suite of evolution models for HD 209458b where we systematically vary both the depth and intensity of internal heating, without specifying the uncertain heating mechanism(s). Our models start with a hot, high entropy planet whose radius decreases as the convective interior cools. The applied heating suppresses this cooling. We find that very shallow heating -- at pressures of $1 - 10 \ \mathrm{bars}$ -- does not significantly suppress cooling, unless the total heating rate is $\gtrsim 10\%$ of the incident stellar power. Deeper heating, at $100 \ \mathrm{bars}$, requires heating at only $1\%$ of the stellar irradiation to explain the observed transit radius of $1.4 R_{\rm Jup}$ after 5 Gyr of cooling. In general, more intense and deeper heating results in larger hot Jupiter radii. Surprisingly, we find that heat deposited at $10^4 \ \mathrm{bars}$ -- which is exterior to $\approx 99\%$ of the planet's mass -- suppresses planetary cooling as effectively as heating at the center. In summary, we find that relatively shallow heating is required to explain the radii of most hot Jupiters, provided that this heat is applied early and persists throughout their evolution.

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arXiv2016

The Role of Non-ionizing Radiation Pressure in Star Formation: The Stability of Cores and Filaments

Stars form when filaments and dense cores in molecular clouds fragment and collapse due to self-gravity. In the most basic analyses of gravitational stability, the competition between self-gravity and thermal pressure sets the critical (i.e. maximum stable) mass of spheres and the critical line density of cylinders. Previous work has considered additional support from magnetic fields and turbulence. Here, we consider the effects of non-ionizing radiation, specifically the inward radiation pressure force that acts on dense structures embedded in an isotropic radiation field. Using hydrostatic, isothermal models, we find that irradiation lowers the critical mass and line density for gravitational collapse, and can thus act as a trigger for star formation. For structures with moderate central densities, $\sim10^3$ cm$^{-3}$, the interstellar radiation field in the Solar vicinity has an order unity effect on stability thresholds. For more evolved objects with higher central densities, a significant lowering of stability thresholds requires stronger irradiation, as can be found closer to the Galactic center or near stellar associations. Even when strong sources of ionizing radiation are absent or extincted, our study shows that interstellar irradiation can significantly influence the star formation process.

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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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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

Planetesimals in Debris Disks

Planetesimals form in gas-rich protoplanetary disks around young stars. However, protoplanetary disks fade in about 10 Myr. The planetesimals (and also many of the planets) left behind are too dim to study directly. Fortunately, collisions between planetesimals produce dusty debris disks. These debris disks trace the processes of terrestrial planet formation for 100 Myr and of exoplanetary system evolution out to 10 Gyr. This chapter begins with a summary of planetesimal formation as a prelude to the epoch of planetesimal destruction. Our review of debris disks covers the key issues, including dust production and dynamics, needed to understand the observations. Our discussion of extrasolar debris keeps an eye on similarities to and differences from Solar System dust.

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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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arXiv2014

Minimum Core Masses for Giant Planet Formation With Realistic Equations of State and Opacities

Giant planet formation by core accretion requires a core that is sufficiently massive to trigger runaway gas accretion in less that the typical lifetime of protoplanetary disks. We explore how the minimum required core mass, M_crit, depends on a non-ideal equation of state and on opacity changes due to grain growth, across a range of stellocentric distances from 5-100 AU. This minimum M_crit applies when planetesimal accretion does not substantially heat the atmosphere. Compared to an ideal gas polytrope, the inclusion of molecular hydrogen (H_2) dissociation and variable occupation of H_2 rotational states increases M_crit. Specifically, M_crit increases by a factor of ~2 if the H_2 spin isomers, ortho- and parahydrogen, are in thermal equilibrium, and by a factor of ~2-4 if the ortho-to-para ratio is fixed at 3:1. Lower opacities due to grain growth reduce M_crit. For a standard disk model around a Solar mass star, we calculate M_crit ~ 8 M_Earth at 5 AU, decreasing to ~5 M_Earth at 100 AU, for a realistic EOS with an equilibrium ortho-to-para ratio and for grain growth to cm-sizes. If grain coagulation is taken into account, M_crit may further reduce by up to one order of magnitude. These results for the minimum critical core mass are useful for the interpretation of surveys that find exoplanets at a range of orbital distances.

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