arXiv subjects

Andrew N. Youdin

Publications and source records attributed to Andrew N. Youdin.

52 records · Page 3Linked to original sources

arXiv2014

On the Minimum Core Mass for Giant Planet Formation at Wide Separations

In the core accretion hypothesis, giant planets form by gas accretion onto solid protoplanetary cores. The minimum (or critical) core mass to form a gas giant is typically quoted as 10 Earth masses. The actual value depends on several factors: the location in the protoplanetary disk, atmospheric opacity, and the accretion rate of solids. Motivated by ongoing direct imaging searches for giant planets, this study investigates core mass requirements in the outer disk. To determine the fastest allowed rates of gas accretion, we consider solid cores that no longer accrete planetesimals, as this would heat the gaseous envelope. Our spherical, two-layer atmospheric cooling model includes an inner convective region and an outer radiative zone that matches onto the disk. We determine the minimum core mass for a giant planet to form within a typical disk lifetime of 3 Myr. The minimum core mass declines with disk radius, from ~8.5 Earth masses at 5 AU to ~3.5 Earth masses at 100 AU, with standard interstellar grain opacities. Lower temperatures in the outer disk explain this trend, while variations in disk density are less influential. At all distances, a lower dust opacity or higher mean molecular weight reduces the critical core mass. Our non-self-gravitating, analytic cooling model reveals that self-gravity significantly affects early atmospheric evolution, starting when the atmosphere is only ~10% as massive as the core.

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arXiv2012

From Disks to Planets

This pedagogical chapter covers the theory of planet formation, with an emphasis on the physical processes relevant to current research. After summarizing empirical constraints from astronomical and geophysical data, we describe the structure and evolution of protoplanetary disks. We consider the growth of planetesimals and of larger solid protoplanets, followed by the accretion of planetary atmospheres, including the core accretion instability. We also examine the possibility that gas disks fragment directly into giant planets and/or brown dwarfs. We defer a detailed description of planet migration and dynamical evolution to other work, such as the complementary chapter in this series by Morbidelli (available at arXiv:1106.4114).

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arXiv2012

Circumbinary Chaos: Using Pluto's Newest Moon to Constrain the Masses of Nix & Hydra

The Pluto system provides a unique local laboratory for the study of binaries with multiple low mass companions. In this paper, we study the orbital stability of P4, the most recently discovered moon in the Pluto system. This newfound companion orbits near the plane of the Pluto-Charon binary, roughly halfway between the two minor moons Nix and Hydra. We use a suite of few body integrations to constrain the masses of Nix and Hydra, and the orbital parameters of P4. For the system to remain stable over the age of the Solar System, the masses of Nix and Hydra likely do not exceed 5e16 kg and 9e16 kg, respectively. These upper limits assume a fixed mass ratio between Nix and Hydra at the value implied by their median optical brightness. Our study finds that stability is more sensitive to their total mass and that a downward revision of Charon's eccentricity (from our adopted value of 0.0035) is unlikely to significantly affect our conclusions. Our upper limits are an order of magnitude below existing astrometric limits on the masses of Nix and Hydra. For a density at least that of ice, the albedos of Nix and Hydra would exceed 0.3. This constraint implies they are icy, as predicted by giant impact models. Even with these low masses, P4 only remains stable if its eccentricity e < 0.02. The 5:1 commensurability with Charon is particularly unstable, Combining stability constraints with the observed mean motion places the preferred orbit for P4 just exterior to the 5:1 resonance. These predictions will be tested when the New Horizons satellite visits Pluto. Based on the results for the Pluto-Charon system, we expect that circumbinary, multi-planet systems will be more widely spaced than their singleton counterparts. Further, circumbinary exoplanets close to the three-body stability boundary, such as those found by Kepler, are less likely to have other companions nearby.

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arXiv2011

The Exoplanet Census: A General Method, Applied to Kepler

We develop a general method to fit the planetary distribution function (PLDF) to exoplanet survey data. This maximum likelihood method accommodates more than one planet per star and any number of planet or target star properties. Application to \Kepler data relies on estimates of the efficiency of discovering transits around Solar type stars by Howard et al. (2011). These estimates are shown to agree with theoretical predictions for an ideal transit survey. Using announced \Kepler planet candidates, we fit the PLDF as a joint powerlaw in planet radius, down to 0.5 R_Eart, and orbital period, up to 50 days. The estimated number of planets per star in this sample is ~ 0.7 --- 1.4, where the broad range covers systematic uncertainties in the detection efficiency. To analyze trends in the PLDF we consider four planet samples, divided between shorter and longer periods at 7 days and between large and small radii at 3 R_Earth. At longer periods, the size distribution of the small planets, with index α= -1.2 \pm 0.2 steepens to α= -2.0 \pm 0.2 for the larger planet sample. For shorter periods, the opposite is seen: smaller planets follow a steep powerlaw, α= -1.9 \pm 0.2 that is much shallower, α= -0.7 \pm 0.2 at large radii. The observed deficit of intermediate-sized planets at the shortest periods may arise from the evaporation and sublimation of Neptune and Saturn-like planets. If the trend and explanation hold, it would be spectacular observational confirmation of the core accretion and migration hypotheses, and allow refinement of these theories.

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arXiv2011

On the Formation of Planetesimals via Secular Gravitational Instabilities with Turbulent Stirring

We study the gravitational instability (GI) of small solids in a gas disk as a mechanism to form planetesimals. Dissipation from gas drag introduces secular GI, which proceeds even when standard GI criteria for a critical density or Toomre's $Q$ predict stability. We include the stabilizing effects of turbulent diffusion, which suppresses small scale GI. The radially wide rings that do collapse contain up to $\sim 0.1$ Earth masses of solids. Subsequent fragmentation of the ring (not modeled here) would produce a clan of chemically homogenous planetesimals. Particle radial drift time scales (and, to a lesser extent, disk lifetimes and sizes) restrict the viability of secular GI to disks with weak turbulent diffusion, characterized by $α\lesssim 10^{-4}$. Thus midplane dead zones are a preferred environment. Large solids with radii $\gtrsim 10$ cm collapse most rapidly because they partially decouple from the gas disk. Smaller solids, even below $\sim$ mm-sizes could collapse if particle-driven turbulence is weakened by either localized pressure maxima or super-Solar metallicity. Comparison with simulations that include particle clumping by the streaming instability shows that our linear model underpredicts rapid, small scale gravitational collapse. Thus the inclusion of more detailed gas dynamics promotes the formation of planetesimals. We discuss relevant constraints from Solar System and accretion disk observations.

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arXiv2010

The Mechanical Greenhouse: Burial of Heat by Turbulence in Hot Jupiter Atmospheres

The intense irradiation received by hot Jupiters suppresses convection in the outer layers of their atmospheres and lowers their cooling rates. "Inflated" hot Jupiters, i.e., those with anomalously large transit radii, require additional sources of heat or suppressed cooling. We consider the effect of forced turbulent mixing in the radiative layer, which could be driven by atmospheric circulation or by another mechanism. Due to stable stratification in the atmosphere, forced turbulence drives a downward flux of heat. Weak turbulent mixing slows the cooling rate by this process, as if the planet was irradiated more intensely. Stronger turbulent mixing buries heat into the convective interior, provided the turbulence extends to the radiative-convective boundary. This inflates the planet until a balance is reached between the heat buried into and radiated from the interior. We also include the direct injection of heat due to the dissipation of turbulence or other effects. Such heating is already known to slow planetary cooling. We find that dissipation also enhances heat burial from mixing by lowering the threshold for turbulent mixing to drive heat into the interior. Strong turbulent mixing of heavy molecular species such as TiO may be necessary to explain stratospheric thermal inversions. We show that the amount of mixing required to loft TiO may overinflate the planet by our mechanism. This possible refutation of the TiO hypothesis deserves further study. Our inflation mechanism requires a deep stratified layer that only exists when the absorbed stellar flux greatly exceeds the intrinsic emitted flux. Thus it would be less effective for more luminous brown dwarfs and for longer period gas giants, including Jupiter and Saturn.

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arXiv2010

Formation of Kuiper Belt Binaries by Gravitational Collapse

A large fraction of 100-km-class low-inclination objects in the classical Kuiper Belt (KB) are binaries with comparable mass and wide separation of components. A favored model for their formation was capture during the coagulation growth of bodies in the early KB. Instead, recent studies suggested that large objects can rapidly form in the protoplanetary disks when swarms of locally concentrated solids collapse under their own gravity. Here we examine the possibility that KB binaries formed during gravitational collapse when the excess of angular momentum prevented the agglomeration of available mass into a solitary object. We find that this new mechanism provides a robust path toward the formation of KB binaries with observed properties, and can explain wide systems such as 2001 QW322 and multiples such as (47171) 1999 TC36. Notably, the gravitational collapse is capable of producing 100% binary fraction for a wide range of the swarm's initial angular momentum values. The binary components have similar masses (80% have the secondary-over-primary radius ratio >0.7) and their separation ranges from ~1,000 to ~100,000 km. The binary orbits have eccentricities from e=0 to ~1, with the majority having e<0.6. The binary orbit inclinations with respect to the initial angular momentum of the swarm range from i=0 to ~90 deg, with most cases having i<50 deg. Our binary formation mechanism implies that the primary and secondary components in each binary pair should have identical bulk composition, which is consistent with the current photometric data. We discuss the applicability of our results to the Pluto-Charon, Orcus-Vanth, (617) Patroclus-Menoetius and (90) Antiope binary systems.

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arXiv2010

The Runts of the Litter: Why planets formed through gravitational instability can only be failed binary stars

Recent direct imaging discoveries suggest a new class of massive, distant planets around A stars. These widely separated giants have been interpreted as signs of planet formation driven by gravitational instability, but the viability of this mechanism is not clear cut. In this paper, we first discuss the local requirements for fragmentation and the initial fragment mass scales. We then consider whether the fragment's subsequent growth can be terminated within the planetary mass regime. Finally, we place disks in the larger context of star formation and disk evolution models. We find that in order for gravitational instability to produce planets, disks must be atypically cold in order to reduce the initial fragment mass. In addition, fragmentation must occur during a narrow window of disk evolution, after infall has mostly ceased, but while the disk is still sufficiently massive to undergo gravitational instability. Under more typical conditions, disk-born objects will likely grow well above the deuterium burning planetary mass limit. We conclude that if planets are formed by gravitational instability, they must be the low mass tail of the distribution of disk-born companions. To validate this theory, on-going direct imaging surveys must find a greater abundance of brown dwarf and M-star companions to A-stars. Their absence would suggest planet formation by a different mechanism such as core accretion, which is consistent with the debris disks detected in these systems.

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arXiv2007

Planetesimal Formation with Particle Feedback

Proposed mechanisms for the formation of km-sized solid planetesimals face long-standing difficulties. Robust sticking mechanisms that would produce planetesimals by coagulation alone remain elusive. The gravitational collapse of smaller solids into planetesimals is opposed by stirring from turbulent gas. This proceeding describes recent works showing that "particle feedback," the back-reaction of drag forces on the gas in protoplanetary disks, promotes particle clumping as seeds for gravitational collapse. The idealized streaming instability demonstrates the basic ability of feedback to generate particle overdensities. More detailed numerical simulations show that the particle overdensities produced in turbulent flows trigger gravitational collapse to planetesimals. We discuss surprising aspects of this work, including the large (super-Ceres) mass of the collapsing bound cluster, and the finding that MHD turbulence aids gravitational collapse.

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arXiv2007

Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations

We describe the diffusion and random velocities of solid particles due to stochastic forcing by turbulent gas. We include the orbital dynamics of Keplerian disks, both in-plane epicycles and vertical oscillations. We obtain a new result for the diffusion of solids. The Schmidt number (ratio of gas to particle diffusivity) is Sc = 1 + (Omega t_stop)^2, in terms of the particle stopping time, t_stop, and the orbital frequency, Omega. The standard result, Sc = 1 + t_stop/t_eddy, in terms of the eddy turnover time, t_eddy, is shown to be incorrect. The main difference is that Sc rises quadratically, not linearly, with stopping time. Consequently, particles larger than ~ 10 cm in protoplanetary disks will suffer less radial diffusion and will settle closer to the midplane. Such a layer of boulders would be more prone to gravitational collapse. Our predictions of RMS speeds, vertical scale height and diffusion coefficients will help interpret numerical simulations. We confirm previous results for the vertical stirring of particles (scale heights and random velocities), and add a correction for arbitrary ratios of eddy to orbital times. The particle layer becomes thinner for t_eddy > 1/Omega, with the strength of turbulent diffusion held fixed. We use two analytic techniques -- the Hinze-Tchen formalism and the Fokker-Planck equation with velocity diffusion -- with identical results when the regimes of validity overlap. We include simple physical arguments for the scaling of our results.

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arXiv2005

Planetesimal Formation without Thresholds. I: Dissipative Gravitational Instabilities and Particle Stirring by Turbulence

We analyze the gravitational collapse of solids subject to gas drag in a protoplanetary disk. We also study the stirring of solids by turbulent fluctuations to determine the velocity dispersion and thickness of the midplane particle layer. The usual thresholds for determining gravitational instability in disks, Toomre's criterion and/or the Roche density, do not apply. Dissipation of angular momentum allows instability at longer wavelengths, lower densities, and higher velocity dispersions than without drag. Small solids will slowly leak into axisymmetric rings since initial collapse occurs over many orbits. Growth is fastest when particle stopping times are comparable to orbital times. Our analysis of particle stirring by turbulence is consistent with previous results for tightly coupled particles, but is generalized to loose coupling where epicyclic motions contribute to random velocities. A companion paper applies these results to turbulent protoplanetary disks.

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arXiv2005

Planetesimal Formation without Thresholds. II: Gravitational Instability of Solids in Turbulent Protoplanetary Disks

We show that small solids in low mass, turbulent protoplanetary disks collect into self-gravitating rings. Growth is faster than disk lifetimes and radial drift times for moderately strong turbulence, characterized by dimensionless diffusivities, $α_g < 10^{-6} -- 10^{-3}$ when particles are mm-sized. This range reflects a strong dependance on disk models. Growth is faster for higher particle surface densities. Lower gas densities and larger solids also give faster growth, as long as aerodynamic coupling is tight. In simple power law models, growth is slowest around ~0.3 AU, where drag coupling is strongest for mm-sized solids. Growth is much faster close to the star where orbital times are short, with implications for in situ formation of short period extrasolar planets. Growth times also decrease toward the outer disk where lower gas densities allow greater particle settling. Beyond roughly Kuiper Belt distances however, solids are sufficiently decoupled from gas that dissipative gravitational instabilities are less effective. Turbulence not only slows growth, but also increases radial wavelengths. The initial solid mass in an unstable ring can be ~0.01 M_Earth or greater, huge compared to km-sized planetesimals. Nonlinear fragmentation, which has not been studied in detail, will lower the final planetesimal mass. We consider applications to the asteroid belt and discuss the alternate hypothesis of collisional agglomeration.

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arXiv2004

Streaming Instabilities in Protoplanetary Disks

Interpenetrating streams of solids and gas in a Keplerian disk produce a local, linear instability. The two components mutually interact via aerodynamic drag, which generates radial drift and triggers unstable modes. The secular instability does not require self-gravity, yet it generates growing particle density perturbations that could seed planetesimal formation. Growth rates are slower than dynamical, but faster than radial drift, timescales. Growth rates, like streaming velocities, are maximized for marginal coupling (stopping times comparable dynamical times). Fastest growth occurs when the solid to gas density ratio is order unity and feedback is strongest. Curiously, growth is strongly suppressed when the densities are too nearly equal. The relation between background drift and wave properties is explained by analogy with Howard's semicircle theorem. The three-dimensional, two-fluid equations describe a sixth order (in the complex frequency) dispersion relation. A terminal velocity approximation allows simplification to an approximate cubic dispersion relation. To describe the simplest manifestation of this instability, we ignore complicating (but possibly relevant) factors like vertical stratification, dispersion of particle sizes, turbulence, and self-gravity. We consider applications to planetesimal formation and compare our work to other studies of particle-gas dynamics.

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arXiv2004

Particle Pile-ups and Planetesimal Formation

Solid particles in protoplanetary disks that are sufficiently super-solar in metallicity overcome turbulence generated by vertical shear to gravitationally condense into planetesimals. Super-solar metallicities result if solid particles pile up as they migrate starward as a result of aerodynamic drag. Previous analyses of aerodynamic drift rates that account for mean flow differences between gas and particles yield particle pile-ups. We improve on these studies not only by accounting for the collective inertia of solids relative to that of gas, but also by including the transport of angular momentum by turbulent stresses within the particle layer. These turbulent stresses are derived in a physically self-consistent manner from the structure of marginally Kelvin-Helmholtz turbulent flows. They are not calculated using the usual plate drag formulae, whose use we explain is inappropriate. Accounting for the relative inertia of solids to gas retards, but does not prevent, particle pile-ups, and generates more spatially extended regions of metal enrichment. Turbulent transport hastens pile-ups. We conclude that particle pile-up is a robust outcome in sufficiently passive protoplanetary disks. Connections to observations of circumstellar disks, including the Kuiper Belt, and the architectures of planetary systems are made.

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arXiv2003

Obstacles to the Collisional Growth of Planetesimals

The debate over whether kilometer-sized solids, or planetesimals, assemble by collision-induced chemical sticking or by gravity-driven unstable modes remains unsettled. In light of recent work showing that gravitational growth can occur despite turbulent stirring, we critically evaluate the collisional hypothesis. Impact speeds in protoplanetary disks reach 50 m/s in a laminar disk and may be larger in turbulent disks. We consider the role of elastic and plastic deformations, restructuring of "rubble piles," and sticky organic matter. Coagulation is possible for dust grains with large surface area-to-volume ratios. Simple energetic arguments show that bouncing, cratering, and fragmentation should dominate collisional dynamics between millimeter and kilometer sizes.

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arXiv2002

Planetesimal Formation by Gravitational Instability

We investigate the formation of planetesimals via the gravitational instability of solids that have settled to the midplane of a circumstellar disk. Vertical shear between the gas and a subdisk of solids induces turbulent mixing which inhibits gravitational instability. Working in the limit of small, well-coupled particles, we find that the mixing becomes ineffective when the surface density ratio of solids to gas exceeds a critical value. Solids in excess of this precipitation limit can undergo midplane gravitational instability and form planetesimals. However, this saturation effect typically requires increasing the local ratio of solid to gaseous surface density by factors of two to ten times cosmic abundances, depending on the exact properties of the gas disk. We discuss existing astrophysical mechanisms for augmenting the ratio of solids to gas in protoplanetary disks by such factors, and investigate a particular process that depends on the radial variations of orbital drift speeds induced by gas drag. This mechanism can concentrate millimeter sized chondrules to the supercritical surface density in < few x 10^6 years, a suggestive timescale for the disappearance of dusty disks in T Tauri stars. We discuss the relevance of our results to some outstanding puzzles in planet formation theory: the size of the observed solar system, and the rapid type I migration of Earth mass bodies.

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