Protoplanet Dynamics in a Shear-dominated Disk

Collins, Benjamin F.; Sari, R.

doi:10.1086/506388

Cited by 11 publications

(11 citation statements)

References 16 publications

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“…The slope of the distribution of excitations dictates the shape of the distribution. This explains the coincidence of the distribution that we derive in this work being exactly that of the distribution of eccentricity of protoplanets in a shear-dominated planetesimal disk, where the probability of changing the eccentricity of a protoplanet is inversely proportional to the size of that change (Collins & Sari 2006;Collins et al 2007). …”

Section: Discussionsupporting

confidence: 77%

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Lévy Flights of Binary Orbits Due to Impulsive Encounters

Collins¹,

Sari²

2008

The Astronomical Journal

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We examine the evolution of an almost-circular Keplerian orbit interacting with unbound perturbers. We calculate the change in eccentricity and angular momentum that results from a single encounter, assuming that the timescale for the interaction is shorter than the orbital period. The orbital perturbations are incorporated into a Boltzmann equation that allows for eccentricity dissipation. We present an analytic solution to the Boltzmann equation that describes the distribution of orbital eccentricity and relative inclination as a function of time. The eccentricity and inclination of the binary do not evolve according to a normal random walk but perform a Lévy flight. The slope of the mass spectrum of perturbers dictates whether close gravitational scatterings are more important than distant tidal ones. When close scatterings are important, the mass spectrum sets the slope of the eccentricity and inclination distribution functions. We use this general framework to understand the eccentricities of several Kuiper belt systems: Pluto, 2003 EL 61 , and Eris. We use the model of Tholen et al. to separate the non-Keplerian components of the orbits of Pluto's outer moons Nix and Hydra from the motion excited by interactions with other Kuiper belt objects. Our distribution is consistent with the observations of Nix, Hydra, and the satellites of 2003 EL 61 and Eris. We address applications of this work to objects outside of the solar system, such as extra-solar planets around their stars and millisecond pulsars.

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Section: Discussionsupporting

confidence: 77%

“…The solution to this equation has been presented in several earlier works, where the authors investigate the eccentricity distribution of the oligarchs in a protoplanetary disk (Collins & Sari 2006;Collins et al 2007):…”

Section: Eccentricitymentioning

confidence: 99%

Lévy Flights of Binary Orbits Due to Impulsive Encounters

Collins¹,

Sari²

2008

The Astronomical Journal

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“…But when the mutual velocity of two bodies are below their mutual Hill velocity (sub-hill), we adopt instead the viscous heating prescription in eq. (13) of Collins et al (2007), calibrated by the numerical simulations of Collins & Sari (2006). GLS give explicit formula for the rate of viscous stirring and dynamical friction, depending on whether the velocities are sub-or super-hill (also called shear-or dispersion-dominated).…”

Section: Dynamical Friction and Viscous Stirringmentioning

confidence: 99%

Conglomeration of Kilometer-Sized Planetesimals

Shannon

Lithwick

2015

ApJ

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We study the efficiency of forming large bodies, starting from a sea of equal-sized planetesimals. This is likely one of the earlier steps of planet formation and relevant for the formation of the asteroid belt, the Kuiper belt and extra-solar debris disks. Here we consider the case that the seed planetesimals do not collide frequently enough for dynamical collisional to be important (the collisionless limit), using a newly constructed conglomeration code, and by carefully comparing numerical results with analytical scalings. In the absence of collisional cooling, as large bodies grow by accreting small bodies, the velocity dispersion of the small bodies (u) is increasingly excited. Growth passes from the well-known run-away stage (when u is higher than the big bodies' hill velocity) to the newly discovered trans-hill stage (when u and big bodies both grow, but u remains at the big bodies' hill velocity). We find, concurring with the analytical understandings developed in Lithwick (2014), as well as previous numerical studies, that a size spectrum dn/dR ∝ R −4 results, and that the formation efficiency, defined as mass fraction in bodies much larger than the initial size, is ∼ a few × R ⊙ /a, or ∼ 10 −3 at the distance of the Kuiper belt. We argue that this extreme inefficiency invalidates the conventional conglomeration model for the formation of both our Kuiper belt and extra-solar debris disks. New theories, possibly involving direct gravitational collapse, or strong collisional cooling of small planetesimals, are required.

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“…Scattering is said to be in the shear‐dominated (dynamically cold) regime when v ≲ v H and in the dispersion‐dominated regime (dynamically hot) if v ≳ v H (Stewart & Ida 2000; Collins & Sari 2006). Shear is induced by the difference between the Keplerian angular velocities of primaries having different radii.…”

Section: Three‐body Hill Approximationmentioning

confidence: 99%

Production of trans-Neptunian binaries through chaos-assisted capture

Lee

Astakhov

Farrelly

2007

Monthly Notices of the Royal Astronomical Society

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The recent discovery of binary objects in the Kuiper-belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary-object formation model based on the notion of chaos-assisted capture. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity, and orbital element distribu- tions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering in the circular Hill four-body problem and find that the chaos-assisted capture mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also addressed.Comment: submitted to MNRA

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Protoplanet Dynamics in a Shear-dominated Disk

Cited by 11 publications

References 16 publications

Lévy Flights of Binary Orbits Due to Impulsive Encounters

Lévy Flights of Binary Orbits Due to Impulsive Encounters

Conglomeration of Kilometer-Sized Planetesimals

Production of trans-Neptunian binaries through chaos-assisted capture

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