A Unified Theory for the Effects of Stellar Perturbations and Galactic Tides on Oort Cloud Comets

Collins, Benjamin F.; Sari, Re’em

doi:10.1088/0004-6256/140/5/1306

Cited by 37 publications

(14 citation statements)

References 17 publications

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“…Gravitational scattering by Neptune is not expected to result in a mean plane different than the invariable plane. These objects are also too close to the Sun to have their angular momentum significantly affected by Galactic tides or stellar flybys (see, e.g., Collins & Sari 2010). It is therefore interesting to consider possible explanations for the measured deviation from the expected mean plane of the more distant KBOs.…”

Section: Summary and Discussionmentioning

confidence: 99%

The Curiously Warped Mean Plane of the Kuiper Belt

Volk

Malhotra

2017

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We measured the mean plane of the Kuiper Belt as a function of semimajor axis. For the classical Kuiper Belt as a whole (the nonresonant objects in the semimajor axis range 42-48 au), we find a mean plane of inclination accord with theoretical expectations of the secular effects of the known planets. With finer semimajor axis bins, we detect a statistically significant warp in the mean plane near semimajor axes 40-42 au. Linear secular theory predicts a warp near this location due to the 18 n nodal secular resonance; however, the measured mean plane for the 40.3-42 au semimajor axis bin (just outside the 18 n ) is inclined 13  to the predicted plane, a nearly 3σ discrepancy. For the more distant Kuiper Belt objects of semimajor axes in the range 50-80 au, the expected mean plane is close to the invariable plane of the solar system, but the measured mean plane deviates greatly from this: it has inclination i 9 . 1 18 W =  - +  . We estimate this deviation from the expected mean plane to be statistically significant at the ∼97%-99% confidence level. We discuss several possible explanations for this deviation, including the possibility that a relatively close-in (a 100  au), unseen, small planetary-mass object in the outer solar system is responsible for the warping.

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Section: Summary and Discussionmentioning

confidence: 99%

The Curiously Warped Mean Plane of the Kuiper Belt

Volk

Malhotra

2017

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“…This approximation neglects the granularity and stochastic variability of the cluster potential caused by encounters with other stars, which are very important in dense environments of clusters (Heggie 1975;Hut & Bahcall 1983;Hut 1983;Heggie & Rasio 1996;Collins & Sari 2008). The cumulative effect of a large number of such encounters is what eventually contributes to the smooth tidal field of the cluster (Collins & Sari 2010); thus, one hopes that in the long run our framework should provide a qualitatively accurate picture of binary evolution in clusters. Nevertheless, in the future we plan to extend our calculation by including the effects of individual stellar encounters on evolution of the binary inner orbit (Weinberg et al 1987).…”

Section: Discussionmentioning

confidence: 99%

“…In doing this we neglect the stochastic effect of individual stellar passages on the orbital elements of the binary. Separating the cumulative effect of multiple stellar encounters from the smooth Galactic tide is a non-trivial exercise, as demonstrated previously by Collins & Sari (2010) and Jiang & Tremaine (2010). Nevertheless, for the purposes of clarity, we prefer to focus here on the effects of the mean tidal field due to the smooth mass distribution inside the cluster -effects of encounters with individual stars will be incorporated later.…”

Section: Introductionmentioning

confidence: 98%

Secular dynamics of binaries in stellar clusters – I. General formulation and dependence on cluster potential

Hamilton

Rafikov

2019

Monthly Notices of the Royal Astronomical Society

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Orbital evolution of binary systems in dense stellar clusters is important in a variety of contexts: origin of blue stragglers, progenitors of compact object mergers, millisecond pulsars, and so on. Here we consider the general problem of secular evolution of the orbital elements of a binary system driven by the smooth tidal field of an axisymmetric stellar cluster (globular, nuclear, etc.) in which the binary orbits. We derive a secular Hamiltonian (averaged over both the inner Keplerian orbit of the binary and its outer orbit within the cluster) valid to quadrupole order for an arbitrary cluster potential and explore its characteristics. This doubly-averaged 'tidal' Hamiltonian depends on just two parameters, which fully absorb the information about the background cluster potential and the binary's orbit within it: a dimensional parameter A setting the secular timescale, and a dimensionless parameter Γ which determines the phase portrait of the binary's inner orbital evolution. We examine the dependence of A and Γ on cluster potential (both spherical and axisymmetric) and on the binary orbit within the cluster. Our theory reproduces known secular results -such as Lidov-Kozai evolution and the effect of the Galactic tide on Oort Cloud comets -in appropriate limits, but is more general. It provides a universal framework for understanding dynamical evolution of various types of binaries driven by the smooth tidal field of any axisymmetric potential. In a companion paper (Hamilton & Rafikov 2019b) we provide a detailed exploration of the resulting orbital dynamics.

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“…This regime is appropriate if one is studying perturbations to the orbits of relatively tight systems (hard binaries), such as millisecond pulsars or hot Jupiters. On the other hand, Collins & Sari (2008) (see also Collins & Sari 2010) considered the opposite regime in which the timescale for the flyby interaction is much shorter than the inner binary period, so that the encounter can be treated in the impulse approximation. This is the correct description when studying the dynamics of the Oort Cloud comets in the Galaxy or very soft binaries in clusters.…”

Section: Stellar Scattering and Other Non-ideal Effectsmentioning

confidence: 99%

Secular dynamics of binaries in stellar clusters – II. Dynamical evolution

Hamilton

Rafikov

2019

Monthly Notices of the Royal Astronomical Society

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Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system driven by the global tidal field of an axisymmetric stellar cluster in which the binary orbits. In a companion paper (Hamilton & Rafikov 2019a) we developed a general Hamiltonian framework describing such systems. The effective (doublyaveraged) Hamiltonian derived there encapsulates all information about the tidal potential experienced by the binary in its orbit around the cluster in a single parameter Γ. Here we provide a thorough exploration of the phase-space of the corresponding secular problem as Γ is varied. We find that for Γ > 1/5 the phase-space structure and the evolution of binary orbital elements are qualitatively similar to the Lidov-Kozai problem. However, this is only one of four possible regimes, because the dynamics are qualitatively changed by bifurcations at Γ = 1/5, 0, −1/5. We show how the dynamics are altered in each regime and calculate characteristics such as secular evolution timescale, maximum possible eccentricity, etc. We verify the predictions of our doubly-averaged formalism numerically and find it to be very accurate when its underlying assumptions are fulfilled, typically meaning that the secular timescale should exceed the period of the binary around the cluster by 10 − 10 2 (depending on the cluster potential and binary orbit). Our results may be relevant for understanding the nature of a variety of exotic systems harboured by stellar clusters.1 To sufficient accuracy, the binary's barycentre follows the trajectory of a test particle, d 2 Rg/dt 2 = −∇Φ where Φ is the smooth cluster potential.

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A Unified Theory for the Effects of Stellar Perturbations and Galactic Tides on Oort Cloud Comets

Cited by 37 publications

References 17 publications

The Curiously Warped Mean Plane of the Kuiper Belt

The Curiously Warped Mean Plane of the Kuiper Belt

Secular dynamics of binaries in stellar clusters – I. General formulation and dependence on cluster potential

Secular dynamics of binaries in stellar clusters – II. Dynamical evolution

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