arXiv subjects

Chris Hamilton

Publications and source records attributed to Chris Hamilton.

35 records · Page 2Linked to original sources

arXiv2023

Relativistic phase space diffusion of compact object binaries in stellar clusters and hierarchical triples

The LIGO/Virgo detections of compact object mergers have posed a challenge for theories of binary evolution and coalescence. One promising avenue for producing mergers dynamically is through secular eccentricity oscillations driven by an external perturber, be it a tertiary companion (as in the Lidov-Kozai (LK) mechanism) or the tidal field of the stellar cluster in which the binary orbits. The simplest theoretical models of these oscillations use a 'doubly-averaged' (DA) approximation, averaging both over the binary's internal Keplerian orbit and its 'outer' barycentric orbit relative to the perturber. However, DA theories do not account for fluctuations of the perturbing torque on the outer orbital timescale, which are known to increase a binary's eccentricity beyond the maximum DA value, potentially accelerating mergers. Here we reconsider the impact of these short-timescale fluctuations in the test-particle quadrupolar limit for binaries perturbed by arbitrary spherical cluster potentials (including LK as a special case), {in particular including 1pN} general relativistic (GR) apsidal precession of the internal orbit. Focusing on the behavior of the binary orbital elements around peak eccentricity, we discover a new effect, relativistic phase space diffusion (RPSD), in which a binary can jump to a completely new dynamical trajectory on an outer orbital timescale, violating the approximate conservation of DA integrals of motion. RPSD arises from an interplay between secular behavior at extremely high eccentricity, short-timescale fluctuations, and rapid GR precession, and can change the subsequent secular evolution dramatically. This effect occurs even in hierarchical triples, but has not been uncovered until now.

astro-ph.GA↗

arXiv2023

The linear response of stellar systems does not diverge at marginal stability

The linear response of a stellar system's gravitational potential to a perturbing mass comprises two distinct contributions. Most famously, the system will respond by forming a polarization 'wake' around the perturber. At the same time, the perturber may also excite one or more 'Landau modes', i.e. coherent oscillations of the entire stellar system which are either stable or unstable depending on the system parameters. The amplitude of the first (wake) contribution is known to diverge as a system approaches marginal stability. In this paper we consider the linear response of a homogeneous stellar system to a point mass moving on a straight line orbit. We prove analytically that the divergence of the wake response is in fact cancelled by a corresponding divergence in the Landau mode response, rendering the total response finite. We demonstrate this cancellation explicitly for a box of stars with Maxwellian velocity distribution. Our results imply that polarization wakes may be much less efficient drivers of secular evolution than previously thought. More generally, any prior calculation that accounted for wakes but ignored modes - such as those based on the Balescu-Lenard equation - may need to be revised.

astro-ph.GA↗

arXiv2023

Eccentricity dynamics of wide binaries -- I. The effect of Galactic tides

A major puzzle concerning the wide stellar binaries (semimajor axes $a\gtrsim 10^3$\,AU) in the Solar neighborhood is the origin of their observed superthermal eccentricity distribution function (DF), which is well-approximated by $P(e)\propto e^α$ with $α\approx 1.3$. This DF evolves under the combined influence of (i) tidal torques from the Galactic disk and (ii) scattering by passing stars, molecular clouds, and substructure. Recently, it was demonstrated that Galactic tides alone cannot produce a superthermal eccentricity DF from an initially isotropic, non-superthermal one, under the restrictive assumptions that the eccentricity DF was initially of power law form and then was rapidly phase-mixed toward a steady state by the tidal perturbation. In this paper we first prove analytically that this conclusion is valid at all times, regardless of these assumptions. We then adopt a thin Galactic disk model and numerically integrate the equations of motion for several ensembles of tidally perturbed wide binaries to study the time evolution in detail. We find that even non-power law DFs can be described by an effective power law index $α_\mathrm{eff}$ which accurately characterizes both their initial and final states, and that a DF with initial (effective or exact) power law index $α_\mathrm{i}$ is transformed by Galactic tides into another power law with index $α_\mathrm{f}\approx (1+α_\mathrm{i})/2$ on a timescale $ \sim 4\,\mathrm{Gyr}\,(a/10^4\mathrm{AU})^{-3/2}$. In a companion paper, we investigate separately the effect of stellar scattering. As the GAIA data continues to improve, these results will place strong constraints on wide binary formation channels.

astro-ph.GA↗

arXiv2023

Galactic bar resonances with diffusion: an analytic model with implications for bar-dark matter halo dynamical friction

The secular evolution of disk galaxies is largely driven by resonances between the orbits of 'particles' (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies - effects which have, with few exceptions, been previously explored only with complex N-body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles' slow actions. We solve this equation for various values of the dimensionless diffusion strength $Δ$, and then apply our theory to the calculation of bar-halo dynamical friction. For $Δ= 0$ we recover the classic result of Tremaine & Weinberg that friction ultimately vanishes, owing to the phase-mixing of resonant orbits. However, for $Δ> 0$ we find that diffusion suppresses phase-mixing, leading to a finite torque. Our results suggest that stochasticity - be it physical or numerical - tends to increase bar-halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time.

astro-ph.GA↗

arXiv2023

Wide binary stars formed in the turbulent interstellar medium

The ubiquitous interstellar turbulence regulates star formation and the scaling relations between the initial velocity differences and the initial separations of stars. We propose that the formation of wide binaries with initial separations $r$ in the range $\sim 10^3~\text{AU} \lesssim r \lesssim 10^5$ AU is a natural consequence of star formation in the turbulent interstellar medium. With the decrease of $r$, the mean turbulent relative velocity $v_\text{tur}$ between a pair of stars decreases, while the largest velocity $v_\text{bon}$ at which they still may be gravitationally bound increases. When $v_\text{tur} < v_\text{bon}$, a wide binary can form. In this formation scenario, we derive the eccentricity distribution $p(e)$ of wide binaries for an arbitrary relative velocity distribution. By adopting a turbulent velocity distribution, we find that wide binaries at a given initial separation generally exhibit a superthermal $p(e)$. This provides a natural explanation for the observed superthermal $p(e)$ of the wide binaries in the Solar neighborhood.

astro-ph.GA↗

arXiv2022

Stream Fanning and Bifurcations: Observable Signatures of Resonances in Stellar Stream Morphology

Recent observations have revealed a trove of unexpected morphological features in many of the Milky Way's stellar streams. Explanations for such features include time-dependent deformations of the Galactic gravitational potential, local disruptions induced by dark matter substructure, and special configurations of the streams' progenitors. In this paper, we study how these morphologies can also arise in certain static, non-spherical gravitational potentials that host a subset of resonantly-trapped orbit families. The transitions, or separatrices, between these orbit families mark abrupt discontinuities in the orbital structure of the potential. We develop a novel numerical approach for measuring the libration frequencies of resonant and near-resonant orbits, and apply it to study the evolution of stellar streams on these orbits. We reveal two distinct morphological features that arise in streams on near-resonant orbits: fans, that come about due to a large spread in the libration frequencies near a separatrix; and bifurcations, that arise when a separatrix splits the orbital distribution of the stellar stream between two (or more) distinct orbit families. We demonstrate that these effects can arise in some Milky Way streams for certain choices of the dark matter halo potential, and discuss how this might be used to probe and constrain the global shape of the Milky Way's gravitational potential.

astro-ph.GA↗

arXiv2022

Wide twin binaries are extremely eccentric: evidence of twin binary formation in circumbinary disks

The Gaia mission recently revealed an excess population of equal-mass "twin" wide binaries, with mass ratio $q\gtrsim 0.95$, extending to separations of at least 1000 AU. The origin of this population is an enigma: twin binaries are thought to form via correlated accretion in circumbinary disks, but the typical observed protostellar disks have radii of $\sim100$ AU, far smaller than the separations of the widest twins. Here, we infer the eccentricity distribution of wide twins from the distribution of their $v$-$r$ angles, i.e., the angle between the components' separation and relative velocity vectors. We find that wide twins must be on extremely eccentric orbits. For the excess-twin population at 400-1000 AU, we infer a near-delta function excess of high-eccentricity system, with eccentricity $0.95 \lesssim e \leq 1$. These high eccentricities for wide twins imply pericenter distances of order $10$ AU and suggest that their orbits were scattered via dynamical interactions in their birth environments, consistent with a scenario in which twins are born in circumbinary disks and subsequently widened. These results further establish twin wide binaries as a distinct population and imply that wide twins can be used as a probe of the dynamical history of stellar populations.

astro-ph.SR↗

arXiv2022

Anatomy of a slow merger: dissecting secularly-driven inspirals of LIGO/Virgo gravitational wave sources

The dozens of compact object mergers detected by LIGO/Virgo raise a key theoretical question: how do initially wide binaries shrink sufficiently quickly that they are able to merge via gravitational wave (GW) radiation within a Hubble time? One promising class of answers involves secular driving of binary eccentricity by some external tidal perturbation. This perturbation can arise due to the presence of a tertiary point mass, in which case the system exhibits Lidov-Kozai (LK) dynamics, or it can stem from the tidal field of the stellar cluster in which the binary orbits. While these secular tide-driven mechanisms have been studied exhaustively in the case of no GW emission, when GWs are included the dynamical behavior is still incompletely understood. In this paper we consider compact object binaries driven to merger via high eccentricity excitation by (doubly-averaged, test-particle quadrupole level) cluster tides - which includes LK-driven mergers as a special case - and include the effects of both general relativistic precession and GW emission. We provide for the first time an analytical understanding of the different evolutionary stages of the binary's semimajor axis, secular oscillation timescale, and phase space structure all the way to merger. Our results will inform future population synthesis calculations of compact object binary mergers from hierarchical triples and stellar clusters.

astro-ph.HE↗

arXiv2022

On the phase-mixed eccentricity and inclination distributions of wide binaries in the Galaxy

Modern observational surveys allow us to probe the phase space distribution function (DF) of wide binaries in the Solar neighbourhood. This DF exhibits non-trivial features, in particular a superthermal distribution of eccentricities for semimajor axes $a\gtrsim 10^3$AU. To interpret such features we must first understand how the binary DF is affected by dynamical perturbations, which typically fall into two classes: (i) stochastic kicks from passing stars, molecular clouds, etc. and (ii) secular torques from the Galactic tide. Here we isolate effect (ii) and calculate the time-asymptotic, phase-mixed DF for an ensemble of wide binaries under quadrupole-order tides. For binaries wide enough that the phase-mixing assumption is valid, none of our results depend explicitly on semimajor axes, masses, etc. We show that unless the initial DF is both isotropic in binary orientation and thermal in eccentricity, then the final phase-mixed DF is always both anisotropic and non-thermal. However, the only way to produce a superthermal DF under phase mixing is for the initial DF to itself be superthermal.

astro-ph.GA↗

arXiv2021

Secular dynamics of binaries in stellar clusters -- III. Doubly-averaged dynamics in the presence of general relativistic precession

Secular evolution of binaries driven by an external (tidal) potential is a classic astrophysical problem. Tidal perturbations can arise due to an external point mass, as in the Lidov-Kozai (LK) theory of hierarchical triples, or due to an extended stellar system (e.g. galaxy or globular cluster) in which the binary resides. For many applications, general-relativistic (GR) apsidal precession is important, and has been accounted for in some LK calculations. Here we generalise and extend these studies by exploring in detail the effect of GR precession on (quadrupole-level) tidal evolution of binaries orbiting in arbitrary axisymmetric potentials (which includes LK theory as a special case). We study the (doubly-averaged) orbital dynamics for arbitrary strengths of GR and binary initial conditions and uncover entirely new phase space morphologies with important implications for the binary orbital evolution. We also explore how GR precession affects secular evolution of binary orbital elements when the binary reaches high eccentricity ($e\to 1$) and delineate several different dynamical regimes. Our results are applicable to a variety of astrophysical systems. In particular, they can be used to understand the high-eccentricity behaviour of (cluster) tide-driven compact object mergers -- i.e. LIGO/Virgo gravitational wave sources -- for which GR effects are crucial.

astro-ph.GA↗

arXiv2021

Resonant and non-resonant relaxation of globular clusters

Globular clusters contain a finite number of stars. As a result, they inevitably undergo secular evolution (`relaxation') causing their mean distribution function (DF) to evolve on long timescales. On one hand, this long-term evolution may be interpreted as driven by the accumulation of local deflections along each star's mean field trajectory -- so-called `non-resonant relaxation'. On the other hand, it can be thought of as driven by non-local, collectively dressed and resonant couplings between stellar orbits, a process termed `resonant relaxation'. In this paper we consider a model globular cluster represented by a spherical, isotropic isochrone DF, and compare in detail the predictions of both resonant and non-resonant relaxation theories against tailored direct $N$-body simulations. In the space of orbital actions (namely the radial action and total angular momentum), we find that both resonant and non-resonant theories predict the correct morphology for the secular evolution of the cluster's DF, although non-resonant theory over-estimates the amplitude of the relaxation rate by a factor ${\sim 2}$. We conclude that the secular relaxation of hot isotropic spherical clusters is not dominated by collectively amplified large-scale potential fluctuations, despite the existence of a strong ${\ell = 1}$ damped mode. Instead, collective amplification affects relaxation only marginally even on the largest scales. The predicted contributions to relaxation from smaller scale fluctuations are essentially the same from resonant and non-resonant theories.

astro-ph.GA↗

arXiv2020

A simple, heuristic derivation of the Balescu-Lenard kinetic equation for stellar systems

The unshielded nature of gravity means that stellar systems are inherently inhomogeneous. As a result, stars do not move in straight lines. This obvious fact severely complicates the kinetic theory of stellar systems because position and velocity turn out to be poor coordinates with which to describe stellar orbits - instead, one must use angle-action variables. Moreover, the slow relaxation of star clusters and galaxies can be enhanced or suppressed by collective interactions ('polarisation' effects) involving many stars simultaneously. These collective effects are also present in plasmas; in that case, they are accounted for by the Balescu-Lenard (BL) equation, which is a kinetic equation in velocity space. Recently several authors have shown how to account for both inhomogeneity and collective effects in the kinetic theory of stellar systems by deriving an angle-action generalisation of the BL equation. Unfortunately their derivations are long and complicated, involving multiple coordinate transforms, contour integrals in the complex plane, and so on. On the other hand, Rostoker's superposition principle allows one to pretend that a long-range interacting $N$-body system, such as a plasma or star cluster, consists merely of uncorrelated particles that are 'dressed' by polarisation clouds. In this paper we use Rostoker's principle to provide a simple, intuitive derivation of the BL equation for stellar systems which is much shorter than others in the literature. It also allows us to straightforwardly connect the BL picture of self-gravitating kinetics to the classical 'two-body relaxation' theory of uncorrelated flybys pioneered by Chandrasekhar.

astro-ph.GA↗

arXiv2020

Noise and waves: a unified kinetic theory for stellar systems

The traditional Chandrasekhar picture of the slow relaxation of stellar systems assumes that stars' orbits are only modified by occasional, uncorrelated, two-body flyby encounters with other stars. However, the long-range nature of gravity means that in reality large numbers of stars can behave collectively. In stable systems this collective behaviour (i) amplifies the noisy fluctuations in the system's gravitational potential, effectively 'dressing' the two-body (star-star) encounters, and (ii) allows the system to support large-scale density waves (a.k.a. normal modes) which decay through resonant wave-star interactions. If the relaxation of the system is dominated by effect (i) then it is described by the Balescu-Lenard (BL) kinetic theory. Meanwhile if (ii) dominates, one must describe relaxation using quasilinear (QL) theory, though in the stellar-dynamical context the full set of QL equations has never been presented. Moreover, in some systems like open clusters and galactic disks, both (i) and (ii) might be important. Here we present for the first time the equations of a unified kinetic theory of stellar systems in angle-action variables that accounts for both effects (i) and (ii) simultaneously. We derive the equations in a heuristic, physically-motivated fashion and work in the simplest possible regime by accounting only for very weakly damped waves. This unified theory is effectively a superposition of BL and QL theories, both of which are recovered in appropriate limits. The theory is a first step towards a comprehensive description of those stellar systems for which neither the QL or BL theory will suffice.

astro-ph.GA↗

arXiv2019

Secular dynamics of binaries in stellar clusters I: general formulation and dependence on cluster potential

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.

astro-ph.GA↗

arXiv2019

Secular dynamics of binaries in stellar clusters II: dynamical evolution

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 (doubly-averaged) 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 element 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 $\gtrsim 10-10^2$ (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.

astro-ph.SR↗

arXiv2019

Compact object binary mergers driven by cluster tides: a new channel for LIGO/Virgo gravitational wave events

The detections of gravitational waves produced in mergers of binary black holes (BH) and neutron stars (NS) by LIGO/Virgo have stimulated interest in the origin of the progenitor binaries. Dense stellar systems - globular and nuclear star clusters - are natural sites of compact object binary formation and evolution towards merger. Here we explore a new channel for the production of binary mergers in clusters, in which the tidal field of the cluster secularly drives the binary to high eccentricity (even in the absence of a central massive black hole) until gravitational wave emission becomes important. We employ the recently developed secular theory of cluster tide-driven binary evolution to compute present day merger rates for BH-BH, NS-BH and NS-NS binaries, varying cluster potential and central concentration of the binary population (but ignoring cluster evolution and stellar flybys for now). Unlike other mechanisms, this new dynamical channel can produce a significant number of mergers out to cluster-centric distances of several pc. For NS-NS binaries we find merger rates in the range $0.01-0.07$ Gpc$^{-3}$ yr$^{-1}$ from globular clusters and $0.1-0.2$ Gpc$^{-3}$ yr$^{-1}$ from cusped nuclear clusters. For NS-BH and BH-BH binaries we find small merger rates from globular clusters, but a rate of $0.1 - 0.2$ Gpc$^{-3}$ yr$^{-1}$ from cusped nuclear clusters, contributing to the observed LIGO/Virgo rate at the level of several per cent. Therefore, cluster tide-driven mergers constitute a new channel that can be further explored with current and future gravitational wave detectors.

astro-ph.GA↗

arXiv2018

Revisiting relaxation in globular clusters

The classical theory of cluster relaxation is unsatisfactory because it involves the Coulomb logarithm. The Balescu-Lenard (BL) equation provides a rigorous alternative that has no ill-defined parameter. Moreover, the BL equation, unlike classical theory, includes the cluster's self-gravity. A heuristic argument is given that indicates that relaxation does not occur predominantly through two-particle scattering and is enhanced by self-gravity. The BL equation is adapted to a spherical system and used to estimate the flux through the action space of isochrone clusters with different velocity anisotropies. A range of fairly different secular behaviours is found depending on the fraction of radial orbits. Classical theory is also used to compute the corresponding classical fluxes. The BL and classical fluxes are very different because (a) the classical theory materially under-estimates the impact of large-scale collectively amplified fluctuations and (b) only the leading terms in an infinite sum for the BL flux are computed. A complete theory of cluster relaxation likely requires that the sum in the BL equation be decomposed into a sum over a finite number of small wavenumbers complemented by an integral over large wavenumbers analogous to classical theory.

astro-ph.GA↗