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.
Based on a simple geometrical approach, we analyze the evolution of the Kozai-Lidov mechanism for stars around shrinking massive black hole binaries on circular orbits. We find that, due to a peculiar bifurcation pattern induced by the Newtonian potential of stellar clusters, the orbit of stars could become highly eccentric. This transition occurs abruptly for stars with small initial eccentricities. Our approach would be also useful for studying the Kozai-Lidov mechanism in various astrophysical contexts.
Using linear perturbation theory, we evaluate the time-dependent force exerted on an eccentric and inclined low-mass planet embedded in a gaseous protoplanetary disc with finite thermal diffusivity $χ$. We assume the eccentricity and inclination to be small compared to the size of the thermal lobes $λ\sim(χ/Ω)^{1/2}$, itself generally much smaller than the scalelength of pressure $H$. When the planet is non-luminous, we find that its eccentricity and inclination are vigorously damped by the disc, over a timescale shorter by a factor $H/λ$ than the damping timescale in adiabatic discs. On the c…
Based on the secular theory, we discuss the orbital evolution of stars in a nuclear star cluster to which a secondary massive black hole is infalling with vanishing eccentricity. We find that the eccentricities of the stars could show sharp transitions, depending strongly on their initial conditions. By examining the phase-space structure of an associated Hamiltonian, we show that these characteristic behaviors are partly due to a probabilistic bifurcation at a separatrix crossing, resulting from the retrograde apsidal precession by the cluster potential. We also show that separatrix crossings…
Converging on the eccentricity of massive black hole binaries in galactic mergers
School of Mathematics and Physics, University of Surrey（萨里大学数学与物理学院）；Dipartimento di Fisica “G. Occhialini（意大利国家核物理研究所米兰比可卡分部）；INFN, Sezione di Milano-Bicocca（海德堡大学天文学计算中心）；Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg
Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in the Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models are highly uncertain. A major difficulty stems from the necessity to model the BHB from the scale of the merger to that of inspiral. Of particular relevance to the GW merger timescale is the binary eccentricity. Here we present a self-consistent numerical study of the eccentricity of BHBs formed in massive gas-free mergers from the early stages of the…
N-body simulations of galactic collisions are employed to investigate the formation of elliptical rings in disk galaxies. The relative inclination between disk and dwarf galaxies is studied with a fine step of five degrees. It is confirmed that the eccentricity of elliptical ring is linearly proportional to the inclination angle. Deriving from the simulational results, an analytic formula which expresses the eccentricity as a function of time and inclination angle is obtained. This formula shall be useful for the interpretations of the observations of ring systems, and therefore reveals the me…
Distribution of eccentricities of very wide (up to 10 kau) low-mass binaries in the solar neighborhood is studied using the catalog of El-Badry and Rix (2018) based on Gaia. Direction and speed of relative motions in wide pairs contain statistical information on the eccentricity distribution, otherwise inaccessible owing to very long orbital periods. It is found that the eccentricity distribution is close to the linear (thermal) one f(e) = 2e$ However, pairs with projected separations <200 au have less eccentric orbits, while f(e) for very wide pairs appears to be slightly super-thermal, with …
Eccentricity of wide binaries is difficult to measure due to their long orbital periods. With Gaia's high-precision astrometric measurements, eccentricity of a wide binary can be constrained by the angle between the separation vector and the relative velocity vector (the $v$-$r$ angle). In this paper, by using the $v$-$r$ angles of wide binaries in Gaia Early Data Release 3, we develop a Bayesian approach to measure the eccentricity distribution as a function of binary separations. Furthermore, we infer the eccentricities of individual wide binaries and make them publicly available. Our result…
We report results on the kinematics of Milky Way (MW) globular clusters (GCs) based on updated space velocities for nearly the entire GC population. We found that a 3D space with the semi-major axis, the eccentricity and the inclination of the orbit with respect to the MW plane as its axes is helpful in order to dig into the formation of the GC system. We find that GCs formed in-situ show a clear correlation between their eccentricities and their orbital inclination in the sense that clusters with large eccentricities also have large inclinations. These GCs also show a correlation between thei…
About a century ago, Jeans (1919) discovered that if binary stars reach a state approximating energy equipartition, for example through many dynamical encounters that exchange energy, their eccentricity distribution can be described by : dN/de = 2e. This is referred to as the thermal eccentricity distribution, and has been widely used for initial conditions in theoretical investigations of binary stars. However, observations suggest that the eccentricity distributions of most observed binaries, and particularly those with masses < 5 Msun, are flatter than thermal and follow more closely to a u…
Future Gaia and Legacy Survey of Space and Time data releases, together with wide area spectroscopic surveys, will deliver large samples of resolved binary stars with phase space coordinates, albeit with low-cadence. Given an eccentricity law $f(ε)$, we derive properties of (i) the velocity distribution $v/\sqrt{G M/r}$ normalised by the value for a circular orbit at the measured separation $r$; (ii) the astrometric acceleration distributions $a/\left(G M/r^2\right)$ again normalised to the circular orbit value. Our formulation yields analytic predictions for the full statistical distribution …
We study the dynamical evolution of eccentric massive black hole binaries (MBHBs) interacting with unbound stars by means of an extensive set of three body scattering experiments. Compared to previous studies, we extend the investigation down to a MBHB mass ratio of $q=m_2/m_1=10^{-4}$, where $m_1$ and $m_2$ are the masses of the primary and secondary hole respectively. Contrary to a simple extrapolation from higher mass ratios, we find that for $q\lesssim 10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {\it circularises} as it shrinks. This behaviour is due to the sub…
The population of young stars near the Supermassive black hole (SMBH) in the Galactic Center (GC) has presented an unexpected challenge to theories of star formation. Kinematics measurements of these stars have revealed a stellar disk structure (with an apparent 20% disk membership) that has provided important clues to the origin of these mysterious young stars. However many of the apparent disk properties are difficult to explain, including the low disk membership fraction and the high eccentricities, given the youth of this population. Thus far, all efforts to derive the properties of this d…
Many gravitational wave (GW) sources in the LISA band are expected to have non-negligible eccentricity. Furthermore, many of them can undergo acceleration because they reside in the presence of a tertiary. Here we develop analytical and numerical methods to quantify how the compact binary's eccentricity enhances the detection of its peculiar acceleration. We show that the general relativistic precession pattern can disentangle the binary's acceleration-induced frequency shift from the chirp-mass-induced frequency shift in GW template fitting, thus relaxing the signal-to-noise ratio requirement…
Aims: Our goal is to investigate how the strength of episodic accretion bursts depends on eccentricity. Methods: We investigate the binary trigger hypothesis in longer-period (>20yr) binaries by carrying out three-dimensional magnetohydrodynamical (MHD) simulations of the formation of low-mass binary stars down to final separations of $\sim$10$\au$, including the effects of gas turbulence and magnetic fields. We ran two simulations with an initial turbulent gas core of one solar mass each and two different initial turbulent Mach numbers, M = 0.1 and M=0.2, for 6500yr after protostar formation.…
