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 merger to the hardening phase, followed by a semi-analytical model down to coalescence. We find that the early eccentricity of the unbound black hole pair is largely determined by the initial orbit. It systematically decreases during the dynamical friction phase. The eccentricity at binary formation is affected by stochasticity and noise owing to encounters with stars, but preserves a strong correlation with the initial orbital eccentricity. Binding of the black holes is a phase characterised by strong perturbations, and we present a quantitative definition of the time of binary formation. During hardening the eccentricity increases in minor mergers, unless the binary is approximately circular, but remains largely unchanged in major mergers, in agreement with predictions from semi-analytical models based on isotropic scattering experiments. Coalescence times due to hardening and GW emission in gas-poor non-rotating ellipticals are <~0.5 Gyr for the large initial eccentricities (0.5 < e < 0.9) typical of galaxy mergers in cosmological simulations.
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.
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…
We evaluate the cosmological coalescence and detection rates for massive black hole (MBH) binaries targeted by the gravitational wave observatory Laser Interferometer Space Antenna (LISA). Our calculation starts with a population of gravitationally unbound MBH pairs, drawn from the TNG50-3 cosmological simulation, and follows their orbital evolution from kpc scales all the way to coalescence using a semi-analytic model developed in our previous work. We find that for a majority of MBH pairs that coalesce within a Hubble time dynamical friction is the most important mechanism that determines th…
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
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, pha…
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…
In recent numerical simulations \citep{matsubayashi07,lockmann08}, it has been found that the eccentricity of supermassive black hole(SMBH) - intermediate black hole(IMBH) binaries grows toward unity through interactions with stellar background. This increase of eccentricity reduces the merging timescale of the binary through the gravitational radiation to the value well below the Hubble Time. It also gives the theoretical explanation of the existence of eccentric binary such as that in OJ287 \citep{lehto96, valtonen08}. In self-consistent N-body simulations, this increase of eccentricity is a…
We investigate a purely stellar dynamical solution to the Final Parsec Problem. Galactic nuclei resulting from major mergers are not spherical, but show some degree of triaxiality. With $N$-body simulations, we show that massive black hole binaries (MBHB) hosted by them will continuously interact with stars on centrophilic orbits and will thus inspiral---in much less than a Hubble time---down to separations at which gravitational wave (GW) emission is strong enough to drive them to coalescence. Such coalescences will be important sources of GWs for future space-borne detectors such as the {\it…
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…
Pulsar timing observations are used to place constraints on the rate of coalescence of supermassive black-hole (SMBH) binaries as a function of mass and redshift. In contrast to the indirect constraints obtained from other techniques, pulsar timing observations provide a direct constraint on the black-hole merger rate. This is possible since pulsar timing is sensitive to the gravitational waves (GWs) emitted by these sources in the final stages of their evolution. We find that upper bounds calculated from the recently published Parkes Pulsar Timing Array data are just above theoretical predict…
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…
Massive black hole binaries are naturally predicted in the context of the hierarchical model of structure formation. The binaries that manage to lose most of their angular momentum can coalesce to form a single remnant. In the last stages of this process, the holes undergo an extremely loud phase of gravitational wave emission, possibly detectable by current and future probes. The theoretical effort towards obtaining a coherent physical picture of the binary path down to coalescence is still underway. In this paper, for the first time, we take advantage of observational studies of active galac…
In currently favoured hierarchical cosmologies, the formation of massive black hole binaries (MBHBs) following galaxy mergers is unavoidable. Still, due the complex physics governing the (hydro)dynamics of the post-merger dense environment of stars and gas in galactic nuclei, the final fate of those MBHBs is still unclear. In gas-rich environments, it is plausible that turbulence and gravitational instabilities feed gas to the nucleus in the form of a series of cold incoherent clumps, thus providing a way to exchange energy and angular momentum between the MBHB and its surroundings. Within thi…
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…
We investigate interactions of stellar binaries in galactic nuclear clusters with a massive black hole (MBH). We consider binaries on highly eccentric orbits around the MBH that change due to random gravitational interactions with other stars in the nuclear stellar cluster. The pericenters of the orbits perform a random walk, and we consider cases where this random walk slowly brings the binary to the Hills tidal separation radius (the so-called empty loss-cone regime). However, we find that in a majority of cases the expected separation does not occur and instead the members of the binary mer…
Massive black hole binaries are predicted to form during the hierarchical assembly of cosmic structures and will represent the loudest sources of low-frequency gravitational waves (GWs) detectable by present and forthcoming GW experiments. Before entering the GW-driven regime, their evolution is driven by the interaction with the surrounding stars and gas. While stellar interactions are found to always shrink the binary, recent studies predict the possibility of binary outspiral mediated by the presence of a gaseous disk, which could endlessly delay the coalescence and impact the merger rates …
The dynamical evolution of binaries of intermediate-massive black holes (IMBHs, massive black holes with a mass ranging between $10^2$ and $10^4 M_{\odot}$) in stellar clusters has recently received an increasing amount of attention. This is at least partially due to the fact that if the binary is hard enough to evolve to the phase at which it will start emitting gravitational waves (GWs) efficiently, there is a good probability that it will be detectable by future space-borne detectors like LISA. We study this evolution in the presence of rotation in the cluster. The eccentricity is strongly …
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.…
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 velocit…
