When a stellar massive compact object, such as a black hole (BH), inspirals into an intermediate massive black hole (IMBH), an intermediate-mass-ratio-inspiral (IMRI) system forms. Such kind of systems are important sources for space-based gravitational wave detectors including LISA, Taiji and Tianqin. Dark matter (DM) minispikes may form around IMBHs. We study the effect of dynamical friction against DM minispike on the evolution of eccentric IMRI. For such investigation we construct the dynamical equations which describes the evolution of eccentric IMRI under the effect of dynamical friction. As dynamical friction is large for small velocity, the dissipation of energy near apastron is more than that near periastron. This will greatly enhance the eccentricity. For instance, with an initial semi-latus rectum of $1\rm AU$, even a moderate DM minispike can make the eccentricity grow from $0.3$ to $0.85$. In the extremal case the eccentricity could be enhanced to near $1$. We also study a specific case which corresponds to an IMRI in the center of a globular cluster (GC) and find the eccentricity can keep its value above $0.95$ until the IMRI enters LISA band. These gravitational wave with enhanced eccentricity by DM minispikes can be easly distinguished from that without DM at $10^{-3}\rm Hz$ due to the eccentricity difference. These anticipations can be tested by future space-based GW detectors such as LISA.
Gravitational waves (GWs) can be produced if a stellar compact object, such as a black hole (BH) or neutron star, inspirals into an intermediate-massive black hole (IMBH) of $(10^3 \sim 10^5)\,M_\odot$. Such a system may be produced in the center of a globular cluster (GC) or a nuclear star cluster (NSC), and is known as an intermediate- or extreme-mass-ratio inspiral (IMRI or EMRI). Motivated by the recent suggestions that dark matter minispikes could form around IMBHs, we study the effect of dynamical friction against DM on the merger rate of IMRIs/EMRIs. We find that the merger timescale of…
When binary black holes form in the field, it is expected that their orbits typically circularize before coalescence. In galactic nuclei and globular clusters, binary black holes can form dynamically. Recent results suggest that $\approx5\%$ of mergers in globular clusters result from three-body interactions. These three-body interactions are expected to induce significant orbital eccentricity $\gtrsim 0.1$ when they enter the Advanced LIGO band at a gravitational-wave frequency of 10 Hz. Measurements of binary black hole eccentricity therefore provide a means for determining whether or not dy…
The inspiral-merger-ringdown (IMR) consistency test checks the consistency of the final mass and final spin of a binary black hole merger remnant, independently inferred via the inspiral and merger-ringdown parts of the waveform. As binaries are expected to be nearly circularized when entering the frequency band of ground-based detectors, tests of general relativity (GR) currently employ quasicircular waveforms. We quantify the effect of residual orbital eccentricity on the IMR consistency test. We find that eccentricity causes a significant systematic bias in the inferred final mass and spin …
Constraining initial orbital eccentricity of inspiral-dominated gravitational-wave events with an analytic approximant
The Chinese University of Hong Kong（香港中文大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；Nikhef—National Institute for Subatomic Physics（NIKHEF-国家亚原子物理研究所）；KU Leuven（荷语鲁汶大学）；The Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理学中心）
The space-based detector LISA may observe gravitational waves from the early inspiral of stellar-mass black hole binaries, some of which could have significant eccentricity. Current gravitational waveform templates are only valid for small orbital velocities (i.e., in a post-Newtonian expansion) and small initial eccentricity $e_0$ ("post-circular" expansion). We conventionally define $e_0$ as the eccentricity corresponding to an orbital frequency of $5 \text{ mHz}$, and we study the convergence properties of frequency-domain inspiral templates that are accurate up to 2PN and order $e_0^6$ in …
Extreme mass ratio inspirals from the Hills mechanism, The eccentricity distribution of Hills EMRIs in LISA
Leiden University（莱顿大学）；Università degli Studi di Trento（特伦托大学）；Università degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN - Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究院）
Although gravitational waves tend to erase eccentricity of an inspiraling binary system, ellipticity can be generated in the presence of surrounding matter. We present a semi-analytical method for understanding the eccentricity distribution of binary black holes in the presence of a supermassive black hole in a galactic center. Given a matter distribution, we show how to determine the resultant eccentricity analytically in the presence of both tidal forces and evaporation up to one cutoff and one matter-distribution-independent function, paving the way for understanding the environment of dete…
We study the effect of tidal interaction between two compact bodies in an eccentric orbit. We assume the tidal fields to be static. Therefore, we ignore the dynamic tides and resonant excitations. Using the results, we find the analytical expression for the phase shift of the emitted gravitational wave. In the process, we find that in the leading order, the initial eccentricity $e_0$ and the dimensionless tidal deformability $Λ$ couple as $\sim e_0^nΛ$, where $n$ is a positive number. We only focus on the dominant contribution, i.e., $e_0^2Λ$. We also compute the accumulated dephasing for bina…
Spin precession effects in the phasing formula of eccentric compact binary inspirals up to the second post-Newtonian order
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Centre for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras（印度马德拉斯理工学院物理系弦、引力和宇宙学中心）；Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University（西北大学天体物理学交叉探索与研究中心）
The localization and distance inference of gravitational waves are two crucial factors for dark sirens as precise probes of cosmology, astrophysics, and fundamental physics. In this Letter, for the first time we investigate the parameter estimation of gravitational waves emitted by the eccentric compact binaries in the mid-frequency (0.1--10 Hz) band. Based on the configuration of one cluster of DECIGO (B-DECIGO), we simulate five types of typical compact binaries in GWTC-3 with component mass ranging from $\mathcal{O}(1\sim100)~M_{\odot}$. For each type of binaries, we assign discrete eccentr…
Spherical harmonic modes of gravitational waveforms for inspiraling compact binaries in eccentric orbits from post-Newtonian (PN) theory accurate to third post-Newtonian order, and those extracted from numerical relativity (NR) simulations for binary black holes (BBHs) are compared. We combine results from the two approaches (PN and NR) to construct time-domain hybrid waveforms that describe the complete evolution of BBH mergers through inspiral-merger-ringdown (IMR) stages. These hybrids are then used in constructing a fully analytical dominant mode ($\ell$=2, $|m|$=2) eccentric IMR model. A …
The intermediate mass-ratio inspiral of a stellar compact remnant into an intermediate mass black hole (IMBH) can produce a gravitational wave (GW) signal that is potentially detectable by current ground-based GW detectors (e.g., Advanced LIGO) as well as by planned space-based interferometers (e.g., eLISA). Here, we present results from a direct integration of the post-Newtonian $N$-body equations of motion describing stellar clusters containing an IMBH and a population of stellar-mass black holes (BHs) and solar mass stars. We take particular care to simulate the dynamics closest to the IMBH…
Eccentricity distribution of extreme mass ratio inspirals
Università degli Studi di Trento（特伦托大学）；Università degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN - Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）
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…
We solve the equations of two-dimensional hydrodynamics describing a circumbinary disk accreting onto an eccentric, equal-mass binary. We compute the time rate of change of the binary semimajor axis $a$ and eccentricity $e$ over a continuous range of eccentricities spanning $e=0$ to $e=0.9$. We find that binaries with initial eccentricities $e_0 \lesssim 0.1$ tend to $e=0$, where the binary semimajor axis expands. All others are attracted to $e \approx 0.4$, where the binary semimajor axis decays. The $e \approx 0.4$ attractor is caused by a rapid change in the disk response from a nearly orig…
External Attention Transformer: A Robust AI Model for Identifying Initial Eccentricity Signatures in Binary Black Hole Events in Simulated Advanced LIGO Data
Extreme mass ratio inspirals (EMRIs) occur when a compact object orbits a much larger one, like a solar-mass black hole around a supermassive black hole. The orbit has 3 frequencies which evolve through the inspiral. If the orbital radial frequency and polar frequency become commensurate, the system passes through a transient resonance. Evolving through resonance causes a jump in the evolution of the orbital parameters. We study these jumps and their impact on EMRI gravitational-wave detection. Jumps are smaller for lower eccentricity orbits; since most EMRIs have small eccentricities when pas…
A parametrized test of general relativity for inspiralling eccentric binaries in LISA
Niels Bohr International Academy, The Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；Center of Gravity, Niels Bohr Institute（引力中心，尼尔斯·玻尔研究所）；Univ Toulouse, CNRS, L2IT（图卢兹大学，法国国家科学研究中心，L2IT）；Institut für Physik und Astronomie, Universität Potsdam（波茨坦大学物理与天文学研究所）
The extreme mass ratio inspiral (EMRI), defined as a stellar-mass compact object inspiraling into a supermassive black hole (SMBH), has been widely argued to be a low-frequency gravitational wave (GW) source. EMRIs providing accurate measurements of black hole mass and spin, are one of the primary interests for Laser Interferometer Space Antenna (LISA). However, it is usually believed that there are no electromagnetic (EM) counterparts to EMRIs. Here we show a new formation channel of EMRIs with tidal disruption flares as EM counterparts. In this scenario, flares can be produced from the tidal…
Relativistic effects in extreme-mass-ratio inspirals within scalar clouds: Eccentric and inclined orbits
CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高级技术学院物理系中心）；Gravitation Astroparticle Physics Amsterdam (GRAPPA), University of Amsterdam（阿姆斯特丹大学引力天体粒子物理学中心）
The inspiral of stellar-mass compact objects, like neutron stars or stellar-mass black holes, into supermassive black holes provides a wealth of information about the strong gravitational-field regime via the emission of gravitational waves. In order to detect and analyse these signals, accurate waveform templates which include the effects of the compact object's gravitational self-force are required. For computational efficiency, adiabatic templates are often used. These accurately reproduce orbit-averaged trajectories arising from the first-order self-force, but neglect other effects, such a…
Extreme-mass-ratio inspiral (EMRI) is an important gravitational-wave (GW) source and it normally consists of one stellar-mass black hole (BH) whirling closely around a supermassive black hole (SMBH). In this Letter, we demonstrate that the small body, in fact, could be a BH binary (BHB). Previous numerical scatting experiments have shown that SMBHs can tidally capture BHBs to bound orbits. Here we investigate the subsequent long-term evolution. We find that those BHBs with a semi-major axis of $a\lesssim5\times10^{-3}$ AU can be captured to tightly-bound orbits such that they will successfull…
The possible formation of stellar-mass binary black holes through dynamical interactions in dense stellar environments predicts the existence of binaries with non-negligible eccentricity in the frequency band of ground-based gravitational wave detectors; the detection of binary black hole mergers with measurable orbital eccentricity would validate the existence of this formation channel. Waveform templates currently used in the matched-filter gravitational-wave searches of LIGO-Virgo data neglect effects of eccentricity which is expected to reduce their efficiency to detect eccentric binary bl…
We estimate the rate of inspiral for a population of stellar mass BHs in the star cluster around the super massive black hole at the center of Milky Way mass galaxies. Our approach is based on an orbit averaged Fokker Planck approach. This is then followed by a post-processing approach, which incorporates the impact of the angular momentum diffusion and the GW dissipation in the evolution of system. We make a sample of 10000 BHs with different initial semi-major and eccentricities with the distribution of $f_c(a)/a$ and $e$, respectively. Where $f_c(a)$ refers to the phase-space distribution f…
We present a time domain waveform model that describes the inspiral-merger-ringdown (IMR) of compact binary systems whose components are non-spinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to non-linear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian …
Secular evolution of orbital parameters for general bound orbits in Kerr spacetime
Division of General Education, Kanazawa Medical University（金泽医科大学通识教育系）；Institute of General Education, Otemon Gakuin University（大东文化大学通识教育研究所）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Faculty of Law, Ryukoku University（龙谷大学法学部）
Scientific analysis for the gravitational-wave detector LISA will require theoretical waveforms from extreme-mass-ratio inspirals (EMRIs) that extensively cover all possible orbital and spin configurations around astrophysical Kerr black holes. However, on-the-fly calculations of these waveforms have not yet overcome the high dimensionality of the parameter space. To confront this challenge, we present a user-ready EMRI waveform model for generic (eccentric and inclined) orbits in Kerr spacetime, using an analytical self-force approach. Our model accurately covers all EMRIs with arbitrary incl…
Constructing a gravitational wave analysis pipeline for extremely large mass ratio inspirals
Sun Yat-sen University (Zhuhai Campus)（中山大学（珠海校区））；Huazhong University of Science and Technology（华中科技大学）；Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；Peking University（北京大学）；Hebei University（河北大学）
Close encounters between stellar-mass black holes (BHs) and stars occur frequently in dense star clusters and in the disks of active galactic nuclei (AGNs). Recent studies have shown that in highly eccentric close encounters, the star can be tidally disrupted by the BH (micro-tidal disruption event, or micro-TDE), resulting in rapid mass accretion and possibly bright electromagnetic signatures. Here we consider a scenario in which the star might approach the stellar-mass BH in a gradual, nearly circular inspiral, under the influence of dynamical friction on a circum-binary gas disk or three-bo…
Gravitational radiation reaction around a static black hole surrounded by a Dehnen type dark matter halo
The Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究所）；Dipartimento di Fisica e Astronomia, Alma Mater Università di Bologna（博洛尼亚大学物理与天文学系）；Istituto Nazionale di Fisica Nucleare, I.S. FLaG, Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）；Alma Mater Research Center on Applied Mathematics (AM 2 )（阿尔玛·mater应用数学研究中心）；Università di Camerino, Divisione di Fisica（卡梅里诺大学物理系）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia（意大利国家核物理研究所佩鲁贾分部）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（法拉比哈萨克国立大学）
