We present results from calculations of the orbital evolution in eccentric binaries of nonrotating black holes with extreme mass-ratios. Our inspiral model is based on the method of osculating geodesics, and is the first to incorporate the full gravitational self-force (GSF) effect, including conservative corrections. The GSF information is encapsulated in an analytic interpolation formula based on numerical GSF data for over a thousand sample geodesic orbits. We assess the importance of including conservative GSF corrections in waveform models for gravitational-wave searches.
Extreme-mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole in a galactic core, are expected to be key sources for LISA. Modelling these systems with sufficient accuracy for LISA science requires going to second (or {\em post-adiabatic}) order in gravitational self-force theory. Here we present a practical two-timescale framework for achieving this and generating post-adiabatic waveforms. The framework comprises a set of frequency-domain field equations that apply on the fast, orbital timescale, together with a set of ordinary differential equati…
We consider extreme mass ratio inspirals during which an electrically charged compact object with mass $m_p$ and the charge to mass ratio $q$ inspirals around a Schwarzschild black hole of mass $M$. Using the Teukolsky and generalized Sasaki-Nakamura formalisms for the gravitational and electromagnetic perturbations around a Schwarzschild black hole, we numerically calculate the energy flux of both gravitational and electromagnetic waves induced by a charged particle moving in circular orbits. With one year observation of these extreme mass ratio inspirals, we show that space-based gravitation…
We present an extension of work in an earlier paper showing high precision comparisons between black hole perturbation theory and post-Newtonian (PN) theory in their region of overlapping validity for bound, eccentric-orbit, Schwarzschild extreme-mass-ratio inspirals. As before we apply a numerical fitting scheme to extract eccentricity coefficients in the PN expansion of the gravitational wave fluxes, which are then converted to exact analytic form using an integer-relation algorithm. In this work, however, we fit to individual $lmn$ modes to exploit simplifying factorizations that lie therei…
We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit, such that the worldline evolves smoothly from one such geodesic to the next. Because a geodesic is uniquely identified by a set of constant orbital elements, the transition between osculating orbits corresponds to an evolution of the elements. In this paper we derive the evolution equations for a convenient set of orbital elements, assuming that the force acts …
We present exact solutions of test particle orbits spiralling inward from the innermost stable circular orbit (ISCO) of a Kerr black hole. Our results are valid for any allowed value of the angular momentum $a$-parameter of the Kerr metric. These solutions are of considerable physical interest. In particular, the radial 4-velocity of these orbits is both remarkably simple and, with the radial coordinate scaled by its ISCO value, universal in form, otherwise completely independent of the black hole spin.
Neutron star (NS) binaries formed dynamically may have significant eccentricities while emitting gravitational waves (GWs) in the LIGO/VIRGO band. We study tidal effects in such eccentric inspiralling NS binaries using a set of hybrid equations. The NS is modelled as a compressible ellipsoid, which can deform nonlinearly due to tidal forces, while the orbit evolution is treated with the post-Newtonian (PN) theory up to 2.5-PN order. We find that in general, the tidal interaction can accelerate the inspiral, and cause orbital frequency and phase shifts. For circular inspirals, our calculations …
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…
We probe the ability of various types of post-Newtonian(PN)-accurate circular templates to capture inspiral gravitational-wave (GW) signals from compact binaries having tiny orbital eccentricities. The GW signals are constructed by adapting the phasing formalism, available in T. Damour, A. Gopakumar, and B. R. Iyer, [Phys. Rev. D 70, 064028 (2004)], employing the orbital energy and the time-eccentricity to describe the orbital evolution. Using the fitting factor estimates, relevant for the initial LIGO, we show that circular templates, based on the adiabatic TaylorT1, complete adiabatic Taylor…
We calculate the kick generated by an eccentric black hole binary inspiral as it evolves through a resonant orbital configuration where the precession of the system temporarily halts. As a result, the effects of the asymmetric emission of gravitational waves build up coherently over a large number of orbits. Our results are calculate using black hole perturbation theory in the limit where the ratio of the masses of the orbiting objects $ε=m/M$ is small. The resulting kick velocity scales as $ε^{3/2}$, much faster than the $ε^2$ scaling of the kick generated by the final merger. For the most ex…
A compact object moving on a quasicircular orbit about a Schwarzschild black hole gradually spirals inward due to the dissipative action of its gravitational self-force. But in addition to driving the inspiral, the self-force has a conservative piece. Within a second-order self-force formalism, I derive a second-order generalization of Detweiler's redshift variable, which provides a gauge-invariant measure of conservative effects on quasicircular orbits. I sketch a frequency-domain numerical scheme for calculating this quantity. Once this scheme has been implemented, its results may be used to…
The inspiral of a stellar mass compact object falling into a massive Kerr black hole can be broken into three different regimes: An adiabatic inspiral phase, where the inspiral timescale is much larger than the orbital period; a late-time radial infall, which can be approximated as a plunging geodesic; and a regime where the body transitions from the inspiral to plunge. In earlier work, Ori and Thorne have outlined a method to compute the trajectory during this transition for a compact object in a circular, equatorial orbit. We generalize this technique to include inclination and eccentricity.
Event horizons are among the most intriguing of general relativity's predictions. Although on firm theoretical footing, direct indications of their existence have yet to be observed. With this motivation in mind, we explore here the possibility of finding a signature for event horizons in the gravitational waves (GWs) produced during the inspiral of stellar-mass compact objects (COs) into the supermassive ($\sim 10^6 M_\odot$) objects that lie at the center of most galaxies. Such inspirals will be a major source for LISA, the future space-based GW observatory. We contrast supermassive black ho…
Action-angle coordinates are a tool commonly used in celestial mechanics to systematically parametrize and store general solutions of the equations of motion of astrophysical bodies. I perturbatively construct action-angle coordinates for bound test particle motion in static, spherically symmetric space-times using a post-circular expansion. Then I specialise the expressions to the motion in the gravitational fields of Schwarzschild black holes and give explicit formulas for the Hamiltonian to the 10th power in the radial action (20th power in eccentricity), and the transformation to angle coo…
We study binary systems in which a stellar mass compact object spirals into a massive black hole, known as extreme mass ratio inspirals, in scenarios with a new fundamental scalar field. Earlier work has shown that, in most interesting such scenarios and to leading order in the mass ratio, the massive black holes can be adequately approximated by the Kerr metric and the imprint of the scalar field on the waveform is fully controlled by the scalar charge of the stellar mass object. Here we use this drastic simplification in the inspiral modelling and consider eccentric equatorial orbits. We stu…
The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of validity of the post-Newtonian approximation by using the gravitational energy flux derived numerically and analytically in the black hole perturbation approach. It is found that the edge of the allowable region behaves quite intricately, including prograde orbits even if we treat higher post-Newtonian orders.
We present a prescription to compute the time-domain gravitational wave (GW) polarization states associated with spinning compact binaries inspiraling along quasi-circular orbits. We invoke the orbital angular momentum ${\bf L}$ rather than its Newtonian counterpart ${\bf L_{\rm N}}$ to describe the orbits and the two spin vectors are freely specified in the source frame associated with the initial direction of the total angular momentum. We discuss the various implications of our approach.
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）
There are three regimes of gravitational-radiation-reaction-induced inspiral for a compact body with mass mu, in a circular, equatorial orbit around a Kerr black hole with mass M>>mu: (i) The "adiabatic inspiral regime", in which the body gradually descends through a sequence of circular, geodesic orbits. (ii) A "transition regime", near the innermost stable circular orbit (isco). (iii) The "plunge regime", in which the body travels on a geodesic from slightly below the isco into the hole's horizon. This paper gives an analytic treatment of the transition regime and shows that, with some luck,…
Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the post-circular scheme of Yunes {\it et al.} [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian…
The bumblebee gravity model, with a vector field nonminimally coupled to gravity, is a natural extension of the Einstein-Maxwell theory. In this theory, a black hole can carry a vector hair, making the metric deviate from the Schwarzschild metric. To investigate the detectability of the vector hair, we consider an Extreme Mass Ratio Inspiral (EMRI) system, where a stellar-mass black hole inspiraling into a supermassive black hole. We find that, with a one-year observation of an EMRI by a space-based gravitational-wave detector, we can probe the vector charge as small as $Q\sim 10^{-3}$ in the …
A rotating star's oblateness creates a deformation in the gravitational field outside the star, which is measured by the quadrupole-moment tensor. We consider the effect of the quadrupole moment on the orbital motion and rate of inspiral of a compact binary system, composed of neutron stars and/or black holes. We find that in the case of circular orbits, the quadrupole-monopole interaction affects the relation between orbital radius and angular velocity, and also the rate of inspiral, by a quantity of order (v/c)^4, where v is the orbital velocity and c the speed of light.
We present a prescription to compute the time-domain gravitational wave (GW) polarization states associated with spinning compact binaries inspiraling along quasi-circular orbits. We invoke the orbital angular momentum $\vek L$ rather than its Newtonian counterpart $\vek L_{\rm N}$ to describe the binary orbits while the two spin vectors are freely specified in an inertial frame associated with the initial direction of the total angular momentum. We show that the use of $\vek L$ to describe the orbits leads to additional 1.5PN order amplitude contributions to the two GW polarization states com…
Compact binaries inspiralling along eccentric orbits are plausible gravitational wave (GW) sources for the ground-based laser interferometers. We explore the losses in the event rates incurred when searching for GWs from compact binaries inspiralling along post-Newtonian accurate eccentric orbits with certain obvious non-optimal search templates. For the present analysis, GW signals having 2.5 post-Newtonian accurate orbital evolution are modeled following the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D \textbf{70}, 064028 (2004)]. We demonstrate that…
[abridged] The inspiral of a stellar compact object into a massive black hole is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of these slowly inspiraling systems. To that end, the use of very precise theoretical waveform templates in the data analysis is required. To build them we need to have a deep understanding of the gravitational backreaction mechanism responsible for the inspiral. The self-force approach describes the inspiral as the action of a local force that can be …
Future space-borne interferometers will be able to detect gravitational waves at $10^{-3}$ to $10^{-1}$ Hz. At this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational wave sources. In this paper, we investigate possibility of testing Kerr hypothesis against a parametrized non-Kerr metric by matching EMRI signals. However, EMRIs from either equatorial orbits or inclined orbits suffer from the "confusion problem". Our results show that, within the time scale before radiation flux plays an important role, small and moderate deviations from the Kerr spacetime($|δ_i|<1$) can b…
Anisotropic emission of gravitational waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and hence gravitational recoil of the system. The loss rate of linear momentum in the far-zone of the source (a nonspinning binary system of black holes in quasicircular orbit) is investigated at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression in harmonic coordinates for the 2.5PN accurate recoil velocity of the binary accumulated in the inspiral phase. We find that the recoil velocity at the end of the inspiral phase (i.e at the innermost sta…
Compact binaries inspiralling along quasi-circular orbits are the most plausible gravitational wave (GW) sources for the operational, planned and proposed laser interferometers. We provide new class of restricted post-Newtonian accurate GW templates for non-spinning compact binaries inspiralling along PN accurate quasi-circular orbits. Arguments based on data analysis, theoretical and astrophysical considerations are invoked to show why these time-domain Taylor approximants should be interesting to various GW data analysis communities.
We calculate the real-space trajectory and spin precession of a generic spinning compact binary inspiral at any time instant using the dynamical renormalization group formalism. This method leads to closed-form analytic solutions to the binary motion through treating radiation reaction as perturbations and resumming the secular growth of perturbative terms. We consider the spin-orbit effects at leading order and the 2.5PN radiation reaction without orbit averaging or precession averaging for arbitrary individual masses and spin magnitudes and orientations. The solutions are written in a moving…
The post-post-Newtonian (2PN) accurate mass quadrupole moment, for compact binaries of arbitrary mass ratio, moving in general orbits is obtained by the multi-polar post Minkowskian approach of Blanchet, Damour, and Iyer (BDI). Using this, for binaries in general orbits, the 2PN contributions to the gravitational waveform, and the associated far-zone energy and angular momentum fluxes are computed. For quasi-elliptic orbits, the energy and angular momentum fluxes are averaged over an orbital period, and employed to determine the 2PN corrections to the rate of decay of the orbital elements.
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）
Probing near-zone magnetic fields with extreme mass-ratio inspirals
School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）；Department of physics, Nanchang University（南昌大学物理系）；Center for Relativistic Astrophysics and High Energy Physics, Nanchang University（南昌大学相对论天体物理与高能物理中心）
We model the inspiral of a compact stellar-mass object into a massive nonrotating black hole including all dissipative and conservative first-order-in-the-mass-ratio effects on the orbital motion. The techniques we develop allow inspirals with initial eccentricities as high as $e\sim0.8$ and initial separations as large as $p\sim 50$ to be evolved through many thousands of orbits up to the onset of the plunge into the black hole. The inspiral is computed using an osculating elements scheme driven by a hybridized self-force model, which combines Lorenz-gauge self-force results with highly accur…
Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by space-based interferometers. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatmen…
Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear. We numerically integrate the motion of a spinning test body in the field of a non-s…
The angular momentum flux from an inspiralling binary system of compact objects moving in quasi-elliptical orbits is computed at the third post-Newtonian (3PN) order using the multipolar post-Minkowskian wave generation formalism. The 3PN angular momentum flux involves the instantaneous, tail, and tail-of-tails contributions as for the 3PN energy flux, and in addition a contribution due to non-linear memory. We average the angular momentum flux over the binary's orbit using the 3PN quasi-Keplerian representation of elliptical orbits. The averaged angular momentum flux provides the final input …
In the context of binary inspiral of mixed neutron star - black hole systems, we investigate the excitation of the neutron star oscillation modes by the orbital motion. We study generic eccentric orbits and show that tidal interaction can excite the f-mode oscillations of the star by computing the amount of energy and angular momentum deposited into the star by the orbital motion tidal forces via closed form analytic expressions. We study the f-mode oscillations of cold neutron stars using recent microscopic nuclear equations of state, and we compute their imprint into the emitted gravitationa…
In this paper we discuss the development of a fast and accurate waveform model for the quasi-circular orbital evolution of extreme-mass-ratio-inspirals (EMRIs). This model simply employs the data of a few numerical Teukoulsky-based energy fluxes and waveforms to fit out a set of polynomials for the entire fluxes and waveforms. These obtained polynomials are accurate enough in the entire evolution domain, and much more accurate than the resummation post-Newtonian (PN) energy fluxes and waveforms, especially when the spin of a black hole becomes large. The dynamical equation we adopted for orbit…
It is standard lore that gravitational radiation reaction circularizes the orbits of inspiralling binary systems. But in recent papers, Loutrel et al. have argued that at late times in such inspirals, one measure of eccentricity actually increases, and that this could have observable consequences. We show that this variable, the magnitude of the Runge-Lenz vector ($e_{\rm RL}$), is not an appropriate measure of orbital eccentricity, when the eccentricity is smaller than the leading non-Keplerian perturbation of the orbit. Following Loutrel et al., we use Newtonian equations of motion plus the …
We investigate the dynamic stability of inspiraling neutron stars by performing multiple-orbit numerical relativity simulations of the binary neutron star inspiral process. By introducing eccentricities in the orbits of the neutron stars, significant changes in orbital separation are obtained within orbital timescales. We find that as the binary system evolves from apastron to periastron (as the binary separation decreases), the central rest mass density of each star decreases, thus stabilizing the stars against individual prompt collapse. As the binary system evolves from periastron to apastr…
We present an improved version of the approximate scheme for generating inspirals of test-bodies into a Kerr black hole recently developed by Glampedakis, Hughes and Kennefick. Their original "hybrid" scheme was based on combining exact relativistic expressions for the evolution of the orbital elements (the semi-latus rectum p and eccentricity e) with approximate, weak-field, formula for the energy and angular momentum fluxes, amended by the assumption of constant inclination angle, iota, during the inspiral. Despite the fact that the resulting inspirals were overall well-behaved, certain path…
