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Register a new userGravitational-wave energy flux for compact binaries through second order in the mass ratio
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Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modelling extreme-mass-ratio inspirals and will be useful in modelling intermediate-mass-ratio systems.
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Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.
The non-linear gravitational wave (GW) memory effect is a distinct prediction in general relativity. While the effect has been well studied for comparable mass binaries, it has mostly been overlooked for intermediate mass ratio inspirals (IMRIs). We offer a comprehensive analysis of the phenomenology and detectability of memory effects, including contributions from subdominant harmonic modes, in heavy IMRIs consisting of a stellar mass black hole and an intermediate mass black hole. When formed through hierarchical mergers, for example when a GW190521-like remnant captures a stellar mass black hole, IMRI systems have a large total mass, large spin on the primary, and possibly residual eccentricity; features that potentially raise the prospect for memory detection. We compute both the displacement and spin non-linear GW memory from the $m eq 0$ gravitational waveforms computed within a black hole perturbation theory framework that is partially calibrated to numerical relativity waveforms. We probe the dependence of memory effects on mass ratio, spin, and eccentricity and consider the detectability of a memory signal from IMRIs using current and future GW detectors. We find that (i) while eccentricity introduces additional features in both displacement and spin memory, it does not appreciatively change the prospects of detectability, (ii) including higher modes into the memory computation can increase singal-to-noise (SNR) values by about 7% in some cases, (iii) the SNR from displacement memory dramatically increases as the spin approaches large, positive values, (iv) spin memory from heavy IMRIs would, however, be difficult to detect with future generation detectors even from highly spinning systems. Our results suggest that hierarchical binary black hole mergers may be a promising source for detecting memory and could favorably impact memory forecasts.
A powerful technique to calculate gravitational radiation from binary systems involves a perturbative expansion: if the masses of the two bodies are very different, the small body is treated as a point particle of mass $m_p$ moving in the gravitational field generated by the large mass $M$, and one keeps only linear terms in the small mass ratio $m_p/M$. This technique usually yields finite answers, which are often in good agreement with fully nonlinear numerical relativity results, even when extrapolated to nearly comparable mass ratios. Here we study two situations in which the point-particle approximation yields a divergent result: the instantaneous flux emitted by a small body as it orbits the light ring of a black hole, and the total energy absorbed by the horizon when a small body plunges into a black hole. By integrating the Teukolsky (or Zerilli/Regge-Wheeler) equations in the frequency and time domains we show that both of these quantities diverge. We find that these divergences are an artifact of the point-particle idealization, and are able to interpret and regularize this behavior by introducing a finite size for the point particle. These divergences do not play a role in black-hole imaging, e.g. by the Event Horizon Telescope.
We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasi-circular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparisons with numerical-relativity simulations.
In the adiabatic post-Newtonian (PN) approximation, the phase evolution of gravitational waves (GWs) from inspiralling compact binaries in quasicircular orbits is computed by equating the change in binding energy with the GW flux. This energy balance equation can be solved in different ways, which result in multiple approximants of the PN waveforms. Due to the poor convergence of the PN expansion, these approximants tend to differ from each other during the late inspiral. Which of these approximants should be chosen as templates for detection and parameter estimation of GWs from inspiraling compact binaries is not obvious. In this paper, we present estimates of the effective higher order (beyond the currently available 4PN and 3.5PN) non-spinning terms in the PN expansion of the binding energy and the GW flux that minimize the difference of multiple PN approximants (TaylorT1, TaylorT2, TaylorT4, TaylorF2) with effective one body waveforms calibrated to numerical relativity (EOBNR). We show that PN approximants constructed using the effective higher order terms show significantly better agreement (as compared to 3.5PN) with the inspiral part of the EOBNR. For non-spinning binaries with component masses $m_{1,2} in [1.4 M_odot, 15 M_odot]$, most of the approximants have a match (faithfulness) of better than 99% with both EOBNR and each other.
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