Modeling multipolar gravitational-wave emission from small mass-ratio mergers

Abstract

Using the effective-one-body (EOB) formalism and a time-domain Teukolsky code, we generate inspiral, merger, and ringdown waveforms in the small mass-ratio limit. We use EOB inspiral and plunge trajectories to build the Teukolsky equation source term, and compute full coalescence waveforms for a range of black hole spins. By comparing EOB waveforms that were recently developed for comparable mass binary black holes to these Teukolsky waveforms, we improve the EOB model for the (2, 2), (2, 1), (3, 3), and (4, 4) modes. Our results can be used to quickly and accurately extract useful information about merger waves for binaries with spin, and should be useful for improving analytic models of such binaries.

Sources of Gravitational Waves: Theory and Observations

“…Much progress has been made in the last twenty years to evolve those equations in a robust, accurate and fast way [209][210][211][212][213][214][215][216], and compute the gravitational waveform h (1) αβ in the wave zone. Today, time-domain RWZ and Teukolsky equations can compute not only the waveform emitted during the very long inspiral stage, but also the plunge, merger and ringdown stages [216][217][218][219][220][221]. Table 6.2 State-of-the-art of PN calculations in BH perturbation theory (i.e., for an extreme mass-ratio compact binary) in the case of quasi-circular orbits.…”

“…To gain more insight and improve the transition from merger to ringdown [216,217,[219][220][221] combined the EOB approch to numerical studies in BH perturbation theory. Concretely, they used the EOB formalism to compute the trajectory followed by an object spiraling and plunging into a much larger BH, and then used that trajectory in the source term of either the time-domain RWZ [202,203] or Teukolsky equation [204].…”

Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms

“…As a consequence, we cannot correct the EOB (2,2) mode to agree with the NR (2,2) mode peak using non-quasicircular amplitude coefficients. This limitation, which also affects the small-mass-ratio limit results [28], is caused by the poor knowledge of PN spin effects in the GW modes and makes the prototype EOB waveforms unreliable for χ i 0.7. Two NR waveforms with nearly extremal spin magnitudes [47,48] became available to us when we were finishing calibration of the spin EOB model.…”

“…III A with those of Ref. [28] to build a prototype EOB model that interpolates between the cal-ibrated EOB waveforms and extends them to a larger region of the parameter space. We also investigate how this prototype EOB model performs with respect to two NR waveforms with nearly extremal spin, which were not used in the calibration.…”

“…After breakthroughs in numerical relativity (NR) [14][15][16], the EOB inspiral-merger-ringdown waveforms were improved by calibrating the model to progressively more accurate NR simulations, spanning larger regions of the parameter space [17][18][19][20][21][22][23][24][25][26][27]. More recently, an EOB model for the dominant (2, 2) mode and four subdominant modes was built for non-spinning binaries of comparable-masses [27] and the small mass-ratio limit [28]. These results, at the interface between numerical and analytical relativity, have already had an impact in LIGO and Virgo searches.…”