Analytical model for gravitational-wave echoes from spinning remnants

Abstract

Gravitational-wave echoes in the post-merger signal of a binary coalescence are predicted in various scenarios, including near-horizon quantum structures, exotic states of matter in ultracompact stars, and certain deviations from general relativity. The amplitude and frequency of each echo is modulated by the photon-sphere barrier of the remnant, which acts as a spin-and frequencydependent high-pass filter, decreasing the frequency content of each subsequent echo. Furthermore, a major fraction of the energy of the echo signal is contained in low-frequency resonances corresponding to the quasi-normal modes of the remnant. Motivated by these features, in this work we provide an analytical gravitational-wave template in the low-frequency approximation describing the postmerger ringdown and the echo signal of a spinning ultracompact object. Besides the standard ringdown parameters, the template is parametrized in terms of only two physical quantities: the reflectivity coefficient and the compactness of the remnant. We discuss novel effects related to the spin and to the complex reflectivity, such as a more involved modulation of subsequent echoes, the mixing of two polarizations, and the ergoregion instability in case of perfectly-reflecting spinning remnants. Finally, we compute the errors in the estimation of the template parameters with current and future gravitational-wave detectors using a Fisher matrix framework. Our analysis suggests that models with almost perfect reflectivity can be excluded/detected with current instruments, whereas probing values of the reflectivity smaller than 80% at 3σ confidence level requires future detectors (Einstein Telescope, Cosmic Explorer, LISA). The template developed in this work can be easily implemented to perform a matched-filter based search for echoes and to constrain models of exotic compact objects.

Quantum Black Holes in the Sky

“…The detection of GW echoes with the third generation GW observatories are discussed in [117,118], and it may be possible to distinguish ECOs with |R| 0.3 from BHs with at 2σ level when SNR ∼ 100 in ringdown, which would be possible for the third-generation GW detectors. The relative error on the reflectivity of would-be horizon is also investigated in [117,118], and the relative error for measurement of relectivity in ground-based detectors is approximately given by where M = 30M , ρ ringdown is the SNR in the ringdown phase, while the distance between the top of the angular momentum barrier and the would-be horizon is assumed to be longer than 50M in the tortoise coordinate. For comparison, we note that the loudest detected BBH event, GW150914, has ρ ringdown 8.…”

Gravitational wave physics and astronomy in the nascent era

“…In the analytical template proposed by Refs. [510,511], the reflection rate at the object's surface is also assumed as a parameter. The reflection rate at the potential barrier is given from BH perturbations.…”

Spicing up the recipe for echoes from exotic compact objects: Orbital differences and corrections in rotating backgrounds

“…Different works presented proposals for echo templates that could be used in the search for echoes in gravitational wave data (see for example [37][38][39]). Some preliminary searches reported evidence for echoes with low significance < 2.5σ [40,41], which were not confirmed by other studies [42][43][44].…”

“…However, it would be possible to fine tune the transfer function to select the same frequencies for both orbits, as in the nonrotating case[29]. A simple example of such a transfer function would be a sum of two gaussians centered at ±ω 0 5 An unrelated modulation of the waveform was reported in[37],where it was noticed that rotation can mix the + and × polarizations in the gravitational case.…”