Analytical template for gravitational-wave echoes: Signal characterization and prospects of detection with current and future interferometers

Abstract

Gravitational-wave echoes in the post-merger ringdown phase are under intense scrutiny as probes of near-horizon quantum structures and as signatures of exotic states of matter in ultracompact stars. We present an analytical template that describes the ringdown and the echo signal for nonspinning objects in terms of two physical parameters: the reflectivity and the redshift at the surface of the object. We characterize the properties of the template and adopt it in a preliminary parameter estimation with current (aLIGO) and future (Cosmic Explorer, Einstein Telescope, LISA) gravitational-wave detectors. For fixed signal-to-noise ratio in the post-merger phase, the constraints on the model parameters depend only mildly on the details of the detector sensitivity curve, but depend strongly on the reflectivity. Our analysis suggests that it might be possible to detect or rule out Planckian corrections at the horizon scale for perfectly-reflecting ultracompact objects at 5σ confidence level with Advanced LIGO/Virgo. On the other hand, signal-to-noise ratios in the ringdown phase equal to ≈ 100 (as achievable with future interferometers) might allow us to probe near-horizon quantum structures with reflectivity 30% ( 85%) at 2σ (3σ) level.

Analytical model for gravitational-wave echoes from spinning remnants

“…Here we generalize the approach of Ref. [32], which considered a source localized near the surface of the ECO. Inspection of Eq.…”

“…Note that the phase of each subsequent echo depends on the combination RR BH , i.e., on the combined action of the reflection by the surface and by the BH barrier. Thus, phase inversion [13,31,32] of each echo relative to the previous one occurs whenever RR BH ≈ −1 for low frequencies (cf. Sec.…”

“…is the real part of the fundamental QNM of the ECO) -the amplitude of the echoes always decreases as [32] |h…”

Quantum Black Holes in the Sky

“…Moreover, even Planckian correction in the dispersion relation of gravitational field [22,23,29] and the BH area quantization [114] may also lead to echo signals. Not only the specific models to reproduce GW echoes but also comprehensive modeling of echo spectra in non-spinning case [115], in spinning case [29,116], and in a semi-analytical way [117,118] have been investigated, which enable us to easily obtain echo spectra. In this section, we review the details of GW echoes by starting with the Chandrasekhar-Detweiler (CD) equation [119,120] that is a wave equation with a purely real angular momentum barrier in the Kerr spacetime.…”

“…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.…”