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

Gravitational-wave echoes in the postmerger 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 postmerger 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 5 sigma confidence level with Advanced LIGO/Virgo. On the other hand, signal-to-noise ratios in the ringdown phase equal to approximate to 100 (as achievable with future interferometers) might allow us to probe near-horizon quantum structures with reflectivity greater than or similar to 30% (greater than or similar to 85%) at 2 sigma (3 sigma) level.