A morphology-independent data analysis method for detecting and characterizing gravitational wave echoes

The ability to directly detect gravitational waves has enabled us to empirically probe the nature of ultracompact relativistic objects. Several alternatives to the black holes of classical general relativity have been proposed which do not have a horizon, in which case a newly formed object (e.g., as a result of binary merger) may emit echoes: bursts of gravitational radiation with varying amplitude and duration, but arriving at regular time intervals. Unlike in previous template-based approaches, we present a morphology-independent search method to find echoes in the data from gravitational wave detectors, based on a decomposition of the signal in terms of generalized wavelets consisting of multiple sine-Gaussians. The ability of the method to discriminate between echoes and instrumental noise is assessed by inserting into the noise two different signals: a train of sine-Gaussians, and an echoing signal from an extreme mass-ratio inspiral of a particle into a Schwarzschild vacuum spacetime, with reflective boundary conditions close to the horizon. We find that both types of signals are detectable for plausible signal-to-noise ratios in existing detectors and their near-future upgrades. Finally, we show how the algorithm can provide a characterization of the echoes in terms of the time between successive bursts, and damping and widening from one echo to the next.

Figure 1

The simulated signals used to evaluate the method. Top panel: A train of sine-Gaussians. Bottom panel: The waveform from a toy model for a mass-ratio $q=1000$ inspiral of a particle in a Schwarzschild spacetime, with Neumann reflective boundary conditions just outside the horizon.

Figure 2

Background distributions for the (log) Bayes factors $B_{S/N}$ (top) and $B_{S/G}$ (bottom), containing 380 trials. The dashed lines show the values of these quantities for the injection of echoes from the inspiral toy model with SNRs of 8, 12, 18, and 25.

Figure 3

The distribution of samples for the case where the injected signal is a comb of sine-Gaussians. Top: Damping factor $\gamma$ against the time $\mathrm{\Delta }t$ between echoes. Bottom: The widening factor $w$ against $\mathrm{\Delta }t$. The colors indicate the number of samples per pixel, while the dashed lines show the true values of the parameters.

Figure 4

The distribution of samples for the case where the injected signal is the inspiral toy model. Again we show $\gamma$ versus $\mathrm{\Delta }t$ (top) and $w$ versus $\mathrm{\Delta }t$ (bottom).

Figure 5

Injected and recovered strain in one of the detectors for the inspiral toy model. The reconstructed signal (shaded orange band showing 90% credible interval) is indeed consistent with the signal that has been injected (solid maroon line). For completeness we also show the full detector data containing both signal and noise (gray background).