# On echo intervals in gravitational wave echo analysis

## TL;DR

This paper evaluates whether constant interval templates are sufficient for gravitational wave echo detection or if variable interval templates are necessary, especially for future high-sensitivity detectors, through simulations and Bayesian analysis.

## Contribution

It demonstrates the potential misinterpretation of signals by constant interval templates and assesses the importance of variable interval templates in future gravitational wave searches.

## Key findings

- CIE templates may misinterpret UIE signals if interval variation exceeds statistical errors.
- Bayesian analysis confirms the importance of UIE templates for accurate signal reconstruction.
- Forecasts show future detectors can constrain echo intervals effectively.

## Abstract

Gravitational wave echoes, if they exist, could encode important information of new physics from the strong gravity regime. Current echo searches usually assume constant interval echoes (CIEs) a priori, although unequal interval echoes (UIEs) are also possible. Despite of its simplicity, the using of CIE templates need to be properly justified, especially given the high sensitivity of future gravitational wave detectors. In this paper, we assess the necessity of UIE templates in echo searches. By reconstructing injected UIE signals with both CIE and UIE templates, we show that the CIE template may significantly misinterpret the echo signals if the variation of the interval is greater than the statistical errors of the interval, which is further confirmed by a Bayesian analysis on model stelection. We also forecast the constraints on the echo intervals given by future GW detectors such as Advanced LIGO and Einstein Telescope.