On echo intervals in gravitational wave echo analysis
  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.
