Two distinct types of echoes in compact objects

TL;DR

This paper compares two physical mechanisms for gravitational wave echoes in compact objects, linking their origins to potential well reflections and discontinuities, and presents a unified framework supported by numerical simulations.

Contribution

It introduces a unified framework for understanding two types of echoes in compact objects, highlighting their different physical origins and independent triggers.

Findings

Both echo types are associated with distinct quasinormal modes.

Numerical simulations demonstrate the independent occurrence of each echo type.

The period of echoes relates to mode spacing in the frequency domain.

Abstract

In the black hole perturbation theory framework, two different physical pictures for echoes in compact objects have been proposed. The first mechanism interprets echoes as repeated reflections of gravitational waves within a potential well, where the echo period is defined by twice the distance related to the spatial displacement operator that separates two local maxima of the effective potential. The second mechanism associates echoes with a discontinuity in the effective potential, potentially associated with specific accretion processes, without necessarily introducing a second local maximum in the effective potential. This discontinuity leads to echo signals that are typically attenuated over time more quickly, with their period dictated by the characteristics of the transfer amplitudes. In both scenarios, the echoes correspond to a new category of quasinormal modes with minor real parts, with their period connected to the spacing between successive modes in the frequency domain. This work elaborates on a unified framework in compact stars that encompasses both echo mechanisms. It suggests that these two types of echoes derive from different physical origins and can be independently triggered. The occurrence and interplay between these two types of echoes are demonstrated through numerical simulations. %The observational relevance of this study is also addressed.