Gravitational wave echo spectra

Exotic compact objects may resemble black holes very closely while remaining horizonless. They may be distinguished from black holes because they effectively give rise to a resonant cavity for the propagation of low frequency gravity waves. In a Green's function approach, the resonance structure appears in a transfer function. The transfer function in turn is modulated by an initial-condition-dependent source integral to obtain the observed spectrum. We find that the source integral displays universal factors that tend to enhance low and negative frequencies, and this increases the complexity of the waveforms in the time domain. These waveforms also display a significant sensitivity to initial conditions. For these reasons a standard matched-filter search strategy is difficult. In contrast, the sharp and evenly spaced resonance spectrum presents a much more robust signal to target. It persists even in the absence of simple echoes. We also describe an additional two-component structure of this resonance pattern.