Astrophysical gravitational-wave echoes from galactic nuclei

Galactic nuclei (GNs) are dense stellar environments abundant in gravitational-wave (GW) sources for the Laser Interferometer Gravitational-Wave Observatory (LIGO), Virgo, and Kamioka Gravitational Wave Detector (KAGRA). The GWs may be generated by stellar-mass black hole (BH) or neutron star mergers following gravitational bremsstrahlung, dynamical scattering encounters, Kozai-Lidov-type oscillations driven by the central supermassive black hole (SMBH), or gas-assisted mergers if present. In this paper, we examine a smoking gun signature to identify sources in GNs: the GWs scattered by the central SMBH. This produces a secondary signal, an astrophysical GW echo, which has a very similar time-frequency evolution as the primary signal but arrives after a time delay. We determine the amplitude and time-delay distribution of the GW echo as a function of source distance from the SMBH. Between similar to 10 per cent and 90 per cent of the detectable echoes arrive within similar to(1-100)M-6 s after the primary GW for sources between 10 and 10 4 Schwarzschild radius, where M-6 = M-SMBH,M-z/(10(6) M-circle dot), and M-SMBH,M-z is the observer-frame SMBH mass. The echo arrival times are systematically longer for high signal-to-noise ratio (SNR) primary GWs, where the GW echo rays are scattered at large deflection angles. In particular, similar to 10 per cent-90 per cent of the distribution is shifted to similar to(5-1800)M-6 s for sources, where the lower limit of echo detection is 0.02 of the primary signal amplitude. We find that similar to 5 per cent-30 per cent (similar to 1 per cent-7 per cent) of GW sources have an echo amplitude larger than 0.2-0.05 times the amplitude of the primary signal if the source distance from the SMBH is 50 (200) Schwarzschild radius. Non-detections can rule out that a GW source is near an SMBH.