Tail wavelets in the merger of binary compact objects

We present a model for tail wavelets, a phenomenon also known as "echo" in the literature. The tail wavelet may appear in signal reconnaissances in the merger of binary compact objects, including black holes and neutron stars. It follows main gravitational waves (GWs) emitted during the merger process. We study, among other generic properties, the pressure of the gravitational waves and their subsequent effects to the surrounding matters/dark matters. We demonstrate that the matters/dark matters surrounding the compact objects lead to the speculated tail wavelet following the main GW. In this scenario, the surrounding matter is first pushed away to some altitude by the main wave, and then splash down to the black hole region, and thereby excites the tail wavelet. We illustrate this idea in a simplified model, where numerical estimations are carried out concerning the specific distribution of the dark matter outside the black hole horizon and the threshold values in accordance with observations. We demonstrate that the tail wavelet can be a natural phenomenon in frame of general relativity, without invoking any modified gravities or quantum effects. Furthermore, in frame of this model one can investigate the distribution of dark matters surrounding the black holes through analysing the waveform of the tail wavelet from the forthcoming data with better resolution, especially those from the third generation GW detectors.