Low-frequency Gravitational-wave Memories from Gamma-Ray Burst Afterglows with Energy Injections

Abstract

Ultrarelativistic gamma-ray burst (GRB) jets are strong gravitational-wave (GW) sources with memory-type signals. The plateau (or shallow decay) phases driven by the energy injection may appear in the early X-ray afterglows of GRBs. In this paper, we investigate GW signals as well as X-ray afterglow emissions in the framework of GRB jets with energy injections, and both short- and long-duration GRBs are considered. We find that, regardless of the case, and because of the antibeaming and time delay effects, a rising slope that emerges in the waveform of the GW signal, due to the energy injection, lags far behind the energy ejection, and the typical frequencies of the characteristic amplitudes fall within a low-frequency region of ∼10−4–10−6 Hz; we also consider that the GW memories triggered by the GRB jets with energy injection have previously not been accounted for and that nearby GRBs with strong energy injections may disturb the measurement of the stochastic GW background. Such GW memory detection would provide a direct test for models of energy injection in the scenario of GRB jets.