2005MNRAS.364.1063H

We discuss the gravitational wave background (GWB) from a cosmological population of gamma-ray bursts (GRBs). Among the various emission mechanisms for the gravitational waves (GWs), we pay particular attention to the vast anisotropic neutrino emissions from the accretion discs around black holes formed after so-called failed supernova explosions. The GWs produced by such mechanisms are known as `burst with memory', and could dominate in the low-frequency regime below ∼10 Hz. To estimate their amplitudes, we derive general analytic formulae for gravitational waveforms from the axisymmetric jets. Based on the formulae, we first quantify the spectrum of GWs from a single GRB. Then, summing the cosmological population, we find that the resultant value of the density parameter becomes roughly Ω_GW~ 10^–20 over the wide-band of the low-frequency region, f∼ 10^–4- 10¹ Hz. The amplitude of the GWB is significantly smaller than that of the primordial GWB originating from the inflationary epoch, and is far below the detection limit.