On the gravitational wave background from compact binary coalescences in the band of ground-based interferometers

This paper reports a comprehensive study on the gravitational wave (GW) background from compact binary coalescences. We consider in our calculations newly available observationbased neutron star and black hole mass distributions and complete analytical waveforms that include post-Newtonian amplitude corrections. Our results show that: (i) post-Newtonian effects cause a small reduction in the GW background signal; (ii) below 100 Hz the background depends primarily on the local coalescence rate r0 and the average chirp mass and is independent of the chirp mass distribution; (iii) the effects of cosmic star formation rates and delay times between the formation and merger of binaries are linear below 100 Hz and can be represented by a single parameter within a factor of ~2; (iv) a simple power-law model of the energy density parameter ΩGW(f) ~ f 2/3 up to 50-100 Hz is sufficient to be used as a search template for ground-based interferometers. In terms of detection prospects of this background signal, we show that: (i) detection (a signal-to-noise ratio of 3) within one year of observation by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors (H1-L1) requires a coalescence rate of r0 = 3 (0.2) Mpc-3 Myr-1 for binary neutron stars (binary black holes); (ii) this limit on r0 could be reduced threefold for two co-located and co-aligned detectors, whereas the currently proposed worldwide network of advanced instruments gives only ~30 per cent improvement in detectability; (iii) the improved sensitivity of the planned Einstein Telescope allows not only confident detection of the background but also the high-frequency components of the spectrum to be measured, possibly enabling rate evolutionary histories and mass distributions to be probed. Finally, we show that sub-threshold binary neutron star merger events produce a strong foreground, which could be an issue for future terrestrial stochastic searches of primordial GWs. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.