This paper reports a comprehensive study on the gravitational wave ( GW ) background from compact binary coalescences .
We consider in our calculations newly available observation-based 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 r _ { 0 } 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 \sim 2 ; ( iv ) a simple power law model of the energy density parameter \Omega _ { GW } ( f ) \sim 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 r _ { 0 } = 3 \hskip { 1.422638 pt } ( 0.2 ) \hskip { 1.422638 pt } Mpc ^ { -3 } \hskip { 1.422638 pt% } Myr ^ { -1 } for binary neutron stars ( binary black holes ) ; ( ii ) this limit on r _ { 0 } could be reduced 3-fold for two co-located and co-aligned detectors , whereas the currently proposed worldwide network of advanced instruments gives only \sim 30 \% 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 .