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

Abstract

This paper reports a comprehensive study on the gravitational wave (GW)\nbackground from compact binary coalescences. We consider in our calculations\nnewly available observation-based neutron star and black hole mass\ndistributions and complete analytical waveforms that include post-Newtonian\namplitude corrections. Our results show that: (i) post-Newtonian effects cause\na small reduction in the GW background signal; (ii) below 100 Hz the background\ndepends primarily on the local coalescence rate $r_0$ and the average chirp\nmass and is independent of the chirp mass distribution; (iii) the effects of\ncosmic star formation rates and delay times between the formation and merger of\nbinaries are linear below 100 Hz and can be represented by a single parameter\nwithin a factor of ~ 2; (iv) a simple power law model of the energy density\nparameter $\\Omega_{GW}(f) ~ f^{2/3}$ up to 50-100 Hz is sufficient to be used\nas a search template for ground-based interferometers. In terms of the\ndetection prospects of the background signal, we show that: (i) detection (a\nsignal-to-noise ratio of 3) within one year of observation by the Advanced LIGO\ndetectors (H1-L1) requires a coalescence rate of $r_0 = 3 (0.2) Mpc^{-3}\nMyr^{-1}$ for binary neutron stars (binary black holes); (ii) this limit on\n$r_0$ could be reduced 3-fold for two co-located detectors, whereas the\ncurrently proposed worldwide network of advanced instruments gives only ~ 30%\nimprovement in detectability; (iii) the improved sensitivity of the planned\nEinstein Telescope allows not only confident detection of the background but\nalso the high frequency components of the spectrum to be measured. Finally we\nshow that sub-threshold binary neutron star merger events produce a strong\nforeground, which could be an issue for future terrestrial stochastic searches\nof primordial GWs.\n