Accessibility of the gravitational-wave background due to binary coalescences to second and third generation gravitational-wave detectors

Compact binary coalescences, such as binary neutron stars or black holes, are among the most promising candidate sources for the current and future terrestrial gravitational-wave detectors. While such sources are best searched using matched template techniques and chirp template banks, integrating chirp signals from binaries over the entire universe also leads to a gravitational-wave background (GWB). In this paper we systematically scan the parameter space for the binary coalescence GWB models, taking into account uncertainties in the star formation rate and in the delay time between the formation and coalescence of the binary, and we compare the computed GWB to the expected sensitivities of the second and third generation gravitational-wave detector networks. We find that second generation detectors are likely to detect the binary coalescence GWB, while the third generation detectors will probe most of the available parameter space. The binary coalescence GWB will, in fact, be a foreground for the third generation detectors, potentially masking the GWB background due to cosmological sources. Accessing the cosmological GWB with third generation detectors will therefore require identification and subtraction of all inspiral signals from all binaries in the detectors’ frequency band.

Figure 1

Number of binaries per 1 Hz frequency bin. For the BNS cases, we assume each star to have mass of $1.4M_{\odot }$, local rate of $R_{\mathrm{local}}=1{\mathrm{Mpc}}^{-3}{\mathrm{Myr}}^{-1}$, and $t_{\min }=20\mathrm{Myr}$ ($P(t_d)\sim 1/t_d$). For the BHNS case, we assume masses of $1.4M_{\odot }$ and $10M_{\odot }$, the local rate $R_{\mathrm{local}}=0.03{\mathrm{Mpc}}^{-3}{\mathrm{Myr}}^{-1}$, and $t_{\min }=100\mathrm{Myr}$. For the BBH case, we assume masses of $10M_{\odot }$, and $t_{\min }=100\mathrm{Myr}$.

Figure 2

Gravitational-wave spectrum ${\Omega }_{\mathrm{GW}}(f)$ computed for the BNS case with $M_c=1.22M_{\odot }$, $\lambda =3\times {10}^{-5}{M}_{\odot }^{-1}$ ($R_{\mathrm{local}}=0.6{\mathrm{Mpc}}^{-3}{\mathrm{Myr}}^{-1}$), star formation rate from 48, and $P(t_d)\sim t_d^{-1}$ with $t_{\min }=20\mathrm{Myr}$. The effect of removing the nearest binaries (with redshifts $z<0.1$ or $z<0.2$) is very small.

Figure 3

Top: Different star formation rates $R_{*}(z)$ are plotted as a function of redshift $z$. Bottom: $I(z)$ as a function of redshift is plotted for different star formation rates, assuming $P(t_d)\sim t_d^{-1}$ and $t_{\min }=20\mathrm{Myr}$.

Figure 4

Accessibility of binary coalescence GWB to current and future gravitational-wave detectors. The two columns correspond to two estimates of the star formation rate: Hopkins and Beacom [48] (left) and Nagamine et al. [51] (right). The three rows correspond to BNS, BBH, and BHNS, respectively, top-to-bottom. For each plot, we show the region in the $\lambda -M_c$ parameter space excluded by the 95% confidence upper limit of LIGO [31]. We also show regions in the $\lambda -M_c$ parameter space that will be probed by the Advanced LIGO collocated detector pair (assuming 1 yr of exposure [5, 6]), and by the Einstein Telescope (assuming two collocated detectors with ET-D sensitivity and 1 yr of exposure [11, 12]) at $2\sigma$ level (that is, assuming the signal-to-noise ratio of 2). These regions are to be compared with the expected local coalescence rates shown as horizontal dashed lines: top-to-bottom they correspond to maximal, optimistic, realistic, and pessimistic estimates presented in 53.

Figure 5

Effect of different $P(t_d)$ choices on the contours for Advanced LIGO (first column) and ET (second column) for the BNS (first row) and BBH (second row). Dashed horizontal lines correspond to realistic estimate (upper-left), optimistic and realistic estimates (lower-left), and pessimistic estimate (lower-right). In the upper-right plot, all contours are below the pessimistic estimate. As in Fig. 4, we assume signal-to-noise ratio of 2 when comparing the models with the expected experimental sensitivities. In all cases we consider several power-law distributions (denoted by the parameters $\alpha$ and $t_{\min }$), as well as the model where we force $t_d=0$. In the BNS case (top row), we also consider the log-normal distribution denoted by the parameters ${\tau }_{*}$ and $\sigma$.