For example, the aLIGO horizon distance is $D_{h} \simeq 450 {\, {\rm Mpc}}$.

Although the sensitivity of a GW detector network depends on the details of the search pipeline and the detector data quality, we follow [@2010CQGra..27q3001A] in considering a single detector with an SNR threshold $\rho \ge 8$ as a proxy for detectability by the network. With this criterion, a simple and common expression to transform the local merger rate to a predicted detection rate $R_D$, given the horizon distance $D_h$ and the merger rate density, ${\cal R}(z)$, evaluated locally (at $z=0$), is: $$\label{eq:LocalUniverseMergerRateFormula}
R_D \simeq  \frac{4\pi}{3} D_{h}^3 \langle w^3\rangle \left<(\mc/1.2 M_\odot)^{15/6}\right>{\cal R}(0) 
$$ In this expression $\langle w^3\rangle^{-1/3}\simeq 2.264$ is a purely geometrical and SNR-threshold-independent factor commonly used to relate sky location- and orientation-averaged distances to optimal detection distances (see Appendix for details) and $\mc=\eta^{3/5}M$ (where $M=m_1+m_2$ is the total mass of the binary and $\eta\equiv m_1m_2/M^2$) is the “chirp mass” [see, e.g., @cutlerflanagan]. This estimate assumes that (1) cosmological effects are negligible (i.e., space is Euclidean to a good approximation), and (2) most of the SNR is accumulated during an inspiral phase which lasts through the entire sensitive band of the detector, where the GW amplitude in 