profile is calibrated to yield a median value of metallicity equal to $1.5\,\zsun$ (or $8.9$ in the “12+log(O/H)” formalism) at redshift $z=0$. This calibration was designed to match the upper $1 \sigma$ scatter of metallicities according to [@yuan] (see their Fig. 2, top-right panel).

The low-end metallicity profile is based on SDSS observations [@panter], from which we infer that one half of the star forming mass of galaxies at $z\sim0$ has $20\%$ solar metallicity, while the other half has $150\%$ solar metallicity.

Waveform models {#wmodels}
===============

Order-of-magnitude estimates {#sec:simplerates}
----------------------------

For any given GW detector the “horizon distance”, $D_h$, is defined as the luminosity distance at which an optimally oriented (face-on, overhead) canonical $(1.4+1.4)~M_\odot$ NS-NS binary would be detected at a fiducial threshold signal-to-noise ratio (SNR), taken to be $8$ in this paper. The expectation value of the SNR, $\rho$, of a signal with GW amplitude $h(t)$ is given by \[SNR\] \^2 = 4\_0\^ df, where $\tilde h(f)$ is the Fourier transform of the signal and $S_n(f)$ is the noise power spectral density of the detector [see e.g. @cutlerflanagan; @poissonwill]. The square root of the noise power spectral density is plotted in Fig. \[fig:noise\] for several advanced interferometers of interest. 