 Solution

Treat the stated $120\mathrm{Mpc}$ as the radius of a complete, volume-limited search, with uniform galaxy density $n_g$. Its surveyed volume and number of galaxies areThe observing time is $\Delta t=117/365.25=0.3203\mathrm{yr}$. One detection estimatesor one merger per approximately $2.3\times 10^4$ years per Milky-Way-type galaxy. The equivalent volume rate is about $431\mathrm{Gp}{\mathrm{c}}^{-3}\mathrm{y}{\mathrm{r}}^{-1}$. The event's actual $40\mathrm{Mpc}$ distance is not the survey radius and must not replace $120\mathrm{Mpc}$ in the exposure.

A representative Galactic core-collapse supernova rate is about two per century, roughly $4.6\times 10^2$ times larger than this merger-rate estimate. The historical ${}^{26}\mathrm{Al}$ estimate was $1.9\pm 1.1$ per century.^[ref] The one-event Poisson uncertainty is large. Detector orientation, duty cycle, completeness and whether the quoted radius is an optimal horizon or an effective range also change the exposure; the boxed value is the specified simple-volume estimate.