tokens: and the fraction of mass of formed stars that are NSs iswith being the IMF, Ψ( t ⋆ ) is our best-fit SFH, and Θ NS ( M ⋆ ) is 1 for star mass ranges of 8 M ⊙ M 20 M ⊙ , and zero otherwise. We drop the metallicity dependence in Θ NS because we only consider a solar metallicity for the galaxy, as a result of our spectroscopic fit. t ⋆ is the time when the progenitor of the NS was formed, therefore satisfying t ′ = t ⋆ + t life , with t life being the lifetime of the progenitor before becoming an NS. We assume a t life = 0.02 Gyr, but our calculation is insensitive to this choice as the typical lifetime of these massive stars (∼0.01–0.03 Gyr) is much shorter than the timescale over which the SFH found for NGC 4993 is changing at late times. We assume a Chabrier IMF, but this choice is not relevant, as we are only exploring the high-mass end of the IMF. Assuming α = 0.002 and the distribution of Δ t NSM from Vangioni et al. ( 2016 , their Figure 3 for solar metallicity), and our best-fit SFH from Equation ( 1 ) with t 0 = 3 Gyr and τ = 0.3, we get an NS formation rate of and a BNS merger rate of for the whole galaxy. Errors reflect the uncertainty on the SFH, which dominates our errors: they represent the two central quartiles of the rates distribution computed with the SFHs of the pixel SED fitting over the galaxy. Given the sensitivity of the BNS merger event rate to the recent SFR of a galaxy, it is somewhat surprising that GW170817 occurred in an old, early-type galaxy. We therefore ask what is the probability of observing such an event in any early-type galaxy within the LIGO-detectable volume. To make this estimate, we integrate the stellar mass function of early-type galaxies from Weigel et al. ( 2016 ) and scale the per-solar-mass rate from Equation ( 2 ) to the mass contained within the LIGO-detectable volume (radius 80 Mpc). We find resulting in expected events. This calculation assumes that the SFH of NGC 4993 is representative of local early-type galaxies. In fact, much of the mass will be contained in more massive, and on average older and less star-forming, galaxies. We contrast this with a similar calculation for all galaxy types, using the cosmic SFR density from Gladders et al. ( 2013 ), finding and ∼0.5 expected events. This result shows that it is unlikely that we observed one such BNS merger with LIGO over the combined nine months of operations in an early-type galaxy. The assumptions in the calculation include the fraction of NS that form in binaries ( α = 0.002) and the delay time distribution, both coming from binary star models (where the progenitors of the BNS were already a bound system) and satisfying Milky Way constraints. If the BNS formation mechanism is via dynamical interaction, our result could point to a higher value of α or a shorter Δ t NSM for systems that recently underwent a galaxy merger, more so for those that have high stellar density (such as early-type galaxies). It is therefore of interest to know the
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