The Gravitational waves merger time distribution of binary neutron star systems

Binary neutron stars (BNS) mergers are prime sites for $r$-process nucleosynthesis. Their rate determines the chemical evolution of heavy elements in the Milky Way. The merger rate of BNS is a convolution of their birth rate and the gravitational radiation spiral-in delay time. Using the observed population of Galactic BNS we show here that the lifetimes of pulsars in observed BNSs are sufficiently short that the ages of BNSs have little to no effect on the observed merger time distribution. We find that at late times ($t\gtrsim 1$ Gyr) the gravitational wave delay time distribution (DTD) follows the expected $ t^{-1}$. However, a significant excess of rapidly merging systems (between $40-60\%$ of the entire population) is apparent at shorter times. Although the exact shape of the DTD cannot be determined with the existing data, in all models that adequately describe the data we find at least $40\%$ of BNSs with merger times less than 1Gyr. This population of rapid mergers implies a declining deposition rate of $r$-process materials that is consistent with several independent observations of heavy element abundances in the Milky Way. At the same time this population that requires initial binary separations of roughly one solar radius clearly indicates that these binaries had common envelope progenitors. Our results suggest that a significant fraction of future LIGO/Virgo BNS mergers would reside in star forming galaxies.