tokens: is obtained by taking the sum of the contributions from all dark matter halos We have made use of the python code colossus (Diemer 2018 ) to generate the dark matter halo mass function using the parameterized formula fitting to an N -body simulation proposed by Tinker et al. ( 2008 ), and the concentration–dark matter halo mass relation proposed by Prada et al. ( 2012 ). We have tested systematics by using Raeymaekers ( 2007 ) for N -body simulation fits for the dark matter halo mass function, and Dutton Macciò ( 2014 ) for the concentration–halo mass relation. The results show a different choice of dark matter halo population modeling will not change the final event rate by orders of magnitude. Assuming f PBH = 100%, the result of Equation ( 10 ) is shown in Figure 1 . The main contribution to the integral in Equation ( 10 ) is from low-mass dark matter halos, therefore the result depends sensitively on the lower end for halo mass. To illustrate the dependence on lower mass cutoff , we plot as a function of in Figure 1 . Also note that the integrand of Equation ( 10 ) does not depend on M PBH due to compensation between the primordial black hole number density and the cross section. To determine the lower limit of the dark matter halo mass for M PBH = 0.01/0.1/1 M ⊙ , we follow the criterion by Equation (11) of Bird et al. ( 2016 ) requiring that the dark matter halo evaporation timescale due to dynamical relaxation exceeds the dark energy domination timescale (∼3 × 10 9 yr). This choice results in the lower integral limit of Equation ( 10 ) being 0.3/3/21 M ⊙ for M PBH = 0.01/0.1/1 M ⊙ . Choosing a lighter dark matter halo cutoff would contribute more binary primordial black hole merger events if the halos would not have evaporated at present and the NFW profile is still preserved. High resolution dark matter N -body simulations are needed to precisely resolve the smallest structure of subsolar mass primordial black hole halos but this is beyond the scope of this paper. Figure 1. Event rate for binary primordial black hole merger as a function of the lower cutoff of dark matter halo mass. The markers are the event rate for M PBH = 0.01/0.1/1 M ⊙ , which are 528/140/45 Gpc −3 yr −1 , respectively. With the above choices of lower integral cutoff, as shown in Figure 1 , the event rate for M PBH = 0.01/0.1/1 M ⊙ is 528/140/45 Gpc −3 yr −1 . As a comparison, for M PBH = 30 M ⊙ , the event rate is Gpc −3 yr −1 , as computed in Bird et al. ( 2016 ). Therefore, the merger rate of subsolar primordial black holes increases by one to two orders of magnitude compared to that of 30 M ⊙ . To compare with observations, the sensitive volume, which is defined to be the orientation-averaged volume assuming a match-filtering signal-to-noise ratio (S/N) > 8 (Abbott et al. 2018b ), is Gpc 3 for M PBH = 0.01/0.1/1 M ⊙ for Advanced LIGO at its design sensitivity. Given the above estimated event rate, under our assumption of delta function mass distribution, the
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