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Observations of the properties of multiple coalescing neutron stars willsimultaneously provide insight into neutron star mass and spin distribution,the neutron star merger rate, and the nuclear equation of state. Not allmerging binaries containing neutron stars are expected to be identical.Plausible sources of diversity in these coalescing binaries can arise from abroad or multi-peaked NS mass distribution; the effect of different and extremeNS natal spins; the possibility of NS-BH mergers; or even the possibility ofphase transitions, allowing for NS with similar mass but strongly divergentradius. In this work, we provide a concrete algorithm to combine allinformation obtained from GW measurements into a joint constraint on the NSmerger rate, the distribution of NS properties, and the nuclear equation ofstate. Using a concrete example, we show how biased mass distributioninferences can significantly impact the recovered equation of state, even inthe small-$N$ limit. With the same concrete example, we show how small-$N$observations could identify a bimodal mass and spin distribution for merging NSsimultaneously with the EOS. Our concordance approach can be immediatelygeneralized to incorporate other observational constraints.

Inferring the neutron star equation of state simultaneously with the population of merging neutron stars