Abstract
The Double Pulsar (PSR J0737-3039) is the only neutron star-neutron star (NS-NS) binary in which both NSs have been detectable as radio pulsars. The Double Pulsar has been assumed to dominate the Galactic NS-NS binary merger rate $R_g$ among all known systems, solely based on the properties of the first-born, recycled pulsar (PSR J0737-3039A, or A) with an assumption for the beaming correction factor of 6. In this work, we carefully correct observational biases for the second-born, non-recycled pulsar (PSR J0737-0737B, or B) and estimate the contribution from the Double Pulsar on $R_g$ using constraints available from both A and B. Observational constraints from the B pulsar favour a small beaming correction factor for A (~2), which is consistent with a bipolar model. Considering known NS-NS binaries with the best observational constraints, including both A and B, we obtain $R_g=21_{-14}{^+28}$ per Myr at 95 per cent confidence from our reference model. We expect the detection rate of gravitational waves from NS-NS inspirals for the advanced ground-based gravitational-wave detectors is to be $8_{-5}{^+10}$ per yr at 95 per cent confidence. We discuss prospects of gravitational-wave detection based on our results. Implications of PSR J1906+0746, which is likely to be another tight NS-NS binary in the Galactic disc supported by recent observation, are also remarked.