The Classifications of Double Neutron Stars and their Correlations with the Binary Orbital Parameters

The statistical distribution of the total mass of 14 double neutron star (DNS) systems (out of 18 pairs observed) is found to be very narrow, with the average and standard deviation as 2.65 0.03 M . For the seven pairs of DNSs with the precisely measured masses of the recycled NSs (first formed) and their non-recycled companions (second formed), their masses are homogeneously distributed as 1.38 0.02 M and 1.29 0.02 M , respectively. It is shown by the Anderson-Darling and Mann-Whitney-Wilcoxon tests that the first-born NSs share a same distribution, which should be formed by the supernova explosion; however, the second-formed NSs have the different statistical origins, which can be ascribed to three formation mechanisms after the further investigations of their orbital parameters and mass values, for instance, supernova explosion (e.g., PSR B1913+16), electron capture (e.g., PSR J0737-3039B), and ultra-stripped cores in close-orbit systems (e.g., PSR J1411+2551). In addition, by means of Fisher's discriminant method, through simulation of the two groups of DNS samples that originated from electron-capture supernova and core-collapse supernova, we obtained the linear discriminant equation (e = −4.5Porb(day) + 1.1) between the eccentricity and orbital period, which can divide the DNSs into two groups involved in NS formed by electron-capture supernova (core-collapse supernova) without (with) kick.