Population synthesis of wide binary millisecond pulsars

Four evolutionary channels leading to the formation of wide binary millisecond pulsars are investigated. The majority of binary millisecond pulsars are found to descend from systems in which the most massive component undergoes a common-envelope phase prior to the supernova explosion leading to the birth of the neutron star. The orbital period distribution of simulated samples of wide binary millisecond pulsars is compared with the observed distribution of Galactic binary millisecond pulsars for a variety of parameters describing the formation and evolution of binaries. The distribution functions typically show a short-period peak below 10 d and a long-period peak around 100 d. The observed distribution is best reproduced by models with highly non-conservative mass transfer, common-envelope efficiencies equal to or larger than unity, a critical mass ratio for the delayed dynamical instability larger than 3, and no or moderate supernova kicks at the birth of the neutron star. Few systems are found with orbital periods longer than 200 d, irrespective of the accretion efficiency of neutron stars. This occurs as a result of the upper limit on the initial orbital periods beyond which the binary avoids the common-envelope phase prior to the supernova explosion of the primary.