Formation and evolution of compact binaries in globular clusters - II. Binaries with neutron stars

In this paper, the second of a series, we study the stellar dynamical and evolutionary processes leading to the formation of compact binaries containing neutron stars (NSs) in dense globular clusters. For this study, 70 dense clusters were simulated independently, with a total stellar mass similar to 2 x 10(7) M-circle dot, exceeding the total mass of all dense globular clusters in our Galaxy. We find that, in order to reproduce the empirically derived formation rate of low-mass X-ray binaries (LMXBs), we must assume that NSs can be formed via electron-capture supernovae with typical natal kicks smaller than in core-collapse supernovae. Our results explain the observed dependence of the number of LMXBs on 'collision number' as well as the large scatter observed between different globular clusters. We predict that the number of quiescent LMXBs in different clusters should not have a strong metallicity dependence. We compare the results obtained from our simulations with the observed population of millisecond pulsars (MSPs). We find that in our cluster model the following mass-gaining events create populations of MSPs that do not match the observations (either they are inconsistent with the observed LMXB production rates, or the inferred binary periods or companion masses are not observed among radio bMSPs): (i) accretion during a common-envelope event with a NS formed through electron-capture supernovae (ECSNe), and (ii) mass transfer (MT) from a white dwarf donor. Some processes lead only to a mild recycling - physical collisions or MT in a post-accretion-induced collapse system. In addition, for MSPs, we distinguish low magnetic field (long-lived) and high magnetic field (short-lived) populations, where in the latter NSs are formed as a result of accretion-induced collapse or merger-induced collapse. With this distinction and by considering only those mass-gaining events that appear to lead to NS recycling, we obtain good agreement of our models with the numbers and characteristics of observed MSPs in 47 Tuc and Terzan 5, as well as with the cumulative statistics for MSPs detected in globular clusters of different dynamical properties. We find that significant production of merging double NSs potentially detectable as short gamma-ray bursts occurs only in very dense, most likely core-collapsed clusters.