A strange star scenario for the formation of isolated millisecond pulsars

According to the recycling model, neutron stars in low-mass X-ray binaries were spun up to millisecond pulsars (MSPs), which indicates that all MSPs in the Galactic plane ought to be harbored in binaries. However, about $20\%$ Galactic field MSPs are found to be solitary. To interpret this problem, we assume that the accreting neutron star in binaries may collapse and become a strange star when it reaches some critical mass limit. Mass loss and a weak kick induced by asymmetric collapse during the phase transition (PT) from neutron star to strange star can result in isolated MSPs. In this work, we use a population-synthesis code to examine the PT model. The simulated results show that a kick velocity of $\sim60~{\rm km~s}^{-1}$ can produce $\sim6\times10^3$ isolated MSPs and birth rate of $\sim6.6\times10^{-7} {\rm ~yr}^{-1}$ in the Galaxy, which is approximately in agreement with predictions from observations. For the purpose of comparisons with future observation, we also give the mass distributions of radio and X-ray binary MSPs, along with the delay time distribution.