Evolution from Canonical to Millisecond Pulsar through the X-ray Accretion Stage

We model the evolution of canonical pulsars from the death line to millisecond pulsars through the X-ray neutron star stage of accretion from a low-mass companion. We trace this evolution in magnetic field strength starting at $B=10^{12}$ to $10^8$ G and in period of about 1 s to milliseconds. Important factors are accretion rate and the decay rate of the magnetic field. A broad swathe is traced in the $B-P$ plane according to the value of these factors, which represent different conditions of the binary pair. An important ingredient is the dependence of the stellar moment of inertia on rotation frequency (time).