Recycling NSs to ultrashort periods: a statistical analysis of their evolution in the μ− P plane

We investigate the statistical evolution of magnetic neutron stars recycled in Low Mass Binary (LMB) systems, simulating synthetic populations. Irrespective to the details of the physical models, we find to be significant the fraction of neutron stars spinning close to their mass shedding limit relative to the millisecond pulsar population. The simulated neutron stars show a tail in their period distribution at periods shorter than 1.558 ms, the minimum detected so far. Crustal magnetic field decay models predict also the existence of massive rapidly spinning neutron stars with very low magnetic moment. 1. Magnetorotational evolution scenario Population synthesis models are evolved within a simple recycling scenario (as outlined e.g. by Lipunov 1992), where the neutron stars (NSs hereon) may experience the phase of ejector, accretor or propeller. The magnetorotational evolution includes the general relativistic effects as modelled in Burderi et al. (1999). We considered two possibilities bracketing uncertainties in the accretion histories of the NSs in LMBs: (i) steady accretion for a time τRLO; (ii) persistent accretion followed by a transient phase during which the mass transfer becomes unsteady, mimicking the quenching of accretion (Ergma et al. 1998). In particular we account for the angular momentum losses by propeller, both for persistent and for non-stationary accretion, during the Roche Lobe Overflow phase. The NSs in our population synthesis models have an initial gravitational mass of 1.4 M⊙. Cook, Shapiro & Teukolsky (1994) showed that all viable equations of state (EoSs) for nuclear matter allow for recycling to ultra-short periods,