Recycling NSs to ultrashort periods: a statistical analysis of their evolution in the "magnetic moment vs period" 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.