Recycling neutron stars to ultrashort periods: A statistical analysis of their evolution in the mu-P plane

In this paper we investigate the statistical evolution of magnetic neutron stars, recycled in binary systems, simulating synthetic populations. To bra cket uncertainties, we consider a soft (FP) and a stiff (PS) equation of st ate (EoS) for nuclear matter and explore the hypothesis that the magnetic h eld is confined in the stellar crust. We follow the magnetorotational evolu tion within a simple recycling scenario. The decay of the magnetic held is modeled imposing at the crust-core boundary either complete field expulsion by the superconducting core or advection and freezing in a very highly con ducting transition shell. Irrespective of the details of the physical model s, we find the presence of a tail in the period distribution of the synthet ic populations at periods shorter than 1.558 ms, the minimum detected so fa r. For the soft EoS, and independent of the details of the magnetic held ev olution, the recycling gives rise to a spin distribution that is increasing monotonically toward short periods, and a clear "barrier" forms at the min imum period for the onset of mass shedding (similar or equal to 0.7 ms). Fo r the stiff EoS, the distribution is flatter, displaying a broad maximum ab out 2-4 ms. On the other hand, if in low-mass binaries the neutron stars ex perience a progressive decrease of the mass accretion rate (due to transien t behavior and/or the quenching of accretion), the magnetospheric propeller produces (together with the magnetic dipole losses) an overall depletion o f neutron stars in the millisecond region of the mu-P plane. The estimated fraction of neutron stars spinning close to their shedding limit over the m illisecond pulsar population is found to be significant. Crustal magnetic h eld decay models also predict the existence of massive rapidly spinning neu tron stars with very low magnetic moment mu < 10(25.8) G cm(3).