Recycling Neutron Stars to Ultrashort Periods: A Statistical Analysis of Their Evolution in the μ‐ P Plane

Abstract

In this paper we investigate the statistical evolution of magnetic neutron stars, recycled in binary systems, simulating synthetic populations. To bracket uncertainties, we consider a soft (FP) and a stiU (PS) equation of state (EoS) for nuclear matter and explore the hypothesis that the magnetic —eld is con—ned in the stellar crust. We follow the magnetorotational evolution within a simple recycling sce- nario. The decay of the magnetic —eld is modeled imposing at the crust-core boundary either complete —eld expulsion by the superconducting core or advection and freezing in a very highly conducting tran- sition shell. Irrespective of the details of the physical models, we —nd the presence of a tail in the period distribution of the synthetic populations at periods shorter than 1.558 ms, the minimum detected so far. For the soft EoS, and independent of the details of the magnetic —eld evolution, the recycling gives rise to a spin distribution that is increasing monotonically toward short periods, and a clear ii barrier ˇˇ forms at the minimum period for the onset of mass shedding (^0.7 ms). For the stiU EoS, the distribution is —atter, displaying a broad maximum about 2¨4 ms. On the other hand, if in low-mass binaries the neutron stars experience a progressive decrease of the mass accretion rate (due to transient behavior and/or the quenching of accretion), the magnetospheric propeller produces (together with the magnetic dipole losses) an overall depletion of neutron stars in the millisecond region of the k-P plane. The esti- mated fraction of neutron stars spinning close to their shedding limit over the millisecond pulsar popu- lation is found to be signi—cant. Crustal magnetic —eld decay models also predict the existence of massive rapidly spinning neutron stars with very low magnetic moment k 1025.8 Gc m3. Subject headings: equation of statestars: magnetic —eldsstars: neutron