The elusiveness of old neutron stars

Old neutron stars (ONSs) that have radiated away their internal and rotational energy may still shine if they are accreting the interstellar medium. Despite their large number, only two promising candidates have been detected so far, and rather stringent limits on their observability follow from the analysis of ROSAT surveys. This contrasts with optimistic theoretical estimates that predicted a large number of sources in ROSAT fields. We have reconsidered the issue of the observability of ONSs, accounting for the spin and magnetic field evolution over the neutron star lifetime. In the framework of a spin-induced held decay model, we show that the total number of ONSs that are at present in the accretion stage is reduced by a factor of similar to 5 over previous figures if the characteristic timescale for crustal current dissipation is similar to 10(8)-10(9) yr. This brings theoretical predictions much closer to observational limits. Most ONSs should be, at present, in the propeller phase; if subject to episodic flaring, they could be observable.