  Old neutron stars (ONSs) which have radiated away their internal and
rotational energy may still shine if 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 ONSs observability, accounting for the spin and magnetic field
evolution over the neutron star lifetime. In the framework of a spin-induced
field decay model, we show that the total number of ONSs which are, at present,
in the accretion stage is reduced by a factor ~5 over previous figures if the
characteristic timescale for crustal current dissipation is ~ 10^8 - 10^9 yr.
This brings theoretical predictions much closer to observational limits. Most
ONSs should be at present in the propeller phase and, if subject to episodic
flaring, they could be observable.
