2000PASP..112..297T

As many as 10⁹ neutron stars populate the Galaxy, but only ~10³ are directly observed as pulsars or as accreting sources in X-ray binaries. In principle, also the accretion of the interstellar medium may make isolated neutron stars shine, and their weak luminosity could be detected in soft X-rays. Recent ROSAT observations have convincingly shown that neutron stars accreting from the interstellar medium are extremely rare, if observed at all, in contrast with earlier theoretical predictions. Until now two possible explanations for their elusiveness have been proposed: their velocity distribution may peak at ∼200-400 km.s^–1, as inferred from pulsar statistics, and this would severely choke accretion; the magnetic field may decay on timescales ∼10⁸-10⁹ yr, preventing a large fraction of neutron stars from entering the accretor stage. The search for accreting neutron stars has produced up to now a handful of promising candidates. While little doubt is left that these objects are indeed isolated neutron stars, the nature of their emission is still controversial. In particular, accreting objects can be confused with much younger, cooling neutron stars. However, a combination of observations and theoretical modeling may help in discriminating between the two classes.