Dim ROSAT isolated neutron star candidates

We model populations of isolated neutron stars in order to investigate them as progenitors of dim soft X-ray sources. We discuss both: old accreting and young cooling neutron stars. For accretors realistic magneto-rotational evolution and evolution in the Galactic potential are taken into account together with a realistic large scale distribution of the interstellar medium. Cooling neutron stars are explored with a simpler model of local sources, but interstellar absorption is additionly taken into account. In the standard assumptions (maxwellian initial velocity distribution with the mean value about 200-300 km s-1, initial magnetic field distribution similar to radiopulsar, no field decay, small initial spin periods) we obtain accretors only if their magnetic field is > 1011-1012 G. So, for polar cap accretion X-ray sources are relatively hard with typical temperature about 300-400 eV. For them interstellar absorption is not very significant, and we predict about 1 source per square degree for fluxes about 10-15-10-16 erg cm-2s-1 for energy range 0.5-2 keV. For young cooling neutron stars, which are soft sources (T 50 eV), absorption is very important, and they are significantly less abundant at low fluxes. For them we predict < 0.1 sources per square degree. With these standard assumptions we cannot explain observed properties of the ROSAT candidates (relatively large number of close bright sources; low temperatures; periods about 10-20 s, which are observed for two candidates: RX J0420.0-5022 and RX J0720-3125). We argue, that most part of these sources can be young cooling neutron stars with typical age about 106 yrs or less, if the total number of neutron stars in the Galaxy is significantly higher, than it comes from radiopulsars statistics. The source RX J0420.0-5022 with the spin period 22.7 s can't be explained as a 'standard' accretor or a 'standard' cooling neutron star. In this case most probably magnetic field decay is operating.