The log N-log S distributions of accreting and cooling isolated neutron stars

We model populations of isolated neutron stars in the Galaxy following their orbital and magnetorotational evolution. It is shown that accretors become more abundant than coolers at fluxes below similar to 10(-13) ergs cm(-2) s(-1), and one can predict that about one accreting neutron star per square degree should be observed at the Chandra and Newton flux limits of similar to 10(-16) ergs cm(-2) s(-1). The soft ROSAT sources associated with isolated neutron stars can be relatively young cooling objects only if the neutron star birthrate in the solar vicinity during the last similar to 10(6) yr is higher than that inferred from radio pulsar observations.