We model Galactic populations of accreting and cooling isolated neutron stars in the attempt to explore their link with a new class of dim soft X-ray sources revealed by ROSAT .
For accretors we follow the magneto-rotational and dynamical evolution in the Galactic potential and a realistic large scale distribution of the interstellar medium is used .
Under standard assumptions old neutron stars enter the accretor stage only if their magnetic field exceeds \approx 10 ^ { 11 } – 10 ^ { 12 } G. We predict about 1 source per square degree for fluxes \approx 10 ^ { -15 } – 10 ^ { -16 } erg cm ^ { -2 } s ^ { -1 } in the energy range 0.5-2 keV .

Cooling neutron stars are explored within a simpler model of local sources , including however interstellar absorption .
They are found to be significantly less abundant at low fluxes , < 0.1 sources per square degree , but dominate over accretors at higher flux levels ( \approx 10 ^ { -12 } – 10 ^ { -11 } erg cm ^ { -2 } s ^ { -1 } ) .
We suggest that the faint sources observed by ROSAT may be young cooling neutron stars with typical age \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 10 ^ % { 6 } yrs , if the total number of young neutron stars in the Solar proximity is \sim 10 times higher than inferred from radiopulsars statistics .