The origin of the local population of young, cooling neutron stars is investigated with a population synthesis model taking into account the contribution of neutron stars born in the Gould Belt, in addition to those originating in the Galactic disk. We estimate their emission in the soft X-ray band as a function of distance and age and construct the Log N -- Log S distribution. It is shown that the inclusion of neutron stars from the Gould Belt provides a good fit to the observed Log N -- Log S distribution. As the Sun is situated inside the Gould Belt, one can naturally explain the comparative local overabundance of massive progenitors and can remove the difficulty of the deficit of relatively bright ($\ga 0.1$ ROSAT PSPC cts s$^{-1}$) cooling neutron stars previously reported from models where only neutron stars from the Galactic disk were accounted for.

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