Context: Isolated cooling neutron stars with thermal X-ray emission remain rarely detected objects despite many searches investigating the ROSAT data. Aims: We simulate the population of close-by young cooling neutron stars to explain the current observational results. Given the inhomogeneity of the neutron star distribution on the sky it is particularly interesting to identify promising sky regions with respect to on-going and future searches. Methods: Applying a population synthesis model the inhomogeneity of the progenitor distribution and the inhomogeneity of the X-ray absorbing interstellar medium are considered for the first time. The total number of observable neutron stars is derived with respect to ROSAT count rates. In addition, we present sky maps of neutron star locations and discuss age and distance distributions of the simulated neutron stars. Implications for future searches are discussed. Results: With our advanced model we can successfully explain the observed logN - logS distribution of close-by neutron stars. Cooling neutron stars will be most abundant in the directions of rich OB associations. New candidates are expected to be identified behind the Gould Belt, in particular in the Cygnus-Cepheus region. They are expected to be on average younger and then hotter than the known population of isolated cooling neutron stars. In addition, we propose to use data on runaway stars to search for more radio-quiet cooling neutron stars.
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