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The study of thermal emission from isolated, cooling neutron stars plays akey role in probing the physical conditions of both the star crust and thecore. The comparison of theoretical models for the star thermal evolution withthe surface temperature derived from X-ray observations of sources of differentage is one of the main tools to investigate the properties of the interior andconstrain the equation of state. Here we propose to use population synthesisstudies as an independent approach to test the physics governing the starcooling. Theoretical Log N - Log S distributions depend on the assumed neutronstar thermal evolution. We have computed distributions for several differentcooling scenarios and found that comparison with the observed Log N - Log S ofisolated neutron stars is effective in discriminating among cooling models.Among the eleven cooling models considered in this paper, all of which mayreproduce the observed temperature vs. age diagram, only at most three canexplain the Log N - Log S distribution of close-by cooling neutron stars. TheLog N - Log S test, being a ``global'' one and despite some limitations,appears capable of complementing the standard temperature vs. age test used upto now.Comment: 10 pages, 7 figures, table extended, references added, final version  to appear in Astron. & Astrophy

Population synthesis as a probe of neutron star thermal evolution