  We introduce a new tool for 'unmasking' the composition of neutron star (NS)
interiors which is based on the fact that the state of matter at high densities
determines the statistics of both NS observables, the temperature-age (TA) data
as well as the mass distribution. We use modern cooling simulations to extract
distributions of NS masses required to reproduce those of the yet sparse data
in the TA plane. By comparing the results with a mass distribution for young,
nearby NSs from population synthesis we can sharpen two NS cooling problems.
The direct Urca (DU) problem consists in a narrowing of the NS population at
the mass value for which the DU process as the most effective cooling mechanism
in the hadronic layer of the star can occur. The Vela mass problem is a
broadening of the population beyond the range of the typical mass window of 1.1
- 1.5 M_sun. Applying this tool to modern EoS we discuss examples for pure
hadronic stars which are in conflict with these constraints while hybrid stars
with a color superconducting quark matter core can predict a satisfactory mass
distribution, provided the smallest diquark pairing gap has a properly defined
density dependence.
