Abstract
We have seen in Sect. 2 that measuring mass and radius of a compact star is not sufficient to deduce the matter composition inside the star; it is neither conclusive for a distinction between nuclear matter and quark matter nor between unpaired quark matter and color-superconducting quark matter. We now turn to an observable which is more sensitive to the microscopic properties of dense matter, namely the temperature of the star. More precisely, its cooling curve, i.e., the temperature as a function of the age of the star. Approximately one minute after the star is born, the temperature has cooled below 1 MeV and the star becomes transparent for neutrinos. Consequently, neutrinos (and antineutrinos) which are produced in the star can leave the system and carry away energy. Neutrino emission is thus the dominant cooling mechanism of a compact star in about the first million years of its life. After that, photon emission takes over. We shall not be concerned with this late regime here.
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