Using the observation of four transiently-accreting neutron stars, the authors provide (under simple assumptions) a lower limit for the star core heat capacity. The limit rules out a large fraction of the core being made up of a quark color-flavor-locked phase. Future observations during cooling periods between accretion outbursts will further constrain the heat capacity and neutrino cooling luminosity of the core.
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Cumming et al. (2017) studied this question.
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