Constraining twin stars with cold neutron star cooling data

We investigate the influence of a phase transition from hadronic matter to a deconfined quark phase inside a neutron star on its cooling behaviour including the appearance of twin star solutions in the mass-radius diagram. We find that while the inferred neutrino luminosity of cold transiently-accreting star in MXB $1659\text{-}29$ is reproduced in all of the constructed twin star models, the luminosity of a colder source, the neutron star in SAX J$1808.4\text{-}3658$, cannot be described by equations of state with quark-hadron transition densities below $1.7$ saturation density, suggesting that twin stars with such low density transitions to the quark phase are not realized in nature. We also discuss how constraints to the quark-hadron phase transition density are strongly dependent on the cooling effectiveness of neutrino reactions in the quark phase.