Recently proposed neutrino emission processes in high-density matter result in the relatively rapid cooling of a neutron star's interior followed by a precipitous drop in the surface temperature. We show that the time interval between the formation of the neutron star and the drop in the surface temperature is primarily determined by the structure of the neutron star and is relatively insensitive to the rapid cooling mechanism itself. Thus, observations of thermal emissions from neutron stars have the potential for constraining the neutron star's structure and the underlying equation of state of dense matter.
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A 1994 study studied this question.