The internal properties of the neutron star crust can be probed by observing the epoch of thermal relaxation .
After the supernova explosion , powerful neutrino emission quickly cools the stellar core , while the crust stays hot .
The cooling wave then propagates through the crust , due to its finite thermal conductivity .
When the cooling wave reaches the surface ( age 10 - 100 yr ) , the effective temperature drops sharply from 250 eV to 30 or 100 eV , depending on the cooling model .
The crust relaxation time is sensitive to the ( poorly known ) microscopic properties of matter of subnuclear density , such as the heat capacity , thermal conductivity , and superfluidity of free neutrons .
We calculate the cooling models with the new values of the electron thermal conductivity in the inner crust , based on a realistic treatment of the shapes of atomic nuclei .
Superfluid effects may shorten the relaxation time by a factor of 4 .
The comparison of theoretical cooling curves with observations provides a potentially powerful method of studying the properties of the neutron superfluid and highly unusual atomic nuclei in the inner crust .