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A critical relation in the study of neutron star cooling is the one betweensurface temperature and interior temperature. This relation is determined bythe composition of the neutron star envelope and can be affected by the processof diffusive nuclear burning (DNB), which occurs when elements diffuse todepths where the density and temperature are sufficiently high to ignitenuclear burning. We calculate models of H-He and He-C envelopes that includeDNB and obtain analytic temperature relations that can be used in neutron starcooling simulations. We find that DNB can lead to a rapidly changing envelopecomposition and prevents the build-up of thermally stable hydrogen columnsy$_H$ > 10$^{7}$ g cm$^{-2}$, while DNB can make helium envelopes moretransparent to heat flux for surface temperatures $T_s$ > 2 $\times 10^6$ K. Weperform neutron star cooling simulations in which we evolve temperature andenvelope composition, with the latter due to DNB and accretion from theinterstellar medium. We find that a time-dependent envelope composition can berelevant for understanding the long-term cooling behaviour of isolated neutronstars. We also report on the latest Chandra observations of the young neutronstar in the Cassiopeia A supernova remnant; the resulting 13 temperaturemeasurements over more than 18 years yield a ten-year cooling rate of $\approx$2%. Finally, we fit the observed cooling trend of the Cassiopeia A neutron starwith a model that includes DNB in the envelope.

Diffusive nuclear burning in cooling simulations and application to new temperature data of the Cassiopeia A neutron star