A critical relation in the study of neutron star cooling is the one between surface temperature and interior temperature .
This relation is determined by the composition of the neutron star envelope and can be affected by the process of diffusive nuclear burning ( DNB ) , which occurs when elements diffuse to depths where the density and temperature are sufficiently high to ignite nuclear burning .
We calculate models of H-He and He-C envelopes that include DNB and obtain analytic temperature relations that can be used in neutron star cooling simulations .
We find that DNB can lead to a rapidly changing envelope composition and prevents the build-up of thermally stable hydrogen columns y _ { H } \gtrsim 10 ^ { 7 } g cm ^ { -2 } , while DNB can make helium envelopes more transparent to heat flux for surface temperatures T _ { s } \gtrsim 2 \times 10 ^ { 6 } K. We perform neutron star cooling simulations in which we evolve temperature and envelope composition , with the latter due to DNB and accretion from the interstellar medium .
We find that a time-dependent envelope composition can be relevant for understanding the long-term cooling behaviour of isolated neutron stars .
We also report on the latest Chandra observations of the young neutron star in the Cassiopeia A supernova remnant ; the resulting 13 temperature measurements 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 star with a model that includes DNB in the envelope .