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

## TL;DR

This paper models diffusive nuclear burning in neutron star envelopes, deriving temperature relations, and applies these models to interpret long-term cooling data of the Cassiopeia A neutron star, highlighting the importance of envelope composition evolution.

## Contribution

It introduces analytic temperature relations incorporating DNB effects into neutron star cooling models and applies them to observational data of Cassiopeia A.

## Key findings

- DNB prevents stable hydrogen buildup in envelopes.
- DNB makes helium envelopes more heat-transparent at high temperatures.
- Envelope composition evolution affects long-term neutron star cooling.

## Abstract

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$_H$ > 10$^{7}$ g cm$^{-2}$, while DNB can make helium envelopes more transparent to heat flux for surface temperatures $T_s$ > 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.