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Abstract: In previous papers, we have shown that, as the rotation of a neutron starslows down, it will be internally heated as a consequence of the progressivelychanging mix of particles rotochemical heating. In previously studied casesnon-superfluid neutron stars or superfluid stars with only modified Urcareactions, this leads to a quasi-steady state in which the star radiatesthermal photons for a long time, possibly accounting for the ultravioletradiation observed from the millisecond pulsar J0437-4715. For the first time,we explore the phenomenology of rotochemical heating with direct Urca reactionsand uniform and isotropic superfluid energy gaps of different sizes. We firstdo exploratory work by integrating the thermal and chemical evolution equationsnumerically for different energy gaps, which uncovers a rich phenomenology ofstable and unstable solutions. To understand these, we perform a stabilityanalysis around the quasi-steady state, identifying the characteristic times ofgrowing, decaying, and oscillating solutions. For small gaps, the phenomenologyis similar to the previously studied cases, in the sense that the solutionsquickly converge to a quasi-steady state. For large gaps $\gtrsim 0.05$ MeV,these solutions become unstable, leading to a limit-cycle behavior ofperiodicity $\sim 10^{6-7} yr, in which the star is hot $T s\gtrsim 10^5$ Kfor a small fraction of the cycle $\sim 5- 20 %$, and cold for a longer time.



Author: Cristobal Petrovich, Andreas Reisenegger

Source: https://arxiv.org/



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