Context. In previous papers, we have shown that, as the rotation of a neutron star slows down, it will be internally heated as a consequence of the progressively changing mix of particles (rotochemical heating). In previously studied cases (non-superfluid neutron stars or superfluid stars with only modified Urca reactions), this leads to a quasi-steady state in which the star radiates thermal photons for a long time, possibly accounting for the ultraviolet radiation observed from the millisecond pulsar J0437-4715.
Aims: For the first time, we explore the phenomenology of rotochemical heating with direct Urca reactions and uniform and isotropic superfluid energy gaps of different sizes.
Methods: We first do exploratory work by integrating the thermal and chemical evolution equations numerically for different energy gaps, which uncovers a rich phenomenology of stable and unstable solutions. To understand these, we perform a stability analysis around the quasi-steady state, identifying the characteristic times of growing, decaying, and oscillating solutions.
Results: For small gaps, the phenomenology is similar to the previously studied cases, in the sense that the solutions quickly converge to a quasi-steady state. For large gaps ( ≳ 0.05 MeV), these solutions become unstable, leading to a limit-cycle behavior of periodicity ~106-7 yr, in which the star is hot (Ts ≳ 105 K) for a small fraction of the cycle (~5-20%), and cold for a longer time.
Astronomy and Astrophysics
- Pub Date:
- April 2011
- stars: neutron;
- dense matter;
- stars: rotation;
- pulsars: general;
- pulsars: individual: PSR J0437-4715;
- Astrophysics - High Energy Astrophysical Phenomena;
- Astrophysics - Solar and Stellar Astrophysics;
- Condensed Matter - Superconductivity
- (8 pages, 11 figures, accepted version to be published in A&