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Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University

The role of r-mode damping in the thermal evoltion of neutron stars. Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University. Outline. Introduction R-mode heating of neutron stars Our results. 1 、 Introduction. Yakovlev et al. (2008) , AIPC,983,379.

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Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University

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  1. The role of r-mode damping in the thermal evoltion of neutron stars Shu-Hua Yang (杨书华) Hua Zhong Normal University

  2. Outline • Introduction • R-mode heating of neutron stars • Our results

  3. 1、Introduction Yakovlev et al. (2008) , AIPC,983,379

  4. The thermal evolution equation with the approximation of isothermal interior

  5. Slow and fast neutrino emission processes

  6. focus on the r-mode instability heating

  7. 2、R-mode heating of neutron stars • R-mode in a perfect fluid star with arbitrary rotation due to the action of the Coriolis force with positive feed back, succumbing to CFS instability. • In contrast, the growth of the modes can be suppressed by the viscosity of the stellar matter. Andersson et al (2001)

  8. R-mode evolution in neutron stars The r-modes of rotating barotropic Newtonian stars are solutions of the perturbed fluid equations having velocity perturbations where is angular velocity of the unperturbed the star, is the dimensionless amplitude of the perturbation, is the magnetic-type vector spherical harmonic:

  9. (Owen et al. 1998) • First-order r-modes In spherical coordinates, solving the linear fluid equations at the first order of the r-mode amplitude( ), we can get the r-mode solutions:

  10. Second-order r-modes At the second order of the r-mode amplitude (Sa 2004) A and N are two constants determined by the initial condition. ● This second-order solution gives a differential rotation, producing large scale drifts of fluid elements along stellar latitudes. ●Sa & Tome (2005) suggested N = 2l -1 and redefined A by introducing a new free parameter K as

  11. The physical angular momentum of the l=2 r-mode calculated up to the second order is(Sa & Tome 2005) For K = -2，J(2) =0， Jrreturn to the first order case. is the total angular momentum of the star, is the magnetic braking timescale.

  12. Thermal evolution of NSs R-mode evolution Spin evolution of NSs

  13. prolongs duration Long-term evolution of isolated NSs enhances the heating effect

  14. Proton superfluidity (model 1p ) No superfluidity Yakovlev et al. (2008) , AIPC,983,379

  15. Problem： Tsuruta et al. (2002) ApJL

  16. 3、Our results:

  17. Thank you!

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