奇异星的体粘滞与极限旋转周期-HKUPhysics.pptVIP

Outline The thermal evolution equation with the approximation of isothermal interior In contrast, the growth of the modes can be suppressed by the viscosity of the stellar matter. 3、Our results: * * Shu-Hua Yang (杨书华) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars Introduction R-mode heating of neutron stars Our results 1、Introduction Yakovlev et al. (2008) , AIPC,983,379 Slow and fast neutrino emission processes focus on the r-mode instability heating 2、R-mode heating of neutron stars Andersson et al (2001) 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. 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: R-mode evolution in neutron stars (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: 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. ● Sa Tome (2005) suggested N = 2l -1 and redefined A by introducing a new free parameter K as ● This second-order solution gives a differential rotation, producing large scale drifts of fluid elements along stellar latitudes. 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， Jr return to the first order case. is the magnetic braking timescale. is the total angular momentum of the star, R-mode evolution Spin evolution of NSs Thermal evolution of NSs Long-term evolution of isolated NSs prolongs durati