1 shu-hua yang ( 杨书华 ) hua zhong normal university the role of r-mode damping in the thermal...

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

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

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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

Page 2: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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Outline

Introduction

R-mode heating of neutron stars

Our results

Page 3: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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1 、 Introduction

Yakovlev et al. (2008) , AIPC,983,379

Page 4: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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The thermal evolution equation with the approximation of isothermal interior

Page 5: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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Slow and fast neutrino emission processes

Page 6: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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focus on the r-mode instability heating

Page 7: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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2 、 R-mode heating of neutron stars

In contrast, the growth of the modes can be suppressed by the viscosity of the stellar matter.

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.

Page 8: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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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

Page 9: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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(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:

Page 10: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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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.

Page 11: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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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,

Page 12: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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R-mode evolution

Spin evolution of NSs

Thermal evolution of NSs

Page 13: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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Long-term evolution of isolated NSs

prolongs duration

enhances the heating effect

Page 14: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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Page 15: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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No superfluidityProton superfluidity

(model 1p )

Yakovlev et al. (2008) , AIPC,983,379

Page 16: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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K9maxcp 108.6T

Page 17: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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Problem :

Tsuruta et al. (2002) ApJL

Page 18: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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Page 19: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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3 、 Our results:

Page 20: 1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars

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Thank you!