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The Braking Indices of Radio Pulsars

The Braking Indices of Radio Pulsars. Wu Fei Dep. Astronomy, Peking University 2003.10.21. Introduction. For rotation-powered pulsars, energy loss rate where  is the angular velocity of rotation. can be obtained observationally.

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The Braking Indices of Radio Pulsars

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  1. The Braking Indices of Radio Pulsars Wu Fei Dep. Astronomy, Peking University 2003.10.21

  2. Introduction • For rotation-powered pulsars, energy loss rate where  is the angular velocity of rotation. can be obtained observationally. • ( ) parameter describing pulsars’ spin-down, employed to test pulsar emission models as well. • The observed braking indices • Dipole radiation

  3. Some efforts • Force-free precession of a distorted neutron star (Macy 1974) • Existence of a companion star (Deminanski 1979) • Neutrino and photon radiation from superfluid neutron vortexes (Peng & Huang 1982) • Multipole field or field evolution (Blandford & Romani 1988) • Non-standard vacuum dipole model (Melatos 1997) • Accretion torque (Menou 2001) • Propeller torque applied by the debris disk (Alpar 2002)

  4. Assumption • Consider the pulsar braking torques due to magnetodipole radiation and unipolar generator. • Energy loss rate of aligned rotators: where • Assumption: where • model-dependent parameters: • Energy conservation:

  5. Application • Xu & Qiao (2001) ApJ: 561,L85 • ICS-induced SCLF model does not work solely on Vela (PSR B0833-45) and PSR B0540-69. • For Vela pulsar, obtained   90o calls for improved pulsar emission models.

  6. Pulsar’s emission models

  7. Inducement • Imperfect points of RS75 model: • The binding energy problem of ions on the neutron star surface • Only half of the neutron stars are applicable • Two scenarios: • Bare strange stars (Xu et al. 1999) • Neutron stars with multipolar surface magnetic fields (Gil & Mitra 2001)

  8. NTVG model • Stronger field Larger ion cohesive energy • Near Threshold Vacuum Gap model (Gil & Mitra, 2001) • Neutron stars with multipolar surface magnetic fields: field curvature radius  neutron star radius: • Different estimates of cohesive energy of surface iron ions • Abrahams & Shapiro 1991 (AS91) • Jones 1986 (J86)

  9. n(P): CR-NTVG model

  10. n(P): ICS-NTVG model

  11. Comparison

  12. Possible picture: VG+OG • It is quite possible that both inner and outer gaps coexist in a magnetosphere (Usov 2000; Xu & Qiao 2001) in order to close the global electric current. • But the interaction between two gaps and the pair plasma properties are very uncertain. • Employ typical parameters: (except B12=10 in NTVG models) • Neglect the possible interaction between gaps.

  13. n(P): CR-VG+OG model

  14. n(P): ICS-VG+OG model • ICS-VG + OG model prefer to work in the pulsar magnetosphere, since other models provides very small n, while observed braking indices range from 1.4 to 2.9

  15. n(P): CR-NTVG+OG model

  16. n(P): ICS-NTVG+OG model

  17. n(P): CR-SCLF+OG model

  18. n(P): ICS-SCLF+OG model

  19. Conclusion & discussion

  20. Thanks!!!

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