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The Absorption Features in X-ray Emission from Isolated Neutron Stars

The Absorption Features in X-ray Emission from Isolated Neutron Stars. 2004 / 04 / 15. Outline. Assumptions & Global Model. Gravitation Effect (see Isothermal NS Case). Strong M field Effect. Anisotropy of the surface temperature Beaming. Lensing Red-shift.

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The Absorption Features in X-ray Emission from Isolated Neutron Stars

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  1. The Absorption Features in X-ray Emission from Isolated Neutron Stars 2004 / 04 / 15

  2. Outline Assumptions & Global Model Gravitation Effect (see Isothermal NS Case) Strong M field Effect • Anisotropy of the surface temperature • Beaming • Lensing • Red-shift Canonical Model & Line profile INS: 1E 1207.4-5209 Results & Discussions OH MY!! What’s going on??

  3. Assumption • Spherical symmetry typical neutron star. • Photons are emitted from the surface of an opaque sphere. • LTE: Iν= Bν.

  4. θ Z axis Global model Changing coordinate Rotation Axis Surface normal Magnetic Axis θp γ θb θ0 θm β Magnetic Axis

  5. Flux(t): (Lightcurve) ∫I(t) cosθ’dΩ’ Spec.: ∫Iν(t) cosθ’dΩ’ ∫Iν(t) cosθ ’dt dΩ’ Note: cosθ’ isqual to 1

  6. Gravitational Effects Self-Lensing Gravitational redshift

  7. Relative total flux v.s ωt R/M M/R 4 0.25 e30 0

  8. Relative specific flux v.s Freq. R/M M/R 4 0.25 e30 0 ν’ ν ν’ ν

  9. B atmosphere envelope core Strong Magnetic field effects • Anisotropy of the surface temperature • Beaming ( In magnetized electron-ion plasma, the scattering and free-free absorption opacities depend on the direction of propagationand the normal modes of EM waves) Dong Lai etc. MNRAS 327,1081 2001 νcyclotron =eB/2πme Ion cyclotron resonance occurs when The E field of the mode rotates in the same direction as the ion gyration

  10. Relative T v.s. θb Heyl etc. MNRA 324,292 2001 Best-fitting model for (a*cos 2θ +b*sin 2θ) for 1012G

  11. Iν (T1) Iν (T1) Iν (T1) θb Iν (T1) Iν (T1) T 1 = T eff Isotropic : Beaming due to B field : B field Iν (T5) Iν (T4) Iν (T4) Iν (T3) Iν (T3) Iν (T2) Iν (T2) Harding etc. ApJ 500:862 1998 Pavlov etc. A&A 297,441 1995 Iν (T1) Iν (T1)

  12. 3D Angles…..|=.=| “

  13. . . Magnetic Axis θp θb θm Surface normal Need to calculate Θm  θB_field  surface temperature Θphoton  Limb-darkening θphoton&B_field Magnetic beaming

  14. Canonical Model M=1.4M⊙ R=10km T =1 sec Rs=2GM/C2 ~ 0.267R θMAX~132∘

  15. 1E1207.4-5209 XMM PN observation Bignami et al. Nature 423:725 2003

  16. Simple Dipole Model Limb-darkening Model Magnetic Beaming Model Results

  17. Cyclotron Resonance Lines Ex. B=1011Gauss @ pole

  18. 50 bin 50 bin 0.5KeV 5KeV 1KeV 3x1017 Hz Line (line1+line2) Conti. (Log Scale) Binning • Given: • Observing time • Effective area • Distance to the source Photon number Line profile in units of σ

  19. Observation Numerical Results N~106 0.2~4KeV 208,000 photons Stellar absorption by NH~1021cm-2 N~103 & Lack of photon ~1KeV and higher energy Note that although we lack of photon at ~ 1KeV and higher energy (“lack” means in our calculus, the theoretical photon number is lower than “1” photon), we can still calculate the residual in units of σ

  20. 40:25 ~102 :1

  21. As a reasonable try , we multiply 103 in each bin to get a similar total photon number with observation. The ratio of the first line and the second line is even worse. (about 103:1)

  22. Discussion Our results show that a direct approach to reproduce the line features for 1E1207.4-5209 is not work well. • Photon number problem The photon number problem might be solved by higher temperature in polar cap or the larger neutron star radius in our model. • Ratio problem The ratio problem is essentially difficult to solved for our considerations.

  23. . The lack of photon numbers in our simulations may also remind us a individual neutron star may not performance like a “typical” neutron star. THE END The regularly spaced line features at 0.7, 1.4, and 2.1 keV in the 2002 August observation for INS 1E207.4-5209 is valuable for our understanding for the nature of neutron stars. A first approach for a typical neutron star with magnetic dipole field effects (such as temperature distribution and beaming effect) and limbdarkening can not produce similar cyclotron resonance lines for the unequal source 1E1207.4-5209. The most problem is the strength ratio of first cyclotron line and the second cyclotron line. The encounter suggests that the line strength ratio of the regularly spaced line features for 1E1207.4-5209 is noticeable. The lack of photon numbers in our simulations may also remind us a individual neutron star may not performance like a “typical” neutron star. The most problem is the strength ratio of first cyclotron line and the second cyclotron line. The encounter suggests that the line strength ratio of the regularly spaced line features for 1E1207.4-5209 is noticeable A first approach for a typical neutron star with magnetic dipole field effects (such as temperature distribution and beaming effect) and limb-darkening can not produce similar cyclotron resonance lines for the unequal source 1E1207.4-5209. The regularly spaced line features at 0.7, 1.4, and 2.1 keV in the 2002 August observation for INS 1E207.4-5209 is valuable for our understanding for the nature of neutron stars.

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