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

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

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

4. Global model Changing coordinate Z axis θ θm Magnetic Axis θb θp Surface normal Magnetic Axis Rotation Axis θ0θ0θ0θ0 β γ

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

7. Gravitational Effects Self-Lensing Gravitational redshift

8. R/M M/R 40.25 e300 Relative total flux v.s ωt

9. R/M M/R 40.25 e300 ν’ ν’ ν ν ’  ν Relative specific flux v.s Freq.

10. 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 propagation and the normal modes of EM waves) Dong Lai etc. MNRAS 327,1081 2001 core envelope atmosphere B ν cyclotron =eB/2πm e Ion cyclotron resonance occurs when The E field of the mode rotates in the same direction as the ion gyration

11. Heyl etc. MNRA 324,292 2001 Best-fitting model for (a*cos 2 θ +b*sin 2 θ) for 10 12 G Relative T v.s. θ b

12. Isotropic : I ν ( T 1 ) I ν ( T 2 ) I ν ( T 3 ) I ν ( T 4 ) I ν ( T 5 ) I ν ( T 4 ) I ν ( T 3 ) I ν ( T 2 ) I ν ( T 1 ) T 1 = T eff I ν ( T 1 ) θb Harding etc. ApJ 500:862 1998 Pavlov etc. A&A 297,441 1995 Beaming due to B field : B field

13. 3D Angles….. |=.=| “

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

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

16. 1E1207.4-5209 XMM PN observation Bignami et al. Nature 423:725 2003

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

18. Cyclotron Resonance Lines Ex. B=10 11 Gauss @ pole

20. Binning Photon number Line profile in units of σ Line (line1+line2) Conti. 0.5KeV 1KeV 3x10 17 Hz 5KeV 50 bin (Log Scale) Given: 1. Observing time 2. Effective area 3. Distance to the source

21. N~10 6 Stellar absorption by N H ~10 21 cm -2 N~10 3 Numerical Results Observation 0.2~4KeV 208,000 photons & 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

22. 40:25 ~10 2 :1

23. As a reasonable try, we multiply 10 3 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 10 3 :1)

24. 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.

25. . The lack of photon numbers in our simulations may also remind us a individual neutron star may not performance like a “typical” neutron star. 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. 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 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  E 