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Pu, Hung-Yi Institute of Astronomy, National Tsing-Hua University

The Effects of Photon Path Bending on the Observed Pulse Profile and Spectra of Surface Thermal Emission from Neutron Stars. Pu, Hung-Yi Institute of Astronomy, National Tsing-Hua University. Spectra calculation:. ∫I’ ν (t) cos θ ’ dΩ’. ( Include photon path bending ). Motivation:.

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Pu, Hung-Yi Institute of Astronomy, National Tsing-Hua University

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  1. The Effects of Photon Path Bending on the Observed Pulse Profile and Spectraof Surface Thermal Emission from Neutron Stars Pu, Hung-Yi Institute of Astronomy, National Tsing-Hua University

  2. Spectra calculation: ∫I’ν(t) cosθ’dΩ’ ( Include photon path bending ) Motivation: Neutron stars with X-ray thermal emission  Iν= Planck function Consider Limb-darkening  Iν= (require ) Application: Determining the inclination and viewing angles for Radio-quiet neutron stars from their X-ray thermal emission

  3. The dependence of model spectra and pulse profiles on the input parameters

  4. Light curveswith different temperature distribution (I) ζ: the viewing angle α: the inclination angle

  5. Light curveswith different temperature distribution (II)

  6. Light curveswith different temperature distribution (III)

  7. Light curveswith and without limb-darkening Dash: without limb-darkening Dot: with limb-darkening

  8. Spectrawith different magnetic field from , Tp=2 x106K Solid curve: Planck function (with suitable normalization) of temperature 2 x106 K

  9. Determining the inclination angleandviewing angleof neutron stars from theirX-ray thermal emissions

  10. Observation: Blackbody Best Fit Temperature (AσT4=4πd2F) 1)Observed Flux 2)Pulse Fraction Model flux Model Pulsed fraction Input parameters: 1) Hot Spot Size 2) M / R 3) αand ζ No Consistent? Yeah Inferred possible range of α and ζ

  11. Observational properties of RX J0806.4-4123

  12. Apply T hot spot = 95.6 eV M/R=0.2 Different hot spot size: 12,13,15,16 from top to down (in unit of canonical polar cap size, ~0.25 degree) Left: computed flux {Flux/28.8x10-13}={0.9,1.0,1.1,1.2} Right: computed pulsed fraction {0.05,0.06,0.07,0.1,0.2,0.3,0.4,0.5}

  13. Computed pulsed fraction contoursfor different mass-to-radius ratio M / R=0.2 M / R=0.01 M / R=0.3 M / R=0.1 The shapes of computed pulsed fraction contours are not change too much for fixed mass-to-radius ratio

  14. Sum of computed RX J0806.4-4123 pulsed fraction contours with values of 6% M / R=0.3 M / R=0.2 M / R=0.1 M / R=0.01

  15. Pulse profilese.x. M/R= 0.1, hot spot size equal to 22 times of the canonical polar cap sizes

  16. Distribution of Radio pulsars in α-ζ plane 117 Radio pulsar geometries reported by Rankin ( 1993 )

  17. M / R=0.3 M / R=0.2 M / R=0.1 M / R=0.01

  18. M/R=0.01 0.1 0.2 0.3 {0.10, 0.12, 0.15, 0.2, 0.3} RX J0420.0-5022

  19. M/R=0.01 0.1 0.2 0.3 {0.06, 0.11, 0.15, 0.2, 0.3} RX J0720.4-3125

  20. Summary • Pulse fraction in general decreases as the gravity increases; Beaming effect in general increases the pulse fraction. • The inferred possible geometry range is broad in the α-ζ plane and we cannot tell if the distribution for radio-quiet neutron stars and radio pulsars are different. • Our computed result depends on the beaming pattern we use.

  21. Thank you!

  22. Lyne 1998 Rotation Axis Hot Spot Magnetic Axis ζ: the viewing angle α: the inclination angle

  23. Calculate (specific) Observed Flux: ∫I’ν(t) cosθ’dΩ’ dΩ’ Distant Observer

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