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On the Emission Site of Gamma On the Emission Site of Gamma Rays from PulsarsRays from Pulsars
Hsiang-Kuang Chang and Cheng HoHsiang-Kuang Chang and Cheng Ho
徐佩君徐佩君清華大學天文研究所清華大學天文研究所
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Gamma-Ray PulsarsGamma-Ray Pulsars
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Their Their spectraspectra
(Thompson et al. 1999)
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ModelsModels• Polar-cap• Outer-gap
(Harding 2000)
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Power-law SpectraPower-law Spectra
(Nolan et al. 1996)
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Photon IndicesPhoton Indices
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• a steady cooling population of charged particles
Synchrotron radiation P=2 → Γ= 3/2
Curvature radiation P=4 → Γ= 5/3
Assumption Assumption
p
p
electronN
2
1
)(
p
photon EEN
3
1
)(
p
photon EEN
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MethodMethodradiation curvature synchrotron
energy loss rate
characteristic energy of the emission
cooling time scale
dynamical time scale
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The distance of the inferred emission site from the stellar center
curvature radiation
synchrotron radiation
Requiring that at the emission site
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Bending Energy (Eb)Bending Energy (Eb) of PSR B1509-58 of PSR B1509-58
(Matz et al. 1994)
~ 50 keV
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Eb of VelaEb of Vela
(Strickman et al. 1996)
10~70 MeV
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Eb of PSR B1706-44Eb of PSR B1706-44
(Ray, Harding & Strickman 1999)
10 keV ~ 30 MeV
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Eb of PSR B1951+32Eb of PSR B1951+32
(Chang & Ho 1997; Chang & Guo 2000)
70 keV ~ 3 MeV
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Eb of GemingaEb of Geminga
(Mayer-Hasselwander et al. 1994) (Jackson et al. 2002)
10~30 MeV
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Eb of PSR B1055-52Eb of PSR B1055-52
(Thompson et al. 1999)
1 keV ~ 70 MeV
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Determining the emission siteDetermining the emission site
(H-K Chang)
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ResultResult
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DiscussionDiscussion• Under the assumption that the gamma-ray
emission comes from a steady cooling population of charged particles, the synchrotron radiation in outer magnetospheres as the emission mechanism is consistent with the spectral behavior of most gamma-ray pulsars.
• Exception: Crab pulsar, PSR B1509-58
• The inverse Compton scattering is not considered in this method
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ReferenceReferencePeter Meszaros, 1992, The University of Chicago Press, “High-Energy Radiation from Magnetized Neutron Stars” Harding A. K., 2000, arXiv:astro-ph/0012268 George B. Rybicki, Alan P. Lightman, New York :Wiley,c1979. “Radiative processes in astrophysics”
Chang H.-K., Guo T.-F., 2000, Chinese Journal of Physics, 38, 429Chang H.-K., Ho C., 1997, ApJ, 479, L125 Jackson M. S. et al., 2002, ApJ, 578,935Matz S. M. et al., 1994, ApJ, 434, 288Mayer-Hasselwander H. A. et al., 1994, ApJ, 421, 276Nolan P. L. et al., 1996, A&AS, 120, C61Ray A., Harding A. K., Strickman M., 1999, ApJ, 513, 919Strickman M. S. et al., 1996, ApJ, 460, 735Thompson D. J. et al., 1999, ApJ, 516, 297
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Thank you !Thank you !
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),()( tSNNt