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

Gamma-Ray PulsarsGamma-Ray Pulsars

Their Their spectraspectra

(Thompson et al. 1999)

ModelsModels• Polar-cap• Outer-gap

(Harding 2000)

Power-law SpectraPower-law Spectra

(Nolan et al. 1996)

Photon IndicesPhoton Indices

• 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

MethodMethodradiation curvature synchrotron

energy loss rate

characteristic energy of the emission

cooling time scale

dynamical time scale

The distance of the inferred emission site from the stellar center

curvature radiation

synchrotron radiation

Requiring that at the emission site

Bending Energy (Eb)Bending Energy (Eb) of PSR B1509-58 of PSR B1509-58

(Matz et al. 1994)

~ 50 keV

Eb of VelaEb of Vela

(Strickman et al. 1996)

10~70 MeV

Eb of PSR B1706-44Eb of PSR B1706-44

(Ray, Harding & Strickman 1999)

10 keV ~ 30 MeV

Eb of PSR B1951+32Eb of PSR B1951+32

(Chang & Ho 1997; Chang & Guo 2000)

70 keV ~ 3 MeV

Eb of GemingaEb of Geminga

(Mayer-Hasselwander et al. 1994) (Jackson et al. 2002)

10~30 MeV

Eb of PSR B1055-52Eb of PSR B1055-52

(Thompson et al. 1999)

1 keV ~ 70 MeV

Determining the emission siteDetermining the emission site

(H-K Chang)

ResultResult

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

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

Thank you !Thank you !

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