A THREE-DIMENSIONAL OUTER MAGETOSPHERIC MODEL FOR GAMMA-RAY PULSARS : GEOMETRY, PAIR PRODUCTION, EMISSION MORPHOLOGIES, AND PHASE- RESOLVED SPECTRA K.S.CHENG, M.RUDERMAN & L.ZHANG M.N.R.A.S 2000, 537,964

Abstract This paper studies three-dimensional geometry of the particle accelerator of the pulsar, with using the outer-gap model. Pair-creation region inside of the gap is discussed. They calculate the expected light-curves following Romani & Yadigaroglu (1995). The synchrotron- self Inverse Compton process is calculated to compare with observed Crab spectrum.

Introduction Particle are accelerated by the electric field parallel to the magnetic field line inside of the light cylinder. Polar Cap model v.s. Outer gap model Outer gap three dimensional geometry easily produces observed light curve features such as two-peaks in a period and phase separation between two peaks (Romani & Yadigaroglu 1995, RY). -Polar cap model has not predicted except for nearly aligned rotator. I J Vela One period γ-ray light curve

Motivation RY did not consider the inwardly γ-rays to avoid appearance of multiple peaks This paper consider 1,where the most pairs are created, 2,whether the inwardly emitted gamma-rays can be ignore or not. ? Where is the pair creation region?

Model Rotating magnetic field Shape of the Polar cap

Model (cont ’ d) Basic idea of pair-creation cascade in the outer gap Acceleration of particles (primary) in the gap γ-ray radiation of primary particles (Γ ～ 10 7 ) (curvature radiation) Pair-creation process between γ-ray and X-ray Pairs produced inside of the gap Pairs (Γ ～ 10 3 ) produced outside of the gap (Secondary) Synchrotron – Inverse Compton process γ-ray X-ray

Model (cont ’ d) Accelerating electric field:thin vacuum outer- gap model (Cheng, Ho & Ruderman 1986) Gap expands until the pairs are created inside of the gap X-ray field (Zhang & Cheng 1997); heated polar cap model of the primary particles

Results; Pair-creation region The total number of pairs produces at distance r per electron and positron; They estimated the distance, in which the most pairs are produced, from the condition;

Photon emission morphology -the direction emissions are expressed by Polar angle from the rotation axis Phase of rotation of the star The phase, in which many photons are piled up, is observed as a pulse phase.

Relativistic effects 1,Aberration -The photons are emitted in the direction of the particle motion 2,Flight time effect Caustic !! :emission direction of the static observer :emission direction of the corotating observer d: distance to the pulsar from the Earth

Polar angle of detection Phase of detection Absolute azimuth of the emission point Azimuth of the emission direction Relativistic effects

Result Emission between null charge surface and the light cylinder Emissivity is constant Outwardly emission Inwardly emission

Acceleration of particles (primary) γ-ray radiation of primary particles (curvature radiation) Pair-creation process between γ-ray and X-ray Pairs produced inside of the gap Pairs produced outside of the gap (Secondary) Synchrotron – Inverse Compton process Crab like Vela like 1GeV1keV Crab Vela

Spectrum

Conclusion The inwardly emissions is fainter than the outwardly emissions, because the pair- creation region is restricted near the inner boundary. The expected light curves including the relativistic effects is good agreement with observations. The synchrotron-Inverse Compton spectra is consistent with the Crab observation.

Their strength of the accelerating electric field must be overestimated. We should take into account the pair-creation process with the X-ray emitted by secondary pairs. 1keV photons collide with above 500MeV photons Outer gap is screened if 500MeV~1GeV photons are emitted. (In the model Eγ ～ 10GeV because kT ～ 100eV of the stellar surface X-ray) Discussion (my opinion)

Relativistic effects 1,Aberration -The photons are emitted in the direction of the particle motion Emission direction in the co-rotating frame