Gamma-ray emission mechanism in pulsar magnetosphere – electrodynamics and models 徐佩君 清大天文所

Contents  Introduction  Models  My work  Summary

Observational motivation EGRET all sky survey (100MeV-10GeV) How the observed gamma-rays are emitted around the pulsars? Thompson et al. 1999

Plasma-filled magnetosphere Force free condition: Goldreich-Julian charge density

Accelerators Poisson’s equation: (one-dimensional) A super dynamo ! Harding 2000 NS

Models Polar cap Outer gap Hirotani & Shibata Cheng, Ho, & Ruderman Slot gap Polar cap … … Arons et al. Muslimov & Harding Ruderman & Sutherland … … Arons & Scharlemann

Polar cap  Sturrock(1971); Ruderman & Sutherland(1975)  Arons, Scharlemann, & Fawley(1977~)

Slot gap  Muslimov & Harding (2004) They explored the SG electrodynamics up to very high altitudes - A narrow region on the boundary of the open field lines developing above the polar cap The extended gap can explain the observed light curve well

Outer gap (geometrical)  Cheng, Ho, & Ruderman(1986)

Pulse profile Romani & Yadigaroglu 1995 Vela Observation Model Outer gap model can explain double peak light curve with bridge emission

However..  Vacuum gap is assumed to solve E ||  In the gap the number of primary charged particles is roughly given by Inconsistency Cheng, Ruderman & Zhang, Crab Inner boundary (E || =0;Φ=0) is at null surface

Extended gap Dyks & Rudak, 2003 An outer gap with inner boundary extended toward the stellar surface can explain the light curve well (off-pulse emission) Vela

Outer gap (electrodynamical)  Hirotani & Shibata e + and e - are accelerated by E || Relativistic e + /e - emit gamma-rays via synchrotron, curvature, and IC processes Gamma-rays collide with soft photons to materialize as pairs in the accelerator

Basic Equations  Poisson Equation  Particle Boltzmann Equations Stationary condition Electric force Curvature radiation reaction force

Basic Equations  Collision Terms  Gamma-Ray Boltzmann Equations The electrodynamical model connects these equations and solves Outer gap structure self-consistently Inverse Compton Scattering Pair production Curvature radiation

Computed spectrum Vela Hirotano et al. 2003

weaknesses of the present electrodynamical model  One-dimensional model (Thick gap)(Thick gap) (Hirotani & Shibata 1999~2004) - can not apply the Crab case (thin gap) - ignore the tarns-field structure  Two-dimensional model (Takata et al. 2004,2006) - do not solve pitch angle - only calculate the curvature radiation

Motivation Synchrotron radiation is important Information about the pitch angle of particles is needed Takata et al Vela

Comparison between some outer gap models ModelRomani & Yadigaroglu (1995) Hirotani et al. (1999) Takata et al. (2004) Hirotani Pei-Chun Geometry3D1D2D Dynamics xooo Pitch-angle xxxo

My work Pair Production Poisson Equation Next step Future work

Some results s

Summary  It is believed that gamma-ray is emitted by relativistic charge particles accelerated in charge depletion region in pulsar magnetosphere.  Many models have been published to explain the observation. And there is no perfect one. We do not know which one is the answer.  We are trying to quantitatively solve two- dimensional electro-dynamical equations for a stationary pair-production cascade in pulsar magnetospheres.

Reference  Cheng, Ho, & Ruderman, 1986, ApJ, 300, 500  Cheng, Ruderman & Zhang, 2000, ApJ, 537, 964  Dyks & Rudak, 2003, ApJ, 598, 1201  Goldreich & Julian, 1969, ApJ, 157,869  Hirotani, Harding & Shibata, 2003, ApJ, 591, 334  Muslimov & Harding, 2004, ApJ, 606, 1143  Romani & Yadigaroglu, 1995, ApJ, 438, 314  Takata, Shibata &Hirotani, 2004, MNRAS, 348, 241

f: Vertical Size  In outer-gap model, the typical energies of the soft X-rays and the  -rays are completely determined by the vertical size and the horizontal extension of the outer gap  Soft X-ray photon:  Curvature  -ray photon evaluated at the half of the light cylinder:  Using pair production condition we obtain:   -ray luminosity

Basic Equations  Poisson Equation 2D form