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

0ˆ

BE

GJ

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 alti

tudes

- 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

GJGJe 4)(42 Inconsistency

Cheng, Ruderman & Zhang, 2000

VndN GJ

0

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 stellarsurface 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 viasynchrotron, curvature, and IC processes

Gamma-rays collide with soft photons to materialize as pairsin the accelerator

Basic Equations Poisson Equation

Particle Boltzmann Equations

Stationary conditionElectric 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) (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 importantInformation about the pitch angle of particles is needed

Takata et al. 2004

Vela

Comparison between some outer gap models

Model Romani & Yadigaroglu (1995)

Hirotani et al. (1999)

Takata et al. (2004)

Hirotani Pei-Chun

Geometry 3D 1D 2D 2D

Dynamics x o o oPitch-angle x x x o

My work

e||E )(

)(

s

sp

e

Pair ProductionPoisson Equation

Next step

Future work

Some results

||

|| coscos

sinsin

vdt

dsc

PeEp

dt

dc

Pp

dt

d

sc

sc

)(

)(

s

sp

s

cosp4/

7000

1000

0

0

||

E

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

ff: Vertical Size: 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 conditionwe obtain:

-ray luminosity

12/54/112

4/14/11108.9 PBfEX

4/74/312

2/38104.1 PBfE

22 )(~ cmEE eX

7/17/121/267/412 ),(5.5 PBfPBf o

),(),(3 PBLPBfL sd

Basic Equations Poisson Equation

WD

2D form