Study on polarization of high-energy photons from the Crab

pulsar

〇 J. Takata (TIARA-NTHU/ASIAA,Taiwan)

　 H.-K. Chang (NTH Univ., Taiwan) 　 K.S. Cheng (HK Univ., Hong-Kong)

TIARA: Theoretical Institute Advanced Research in Astrophysics

ASIAA: Academia Sinica Institute of Astronomy and Astrophysics

NTHU : National Tsing Hua University

Contents

1. Introduction

2. Synchrotron model for the Crab pulsar

3. Results

4. Discussion

5. Summary & Conclusion

1, Introduction; Gamma-ray pulsar

Vela

Crab

Where and how are the particles accelerated and the gamma-rays radiated in the pulsar magnetosphere?

Gamma-ray emission models

1, Introduction

Pulsar as a huge electric dynamo

Particle acceleration ( ) via electric field (E||) parallel to magnetic field line in gap, where

Gamma-ray emissions (~a few GeV) via curvature process

Last open line

Rotation phase

Emission direction =particle motion direction-aberration-time delay

Outer gap & Caustic

Polar cap

Vie

win

g an

gle

Double peak light curve

1, IntroductionPolar cap

Caustic

Outer gap

Why polarization?

Polarization data will play an important role to discriminate the various models

Polarization measurement will increase (2 times) number of observed parameter; polarization position angle (P.A.) swing and polarization degree (P.D.)

So far, Crab optical data is available. In future, Compton telescope will measure in MeV-bands for the Crab pulse.

1, Introduction

Crab optical data

40%

40%

Smith et al 1988 Kanbach et al 2004

Observation

-fast swing P.A. through peaks

-constant P.A. in off-pulse phase

-min. in P.D. at both peaks

-~40% of max. in P.D.Po

lari

zati

on

degr

ee (

P.D

.) P

osit

ion

angl

e (P

.A.)

Inte

nsit

y1, Introduction

bridge off pulse

Cheng, Ruderman & Zhang (2000) model for Crab pulsar

Synchrotron and inverse-Compton process of secondary pair produces photons in wide energy bands (optical to GeV).

Outer gap

C.R.

S.R.

We examine the polarization characteristics predicted by the synchrotron model

2,previous studies

Expected Synchrotron phase-ave. spec.

1MeV1eV

3 polarizations

*Synchrotron radiation

Projected B on the skey

observer

•Polarization characteristics are described by Stokes parameters, I, Q, U,V-Linearly Degree of polarization-Position angle of polarization plane

3 Synchrotron emission model

Emission direction

(particle motion direction)

=edge of cone with

Acceleration

Observed electric vector of EM wave with aberration effect

gyration

Model; Stokes parameters

At each point and at each radiation…..

1, linearly polarized radiation at

2,Stokes parameters

3, Intensity

(projected rotation axis on the sky)

3,synchrotron model

Vie

win

g an

gle

Phase90

•Observed P.D. and P.A. after collecting photons

•Collecting of photons

Fig. Emission position projected on plane for the outer gap model

Fig., predicted Crab spectrum by KS2000

Emissivity & model parameters

Model,Outer gap model - Cheng, Ruderman & Zhang (2000)

　　　　　　 -Emission region starting from null charge surface

Model parameters

Emission region is upper surface of the gap

4,Results; Outer gap model

Fast P.A. swing at both peaks and in bridge phase.

Maximum in P.D. (~60%) near both peaks

1eV 300eV 100keV

P.D.

10%

60%

40°0

-40°

P.A.

1.5 phase

A

Maximum in P.D. near the peaks

P.A.

P.D.

A

P1

P2

80

80

4, Results; Crab data .Vs. model results

40％

P.D.

P.A.

60%

*Model explains observed features of1, Fast swing at both peaks,2, relatively constant at bridge 4, relatively small P.D.

But, it is difficult to explain 1,pattern of P.D.2,off pulse emission

1.5 phase

5, Discussion What the observation indicates?

Observation may indicate that present model is very simple….1, gap geometry -outer gap will extending inside of the null surface2, only outward emission by the outgoing particles , -inward emission via ingoing particles may be observed 3, constant power low index (p=2) of particle distribution,

-more realistic particle distribution may be important,4 rotating dipole field? Crab optical data will reflect more detail structure of pulsar

magnetosphere.

In fact, outer gap will start from insider of the null charge surface

No currents !

Bound. of vacuum gap　　　　（ ρ=0)

Jmax=0.4

0.3

null surfa

ce Hei

ght

Radius in units of light radius

0.2Jmax=0.3

5, Discussion; Outer gap geometry

Current

Takata et al. (2004, 2006)

Inward emission

90°

Outward emission

Modified emission map

5, Discussion;

Electric field

Fie

ld-a

lign

ed e

lect

ric

fiel

ds

Distance along field linein units of light radius

null surface

Vacuum gap

Jmax=0.4

Jmax=0.3

5, Discussion;

Expected light curve

Outward emission

Inward emission

90°

5, Discussion;

6,Summary

The polarization characteristics by the synchrotron emission, which is favor for Crab spectrum, were calculated with traditional outer gap model.

-Model explains observed small value of P.D. and the constant of P.A. at bridge

-Predicted pattern of P.D. is problematic. None of the present models was able to explain both of P.A. and

P.D. for Crab optical data. The light curves with the outer gap starting from near the stellar

surface have multi peaks.

P.A. at bridge / off pulse phase

B

Ω

Dipole fieldRotating dipole field

0 deg90 deg270 deg

0.1

P.A.

Outer gap Caustic model

Curvature radiation Synchrotron radiation

Which one more similar to observation?

Gamma-ray emission models

Polar cap

Caustic

Outer gap

3 polarizations of Curvature Vs. Synchrotron

* Curvature radiation *Synchrotron radiation

Projected B on the skey Projected B on the skey

Fig., predicted Crab spectrum by KS2000

Emissivity & model parameters

Model1,Outer gap model - Cheng, Ruderman & Zhang (2000)

　　　　　　 -Emission region starting from null charge surface

Model 2,Caustic model -emission region starting from stellar surface

-constant emissivisity Model parameters

Emission region is upper surface of the gap

4, Results; Caustic model

Caustic model explains off pulse emission of Crab pulsar

1,Maximum in P.D. (~15%) at peak or trailing of peaks

2,P.A. at off pulse…

-relatively constant

-similar value with bridge phase

15%

Off pulse bridge

P.D.

P.A. A0

Previous studies (Dyks et al. 2004)

Curvature emission model predicts

-high Polarization degree (P.D)

-large P.A. swing at off-pulse phase

2,previous studies

There are no curvature emission model for the Crab spectrum

Inte

nsit

y P

osit

ion

angl

e (P

.A.)

Pola

riza

tion

de

gree

(P.

D.)

Polar cap Caustic Outer gapData

40% 80%

Observed polarization plane　 with aberration effect

* No aberration effect * With aberration effect