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Study on polarization of highenergy 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.
2.
3.
4.
5.
Introduction
Synchrotron model for the Crab pulsar
Results
Discussion
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?
1, Introduction
Gamma-ray emission models
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
Last open line
process

1, Introduction
Polar cap
Polar cap
Viewing angle
Double peak light curve
Emission direction
=particle motion direction
-aberration
-time delay
Caustic
Outer gap & Caustic
Outer gap
Rotation phase
1, Introduction
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
Polarization
Position
degree (P.D.) angle (P.A.)
Intensity
Crab optical data
40%
40%
Smith et al 1988
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.

bridge off pulse
Kanbach et al 2004
2,previous studies
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).
We examine the polarization
characteristics predicted by
the synchrotron model

S.R.
C.R.
Expected Synchrotron phase-ave.
spec.
1eV
1MeV
3 polarizations
*Synchrotron radiation
observer
Projected B on the skey
•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

gyration

Acceleration

Observed electric vector of EM
wave with aberration effect
3,synchrotron model
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)
•Collecting of photons
•Observed P.D. and P.A.
after collecting photons
90
Phase
Fig. Emission position projected
on
plane for
the outer gap model
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

Fig., predicted Crab
spectrum by KS2000
4,Results; Outer gap model
1eV


300eV
Fast P.A. swing
at both peaks
40°P.A. A
and in bridge
0
phase.
Maximum in P.D.40
60%
(~60%) near
P.D.
°
both peaks
10%
1.5 phase
100keV
Maximum in P.D.
near the peaks
P1
80
P2
P.A.
P.D.
80
A
4, Results; Crab data .Vs. model results
*Model explains observed
features of
1, Fast swing at both peaks,
2, relatively constant at
bridge
4, relatively small P.D.
P.A.
40
％
P.D.
1.5 phase
60
%
But, it is difficult to explain
1,pattern of P.D.
2,off pulse emission
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 surface
2, 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.

5, Discussion; Outer gap geometry
Bound. of vacuum gap
（ρ=0)

In fact, outer gap
will start from
insider of the null
charge surface
Radius in units of light radius
Jmax=0.3
0.2
0.3
No currents !
Jmax=0.4
Current
Takata et al. (2004, 2006)
5, Discussion;
Modified emission map
90°
Outward emission
Inward emission
Field-aligned electric fields
5, Discussion;
Electric field
Vacuum gap
Jmax=0.3
Jmax=0.4
null surface
Distance along field line
in units of light radius
5, Discussion;
Expected light curve
Outward emission
90°
Inward emission
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
Ω
B
0 deg
90 deg
270 deg
Rotating
dipole
field
Dipole
field
P.A.
0.1
Curvature radiation
Synchrotron radiation
Outer gap
Which one more similar to observation?
Caustic model
Gamma-ray emission
models
Polar cap
Caustic
Outer gap
3 polarizations of Curvature Vs.
Synchrotron
* Curvature radiation
Projected B on the skey
*Synchrotron radiation
Projected B on the skey
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

Fig., predicted Crab
spectrum by KS2000
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
0
2,P.A. at off pulse…
-relatively constant
15%
-similar value with bridge
phase

Off pulse
P.A.
P.D.
bridge
A
2,previous studies
Previous studies (Dyks et al. 2004)
Data
Curvature emission
model predicts
-high Polarization degree
(P.D)
-large P.A. swing at offpulse phase
Polar cap
There are no curvature
emission model for the
Crab spectrum
Position
Polarization
degree (P.D.) angle (P.A.)

Intensity

40%
80%
Caustic
Outer gap
Observed polarization plane with
aberration effect
* No aberration effect
* With aberration effect