study on polarization of high- energy photons from the crab pulsar 〇 j. takata...
TRANSCRIPT
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
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)
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;
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.
Outer gap Caustic model
Curvature radiation Synchrotron radiation
Which one more similar to observation?
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%