The Phase-Resolved Spectra of the Crab Pulsar

Jianjun Jia

Jan 3, 2006

Outline

Review of the high energy pulsars Theoretical models The Crab pulsar Conclusions

Observations of high energy pulsars Light curves spectra

Theory of high energy pulsars

Magnetic dipole approximation

Geometry of the magnetic field lines

The field lines can be traced by numerical calculations.

]ˆ)ˆ(3[13

μμ −⋅= rrr

Bv

Geometry of the magnetic field lines footprints last closed field lines

Goldreich & Julian model

0=××Ω

+ Bcr

Evvv

v

Outer gap model

Global currents flow through the null charge surface results in large regions of charge depletion, which form the gaps in the magnetosphere. The gap extends from the null charge surface to the light cylinder.

Parallel electric field is induced in the gap, which can accelerate the electrons to extremely relativistic speed. (CHR, 1986a,b)

Outer gap model

e+e- pairs are accelerated to extremely relativistic velocity by the parallel electric field

Relativistic pairs radiate high energy photons

through curvature/ synchrotron /ICS mechanisms

The high energy photons collide with the soft photons to materialize as e+e- pairs

The Crab Pulsar

Pulsation of the Crab pulsarenergy dependant light curves phase bins

Modified structure of the outer gap The inner boundary of the outer gap is not

located at the null charge surface, and can shift inwardly to the near surface region (~0.02RL). (Hirotani, 2005)

Thus, the azimuth extension can be larger than 1800, and we get the radiation from both poles.

Radiation morphologies

gap geometry emission from the gaps

Radiation morphologies

relativistic aberration time of flight

x

xx u

uu

ββ

−−

=1

'

x

yy u

uu

ββ

−−

=1

1 2'

x

zz u

uu

ββ

−−

=1

1 2'

Lu

z

R

ur

u'

'

ˆˆ

cos

'

⋅−−=Φ

=

φ

ζ

Numerical results

light curve emission projection

Phase-Resolved Spectra

Synchrotron Self-Compton (SSC) mechanism e+e- pairs interact with the magnetic field to generate

synchrotron photons

high energy synchrotron photons interact with the field to

generate relativistic pairs

relativistic pairs collide with soft photons via ICS to emit high energy photons

Local properties of the magnetosphere Curvature radius

Lorentz factor

Curvature photon energy

Magnetic field

LrRrs =)(

8/1

2/3113 )(1053.1)(

)(2

3−

⎟⎟⎠

⎞⎜⎜⎝

⎛×==

LLecur R

rRf

rsc

rE γh

8/1

4/1

||2

2

)(2

3)( rcreE

ce

sre ∝⎥

⎦

⎤⎢⎣

⎡=γ

3)( −∝ rrB

Free parameters: pitch angle ( ) and beam solid angle ( ) trailing wing 1, bridge, leading wing 2:

leading wing 1: peak 1: Peak 2: trailing wing 2: phase-averaged :

βΔΩ

0.5,06.0)(sin =ΔΦ=LRβ0.1,02.0)(sin =ΔΦ=LRβ

5.3,04.0)(sin =ΔΦ=LRβ

0.3,07.0)(sin =ΔΦ=LRβ

0.6,03.0)(sin =ΔΦ=LRβ

0.5,05.0)(sin =ΔΦ=LRβ

Phase-resolved spectra

Phase-averaged spectrum

Conclusions

Inclination angle: Viewing angle: The phase-resolved spectra in the energy

range from 100eV to 3GeV of the Crab pulsar can be fitted well.

The photons beyond 1GeV may be the residual curvature photons emitted by the first generation pairs.

050=α075=ς

Thank you!