Transcript The Phase-Resolved Spectra of the Crab Pulsar

The Phase-Resolved Spectra
of the Crab Pulsar
Jianjun Jia
Jan 3, 2006
Outline
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Review of the high energy pulsars
Theoretical models
The Crab pulsar
Conclusions
Observations of high energy pulsars
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Light curves

spectra
Theory of high energy pulsars
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Magnetic dipole approximation
 1
B  3 [3(   rˆ)rˆ   ]
r
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Geometry of the magnetic field lines
The field lines can be traced by numerical
calculations.
Geometry of the magnetic field lines
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footprints
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last closed field lines
Goldreich & Julian model
 
  r 
E
B 0
c
Outer gap model
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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 pulsar
energy dependant light curves
phase bins
Modified structure of the outer gap
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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
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relativistic aberration
ux  
u 
1  u x
'
x
u 'y 
uy 1  2
1  u x
2
u
1


u z'  z
1  u x

time of flight
cos   u
'
z
rˆ  uˆ '
  u ' 
RL
Numerical results
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light curve
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emission projection
Phase-Resolved Spectra
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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
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Curvature radius
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Lorentz factor 
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Curvature photon energy
Ecur

s(r )  rRL
3 s

(
r
)

eE
(
r
)
c
e
||
 2

2
e
c


2
1/ 4
 r 1/ 8
 r 
3
c
  e3 (r )
 1.53 1011 f 3 / 2 ( RL ) 
2
s(r )
 RL 
Magnetic field
B( r )  r
3
1 / 8
Free parameters: pitch angle ( ) and beam
solid angle ()
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trailing wing 1, bridge, leading wing 2:
sin  ( R L )  0.06,   5.0
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leading wing 1: sin  (RL )  0.02,   1.0
sin  ( R L )  0.04,   3.5
peak 1:
sin  ( R L )  0.07,   3.0
Peak 2:
trailing wing 2: sin  (R L )  0.03,   6.0
phase-averaged : sin  (R L )  0.05,   5.0
Phase-resolved spectra
Phase-averaged spectrum
Conclusions
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Inclination angle:   500
  750
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.
Thank you!