the phase-resolved spectra of the crab pulsar jianjun jia jan 3, 2006
TRANSCRIPT
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
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
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
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
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
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