Transcript a three-dimensional outer mangetosphereric model for gamma

A THREE-DIMENSIONAL OUTER
MAGETOSPHERIC MODEL FOR
GAMMA-RAY PULSARS:
GEOMETRY, PAIR PRODUCTION,
EMISSION MORPHOLOGIES, AND PHASERESOLVED SPECTRA
K.S.CHENG, M.RUDERMAN & L.ZHANG
M.N.R.A.S 2000, 537,964
Abstract
This paper studies three-dimensional
geometry of the particle accelerator of the
pulsar, with using the outer-gap model.
Pair-creation region inside of the gap is
discussed.
They calculate the expected light-curves
following Romani & Yadigaroglu (1995).
The synchrotron- self Inverse Compton
process is calculated to compare with
observed Crab spectrum.
Introduction
Particle are accelerated by the electric
field parallel to the magnetic field line
inside of the light cylinder.
J
I
Polar Cap model v.s. Outer gap model
Outer gap three dimensional geometry
easily produces observed light curve
features such as two-peaks in a period
and phase separation between two
peaks (Romani & Yadigaroglu 1995, RY).
-Polar cap model has not predicted except
for nearly aligned rotator.
γ-ray light curve
Vela
One period
Motivation
?
RY did not consider
the inwardly γ-rays
to avoid appearance
of multiple peaks
This paper consider
1,where the most pairs
are created,
2,whether the inwardly
emitted gamma-rays
can be ignore or not.
Where is the pair creation region?
Model
Rotating magnetic
field
Shape of the Polar cap
Model (cont’d)
Basic idea of pair-creation cascade in the outer gap
Acceleration of particles (primary) in the gap
γ-ray radiation of primary particles (Γ～107)
(curvature radiation)
γ-ray
Pair-creation process between γ-ray and X-ray
X-ray
Pairs produced inside of the gap
Pairs (Γ～103) produced outside of the gap (Secondary)
Synchrotron – Inverse Compton process
Model (cont’d)
Accelerating electric field:thin vacuum outergap model (Cheng, Ho & Ruderman 1986)
Gap expands until the pairs are created
inside of the gap
X-ray field (Zhang & Cheng 1997); heated
polar cap model of the primary particles
Results;Pair-creation region
The total number of pairs produces at
distance r per electron and positron;
They estimated the distance, in which
the most pairs are produced, from the
condition;
Photon emission
morphology
Photon emission
morphology
-the direction emissions are
expressed by
Polar angle from the rotation axis
Phase of rotation of the star
The phase, in which many photons are piled up, is
observed as a pulse phase.
Relativistic effects
1,Aberration
-The photons are emitted in the
direction of the particle motion
Caustic !!
:emission direction of the static observer
:emission direction of the corotating
observer
2,Flight time effect
d: distance to the pulsar from the Earth
Relativistic effects
Polar angle of detection
Phase of detection
Absolute azimuth of the emission point
Azimuth of the emission direction
Result
Emission between null charge
surface and the light cylinder
Emissivity is constant
Outwardly emission
Inwardly emission
Crab
Acceleration of particles (primary)
Vela
γ-ray radiation of primary particles
(curvature radiation)
Pair-creation process between γ-ray and X-ray
1keV
1GeV
Vela like
Pairs produced inside of the gap
Pairs produced outside of the gap (Secondary)
Synchrotron – Inverse Compton process
Crab like
Spectrum
Conclusion
The inwardly emissions is fainter than the
outwardly emissions, because the paircreation region is restricted near the inner
boundary.
The expected light curves including the
relativistic effects is good agreement with
observations.
The synchrotron-Inverse Compton spectra is
consistent with the Crab observation.
Discussion (my opinion)
Their strength of the accelerating electric
field must be overestimated.
We should take into account the pair-creation
process with the X-ray emitted by secondary
pairs.
1keV photons collide with above 500MeV photons
Outer gap is screened if 500MeV~1GeV photons are emitted.
(In the model Eγ～10GeV because kT～100eV of the stellar
surface X-ray)
Relativistic effects
1,Aberration
-The photons are emitted in the direction of the
particle motion
Emission direction in the co-rotating frame