Download Gap

＠FAN3
22 June 2012
The Structure of
the Pulsar Magnetosphere
via Particle Simulation
S. Shibata 柴田 晋平
Yamagata Univ.山形大学
Department of Phys 物理学科
Aim of our numerical study
via particle simulation, the main problems to
be challenged are
1. To give the theoretical proof of the
outer gap (the mechanism has been
proposed)
2. To look for other particle
acceleration sites; polar cap, & slot
gap to be confirmed, and look for
other possibilities?
3. To study the pulsar wind formation
Although pulse profiles have some varieties,
青系
Ｐ１＋Ｐ２＋Ｐ３以上
2%
7% 1%
黄色系
Ｐ１ メインピーク一つ
9%
5%
11%
65%
緑系
Ｐ１＋Ｐ２ ２ピーク＋ブリッジ
Ｍ型
1
1'
2
M
2'
3
4
４４サンプル
From “The First Fermi Large
Area Telescope Catalog of
Gamma-ray Pulsars,
Abdo et al., astroph/0910.168v2
Observation (Vela)
Double peak and bridge emission can be
understood if emission is along the last
open field lines; due to multi-ply
superposition of photon arrival times:
caustic.
model
Two-pole caustic (TPC) geometry
(Dyks & Rudak, 2003)
Favors Slot gap / Outer gap
Caustic in human life
Double pulses and spectrum support the outer gap model
 to give the proof of the outer gap.
3rd peak, 4th,,,,,many components are observed
and shall be observed in the future. look for
other acceleration sites by simulation.
Third peak, may not be caustic
After Ray & Parkinson 2010
Astro-ph 1007.2183
The rotation power is mostly carried off by the pulsar
wind. formation of the pulsar wind.
Q1 how much fraction of the wind energy is carried by
electromagnetic flux (Poynting flux), and how much by
kinetic energy of particles; acceleration efficiency
Q2 where the wind acceleration takes place; near the l.c. or
gradually in a long distance to the nebula.
X-ray image of Crab Nebula, which is exited by
the pulsar wind, but the contents of the wind is
not certain
Basic Physics I
Model:
NS  magnetized electrically conducting
sphere; B=10^12 G, rotating wiht P= 0.1sec
charge
separation
Electric potential difference appears between
the poles and the equator.
Rotating magnet has emf
B
V
-v
+
B
ー
ー
ー
V
＋ ＋ ＋
F
Release of rotational energy (in reality ]: how?
Unipolar inductor:
rotating magnet produces emf
Note ∂B /∂t =0
Electric potential difference appears between
the poles and the equator.
B
V
-v
+
For oblique rotator, potential difference becomes
φ=(Ωμ/cR^3) [(x^2+y^2)cos χ – zx sin χ]
By forming a closed current circuit, one can extract
energy: one can light the lamp.
magnetic field
current
As a back reation, electromagnetic breaking on the
magnet causes spin-down: Thus rotational energy of the
neutron star
is extracted.
The rate of energy loss L_rot is (by
dimensional analysis within the classical
physics)
One can estimate μ
by this relation.
One must notice that the circuit experiences a force in such a direction
that the circuit is force to corotate with the star. Thus the circuit and
the plasma around the neutron star have strong tendency of corotation.
Co-rotation
speed
becomes c
magnetic field
If the ciruit
corotates with the
star, no mutual
motion, no extraction
of emf.
current
hν/c or γmc
Angular momentum is lost by photons  back reaction
on the emitting material make mutual mo.  extraction
possible
If the lever-arm distance is c/Ω, angular momentum is properly lost.
Summary:
The extraction of rotation energy can be kept
continuously by emission of photons and particles
near and beyond the light cylinder with levar-arm
distance of c/Ω. As a corollaly, the polar cap and any
other radiations well within LC cannot be a dominant
emission site. I think that most of the rotation power
is emitted tangentially from the light cylinder by a
mixture of photons and relativistic particles, called
the pulsar wind.
Breaking index
n<3?
Younger pulsars may have worse efficiency (?)
Basic Physics II
We are working on higher
order approximation!
If there is enough plasma, it corotates with the star.
However, because of relativity principle, the corotation
is limited within the LC.
In 1973, Holloway thought that if some plasma is leaked
from the LC , there appears a gap in the corotation
region.
(Holloway N.J.,1973 Nat. Phys. Sci 246, 6)
Eq. of motion:
BC; rigid rotation of the star; star is a good conductor
Co-rotation electric field
Drift is corotation; for oblique rotator
The corotation electric field is supported by the
“corotation charge density”, GJ density
In number density,
“quasi-neutral plasma?”
This charge density is difficult to realize in the pulsar
magnetosphere because of large gravity and because
source of plasma is limited. We do not have quasineutral plasma in the pulsar magnetosphere as far as
electron-positron pair creation, which we shall discuss
later, takes place.
Let us suppose somewhat idealized situation where the electric field
is the corotaional one (no field-aligned comp.) and therefore the
charge density is GJ. The plasma is supported against gravitational
force from the star so that the plasma is completely charge
separated. Let us add a perturbation that some plasma is leaked from
LC by say centrifugal force.
GJ negative
Positive GJ
GJ negative
Holloway 1973
strong
charge
separation
causes
gaps
Deficiency of plasma within the LC manifests itself as a gap round
the boundary between the negative and positive GJ density.
For the first time, the particle simulation is applied for
this situation by Krause-Polstorf and Michel (1985).
Light
cylinder
Field-aligned Electric field
electrons
Gap
Gap
star
positrons
These pictures are reproduced by our code.
In the gap, GJ density is not filled, and the electric
field deviates from the co-rotation filed.
Inertial force, non-EM forces must balance EM
force; Particle acceleration
Evacuated space (Gap) is unstable against pair
creation. As a result, Holloway gap creates
pairs continuously or quasi-periodically. This is
the outer gap.
By many authors, the gap structure is calculated
but is affected by many factors: e.g., geometry
of back ground magnetic field, soft-photon field,
radiation process taken into account, boundary
conditions for the electric field.
(Hirotani & Shibata 1999, Takata Shibata &
Hirotani 2004, Hirotani 2008, Takata Wang &
Cheng 2010,,,,)
One can in principle calculate the structure of
the outer gap if sufficient conditions are given.
However, we do not think the outer gap
structure can be determined as far as it is local
model. We always have free parameter, which
must be free to adjust with the surroundings,
especially the pulsar wind. More specifically the
total current and current distribution in the gap
is controlled by the pulsar wind. Thus the model
must be global , and the outer gap must be
solved together with the wind.
Particle simulation.
(Wada & Shibata 2007, Wada & Shibata 2011,
Yuki & Shibata 2012)
Method of
Particle Simulation
Plasmas are represented by
several tens of thousands of
super-particles.
60RL
60RL
60RL
(number of particles are not fixed,
but particles are added suitably
from the stellar surface or
because of pair creation.)
Cal .Domain is 3D (60RL)^3
For the case of axisymmetry,
[email protected]
Special purpose computer for
Astrononomical N-body Problem
We iteratively solve the equation of mo. and EM field
[email protected]
Special purpose computer for
Astrononomical N-body Problem
With this method, the corotation boundary (i.e. emf of
the star) is strictly satisfied,
with
In general, surface charge on the star exists, but it is
replaced by simulation particles (free emission) until no
surface charge is emitted from the stellar surface.
For the magnetic field, we use
Treatment for pair creation:
Gap is unstable against e+e- pair creation
Unscreened Gap Electric field
B
γ＋B e+ ＋ e-
γ＋X-ray e+ ＋ eTwo photon pair creation
A simple treatment
If E > Ec, n=f * int(E/Ec) pairs are created
(on the spot approx.)
1. Particles flows
NS
Curvature
radiation
2. (m, q) are chosen so
that any plasma
drift motions are
tracked correctly.
3. Radiation drag
force is taken into
account in the
lowest order
approximation.
Results of
Particle Simulation
The outer gap is proven by the particle simulation.
Ingredients are eq. of mo., Maxwell’s eq., BC rotating NS
and pair creatoin if E//>Ec
＊Outer gap is formed with
continuous pair creation &
E//
just aboe
Ec
Rotating
plasmas
makes toroidal current
Paris
are separated
in the
to open
some magnetic
gap
by E//
flux.
＊outgoing
flow
LC
Particles on
the
open
＊ingoing
magneticflow
fluxStar
flows
out along the magnetic
field.
The outgoing flow rotate with high Lorentz factor, so that curvature
radiation carries off the angular momentum. Back reaction of the
curvature radiation is in –φ direction  cross drift motion.
In going flow from the outer gap fall on to the star. If this continues, the
star is charged up and up. So steady state is reached by emission of
pariticles from the polar cap. There must be accelerating field to extract
particles from the polar cap.
E// map
E// is just above Ec: necessary minimum for pair creation.
Map of Φ(Non-corotational electric potential)
The non-corotaion potential Φ= φ- Ωxr・Ａ
constant on the star, it is set to be zero.
is
If Φ=0, the
potential is
as the same
as the star,
Co-rotation
and E//=0
Dead zone
E//= -B ・∇Φ
Map of Φ(Non-corotational electric potential)
We find another
dead zone in the
middle latitudes.
This dead zone
locates on the field
lines which
separates the
outgoing current and
ingoing current.
Dead zone
Let us call this dead
zone the current
neutral dead zone.
Light cylinder
Super- rotatoin
Discussion
Discussion
The ploidal current loop is
such that it start from
the star, go through the
outer gap, goes to the
nebula, and go back to the
star in higher latitudes.
We have two dead
zones:
One is the dead zone in
the equatorial closed
magnetic flux.
The other extends
along the separatrix of
the oppositely directed
currents.
Discussion
Φ = 0 in the dead zone.
The outer gap is
sandwiched by two dead
zone. Therefore,
previous boundary
conditions used for the
outer gap is correct.
Discussion
The polar current is
surrounded by the
current neutral zone;
Inside of hollow cone of
the current neutral
zone. If there is slotgap, it resides above
the current neutral
dead zone.
Discussion
Some particles leak due
to radiation drag drift.
It is noticeable that E
is larger than B in this
region.
Udzdenski のforce free 解
（Uzdensky, 2003）
light cylinder
Map o f E/B
PIC simulation for an axisymetric Ypoint
初期の磁力線
t ～ 4 x 10^5 ⊿ t
での磁力線
（Uzdensky, 2003）
0.02
0.02
0.00
赤道面
Z / RLC
Z / RLC
0.01
0.01
0.00
0.99
1.00
R / RLC
1.01
Magnetic reconnection takes place
⇒ heating and acceleretion
Discussion
Flow out of magnetic
islands with pairs.
Thin current sheet with
outgoing positrons and
backward electron beam
along last open field line
 another component
Future work
Number of particles must be still larger
(now Ndot = 0.7 GJ
Electric field in the polar flow has not been
resolved.)
Gamma-ray coming into the screened region also
make pairs. These pair must be included.
Oblique rotator (not Grape, PIC)
Realistic pair creation process (include photons)
GR effect near the star.
Thank you!