1. The structure of the pulsar magnetosphere via particle simulation
1. パルサー磁危険の様子を描いた想像図(次へ)
Shinpei Shibata (1),
Shinya Yuki (1), Tohohide Wada (2),Mituhiro Umizaki (1)
(1)Department of Phys. Yamagata University
(2)National Astronomical Obvsevatory of Japan

2. Introduction
Pulsars

3. Neutron Star about 1M_sun 10km in size Pulsars: B_d ～ 10^9 – 10^13 G
P～ 1.5msec – several seconds
Emf～ 10^14 Volt
particle acc. radaton:
rotation powered
pulsars
magnetic powered
pulsars
Neutron Star
about 1M_sun
10km in size
1. パルサー磁危険の様子を描いた想像図(次へ)
Magnetars:
Small subclass of magnetic neutron stars
magnetic active regions with B～ (maybe)10^15G

4. Pulsar Wind radiation is Beamed: observed as pulsed
Rotation axis
radiation is
Beamed:
observed as pulsed
particles acc.byE//
1 ly
Pulsar
Wind
(relativistic
outflow of
magnetized
plasma
γ～ 10^6)
Size of the magnetosphere:
the light cylinder with R_L= c/Ω～4.8×10^4 R_ns

5. SED(spectral energy density plot)
keV
SED(spectral energy density plot)
GeV
TeV
Pulsed emission
magnetospheric
Size: RL=c/Ω
Emf: Vacc=RL*BL =μΩ^2/c^2
Curvature rad. byＥ// acceleration BB
Spectrum of beamed emission
E// + e/p
Unpulsed emission
Nebula
Rs=(Lwind/4πPext)^1/2
sync
Vacc=Rs*Bn with Pext=Bn^2/8π ＩＣ
Aharonian, F.A. & Atoyan, A.M., 1998

6. What magnetospheric models to explain pulsed emission?

7. Polar cap Outer gap Slot gap Models based on observatons: PC, SG, OG
Light cylinder Ω B
Polar cap
Open field region
Outer gap
Closed field
(dead zone)
Null surface
Dead zone
Slot gap

8. Polar cap Outer gap Slot gap Models based on observatons: PC, SG, OG
Are all the three correct?
if so, what is the mutual relation?
We attempted to solve this basic problem form the
first principles via particle simulation.
γ-ray pulse shape and relation to radio pulses are well explained if γ from OG/SG. Radio from PC
Two-pole caustic (TPC) geometry
(Dyks & Rudak, 2003)
Light cylinder Ω B
Polar cap
Open field region
Outer gap
Radio pulse
Closed field
(dead zone)
Null面
Dead zone
Slot gap

9. E// (field-aligned acceleration)

10. E vacuume Unipolar Inductor Roation × magnetization
makes emf >> gravity, work function E
Magnetic neutron star
vacuume
What is the fate of the particles which jump up into the magnetosphere  simulation

11. By strong emf, charged particles are emitted from the neutron star and forms steady clouds.
Rotation axis
Polar domes of electrons
Magnetic neutron star
Equatorial disc
with positive paritcles

12. e+/e-pairs fills the gap
- The clouds are corotating. E//=0
- Vaccume gap E// not zero
- Cloud-gap boundary is stable (FFS)
(ref. Wada and Shibata 2003)
emf makes the gap vs
e+/e-pairs fills the gap
 Final state
Map of E// E
gap
The gap is unstable against pair creation.

13. Particle simulation

14. particle code acceleration Gamma-ray Strong B radiation from the star
Non neutral plasma
E// appears
Particle inertia is effective in the wind zone γ～10^7
Radiation reaction force
Radiated photons make e+/e- pairs
particle code
acceleration ―
Gamma-ray ― ―
Strong B
radiation from the star

15. Particle code
for the axis-symmetric steady solution, d /dt =0, Particle motion and the electromagnetic fields are solved iteratively.
For the EM field
Emf is included in the BC
For the particle motion

16. We use Grape-6, the special purpose computer for astrononomical N-body problem at NAOJ.
Gravitational interaction
For the electric field
For the magnetic field

17. Particle creation and loss
- Particles are emitted from the star if there is E// on the surface.
- On the spot approximation: e+/e- are created if E//>Ec
- Particles are removed through the outer boundary: loss by the puslar wind.
The system settles in a steady state when the system charge becomes constant:
steadily pairs are created in the magnetosphere and lost as the wind.

18. Results

19. E// localized Outer gap
The outer gaps steadily create pairs with E// kept just above E> Ec . The proof of OG.
Rotation axis
Light cylinder
Particle distribution and motion
Strength of E//
E// localized Outer gap
Pair creation
Current sheet begins to form.
Magnetic neutron star

20. Global current in the meridional plane
(do not forget plasma rotating and Bφ<0)
Rotation axis
Return current
Current-neutral dead zone
Slot gap
Fast rotation and
Emition in φ-direction
Outer gap
Polar cap
Outward current ( r )
Dead zone
Magnetic neutron star
Magnetic field (θ)
Radiation reaction force (φ）

21. E/B map
Light cylinder
E>B
(break down of the ideal-MHD cond.), when we look at the inside of the current sheet.
Light cylinder
Uzdensky 2003
Force-free approximation also gives E>B

22. E/B map
E>B
(break down of the ideal-MHD cond.), when we look at the inside of the current sheet.
Light cylinder
Umizaki et al. 2010
磁気リコネクション

23. Summary
The outer gap, which is the candidate place of the particle acceleration and gamma-ray emission, is proven from the first principles by particle simulation. OG, SG and PC, all exist self-consistently.
Due to radiation reaction force, some particles escape through the closed field lines.
At the top of the dead zone, we find strong E field larger than B, i.e., break down of the ideal-MHD condition, and in addition PIC simulation indicates reconnection driven by the centrifugal force.
There are two places in which magnetic reconnection may play an important role.
Close-open boundary near the light cylinder (Y-point)
Termination shock of the pulsar wind

24. Pulsar aurora Polar cap Slot gap Outer gap Magnetic Reconnection
Magnetic axis
Rotation axis Ω
Polar cap
Slot gap
Light cylinder
Outer gap
Ｔｈｉｃｋ　ｗｉｎｄ
Neutral sheet
Magnetic Reconnection
Pulsar aurora

25. 1. EMF and charge separation
Basic properties of the pulsar magnetosphere
1. EMF and charge separation
Unipolar Induction
Motional field
As compared with required charge separation, plasma source is limited
　gap E//

26. In reality, plasma is extracted from the stellar surface by E//: maybe, complete charge separation
Corotation speed becomes the light speed
Negative space charge
Relativistic
centrifugal wind
Positive space charge
Goldreich-Julian model (1969)

27. Gap formation Positive space charge Null charge surface
Strong charge separation in a rotating magnetosphere makes the gap, non-zero E//
Negative space charge
Null charge surface
Gap formation
Positive space charge
Goldreich-Julian model (1969)

28. SED(spectral energy density plot)
keV
SED(spectral energy density plot)
GeV
TeV
Pulsed emission
magnetospheric
RL=c/Ω
Vacc=RL*BL=μΩ^2/c^2
Ｅ// 加速
1. High Energy Pulses
BB 加熱
3. Radio Pulses
E// + e/p
2. Pulsar Wind Lwind=ηw Lrot
Unpulsed emission
Nebula
Rs=(Lwind/4πPext)^1/2
sync
Vacc=Rs*Bn with Pext=Bn^2/8π ＩＣ
垂直衝撃波加速の困難
Aharonian, F.A. & Atoyan, A.M., 1998