The structure of the pulsar magnetosphere via particle simulation
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The structure of the pulsar magnetosphere via particle simulation
Shinpei Shibata (1), Shinya Yuki (1), Tohohide Wada (2),Mituhiro Umizaki (1)
(1)Department of Phys. Yamagata University(2)National Astronomical Obvsevatory of Japan
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Introduction
Pulsars
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Neutron Starabout 1M_sun10km in size
Pulsars:B_d ~ 10^9 – 10^13 GP ~ 1.5msec – several seconds
Emf ~ 10^14 Voltparticle acc. radaton: rotation powered pulsars
Magnetars: Small subclass of magnetic neutron starsmagnetic active regions with B ~ (maybe)10^15G
magnetic powered pulsars
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Rotation axis
PulsarWind(relativisticoutflow ofmagnetizedplasmaγ ~ 10^6)
Size of the magnetosphere: the light cylinder with R_L= c/Ω ~ 4.8×10^4 R_ns
1 ly
radiation isBeamed:observed as pulsedparticles acc.byE//
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SED(spectral energy density plot)
magnetospheric
Nebula
Aharonian, F.A. & Atoyan, A.M., 1998
Unpulsed emission
Pulsed emission
E// + e/p
BB
Curvature rad. by E // acceleration
IC
sync
Size: RL=c/Ω
Rs=(Lwind/4πPext)^1/2
Emf: Vacc=RL*BL
=μΩ^2/c^2
Vacc=Rs*Bn with Pext=Bn^2/8π
keVGeV
TeV
Spectrum of beamed emission
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What magnetospheric models to explain pulsed emission?
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Ω B
Dead zone
Null surface
Light cylinder
Polar cap
Slot gap
Outer gap
Models based on observatons: PC, SG, OG
Closed field(dead zone)
Open field region
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Ω B
Dead zone
Null面
Light cylinder
Polar cap
Slot gap
Outer gapClosed field
(dead zone)
Open field region
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)
Radio pulse
Models based on observatons: PC, SG, OGAre all the three correct?if so, what is the mutual relation?
We attempted to solve this basic problem form thefirst principles via particle simulation.
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E// (field-aligned acceleration)
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Roation × magnetizationmakes emf >> gravity, work function
Unipolar Inductor
E
What is the fate of the particles which jump up into the magnetosphere simulation
Magnetic neutron
starvacuume
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By strong emf, charged particles are emitted from the neutron star and forms steady clouds.
Polar domes of electrons
Equatorial disc with positive paritcles
Magnetic neutron star
Rotation axis
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- The clouds are corotating. E//=0- Vaccume gap E// not zero- Cloud-gap boundary is stable (FFS)
(ref. Wada and Shibata 2003)
gap
The gap is unstable against pair creation.
E
Map of E//
emf makes the gapvs
e+/e-pairs fills the gap Final state
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Particle simulation
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part
icle
code
―
acceleration
Gamma-ray―
―
radiation from the starStrong B
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Particle codefor the axis-symmetric steady solution, d /dt =0, Particle motion and the electromagnetic fields are solved iteratively.
Emf is included in the BC
For the EM field
For the particle motion
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• Gravitational interaction
• For the electric field • For the magnetic field
We use Grape-6, the special purpose computer for astrononomical N-body problem at NAOJ.
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- 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.
Particle creation and loss
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Results
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Light cylinder
E// localized Outer gap
The outer gaps steadily create pairs with E// kept just above E> Ec . The proof of OG.
Particle distribution and motion Strength of E//
Pair creation
Rotation axis
Magnetic neutron starCurrent sheet begins to form.
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Pola
r cap
Global current in the meridional plane(do not forget plasma rotating and Bφ<0)
Slot
gap
Outer gap
Return current
Current-neutral dead zone
Dead zone
Fast rotation andEmition in φ-direction
Outward current ( r )
Radiation reaction force (φ )
Magnetic field (θ)Magnetic neutron star
Rotation axis
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Light cylinder
E/B mapE>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
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Light cylinder
E/B map
磁気リコネクション
Umizaki et al. 2010
E>B(break down of the ideal-MHD cond.), when we look at the inside of the current sheet.
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Summary1. 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.
2. Due to radiation reaction force, some particles escape through the closed field lines.
3. 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
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Ω
Magnetic axis
Thick windNeutral sheet
Magnetic Reconnection
Pulsar aurora
Rotation axis
Lig
ht
cylin
der
Outer gap
Polar cap
Slot gap
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1. EMF and charge separation
Unipolar Induction
Basic properties of the pulsar magnetosphere
Motional field
As compared with required charge separation, plasma source is limited gap E//
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Goldreich-Julian model (1969)
In reality, plasma is extracted from the stellar surface by E//: maybe, complete charge separation
Positive space charge
Negative space charge
Corotation speed becomes the light speed
Relativistic
centrifugal wind
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Goldreich-Julian model (1969)
Strong charge separation in a rotating magnetosphere makes the gap, non-zero E//
Positive space charge
Negative space charge Null c
harge surfa
ce
Gap formation
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SED(spectral energy density plot)
magnetospheric
Nebula
2. Pulsar Wind Lwind=ηw Lrot
Aharonian, F.A. & Atoyan, A.M., 1998
Unpulsed emission
Pulsed emission
E// + e/p
BB 加熱
E // 加速
IC
sync
RL=c/Ω
Rs=(Lwind/4πPext)^1/2
Vacc=RL*BL=μΩ^2/c^2
Vacc=Rs*Bn with Pext=Bn^2/8π
keVGeV
TeV
垂直衝撃波加速の困難
1. High Energy Pulses1. High Energy Pulses3. Radio Pulses
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