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

Introduction Pulsars

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

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

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

What magnetospheric models to explain pulsed emission?

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

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

E// (field-aligned acceleration)

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

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

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.

Particle simulation

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

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

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

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.

Results

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

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）

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

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

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

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

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//

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)

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)

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