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

Introduction Pulsars

Neutron Star about 1M_sun 10km in size Pulsars: B_d ～ 10^9 – 10^13G P ～ 1.5msec – several seconds Emf ～ 10^14 Volt rotation powered pulsars Magnetars: Small subclass of magnetic neutron stars magnetic active regions with B ～ (maybe)10^15G Emf ～ 10^14 Volt magnetic powered pulsars

Rotation axis Pulsar Wind (relativistic outflow of magnetized plasma γ ～ 10^6) Size of the magnetosphere: c/Ω ～ 4.8×10^4 R_ns 1 ly Beamed radiation Observed as pulsed radiation

SED (spectral energy density plot) magnetospheric Nebula 2. Pulsar Wind L wind =η w L rot Aharonian, F.A. & Atoyan, A.M., 1998 Unpulsed emission Pulsed emission E// + e/p BB 加熱 Ｅ // 加速 ＩＣ sync R L =c/Ω R s =(L wind /4πP ext )^1/2 V acc =R L *B L =μΩ^2/c^2 V acc =R s *B n with P ext =B n ^2/8π keV GeV TeV 垂直衝撃波加速の困難 1. High Energy Pulses 3. Radio Pulses

E// (field-aligned acceleration)

Roation × magnetization makes emf  charge separation Unipolar Inductor E ⊥

If pair creation is suppressed, charged particles are emitted from the neutron star and forms steady clouds.

Particle Simulation for the screening. (ref. Wada and Shibata 2003) gap The gap is unstable against pair creation.

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//

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

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

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

Ω B Dead zoneNull 面 Light cylinder Polar cap Slot gap Outer gap Closed field (dead zone) Open field region γ -ray pulse shape and relation to radio pulses are well explained if γ from OG and radio from PC Two-pole caustic (TPC) geometry (Dyks & Rudak, 2003) Radio pulse Models based on observatons: PC, SG, OG

Particle simulation

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 ― ― radiation from the star Strong B

Particle code Particle motion and the electromagnetic fields are solved iteratively for the axis-symmetric steady solution. Emf is included in the BC For the EM field For the particle motion

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

- 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: seteadily pairs are created in the magnetoschpere and lossed as the wind. Particle creation and loss

Result

Modificaton of the magnetic field Light cylinder Outer gap The outer gaps steadily create pairs. Gap electric fileld is kept above Ec as to create pairs. Particle distribution and motion Strength of E// Pair creation Not so strong: limitation of particle number

Polar cap current circulation seen Slot gap Outer gap Outward current Retun current Current-neutral dead zone Dead zone

Light cylinder E/B map E>B Bread down of the ideal-MHD cond. 磁気リコネク ション

Summary and Discussion 1.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. 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 possibility of 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 -Termination shock of the pulsar wind

Ω Magnetic axis Ｔｈｉｃｋ ｗｉｎｄ Neutral sheet Magnetic reconnection パルサーオーロラ Rotation axis Light cylinder Outer gap Polar cap Slot gap

SED (spectral energy density plot) magnetospheric Nebula 2. Pulsar Wind L wind =η w L rot Aharonian, F.A. & Atoyan, A.M., 1998 Unpulsed emission Pulsed emission E// + e/p BB 加熱 Ｅ // 加速 ＩＣ sync R L =c/Ω R s =(L wind /4πP ext )^1/2 V acc =R L *B L =μΩ^2/c^2 V acc =R s *B n with P ext =B n ^2/8π keV GeV TeV 垂直衝撃波加速の困難 1. High Energy Pulses 3. Radio Pulses