The structure of the pulsar magnetosphere via particle simulation

1. 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

2. Introduction Pulsars

3. 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 Magnetars: Small subclass of magnetic neutron stars magnetic active regions with B～ (maybe)10^15G

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

5. keV SED(spectral energy density plot) GeV TeV Pulsed emission magnetospheric Size: RL=c/Ω Curvature rad. byＥ// acceleration Emf: Vacc=RL*BL =μΩ^2/c^2 BB Spectrum of beamed emission E// + e/p Unpulsed emission Nebula sync Rs=(Lwind/4πPext)^1/2 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. Models based on observatons: PC, SG, OG Ω B Light cylinder Polar cap Open field region Outer gap Closed field (dead zone) Nullsurface Dead zone Slot gap

8. 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 γfrom OG/SG. Radio from PC Ω B Light cylinder Polar cap Open field region Outer gap Radio pulse Closed field (dead zone) Null面 Dead zone Slot gap Two-pole caustic (TPC) geometry (Dyks & Rudak, 2003)

9. E// (field-aligned acceleration)

10. 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 domesof electrons Magnetic neutron star Equatorial disc with positive paritcles

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

13. Particle simulation

14. 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 includedin 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. 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. Light cylinder E/B map 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. 磁気リコネクション 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

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

25. 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. 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. 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=ηwLrot Unpulsed emission Nebula sync Rs=(Lwind/4πPext)^1/2 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