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 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

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//

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

What magnetospheric models to explain pulsed emission?

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

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.

E// (field-aligned acceleration)

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

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

- 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

Particle simulation

part

icle

code

―

acceleration

Gamma-ray―

―

radiation from the starStrong B

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

• 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.

- 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

Results

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.

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

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

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.

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

Ω

Magnetic axis

Ｔｈｉｃｋ　ｗｉｎｄNeutral sheet

Magnetic Reconnection

Pulsar aurora

Rotation axis

Lig

ht

cylin

der

Outer gap

Polar cap

Slot gap

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 c

harge surfa

ce

Gap formation

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