Particle simulation forRotating White Dwarf magnetosphere

The 13th Marcel Grossmann Meeting at Stockholm 2012 1 July (Sun.) - 7 July (Sat.), 2012

Tomohide Wada*Center for Computational Astrophysics., National Astronomical Observatory Japan

Kotaro FujisawaUniversity. Tokyo

email: tomohide.wada @ nao.ac.jp

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Outline of presentationGM13th@Stockholm

1. Rotating magnetized star(for simplicity, we treat isolated case)2. Aim of study3. Outline of particle simulation(method)4. Results5. Summary

How does pulsar(conventionally, believed magnetized rotating NS) accelerate plasma?Is there any candidates except for neutron star?

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Axisymmetric steady model

Rotating manetized star (conductive sphere) become unipolar dynamo. Induced E pushes out plasma from the surface.We can follow Jackson’s Gedankenexperiment (Jackson 1976 ApJ) with particle simulation.

: positive charge: negative charge: magnetic field line: electric field line

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It’s a just only rotating magnetized star in vacuum

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mag

netic

fiel

d lin

e

Magnetized rotating starGM13th@Stockholm

Magnetized rotating star become unipolar dynamo!

light

cyl

inde

r

magnetic surface

dead zone(static electrosphere)

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Curvature radiation & Pair cascadingGM13th@Stockholm

magnetic field line

acceleratingelectric field

guiding centerof electron

curvature radius

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Death lineGM13th@Stockholm

magnetosphere

White dwarf

e+e-

gamma-ray

rotation period (P)

surfa

ce |B

|

To maintain activity,

active magnetosphere(pulsar wind & gamma-ray beam)

quiet magnetosphere

Death linemean free path of gamma-ray

e.g., Kashiyama 2011 PhRvD

Bdip

Bquad

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Motivation of our studyGM13th@Stockholm

Bdip, Equad

rotation &magnetized axes

electric field line

Bquad, Eocto

magnetic field line

Bquad, R0=106cmBdip, R0=106cmBquad, R0=109cmBdip, R0=109cm

young NSmillisecond PSRhigh B WD(B0=108gauss, P=100sec)

gamma-ray

EUVE J0317 855AE Auarii

If multipole stellar magnetic field is considered, it can maintains pair creation with larger P.

How are plasmas accelerated in WD’s magnetosphere? ->We use particle simulation to investigate the magnetosphere in case of low density plasma.

Bquad case

Bdip case

NS; R0=106cm

WD; R0=109cm

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Basic equations(with steady condition)

B.C.Elec

tric field

E//gamma-rayradiation

drag forceB

B

BijEij

Static electro-magnetic interaction is calculated by special purpose programmable computer, GRAPE-DR.CfCA web site: http://www.cfca.nao.ac.jp

positive charge

negative charge

Equation of motion(3D)

To obtain steady solution, we solve Maxwell’s equations in steady state and EOM iteratively.

Mag

netic

field

guiding center of particleB.C.

; quadrepole+monopole+octopole

; dipole+quadrupole

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Outline of particle method

1. calculate surface charge density2. replace surface charge density with simulation particle3. calculate fields (stellar field plus field by space charge and current) at the position of particle and solve equation of motion for each particles4. delete particle outside of the outer boundary5. repeat 1-4 until steady state is obtained

1 2 3

positive charge

negative charge

magnetic field line(magenta curves)

We obtain the steady magnetosphere•without pair creation(Bdip, Bquad)•with pair creation

<-current work<-future work

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ResultGM13th@Stockholm

Bdip<Bquad

magnetic field line

light cylinder

equatorial plane

If pair plasma is suppressed and Bquad is dominant near the star rather than Bdip,

accelerating region

(E// remains)

•asymmetric stellar field(Bp, induced Ep) •(quasi-)static electrosphere, no wind•asymmetric accelerating region on both sides of equatorial plane(see, right panel)

•the number of returning plasma might differ in the north and south hemisphere

->It makes asymmetric Polar Cap?

poloidal plane

: positive charge: negative charge

light

cyl

inde

r

3D-distribution of particles in 1 rotation periodBdip+Bquad case

inte

nsity

of E

//

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Effect of pair creation Before talking about summary, I show that the effect of pair creation in our previous model. It would be useful to explain our future work.We had carried out particle simulation for axisymmetric pulsar magnetosphere although then we only treated dipole magnetic field in previous model. It is a steady solution with pulsar wind and accelerating regions in middle latitude.Although we consider NS’s magnetosphere, we expect to obtain same result in WD’s magnetosphere.

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Overview of our particle method

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SummaryGM13th@Stockholm

E//path of

gamma-ray

electron

Multipole B field modifies the structure of static electrosphere(compared with Bdip case). We demonstrated particle simulation for isolated axisymmetric WD’s magnetosphere. If pair cretion is suppressed,1.Static asymmetric electrosphere is obtained2.Asymmetric accelerating region(should be pair

creating region if Bdip+Bquad) around equatorial plane

In future work, we will carry out the simulation taking account for pair creation(e.g., see, right panel) from the present result. And, then static electrosphere will be changed drastically.The simulation had just started. It is still ongoing now...

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Acknowledgement

FOUR-DIMENSIONAL DIGITAL UNIVERSE PROJECT

I would like to thank Hiroyuki Takahashi, Syota Kisaka, Kotaro Fujisawa for insightful suggestion and fruitful discussion. I am grateful for all the help and discussion for everyone in the workshop. Numerical simulation and visualization of the result were carried out on system at Center for Computational Astrophysics(CfCA), NAOJ and supported by Four-dimensional digital universe project(4D2U), NAOJ.

-CfCA: http://www.cfca.jp-4D2U: http://www.4d2u.nao.ac.jp/

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End

Thanks

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