Axisymmetric Pulsar Magnetosphere with Particle Method III: Dipole - - PowerPoint PPT Presentation

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Axisymmetric Pulsar Magnetosphere with Particle Method III: Dipole - - PowerPoint PPT Presentation

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Axisymmetric Pulsar Magnetosphere with Particle Method III: Dipole and Quadrupole magnetic field case Tomohide Wada* ( National Astronomical Observatory Japan ) Kotaro Fujisawa ( University of Tokyo ) Shinpei Shibata ( Yamagata university )

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SLIDE 1

Axisymmetric Pulsar Magnetosphere with Particle Method III:

Dipole and Quadrupole magnetic field case

Tomohide Wada* (National Astronomical Observatory Japan) Kotaro Fujisawa (University of Tokyo) Shinpei Shibata (Yamagata university)

email: tomohide.wada @ nao.ac.jp

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 2

Rotation powered pulsars

Crab nebula: image credit: NASA

Pulsar exists inside the nebula as a central engine. The rotational energy of star is released by radiation & plasma. Pulsar is identified highly magnetized(1012G) and rapidly rotating(P<1sec) neutron star and one of the brightest source of gamma-ray. electron

pulsar magnetosphere synchrotron nebula

positron Pulsar wind ～ Lsd

accelerated plasma(Lorentz factor=107)

Gamma-ray beam < 10% of Lsd

Lsd; spin down luminosity

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 3

Outline of presentation

  • 1. Axisymmetric magnetosphere model
  • 2. Effect of Quadrupole B field
  • 3. Outline of particle simulation(method)
  • 4. Results
  • 5. Summary

How does pulsar release the rotational energy by accelerated plasma and HE-radiation? Fermi observation has been important for pulsar.

Outer gap, Slot gap, Polar cap.... How are the gap(s?) formed?

higher order component of poloidal magnetic field

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 4

Dipole & Quadrupole B field

Kojima Y & Kisaka S MNRAS 2012; Evolution(decay) stellar magnetic field by hall drift effect →Possibility of multipolar poloidal B(higher order of dipole) field dominant phase.

Suppose axial symmetry & steady condition, analytical vacuum solution of B is given by

B.C.

magnetic field line e l e c t r i c fi e l d l i n e Neutron star

Dipole; term B1 Quadrupole; term B2

Bn; surface field intensity at pole R0; stellar radius θ; colatitude r; radius of spherical coordinate Pn; Legendre polynomial function P1n; Associated Legendre polynomial function Rotating magnetized star induces unipolar electric field. Pulsar is one of the greatest accelerator of plasma.

equatorial plane

Anti-symmetry to equatorial plane Symmetry to equatorial plane

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 5

Dipole + Quadrupole B field case

Quadrupole B dominant case; B1=2B0

polar cap

+

dipole Quadrupole

Magnetic stream function in spherical coordinate This function is constant along a B line, and then

; light radius

last closed line Polar cap radius

Quadrupole B field changes the area of polar cap

～

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 6

Magnetic neutral region(MNR)

  • NS of dipole case is

modified and another NS is added

  • MNR above the south

pole → not magnetized region

maybe Eperp acceleration?

null surface; dipole case null surface

Suppose force-free condition and consider only inside light radius, Goldreich-Julian space charge density is given,

  • > null surface(NS)

Bquad>Bdip Bquad<Bdip

B field intensity on poloidal plane B fi e l d l i n e ; B

d i p

+ B

q u a d

equatorial plane Goldreich-Julian space charge density

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 7

Pulsar magnetosphere

Acceleration Radiation Pair creation

  • Eparallel acceleration
  • Eperp acceleration(if it is needed)
  • drift motion
  • inertia
  • radiation drag
  • magnetospheric charge & current

modifies stellar EB field

  • magnetic dissipation(recconection)
  • Bremsstrahlung

(Curvature radiation; CR)

  • Synchrotron radiation
  • Inverse Compton scattering
  • Magnetic pair creation process

hereafter, B-gamma

  • Photon collision process

hereafter, X-gamma

To understand the structure of pulsar magnetosphere, we have to solve below effects at once.

For simplicity, we treat only CR photon by primary accelerated plasma in present case.

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 8

Outline of our particle method

  • 1. calculate surface charge density
  • 2. replace surface charge density with simulation particle
  • 3. calculate fields (stellar field plus field by space charge and current) at the

position of particle and solve 3-D equation of motion for each particles

  • 4. Gamma-ray photons by CR are estimated by E// and converts into e+e-(X-

gamma collision)

  • 5. delete particle outside of the outer boundary
  • 6. repeat 1-5 until steady state is obtained

1 2 3

positive charge negative charge magnetic field line (magenta curves)

Solving static fields and motion of particle iteratively, we finally obtain the steady magnetosphere.

4

gamma-ray emitting region (yellow volume)

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 9

Solving acceleration

To solve pulsar equation, some constraint or boundary condition is imposed at light cylinder. Usually, it is difficult to solve.

Axisymmetric force-free model

  • axial symmetry
  • steady condition (time independent)
  • Particle method with axisymmetric model

Because of solving EOM, the nature at LC is determined by basic eqs. And therefore, it has no singular surface at light cylinder. But it usually needs a large computational time. + maxwell’s eqs

  • >

light cylinder singular surface

We gave up to find analytical solution...

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SLIDE 10

Basic equations(with steady condition)

B.C. Electric field

E//

gamma-ray radiation drag force

B B Bij Eij

positive charge negative charge

Equation of motion(3D) To obtain steady solution, we solve Maxwell’s equations in steady state and EOM iteratively.

Magnetic field guiding center of particle B.C.

; stellar field stellar fields(2D)+magnetospheric field(3D) ; stellar field ; field by particle ; field by particle

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SLIDE 11

Radiation model

～105yr ～103yr Thompson 2004

ρ,j,E,B nγ,εγ

energy spectrum of various age pulsar

  • > time evolution of spectra

Young PSR

  • CR, SR, IC
  • > complicated system

Old PSR(but may emits gamma-ray)

  • CR, SR, IC
  • > might be simple system

For simplicity, we treat only CR process and the gamma-rays

SR

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SLIDE 12

Treatment of pair creation

X-gamma

; c

  • l

l i s i

  • n

a n g l e

; Thomson cross section

B-gamma

;perpendicular component

  • f magnetic field for

propagating direction of gamma-ray emitting region E//>Ecr

If photon moves

  • ut numerical outer

boundary(10Rl), it removed.

  • uter boundary

1 1 1 2 2 3 4

gamma-ray photons

lp

numerically, mean free path is estimated with lp x f, where f is robability distribution function given by random number

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SLIDE 13

Overview of result

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 14

Result; Bdip case

+charge

  • charge

time normalized by rotation period

Our particle method reconstruct gaps & wind steady solution

particle distribution on poloidal plane

Cheng K S et al ApJ 1987b Outer gap model This is a conventional model for acceleration of plasma main source of plasma is gap in middle latitudes

similar structure

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 15

time normalized by rotation period

+charge

  • charge

light cylinder

Result; Bdip & Bquad case

charge distribution on poloidal plane OG OG dead zone d e a d z

  • n

e dead zone d e a d z

  • n

e e+ e- Main source of plasma is also outer gaps, It is a same global feature (wind & gaps) in previous work (e.g., WS2011)

But the system had not become perfectly steady, It needs more calculation time. rotation period/2 months

Preliminary result!

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 16

light cylinder

last closed line

Asymmetry of Available Voltage

colatitude (degree) Open field line voltage in force- free limit with dipole case Available maximum voltage in force-free limit with Bdip+Bquad case Different potential drops are obtained!

dead zone 1 dead zone 2

d e a d z

  • n

e 1

dead zone 2

light cylinder neutron star

  • pen zone 1
  • pen zone 2

dead zone

north-pole south-pole

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

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SLIDE 17

Summary

We demonstrated the particle simulation for axisymmetric pulsar

  • magnetosphere. Steady outflow of accelerated plasma & local accelerating

regions(in middle latitudes)

The effect of quadrupole stellar magnetic field

  • 1. Asymmetry of Charge & Current distribution around the

equatorial surface, especially in the vicinity of star.

  • 2. If Bquad become dominant, MNR & another dead zone is

formed.

In the future work, we will try to taking account to magnetic pair creation process, and then

  • Super GJ-space charge density

region formed around MNR?

  • r Eperp acceleration?
  • asymmetric beam radiation from

north and south hemisphere.

2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

テキスト

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SLIDE 18

Acknowledgement

FOUR-DIMENSIONAL DIGITAL UNIVERSE PROJECT

I would like to thank Syota Kisaka and Junpei Takata for insightful suggestion and fruitful discussion. And 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).

  • CfCA: http://www.cfca.jp
  • 4D2U: http://www.4d2u.nao.ac.jp/
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SLIDE 19

End

Thanks!

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SLIDE 20

It costs 5N2 calculation (N; number of particle).

  • > calculate them with super computer.

star is assumed to be perfect conductive sphere

Solution of field by particles

The static fields by particles around conductive sphere (star) are determined by superimposition of Green function, which is analytical solution.

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SLIDE 21

Particle in Cell method

Equation of motion

PIC is one of the best method to solve the problem. It solves Maxwell’s eqs & EOM simultaneously, and therefore time-dependent solution is obtained. To resolve the local accelerating region in global structure, it need large number of grids (cells) and therefore, it is too difficult to carry out.

  • > We use more simple form for steady solution.

maxwell’s equations

  • q

+q E B

fields are defined on grid

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SLIDE 22

c u r r e n t v e c t

  • r

m a p

  • n

e q u a t

  • r

i a l p l a n e light cylinder e q u a t

  • r

i a l p l a n e rotation axis dipole magnetic field line p

  • l
  • i

d a l p l a n e light cylinder poloidal toroidal current poloidal field toroidal field distorted magnetic field line light cylinder rotation axis e q u a t

  • r

i a l p

  • l
  • i

d a l p l a n e

Result: structure of magnetic field

Bdip+Bmag(B-gamma) pure dipole Bdip+Bmag(X-gamma)

magnetic field line

  • n poloidal plane

light cylinder

  • stellar magnetic field is modified by magnetospheric current
  • >structure of gap is changed
  • >open field encourages outflow of particle

While many part of poloidal magnetic surface is closed in our low plasma number density model, poloidal current can be possible.

The motion traversing magnetic surface is caused by

  • fradxB drift
  • Electric field dominant region around the equatorial plane in

the vicinity of LC (explain next slide) last close line of dipole field