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
GM13th@Stockholm
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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
GM13th@Stockholm
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
GM13th@Stockholm
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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
GM13th@Stockholm
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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.
GM13th@Stockholm
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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/
GM13th@Stockholm
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End
Thanks
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