Pulsar Magnetosphere

1
Pulsar Magnetosphere
Theoretical Astrophysics Seminar

• Xuening Bai
• Dept. of Astrophysical Sciences

2
Outline

• A Quick View
• Qualitative Approach
• Pulsar Equation
• Oblique Rotator
• Radiation Mechanism
• Open Problems

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A Quick View
4
A Quick View

• Beam radiation
• Magnetic dipole
• Energy loss (vacuum)
• Spin down
• Braking index

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A Quick View

• Characteristic Age
• B determination
• Rotation-powered
• Accretion-powered
• Magnetar

Pulsar Zoo
Time evolution
(Manchester 2004)
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Qualitative Approach
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Vacuum or Not?

• Unipolar induction
• Aligned rotator
• Magnetic dipole field -gt
• Electric quadrupole field
• does not vanish outside
• Strong Electric field up to

-gtCannot be surrounded by a vacuum!
(Goldreich Julian 1969)
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Basic Assumption

• Aligned rotator (axisymmetry)
• Steady state
• Perfect conduction, no resistivity (ideal MHD)
• Electromagnetic force dominated (particle
  iner-tia and thermal pressure ignored)
• Magnetic lines are equipotentials

Plasma supplied either directly by NS surface or
by further pair production and cascade Near zone
/ wind zone / boundary zone
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Near Zone

• Charged particles move along B line
• G-J charge density
• Modification to poloi-dal magnetic field

Charge separation is assumed
(Goldreich Julian 1969)
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Wind Zone

• Poloidal fields asy- mptotically radial
• Toroidal field
• dominate
• Charges escape radially
• Current closed in the boundary zone

(Goldreich Julian 1969)
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Energy loss Spin down

• Braking torque
• Energy loss through Poynting flux
• Spin down rate
• Losing energy electromagnetically. Plasma plays
  an essential role!

An aligned rotator surrounded by plasma spins
down!
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Pulsar Equation
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Pulsar Equation

• In cylindrical coordinates, introducing the flux
  function 1 such that
• where is an unknown function (current
  function).
• Force-free condition can be reduced to
• where
• Singularity at the light cylinder
• Uncertainty of
• Aim Solve the PDE with dipole boundary
  condition, smoothly cross LC with a consistent
  current function.

(Michel 1973a)
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Early Attempts
Self-consistent Monopole solution
No current No spin down
(Michel 1973a,b. Figure from Contopoulos et al.
1999)
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First solution
Asymptotic monopole solution at large radius

• Critical condition
• Iterative method
• Self-consistent dipole field
• Spin down rate

Current
Separatrix
Return Current Sheet
No toroidal field
(Contopoulos et al. 1999, Gruzinov 2005)
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Other possibilities
Different locations of Y-point
(Spitkovsky 2006)
(Timokhin 2006)
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Oblique Rotator
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Force-free Electrodynamics

• Magnetosphere filled with plasma
• (through pair production)
• Flux-freezing-gtRelativistic MHD
• Strong Field plasma inertia and pressure
  unimportant -gtForce-free Electrodynamics
• Solve dynamics of fields instead of plasma motion

(Blandford 2002)
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Numerical Simulation
Magnetic field configu-ration for an oblique
rotator
Energy loss
Y-Point
current sheet
(Spitkovsky 2006)
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Radiation Mechanism
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Radio emission profile
(KarastergiouJohnston 2007)

• Narrow beam radiation
• Core and Cone components
• Highly polarized (coherent)
• Drift of subpulses
• Frequency dependent profile

(DeshpandeRankin 1999)
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?-ray emission profile
Properties of ?-ray pulse

• Widely separated two peaks
• Phase offset be- tween radio and ?-ray pulses
• Incoherent
• Cutoff at tens of GeV

(Thompson 2004)
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General consideration

• Emissions originate from particle acceleration in
  gap regions with ( starvation of
  charge to meet G-J charge density )
• Polar Cap
• Polar surface region
• Slot Gap
• Narrow region along
• last open field line
• Outer Gap
• Region between the
• null surface and LC

(Hirotani 2006)
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Radiation Mechanism

• Radio emission
• Generated from polar cap region
• Related to two-stream plasma instability
• Plasma waves trap and propagation
• Gamma-ray emission
• Originated from curvature and IC radiation
  of electrons and positrons in gap regions
• Still far from well understood!

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Theory vs. Observation

• Magnetic field configuration
• Radiation mechanism
• Predicted emission profile, spectrum and
  polarization
• Compare with observation

• Up polar cap shape of a retarded dipole
• Middle observed ? ray profile
• Bottom fitted profile

(Dyks et al. 2004)
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Open Problems

• Emission mechanism
• Idealization of numerical simulation
• The physics of Y-point
• Reconnection
• Gaps and particle acceleration
• Braking index
• Age dependence
• ......

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References

• Arons J., 2007, arxiv0708.1050
• Contopoulos I. et al., 1999, ApJ, 511, 351
• Dyks J. et al., 2004, ApJ, 606, 1125
• Goldreich P., Julian W. H., 1969, ApJ, 157, 869
• Grenier I. A., Harding A. K., 2006, AIPC, 861,
  630
• Gruzinov A., 2005, PRL, 94, 021101
• Hirotani K., 2006, ApJ, 652, 1475
• Manchester R. N., Science, 304, 542
• Michel F. C., 1973a, ApJ, 180, L133
• Michel F. C., 1973b, ApJ, 180, 207
• Qiao G. J. et al., 2007, ASPC, 362, 126
• Spitkovsky A., 2006, ApJ, 648, L51
• Spitkovsky A., 2006, astro-ph/0603212
• Thompson D. J., 2004, ASSL, 304, 149
• Timokhin A. N., 2006, MNRAS, 368, 1055