Pulsar Emission Models

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Pulsar Emission Models
Alice Harding
NASA Goddard Space Flight Center
2
Force-free magnetosphere
Goldreich Julian 1969

• In vacuum E gtgt Fgrav at NS surface
• Vacuum conditions (Deutsch 1955) cannot exist!
• If charge supply creates force-free conditions,
• Goldreich-Julian charge density
• Corotating dipole field
• NO particle acceleration

3
Possible sites of particle acceleration
Ideal MHD in most of magnetosphere
Deficient charge supply acceleration
Solve Poissons Eqn
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Accelerators and global models
Accelerator gaps
Global currents
Charges (ee-)
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Polar Cap Pair Formation Front (SCLF)
e-

• Curvature radiation pair front
• complete screening

e

• Inverse Compton scattering pair front
• incomplete screening

Closed field region
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Slot gap model

• Pair-free zone near last open field-line
• (Arons 1983, Muslimov Harding 2003,
  2004)
• Slower acceleration
• Pair formation front at higher altitude
• Slot gap forms between conducting walls
• E acceleration is not screened

SR
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Which pulsars have slot gaps?
Harding Muslimov 2002
Only the younger pulsars above the death line for
production of curvature radiation pairs will have
SLOT GAPS
SLOT GAPS
NO SLOT GAPS Pair starved
Older pulsars below the death line for production
of curvature radiation pairs will have unscreened
E and NO SLOT GAPS
?
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Polar cap pair cascades
Magnetic pair production Threshold eth
mc2/sinq Spectral attenuation is
super-exponential
SR
CR
ICS
kT
Mp 102 - 105
Mp lt 10

• Daugherty Harding 1982
• Zhang Harding 2000
• Sturner Dermer 1994
• Hibschmann Arons 2001

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Pair production spectral cutoff
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Measuring spectral cutoffs
Super-exponential (PC) or exponential cutoff (OG)
?
Is there a real EC vs. B0 trend?
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Vela Phase-averaged spectrum
Consistent with b1 (simple exponential)
b2 (super-exponential) rejected at 16.5s
No evidence for magnetic pair attenuation Near-su
rface emission ruled out
Abdo et al. 2009
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Fermi pulsars what have we learned?

• Young pulsars
• Majority have double g-ray peaks with phase
  separation 0.2 0.5
• g-ray peaks are not aligned with radio peak(s)
• g-ray beams are must larger that radio beams
• Spectra are power-laws with simple exponential
  cutoffs
• High-energy emission comes from the outer
  magetosphere
• Millisecond pulsars (C. Venters talk)
• most g-ray peak(s) lag radio peak(s)
  pair screening OG/SG gap emission
• some g-ray peak(s) lead radio peak(s)
  pair-starved polar cap emission

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Relativistic Effects

• Aberration
• Time-of-flight delays
• Magnetic field retardation

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Caustic emission
Morini 1983, Romani
Yadigaroglu 1995

• Particles radiate along last open field line from
  polar cap to light cylinder
• Time-of-flight, aberration and phase delay cancel
  on trailing edge emission from many
  altitudes arrive in phase caustic peaks
  in light curve

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Formation of caustics
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Formation of caustics

• Emission on trailing field lines
• Bunches in phase
• Arrives at inertial observer simultaneously

• Emission on leading field lines
• Spreads out in phase
• Arrives at inertial observer at different times

• Caustic emission
• Dipole magnetic field
• Outer edge of open volume

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Elba caustics
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Sky distribution of intensity
a 300
a 600
a 900
Slot gap
Observer angle
Outer gap
Phase
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Slot gap and outer gap geometry
Slot gap
Dyks Rudak 2003 Dyks, Harding Rudak 2004
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Slot gap and outer gap geometry
outer gap
Romani Yadigaroglu 1995 Cheng, Ruderman Zhang
2000 Dyks, Harding Rudak 2004
No off pulse emission in traditional OG model
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Slot gap particle acceleration and radiation
Resonant absorption of radio photons
when (Lyubarski Petrova 1998)
W
ee- pairs
primary e-
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Crab pulsar Model profiles
a 450, z 1000
Harding et al. 2008
X-rays from pairs
g-rays from primaries
Observer Angle z
Radio cone emission
Phase
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Phase-averaged spectrum
Harding et al. 2008
Fermi
Correlations with radio variability only below
200 MeV
Primary CR
Pair SR
Primary SR
Simple exponential cutoff of CR spectrum
Kuiper et al. 2000
Primary ICS
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(New) Outer gap model
Hirotani 2006, Takata et al. 2006
Outer gap exists below the null surface visible
emission from both poles More like extended slot
gap!
Improved profile for Crab
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Outer gap model spectra
Crab pulsar
Takata et al. 2007
Primary ICS
Primary CR
Pair SR
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Emission from a striped pulsar wind
Kirk Petri 2005
Assumed size of dissipation region
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What we can learn from phase-resolved spectroscopy

• Fermi will be able to measure spectral index and
  exponential cutoff vs. phase for the bright
  pulsars
• Outer magnetosphere models map phase to emission
  radius and radius of curvature
• Can map particle acceleration energy and electric
  field with emission radius
• Potentially very powerful model discriminator

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Magnetic field lines projected in observer angle
vs. phase plane
TPC
Outer gap
Phase
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Emission radius vs. phase in SG and OG models
Dyks, Harding Rudak 2004
In both SG and OG models, emission at each phase
comes from small radius range
See also Cheng et al. 2000
Maximum emission radius
Minimum emission radius
Romani 1996
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Emission radius vs. phase for other a and z
1.0
z 60o
0.8
z 70o
0.6
r/rLC
0.4
0.2
0.0
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Mapping particle energy to emission radius
Continuous acceleration in gap -gt particles
reach radiation reaction limit

• Balance CR losses with acceleration gain
• Steady-state Lorentz factor
• Curvature radiation peak energy

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Vela energy dependent profiles

• P3 shifts to higher phase with energy
• P1/P2 decreases with energy
• Explained in slot gap model if
• and E r1/2 decreases with r/rLC

Emission radius lt 0.95 r/rLC
lt 0.8 r/rLC
lt 0.6 r/rLC
Abdo et al. 2009
Energy dependence of light curves map
acceleration in magnetosphere!
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Peak separations and radio lags
Watters et al. 2009
Good model discriminator
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Global models
Contopoulos, Kazanas Fendt 1999
Force-free electrodynamics
everywhere No accelerator gaps!
a 00
Spitkovsky 2008
a 600
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Global currents
Timokhin 2007
Pair cascade (assumed) current
Global current solutions
They dont match!
Timokhin 2006
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Toward a self-consistent magnetosphere

• Can PC pair cascades generate global currents and
  screen E?
• If not, allow component of in
  global model
• Check output profiles, spectra with 3D radiation
  model

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Predicted Fermi pulsar populations
Gonthier et al. 2007 Jiang Zhang 2006 Story et
al. 2007
Few radio-loud pulsars for high-altitude
accelerators
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Summary

• We are finally answering fundamental questions of
  g-ray pulsar astrophysics but raising new ones
• High-energy emission comes from outer
  magnetosphere
• Most millisecond pulsars have narrow gaps
  screening of E
• High magnetic multiples near surface?
• Higher E (higher masses, more compact NS)?
• Fermi has so far detected about 48 g-ray pulsars
  - including ms pulsars many radio-quiet more
  to come!
• Ratio of radio-loud/radio-quiet pulsars
  discriminates between high and low altitude
  accelerators
• Measurement of light curve parameters for many
  pulsars
• Phase-resolved spectroscopy of more sources