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Linear Acceleration Emission in Radio Pulsars
Mohammad Rafat School of Physics University of Sydney Supervisors: D. B. Melrose and Q. Luo


Outline
Pulsars: basic introduction Pulsar magnetosphere: vacuum model, corotating model, oscillating model Pulsar Emission: radio (coherent), high energy (incoherent) Linear Acceleration Emission


Common cartoon

(Wikipedia)


Magnetosphere models
Vacuum model:
magnetic dipole radiation in vacuum

Corotating model:
magnetosphere populated by corotating plasma

Unacceptable features present in both models Standard models borrow features from both models


Vacuum electric field
Interior of a neutron star is an excellent conductor, = Ohm's Law, J = [E + ( в x) в B], in corotating frame inside the star implies E = 0 In an inertial rest frame inside the star E = - ( в x) в B Boundary conditions imply a nonzero charge density at the surface of the star Ez = 0 along B above star


Vacuum Model
Vacuum field can accelerate charges to cause pair cascade
no longer vacuum

Magnetic dipole radiation in vacuum at frequency



transverse wave cannot propagate below plasma frequency

EM torque due to escaping radiation causes alignment of magnetic and rotation axes
not observed


Corotating Model
A corotating electric field, E = - ( в x) в B, must be present everywhere Corotation speed exceed speed of light beyond light cylinder Separate magnetosphere into closed and open regions
(Sturrock 1971)

A minimum charge density, GJ = 0 · E, required to maintain corotation (Goldreich & Julian 1969)


Pair Formation Fronts

GJ

= 0 (-2 · B + в x ·

в B)

GJ can be set up by Ez , resulting in charge-limited outflow Additional source of charge required to maintain Deviations from
GJ GJ

leads to a (vacuum) `gap'

vacuum-type Ez develops

Particles accelerated resulting in pair cascade Concentrated in narrow range of heights: PFFs.


Oscillating model
Parallel electric field screened above PFF Common assumption: time-independent magnetosphere (Arons & Scharlemann 1979) в B = µ0 J + 1 E c 2 t
ignored

Any mismatch between µ0 J and в B must be balanced by a displacement current This leads to an oscillating model (Sturrock 1971)


Large-amplitude oscillations
Numerical solution of one dimensional equations (fluid, continuity, Maxwell's)

(Levinson et al. 2005)


Large-amplitude Electrostatic Wave
Outward propagating superluminal large-amplitude electrostatic waves (LAEW)

(Luo and Melrose 2008)


Pulsar Emission
Radio emission: Tb > 1025 K = coherent Coherent mechanisms
curvature emission by bunches (localization in p & x) reactive instability (localization in p) maser (negative absorption)

LAE is a maser mechanism (Melrose 1978) High energy emission: synchrotron, IC and RIC
(Melrose 2004)


Procedure
Integrate dp µ ( ) = qF d to obtain u µ ( ) and x µ ( )
µ

( ) u ( )

Fourier transform the current density


J (k ) = q
-

µ

d u µ ( ) e

ikx ( )

Power radiated per unit frequency per unit solid angle (k ) = 2 1 |e (k ) J µ (k ) |2 3 c 3 µ T 16 0


LAE in LAEW
Characteristic maximum frequency of the LAE is 3/2 2 c max p max For 106 s -1 and max 106 - 107 we have c 1018-20 s -1 LAE may explain pulsar emission up to hard X-rays, but not -rays. Power spectrum
4/3

at



c

(Melrose, Rafat & Luo 2009; Melrose & Luo 2009)


LAE in other fields
Particle
in a constant electric field; in a waveform describing a double layer; and undergoing simple harmonic motion
2 Characteristic cutoff frequency c max

Power spectrum is flat for electric field
(Reville & Kirk 2010)

c for constant


Summary
An oscillating model is more realistic for pulsars LAE may explain pulsar emissions up to hard X-rays LAE is implausible as a -ray emission mechanism High frequency spectrum not very sensitive to waveform, however, low frequency emission is sensitive Future work: detailed investigation of applicability of LAE to to radio emission and also high energy emission


Thank you