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Pulsar radio emission - oscillating model
M. Verdon, D. Melrose
University of Sydney

10

th

June, 2010


Outline

Problems understanding pulsar radio emission
Magnetosphere model Emission mechanisms

Oscillating model Wave modes
Time-dependence Coupling


What is a pulsar?

rotation axis magnetic axis

polar cap open field line region

closed field line region


Emission models

Production of emission is not well understood Must be a coherent process Variety of proposed mechanisms Most involve time-stationary magnetosphere


Pulsar fields

Rotating magnetic field generates large electric field Particles pulled from pulsar, generate secondary particles Magnetosphere populated with plasma, corotates Goldreich-Julian density to enforce corotation (Goldreich &
Julian, 1969)


Time-stationary models
Pairs produced due to the extremely strong electric field, forming a charge layer to screen the parallel field
(eg Ruderman & Sutherland 1975)
E || E || = 0

primary

e- e- e
+

(Shibata et al, 2002)

e- e+

Steady plasma outflow above the PFF


Problems

Very unlikely to have steady, time-stationary flow (Sturrock
1971)

Initial parallel electric field is inductive, curl E = 0; field from Goldreich-Julian density electrostatic, curl E = 0 Time-stationary models violently unstable (Levinson et al 2005)


Radiation mechanisms

Three basic types (Ginzberg & Zheleznyakov, 1975) Coherent curvature emission N particles I N
2

Emission is from 'bunches' of particles (or solitons), uses changing curvature of pulsar's magnetic field - localization in position and momentum space (Ruderman & Sutherland 1975,
Melikidze, Gil, Pataraya 2000)

Partially screened gap with columns of outflow Problems - bunch formation, back-reaction


Radiation mechanisms

Plasma instabilities Masers - rapid wave growth in some mode due to negative absorption (population inversion) Reactive instabilities - intrinsic growth in a wave, eg two-stream instability (localization in momentum space)


Radiation mechanisms

Appealing to plasma instabilities works only with a high growth rate Most models use a thin beam through a background plasma 1 nb Growth rate ( )1/2 1/2 3/2 (Gedalin et al. 2002) np 2p
b

Beams much less dense, very low growth rates - contrived solutions? (Usov 1987, Ursov & Usov 1988)


Wave growth

Currently favoured theory uses plasma instability to generate waves Growth occurs with certain growth rate in each mode After long time expect radiation predominantly in the faster growing mode, single polarization


OPMs
Observed that emission has (sometimes nearly equal) mixture of two orthogonal modes

PSR B1745-12 (Mitra, Sarala & Rankin)

Polarization is often substantially elliptical


OPMs

Need coupling into two different modes Efficient coupling only near a point where polarization of the modes is changing rapidly Sufficient rapid change occurs only near cyclotron resonance Elliptical polarization also needs cyclotron resonance Waves generated near p , orders of magnitude below c


Problems - summary

Must be coherent, fast enough growth OPMs are hard to generate Time-stationary models unstable


Oscillating model
Introduced as the result of perturbing the stationary model
(Levinson et al., 2005)

Oscillations as large-amplitude outward-propagating waves

Large-amplitude wave

Polar cap

(Luo & Melrose, 2008)


Oscillating model

Include displacement current, allow system to evolve Model has counterstreaming electrons and positrons in the magnetosphere Relative streaming Lorentz factor varies from 1 to 106 Counterstreaming instabilities present Cyclotron frequency c
1

oscillates over wide range


Linear response

Wave dispersion properties important for understanding generation of emission Model as a 1D pair plasma, treat in centre of momentum frame Calculate linear response and find available wave modes Plot as a function of for some k


Wave dispersion
vs. , c = 3p , k = 30

A

5 / p 4 3 2 1 0 0 0.2 0.4 0.6 0.8

B

B

A
1


Mode coupling

Mode coupling is expected to occur when the polarization is changing most rapidly Look for polarization swings near mode crossings Mode coupling in intrinsically time-dependent medium is nontrivial


Polarization ellipse

TM 1

Mode coupling strong when polarization ellipse changes shape rapidly TM = ±1 -- circular, TM = 0, -- linear Can plot TM as a function of k or once the modes are identified Compare with shape of dispersion curves, position of resonances Cyclotron resonance at = c / ± kc


Polarization and dispersion as a function of
5 / p 4 3 2 1 0 0
TM 5 2.5 0.2 -2.5 -5 -7.5 -10 0.4 0.6 0.8 1

vs. , c = 3p

7.5

0.2

0.4

0.6

0.8

1

axial ratio vs. , c = 3p


What should we see?

We expect backward emission, esp. at low frequency - model should produce emission in both directions Elliptical polarization can be explained Low frequency emission, at 3 c /Rc , dominated by curvature effects (we see emission from a short time) Models with high- outflow must be curvature dominated below this frequency; oscillating model has phases where much lower, perhaps coherent emission signatures at low frequency


Conclusion
Pulsar radio emission not well understood
Magnetospheric models unstable OPMs hard to explain Efficient coupling requires cyclotron resonance

Oscillating model provides some solutions
Including displacement current gives more realistic model Allow interaction with cyclotron resonance Rapid polarization change near resonance point, coupling c 1/ can be below p in phase where is maximum Observational effects include expectation of backwards emission Same emission should be observed at lower frequencies