Aristeidis NoutsosUniversity of Manchester

Pulsar PolarizationPulsar radiation is elliptically polarised with a high degree of linear polarization.

PA swing

A transition between the two OPMs across the pulse is seen as a 90º jump in the PA profiles

90º

The linear polarization is the sum of two orthogonal modes (OPMs).

OPMs

On the Stokes plane, the OPMs are anti-parallel vectors; the sum (dominant mode) is always parallel to either of the two modes.

U

Q

Sum

π

XO

Scattering Effects on PolarizationHowever, observations have revealed smooth PA transitions between the two modes

90º

how are these generated?

XO

PSR J1644 – 4559 20 cm

PSR J1326–5859Also, deformities have been observed in the, otherwise, smooth PA swings.

Karastergiou (2009, MNRAS) simulated pulse profiles and convolved them with scattering tails of various lengths. It was shown that ISM scattering can reproduce the observed PA features.

PA(deg)

Intensity scatteredoriginal

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Scattering Effects on PolarizationSimulations show that scattering distorts PA profiles with steep gradients:

orthogonal jumps located near steep PA slopes become flatter and the orthogonality is destroyed

Scattering screen

PA profile

pulsar

Example animation (not to scale!)

observer

•Power from earlier phases is transferred to later ones. •Polarised emission corresponding to different regions in the

magnetosphere arrives at the same phase bin. •The PA profiles are smeared towards later phases, destroying

the orthogonality of the original emission.

Scattering flattens PAs

PA

Scattering Effects on Rotation Measure

•Pulsar RMs are solely a property of the intervening ISM. So, they are not expected to vary across the pulse phase.

•However, since the effect of scattering on the PA profiles is frequency-dependent, the PA profiles change across the band. This induces a PA rotation that is independent of interstellar Faraday Rotation.

High sensitivities and broad bandwidths of current instruments allow us accurate determination of the interstellar Faraday Rotation.LOFAR will have the advantage of low frequencies, where this effect is strong.

Flat PA curve: no rotation

Steep PA curve: rotation occurs across band

•The effect is strongest near steep PA gradients, as the scattered power causes significant changes in the PA, there.

ΔPAscat

Scattering Effects on Rotation Measure

Simulations by Karastergiou (2009) showed that scattering can produce phase-resolved RM variations across the pulse profile. Each RM across the pulse could be fitted well with a λ2-law.

These effects are evident even for small scattering time-scales (τscat ~ 2 ms).

Observational EvidenceWe calculated phase-resolved RM profiles for the 19 strongest, highly polarised pulsars in Noutsos et al. (2008).

In 9 cases we saw significant RM variations across the profile: e.g.

RM

PA

Δ(RM) ~13 rad m–2 Δ(RM) ~ 37 rad m–2 Δ(RM) ~ 52 rad m–2

Observational Evidence

We checked the quality of the fits that produced the RMs:

The effect that causes the RM variations is inseparable from the λ2-law of interstellar Faraday Rotation.

RM

Generalised Faraday Rotation?The theory of Generalised Faraday Rotation is still immature (see e.g. Kennet & Melrose 1998).One of its predictions is the partial conversion of linear to circular polarization, as the elliptically polarised electromagnetic emission propagates through the pulsar’s magnetosphere.

It is a frequency-dependent effect.

If GFR triggers both V and RM variations, we expect a correlation between ΔRM and ΔV.

RM

ΔV

There is little evidence for correlation between ΔV and ΔRM

Hence, to a first order, GFR is unlikely.

However, the presence of quasi-orthogonal modes (see e.g. Ramachandran et al 2004) can affect the RM measurements, if the strength ratio of the initial modes is a function of frequency (Smits et al. 2006).

PAº

φ

Quasi-orthogonal Emission Modes

We could not reproduce the observed rotations of ΔPA~20º and have L>10%.Hence, quasi-orthogonal modes are not the reason for the changes in RM.

By simulating mode summation with a power-law variation (γ = –0.5) across 256 MHz, we estimated ΔPA as a function of L% and φ. φ

ΔPA

• The superposition of strictly orthogonal modes results in emission of the strongest mode. • The direction of the resulting mode is independent of strengths of the initial modes.

180º

ScatteringIf scattering is the reason for the observed RM variations, then we would expect to see the largest variations in highly scattered pulsars.While it is difficult to obtain τscat for all the pulsars in our sample, the DM is a good approximation of the amount of scattering (Bhat et al. 2004):

We plotted the ΔRMp–p against DM for pulsars with evident variations.

ΔR

Mp–p

(ra

d m

–2)

DM (pc cm–3)

Pulsars that typify large ΔRM are also high-DM pulsars.

It is a simple and attractive explanation of this

phenomenon.

Summary & Discussion

• Future studies should account for this effect. RM determination from only a few, high-s/n bins can lead to erroneous estimates, and averaging may be required (but beware of depolarization!).

• We have detected significant RM variations, as a function of pulse phase, for 9 highly polarised pulsars observed with the Parkes telescope, at 20 cm.

• The possibility that this is caused by frequency-dependent quasi-orthogonal emission modes was ruled out.

• Generalised Faraday Rotation was deemed unlikely, but may still play a role. The theory of GFR gives little information on the magnitude of its effect.• Scattering on polarization has been studied by Li & Han (2003) and more recently by Karastergiou (2009). We have found a good correlation between scattering and the amount of RM variation, which makes this explanation simple and appealing.

• We have detected significant RM variations, as a function of pulse phase, for 9 highly polarised pulsars observed with the Parkes telescope, at 20 cm.

• The possibility that this is caused by frequency-dependent quasi-orthogonal emission modes was ruled out.

• Generalised Faraday Rotation was deemed unlikely, but may still play a role. The theory of GFR gives little information on the magnitude of its effect.• Scattering on polarization has been studied by Li & Han (2003) and more recently by Karastergiou (2009). We have found a good correlation between scattering and the amount of RM variation, which makes this explanation simple and appealing.• Future studies should account for this effect. RM determination from only a few, high-s/n bins can lead to erroneous estimates, and averaging may be required (but beware of depolarization!).