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Polarised foreground removal using Faraday

tomography -recovering the EoR

signature

Testori et al. (2004), Wolleben et al. (2005)

Paul M Geil (U. Melb.)Bryan M Gaensler (U. Syd.)

Testori et al. (2004)Wolleben et al. (2005)

21 January 2009 MWA project meeting - Mt Stromlo 2

Outline

• Problem

• Strategy

• Preliminary results

• Further considerations

21 January 2009 MWA project meeting - Mt Stromlo 3

Problem

• How can we distinguish between leakage and EoR signal?• How can we remove contamination in I by polarised foregrounds?

So…

• EoR signal in Stokes I buried under non-polarised foreground emission

• Gain errors & non-ideal feeds conspire to contaminate I further (instrumental polarisation or leakage)

I´ = IEoR + INPFG + L · P

P = Q + iU (complex linear polarisation)

21 January 2009 MWA project meeting - Mt Stromlo 4

Strategy (RM synthesis)

RM synthesis or spectro-polarimetry (Burn 1966; Killeen et al. 2002; Brentjens & de Bruyn 2005)

Exploits the Fourier relationship: P(2) F()Fourier pair: (2, )

Faraday depth

very long ‘baselines’ in 2 space high ‘resolution’ in space

21 January 2009 MWA project meeting - Mt Stromlo 5

Strategy (Mueller transformation)

• Single baseline

Coherency Stokes representation : Mueller operator (Hamaker-Sault notation)

e.g. Stokes I (non-polarised + EoR signal)

• Full array (N antennae)

+ conjugate

∑ baselines required due to S/N requirements

21 January 2009 MWA project meeting - Mt Stromlo 6

Strategy (removal)

Cleaning algorithm: cf. Hogbom (1974)

1. identify largest peak in |FI|()2. fit for max, FI (max) & (0

2)3. subtract corresponding RM spread function R() (with loopgain)

Continue until |FI|() peaks meet threshold criteria (‘S/N’ in |FI|)

e.g.

fit

signal

21 January 2009 MWA project meeting - Mt Stromlo 7

Simulation & modelling (sources)

See, for example:

Geil et al. (MNRAS 390, 1496, 2008)

Jelic et al. (astro-ph:0804.1130v3, 2008)

McQuinn et al. (ApJ 653, 815, 2006)

Jeli

c et

al.

(200

8)

21 January 2009 MWA project meeting - Mt Stromlo 8

Simulation & modelling (instrumental)

Channel depolarisation

• Beam depolarisation

• Frequency dependent leakage

• Altitude/sky position dependence

• 3d power spectra

Unresolved polarised sources within the beam will superimpose detructively.This effect should be included in the simulations due to finite size the synthesised beam.

The integrated complex polarisation over each frequency channel will suffer from depolarisation due to the deconstructive summation of linear polarisation vectors within the small but finite range of frequencies in each channel.

21 January 2009 MWA project meeting - Mt Stromlo 9

Preliminary results

Smooth non-polarised FG already removed usinglog-polynomial fit

Example: B = 8 MHz centred on 154 MHzionisation field (slice @ 154 MHz)

Model EoR signal

Tb profile (central los)

21 January 2009 MWA project meeting - Mt Stromlo 10

Thank you

Comments, questions & suggestions are very welcome(pmgeil@unimelb.edu.au)