SKA polarimetry specication

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Brendan Moses Hubbard
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1 specication Does the SKA really need to achieve its high polarimetric purity (and sensitivity) spec? Onsala Space Observatory Chalmers University, Sweden AAVP workshop, Cambridge, 8 Dec 2010

2 SKA Polarimetry Brief "Polarization purity" is a key parameter in SKA specication a.k.a cross-polarization ratio (XPR), xpol isolation, xpol discrimination, instrumental pol, pol leakage, cross-talk, etc Several SKA Key Science Projects need good polarimetry Table: SKA KSP polarization purity requirements KSP raw PP [db] EoR -30 Cosmic magnetism -30 Pulsar timing -40 These values are demanding!

3 Basic Problem of Polarimetry The economics and technical challenges of polarimetry Az=0 El=0 Good polarimetry is expensive Requires good channel isolation Low cross-polarization over (almost) entire celestial hemisphere Possible solution: improve polarimetry in post-processing Calibration needs to done anyways 180 Is this possible and to what extent?

4 Raw Polarimetry Formulation Basic (Jones) Measurement Equation for interferometer element is V = Je where V is measured voltages, e is Jones vector and J is Jones matrix. Consider the toy model of a good but leaky polarimeter ( ) 1 d J toy = G d 1 d 1 and let the raw estimate of the Jones vector be ê raw = V/G. Then total relative error of the raw estimate is RMS(ê raw ) < d + V / V where V / V is a function of A eff /T sys.

5 XPR Motivation The o-diagonal Jones matrix components squared, i.e. d 2 is the raw cross-polarization ratio (or simply XPR) XPR is a term in the relative error of raw polarimetry

6 Motivation Full Calibration Polarimetry Can do better than raw calibration. Full polarimetric calibration is ê = J 1 V This seems to give prefect solutions, rendering XPR meaningless... This is the conventional wisdow behind using the concept raw XPR for specing polarimetry.

7 IXR Motivation But in reality we have noise V and an imprecise knowledge of Jones J, so there is still a nonvanishing tot. rel. err. RMS(ê) e ( )( e J +... IXR J + V ), V where IXR is the intrinsic cross-polarization ratio dened as IXR = g max + g min g max g min and g max, g min are max and min amplitude gains. So the polarimetric error depends on IXR also after calibration. IXR is newly dened parameter given in Carozzi, Woan arxiv:

8 Comparison of IXR and XPR It can be seen as an invariant XPR since any Jones matrix can be written as ( 1 IXR J = gu )V, U,V unitary IXR 1 So for toy model, IXR=XPR But for general Jones matrix (U,V 1) IXR XPR, and then raw XPR is only relevant to raw calibration, while IXR is relevant even after full calibration. Therefore IXR is a better fundamental gure-of-merit for a polarimeter than generic XPR.

9 Motivation What Should SKA Polarization Purity Be? Depends on calibration & science: If only raw calibration => IXR (or raw XPR) needs to be good If full calibration => IXR can be much less! IXR useful in all cases

10 Motivation Polarimetric Antenna Sensitivity Sensitivity Pulsars EoR Wideeld polarimetry Sensitivity can be extended polarimetrically A eff T M = T where M is the eective Mueller matrix, T is the Stokes antenna temperature and is a matrix/vector norm. A related parameter is SNR of the Stokes estimate from the telescope ( )( ) S S 1 2 M M S IXR T M

11 Sensitivity Pulsars EoR Wideeld polarimetry Polarization purity eects on Pulsar timing Results of end-to-end Monte-Carlo simulations using dierent timing methods versus IXR Method I: Intensity timing (raw) Method II: Invariant interval (raw) Method III: Matrix template matching (calibrated) Figures by R. Paulin in Karastergiou et al. (to be submitted 2010)

12 Sensitivity Pulsars EoR Wideeld polarimetry EoR & polarization leakage in AA-lo 30 At low frequencies SKA is approximated by short dipoles in a plane. Its Jones matrix is ( ) 1 n lm J = 1 m² 0 1 m² for which IXR M = 1 + n² 1 n² IXR M [db] Angle off axis [deg] EoR contamination O-zenith, polarized galactic foreground leaks into intensity. Jeli et al. (2010) Leaked polarized to total power ratio is 1/IXR M

13 Sensitivity Pulsars EoR Wideeld polarimetry Dense AA Wideeld Polarimetry Issues Dierences in E&H-plane versus D-plane E-H planes D-planes This makes wideeld polarimetry dicult and impacts on for instance Cosmic Magnetism... Suggested solution Polarization diversity by varying tile orientations Ref. Carozzi, Maaskant (2010) Proceedings of Wide eld Science for SKA

14 Sensitivity Pulsars EoR Wideeld polarimetry Dense AA Polarimetry Performance Instantaneous 40 FoV E&H planes (mea D planes (mean) 35 Beamforming 30 Gain [db] [deg.]

15 Conclusions Motivation SKA ought to have an IXR spec rather than raw XPR Raw calibrated data requires good XPR Fully calibrated data requires moderate IXR Polarization purity is import for SKA science since it aects nal data SNR (i.e. not just sensitivity) pulsar timing EoR contamination SKA can fulll KSPs with lower IXR (or XPR) than in current spec!

Specifying Polarisation Properties For Radio Telescopes

Specifying Polarisation Properties For Radio Telescopes Bruce Veidt NRC Herzberg Astronomy and Astrophysics, Penticton, BC, Canada PAF Workshop, Sydney, 14 16 November 2017 Outline Motivation: Polarised