Planck Pre-Launch Status Papers - APC - Université Paris Diderot ...

J. P. Leahy et al.: Planck pre-launch status: Expected LFI polarisation capabilityResults are shown in Fig. 13.Theprimaryvariableisthereferencephase of the cycloid scanning strategy, Φ 0 .Theapproximateorbit used in our simulations 9 does not affect the basicgeometry, in particular the phases at which the scan angles becomedegenerate and hence the errors diverge, at Φ 0 ≈ 65 ◦ and275 ◦ .Forn = 0(forwardprecession)themajorchangeisthatthe scan degeneracies occur at Φ 0 ≈ 115 ◦ and 265 ◦ .Avoidingthese bad phases is one of the more significant constraints on thechoice of scan strategy.The figures show that we can obtain precisions of better than0. ◦ 5degreesforabouthalfoftheRCAs,withonlythethreeawkwardly-oriented RCAs at 70 GHz being significantly worsethan 1 ◦ .WheretheuncertaintyisapproximatelyconstantwithΦ 0 ,theerrorsaredominatedbyourassumedbackgroundfluctuations;these are 1σ upper limits and may be significant overestimatesat 44 and 70 GHz, since they are derived from WMAPStokes Q and U data at Q, V, and W bands where there is nosecure detection of fluctuations in our background annuli.These measurements determine the relative orientation of thefeed horn to the Crab’s net polarisation angle Θ at the effectiveobserving frequency. This will unambiguously reveal any misalignmentsbetween feeds in each band, but to give us the desiredabsolute angle we need external measurements of Θ(ν).Theory tells us that the polarisation of a synchrotron sourcesuch as the Crab will change only very slowly with frequencyin the Faraday-thin regime. Faraday rotation in the Crab hasameanrotationmeasureRM ≈ −23 rad m −2 and an rms ofσ RM = 14 rad m −2 (Bietenholz & Kronberg 1991); this correspondsto rotations of 0. ◦ 08 at 30 GHz, which we can indeedneglect. The remaining effect is that the Crab’s net polarisationis a vector average over the rather tangled polarisation structureof the nebula; since the spectral index is not exactly the same atall positions in the nebula, the weighting in the average changesslowly with frequency. Fortunately, over the LFI band such spectralindex variations are remarkably small: Green et al. (2004)show that the spectral index between 1.5 and 350 GHz variesby ≈±0.02 over the bright part of the nebula, which dominatesthe total flux, corresponding to a change of weight of typically≈±1.7% between 30 and 70 GHz.The current best direct measurements of the Crab polarisationin the LFI frequency range are those from WMAP. Pageet al. (2007)presentedpreliminarymeasurementsbasedonsimpleaperture photometry, with typical errors of 1 ◦ –3 ◦ ,butweestimatethat with optimal fitting, the 5-year data will yield randomerrors (including background fluctuations) ranging from 0. ◦ 14 atKbandto0. ◦ 9atWband.Pageetal.estimatethattheirabsoluteorientations are known from pre-launch data to