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A&A 520, A8 (2010)Fig. 11. Simulated pattern on the sky for the axial ratio of the (Q, U)error ellipse for worst-case geometric assumptions at 30 GHz (top) and44 GHz (middle). Note that the colour scale for 30 GHz covers only20% of the range for 44 GHz. Maps are in galactic coordinates. Theactual pattern for the WMAP 5-year V band is show at bottom, on thesame colour scale as for <strong>Planck</strong> at 44 GHz.U (±90 ◦ in the (Q, U)plane).Ingeneraltheerrorellipsewillberotated from this orientation by 2ψ.The Crab polarisation angle of ≈−88 ◦ in galactic coordinates(Page et al. 2007)translatesto−28 ◦ in ecliptic coordinates,hence −56 ◦ in (Q, U). Therefore, for horns with ψ = 22. ◦ 5, themajor axis of the error ellipse is along 135 ◦ /−45 ◦ ,withinabout10 ◦ of the Crab’s (Q, U) vector.Asaresultwegetarelativelypoor measurement of the polarisation amplitude but a good measurementof the angle. Conversely, for horns with ψ = −22. ◦ 5weget a relatively poor measurement of the angle.Each LFI horn will make an independent measurement of theCrab from the two visits in each year of observations. Optimalfitting to the calibrated and background-subtracted time-orderedFig. 12. Scanning the spin axis away from the Ecliptic allows us to obtainsignificantly misaligned scan circles even for a source like the Crabnebula that is sited on the Ecliptic. As in Fig. 1, red arrows and circlesshow the spin axis and scan circle, in this case for the two visits to theCrab in each year (the Crab is at the point just below the Ecliptic wherethe two scan circles intersect). The view is centred at ecliptic coordinates(90 ◦ , 10 ◦ ). Also shown is the 180 ◦ period cycloid path of the spinaxis (for n = 0). Top: near-optimal cycloid phase. Bottom: worst-casecycloid phase giving degenerate scans.data will be used; that is, the known Mueller-matrix beam patternsfor each detector (M QI , M QQ , M QU ), synthesised over theband using the known spectral index of the Crab, will determinethe weight of each sample of the ˜Q H signal, and the best-estimate(Q, U)willbederivedbyleastsquaresfitting.We have simulated the uncertainty in the Crab polarisationangle from this process, using the current best estimates for theLFI detector noise, and nominal background fluctuations withrms [17, 25, 25] µK at30,44,70GHz,respectively,foreachofQ and U.Thefluctuationvaluesareupperlimitstothesignal(asopposed to noise) fluctuations derived in annuli around the Crabin the WMAP 5-year maps, for the nearest frequency channels.Page 16 of 26
J. P. Leahy et al.: <strong>Planck</strong> 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
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A&A 520, E1 (2010)DOI: 10.1051/0004
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ABSTRACTThe European Space Agency
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A&A 520, A1 (2010)Fig. 2. An artist
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A&A 520, A1 (2010)Fig. 4. Planck fo
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A&A 520, A1 (2010)Fig. 6. The Planc
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A&A 520, A1 (2010)Table 4. Summary
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A&A 520, A1 (2010)three frequency c
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A&A 520, A1 (2010)Fig. 12. The left
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A&A 520, A1 (2010)Fig. 14. Left pan
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A&A 520, A1 (2010)flux limit of the
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A&A 520, A1 (2010)- University of C
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A&A 520, A1 (2010)57 Instituto de A
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A&A 520, A2 (2010)Fig. 1. (Left) Th
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A&A 520, A2 (2010)Fig. 3. (Top)Twos
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A&A 520, A2 (2010)Table 2. Predicte
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Table 3. Predicted in-flight main b
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A&A 520, A2 (2010)materials. Theref
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A&A 520, A2 (2010)Fig. 11. Comparis
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A&A 520, A2 (2010)Table 5. Inputs u
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A&A 520, A2 (2010)Fig. 16. Three cu
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A&A 520, A2 (2010)Table 7. Optical
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A&A 520, A2 (2010)Fig. A.1. Dimensi
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A&A 520, A2 (2010)5 Università deg
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A&A 520, A3 (2010)Horizon 2000 medi
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A&A 520, A3 (2010)Fig. 1. CMB tempe
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A&A 520, A3 (2010)Ω ch 2τn s0.130
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A&A 520, A3 (2010)Fig. 6. Integral
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A&A 520, A3 (2010)Table 2. LFI opti
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3.3.1. SpecificationsThe main requi
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A&A 520, A3 (2010)Fig. 11. Schemati
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A&A 520, A3 (2010)features of the r
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A&A 520, A3 (2010)Fig. 13. Level 2
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A&A 520, A3 (2010)Fig. 15. Level 3
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A&A 520, A3 (2010)GUI = graphical u
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A&A 520, A3 (2010)23 Centre of Math
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A&A 520, A4 (2010)In addition, all
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A&A 520, A4 (2010)Table 2. Sensitiv
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A&A 520, A4 (2010)Fig. 2. Schematic
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A&A 520, A4 (2010)Fig. 6. LFI recei
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A&A 520, A4 (2010)Fig. 9. Schematic
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A&A 520, A4 (2010)Table 4. Specific
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A&A 520, A4 (2010)Fig. 15. DAE bias
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A&A 520, A4 (2010)Fig. 19. Picture
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A&A 520, A4 (2010)Table 10. Main ch
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Table 13. Principal requirements an
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A&A 520, A5 (2010)DOI: 10.1051/0004
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A. Mennella et al.: LFI calibration
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A. Mennella et al.: LFI calibration
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P. A. R. Ade et al.: Planck pre-lau
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P. A. R. Ade et al.: Planck pre-lau
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A&A 520, A12 (2010)Table 1. Summary
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arrangement was also constrained by
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A&A 520, A12 (2010)frequency cut-of
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A&A 520, A12 (2010)Fig. 9. Gaussian
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A&A 520, A12 (2010)the horn-to-horn
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A&A 520, A12 (2010)Fig. 19. Broad-b
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A&A 520, A13 (2010)DOI: 10.1051/000
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C. Rosset et al.: Planck-HFI: polar
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of frequencies and shown to have po
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