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

A&A 520, A2 (2010)Fig. 16. Three cuts through the main beam in the telescope symmetryplane (φ = 0 ◦ in Fig. 5)at30,100,and353GHz.Thehorizontalaxisisθas in Fig. 5;theverticalaxisisindBi.Thehorizontallinesshowthelevelsat which Sun, Moon, and Earth would induce a signal of 1 µKinthedetectors; and the angular regions where each object has an influence.Solar system objects may also produce a signal as they travelthrough the far-sidelobes of the beam patterns. In the coordinatesystem of Fig. 5 and with the current baseline orbit, the Suntraces a path within the region from θ ∼ 170 ◦ to 190 ◦ ,theEarthfrom θ ∼ 165 ◦ to 195 ◦ ,andtheMoonfromθ ∼ 148 ◦ to 180 ◦ .For the signal produced by the object to be weaker than 1 µK,the pattern directivity in this region should be less than −46 dBi(Sun), −33 dBi (Earth) and −19 dBi (Moon) 10 .Theflightpredictionmodel meets this requirement with at least a margin of20 dB at 30 GHz, increasing to margin of more than 30 dB at353 GHz (see Fig. 16), but note that this margin may be erodedsignificantly at higher frequencies because of the presence ofdust (see Fig. 17).The level of polarised straylight was estimated in a simplifiedway (Hamaker & Leahy 2004). Typical peak values foundfor Stokes U and Q Galactic straylight at 30 GHz are 1−1.5 µK,resulting from leakage of Stokes I. Atfrequenciesneartheminimumof Galactic emission, the polarised straylight amplitudeshould be much lower (Hamaker & Leahy 2004, estimatebyafactor of ∼10). In polarisation, the dipole straylight is relativelyweak compared to the Galactic contribution; this is because ofthe presence of both positive and negative features in both sidelobecomplexes, which tends to cancel large-scale structures.8.1. The effect of dustDust deposited on the telescope reflectors absorbs and scatterslight and therefore modifies the radiation pattern produced by aclean reflecting surface. The effect on the pattern depends sensitivelyon the number, size, shape, and type (composition) ofthe dust particles. None of these quantities can be predicted withaccuracy for the case of Planck in-flight. In particular, the depositionof particles from the rocket fairing could dominate thedust deposited on the reflectors in-flight, and yet this componentof the dust distribution is very poorly known. Nonetheless,analyses have been performed to estimate the potential impactof dust on the beam patterns. This analysis was first described in10 To be compared to typical peak directivity levels of 51 dBi (30 GHz),61.6 dBi (100 GHz) and 69.3 dBi (353 GHz).Fig. 17. The estimated effect of dust on a beam pattern at 353 GHz foran obscuration level of 5000 ppm. The coloured lines reflect differentassumptions about the aggregation of dust over time on the reflectors;the most robust estimate corresponds to α ∼ α 3 .At100GHz,theestimatedeffect is negligible with respect to the gain from the clean surface.At 857 GHz, the estimated effect is increased by an order of magnitude(in dBi).De Maagt et al. (2000) and later reiterated to include the mostaccurate estimates of dust characteristics for Planck. It assumesthat:– The characteristics of the dust particles (shape, type, andsize distribution) are those found in clean rooms, which havebeen measured and standardised (MIL-STD1246) 11 ,modifiedby deposition onto vertical surfaces and the integratedexposure time 12 .– The multipole expansion (MPE) method is used to estimatethe scattering of particles 13 .Itallowsustocalculatethe bi-reflectance distribution function (BRDF), which isthe effective angular scattering function, for the particles onthe reflectors.– The amount of dust on the reflectors in-flight is representedby an obscuration level of ∼5000 ppm 14 ,whichleadstoapeak BRDF of order 0.08 sr −1 at 353 GHz (lower by an orderof magnitude at 100 GHz, and higher by a factor of ∼5at 857 GHz).– The effect of dust on the surface of the baffle hasbeenignored.With the above assumptions, De Maagt et al. (2000)derivearelationshipbetween the forward gain of a clean surface and a contaminatedone:G real ≈ G 0 (θ) + 10Log(K 0 ) + 10Log(1 + g s (θ)) (1)g s (θ) = 2πBRDF(θ)10 −G 0 (θ)10, (2)K 0where K 0 is the attenuation factor due to the obscuration by dust.11 Particles gathered from clean rooms used for Planck have been analysedand their dielectric indices used in this analysis.12 Particles deposited on surfaces tend to aggregate into “fiber”-likeshapes and therefore their size distribution changes with exposure time.This process is modelled via a so-called “Hamberg” relation; the relateduncertainty is one of the largest in the whole analysis.13 Other methods are available, but MPE has been found to be the mostconservative choice in the sense of producing the greatest disturbance.14 A very conservative in-flight prediction is in the range3000−6000 ppm for each reflector, of which the launch componentis estimated between 1000 and 4000 ppm. However, the latter isvery likely to be at the low end of its range.Page 16 of 22