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

N. Mandolesi et al.: The Planck-LFI programmeThe latter are also known as generalized least squares (GLS)methods and are accurate and flexible. Their drawback is that,at the size of the Planck data set, they require a significantamount of massively powered computational resources(Poutanen et al. 2006; Ashdown et al. 2007, 2009) andarethusinfeasible to use within a Monte Carlo context. To overcomethe limitations of GLS algorithms, the LFI community has developedso-called “hybrid” algorithms (Keihänen et al. 2005;Kurki-Suonio et al. 2009; Keihänen et al. 2010). These algorithmsrely on a tunable parameter connected to the 1/ f kneefrequency, a measure of the amount of low frequency correlatednoise in the time-ordered data: the higher the knee frequency,the shorter the “baseline” length needed to be chosen toproperly suppress the 1/ f contribution. From this point of view,the GLS solution can be thought of as the limiting case whenthe baseline length approaches the sampling interval. Providedthat the knee frequency is not too high, hybrid algorithms canachieve GLS accuracy at a fraction of the computational demand.Furthermore, they can be tuned to the desired precisionwhen speed is an issue (e.g., for timeline-to-map Monte Carloproduction). The baseline map-making algorithms for LFI is ahybrid code dubbed MADAM.Map-making algorithms can, in general, compute the correlation(inverse covariance) matrix of the map estimate that theyproduce (Keskitalo et al. 2010). At high resolution this computation,though feasible, is impractical, because the size of thematrix makes its handling and inversion prohibitively difficult.At low resolution, the covariance matrix will be produced instead:this is of extreme importance for the accurate characterizationof the low multipoles of the CMB (Keskitalo et al. 2010;Gruppuso et al. 2009).AkeytierofPlanck data analysis is the separation of astrophysicalfrom cosmological components. A variety of methodshave been developed to this end (e.g., Leach et al. 2008).Point source extraction is achieved by exploiting non-Planck catalogues,as well as filtering Planck maps with optimal functions(wavelets) capable of recognizing beam-like patterns. In additionto linearly combining the maps or fitting for known templates,diffuse emissions are separated by using the statistical distributionsof the different components, assuming independence betweenthem, or by means of a suitable parametrization and fittingof foreground unknowns on the basis of spatial correlationsin the data or, in alternative, multi-frequency single resolutionelements only.The extraction of statistical information from the CMBusually proceeds by means of correlation functions. Since theCMB field is Gaussian to a large extent (e.g. Smith et al. 2009),most of the information is encoded in the two-point functionor equivalently in its reciprocal representation in spherical harmonicsspace. Assuming rotational invariance, the latter quantityis well described by the set of C l (see e.g., Gorski 1994).For an ideal experiment, the estimated power spectrum could bedirectly compared to a Boltzmann code prediction to constrainthe cosmological parameters. However, in the case of incompletesky coverage (which induces couplings among multipoles)and the presence of noise (which, in general, is not rotationallyinvariant because of the coupling between correlated noise andscanning strategy), a more thorough analysis is necessary. Thelikelihood function for a Gaussian CMB sky can be easily writtenand provides a sound mechanism for constraining modelsand data. The direct evaluation of this function, however, posesintractable computational issues. Fortunately, only the lowestmultipoles require exact treatment. This can be achieved eitherby direct evaluation in the pixel domain or sampling theposterior distribution of the CMB using sampling methods suchas the Gibbs approach (Jewell et al. 2004; Wandelt et al. 2004).At high multipoles, where the likelihood function cannot be evaluatedexactly, a wide range of effective, computationally affordableapproximations exist (see e.g., Hamimeche & Lewis 2008;and Rocha et al., in prep., and references therein). The low andhigh l approaches to power spectrum estimation will be joinedinto a hybrid procedure, pioneered by Efstathiou (2004).The data analysis of LFI will require daunting computationalresources. In view of the size and complexity of its data set, accuratecharacterization of the scientific results and error propagationwill be achieved by means of a massive use of Monte Carlosimulations. A number of worldwide distributed supercomputercentres will support the DPC in this activity. A partial list includesNERSC-LBNL in the USA, CINECA in Italy, CSC inFinland, and MARE NOSTRUM in Spain. The European centreswill benefit from the Distributed European Infrastructure forSupercomputer Application 7 .3. Instrument3.1. OpticsDuring the design phase of LFI, great effort was dedicated to theoptical design of the focal plane unit(FPU).Asalreadymentionedin the introduction, the actual design of the Planck telescopeis derived from COBRAS and specially has been tunedby subsequent studies of the LFI team (Villa et al. 1998) andThales-Alenia Space. These studies demonstrated the importanceof increasing the telescope diameter (Mandolesi et al.2000), optimizing the optical design, and also showed how complexit would be to match the real focal surface to the horn phasecentres (Valenziano et al. 1998). The optical design of LFI isthe result of a long iteration process in which the optimizationof the position and orientation of each feed horn involves atrade-off between angular resolution and sidelobe rejection levels(Sandri et al. 2004; Burigana et al. 2004; Sandri et al. 2010).Tight limits were also imposed by means of mechanical constraints.The 70 GHz system has been improved in terms of thesingle horn design and its relative location in the focal surface.As a result, the angular resolution has been maximized.The feed horn development programme started in the earlystages of the mission with prototype demonstrators (Bersanelliet al. 1998), followed by the elegant bread board (Villa et al.2002) andfinallybythequalification(D’Arcangelo et al. 2005)and flight models (Villa et al. 2009). The horn design has a corrugatedshape with a dual profile (Gentili et al. 2000). This choicewas justified by the complexity of the optical interfaces (couplingwith the telescope and focal plane horn accommodation)and the need to respect the interfaces with HFI.Each of the corrugated horns feeds an orthomode transducer(OMT) that splits the incoming signalintotwo orthogonal polarisedcomponents (D’Arcangelo et al. 2009a). The polarisationcapabilities of the LFI are guaranteed by the use of OMTsplaced immediately after the corrugated horns. While the incomingpolarisation state is preserved inside the horn, the OMT dividesit into two linear orthogonal polarisations, allowing LFIto measure the linear polarisation component of the incomingsky signal. The typical value of OMT cross-polarisation isabout −30 dB, setting the spurious polarisation of the LFI opticalinterfaces at a level of 0.001.7 http://www.deisa.euPage 9 of 24