S. Leach

Component separation methods for the PLANCK mission

Context. The PLANCK satellite will map the full sky at nine frequencies from 30 to 857 GHz. The CMB intensity and polarization that are its prime targets are contaminated by foreground emission. Aims. The goal of this paper is to compare proposed methods for separating CMB from foregrounds based on their different spectral and spatial characteristics, and to separate the foregrounds into “components” with different physical origins (Galactic synchrotron, free-free and dust emissions; extra-galactic and far-IR point sources; Sunyaev-Zeldovich effect, etc.) Methods. A component separation challenge has been organised, based on a set of realistically complex simulations of sky emission. Several methods including those based on internal template subtraction, maximum entropy method, parametric method, spatial and harmonic cross correlation methods, and independent component analysis have been tested. Results. Different methods proved to be effective in cleaning the CMB maps of foreground contamination, in reconstructing maps of diffuse Galactic emissions, and in detecting point sources and thermal Sunyaev-Zeldovich signals. The power spectrum of the residuals is, on the largest scales, four orders of magnitude lower than the input Galaxy power spectrum at the foreground minimum. The CMB power spectrum was accurately recovered up to the sixth acoustic peak. The point source detection limit reaches 100 mJy, and about 2300 clusters are detected via the thermal SZ effect on two thirds of the sky. We have found that no single method performs best for all scientific objectives. Conclusions. We foresee that the final component separation pipeline for PLANCK will involve a combination of methods and iterations between processing steps targeted at different objectives such as diffuse component separation, spectral estimation, and compact source extraction.

The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths

We present the Planck Sky Model (PSM), a parametric model for generating all-sky, few arcminute resolution maps of sky emission at submillimetre to centimetre wavelengths, in both intensity and polarisation. Several options are implemented to model the cosmic microwave background, Galactic diffuse emission (synchrotron, free-free, thermal and spinning dust, CO lines), Galactic HII regions, extragalactic radio sources, dusty galaxies, and thermal and kinetic Sunyaev-Zeldovich signals from clusters of galaxies. Each component is simulated by means of educated interpolations/extrapolations of data sets available at the time of the launch of the Planck mission, complemented by state-of-the-art models of the emission. Distinctive features of the simulations are spatially varying spectral properties of synchrotron and dust; different spectral parameters for each point source; modelling of the clustering properties of extragalactic sources and of the power spectrum of fluctuations in the cosmic infrared background. The PSM enables the production of random realisations of the sky emission, constrained to match observational data within their uncertainties. It is implemented in a software package that is regularly updated with incoming information from observations. The model is expected to serve as a useful tool for optimising planned microwave and sub-millimetre surveys and testing data processing and analysis pipelines. It is, in particular, used to develop and validate data analysis pipelines within the Planck collaboration. A version of the software that can be used for simulating the observations for a variety of experiments is made available on a dedicated website.

Planck Pre-Launch Status: Expected LFI Polarisation Capability

We present a system-level description of the Low Frequency Instrument (LFI) considered as a differencing polarimeter, and evaluate its expected performance. The LFI is one of the two instruments on board the ESA Planck mission to study the cosmic microwave background. It consists of a set of 22 radiometers sensitive to linear polarisation, arranged in orthogonally-oriented pairs connected to 11 feed horns operating at 30, 44 and 70 GHz. In our analysis, the generic Jones and Mueller-matrix formulations for polarimetry are adapted to the special case of the LFI. Laboratory measurements of flight components are combined with optical simulations of the telescope to investigate the values and uncertainties in the system parameters affecting polarisation response. Methods of correcting residual systematic errors are also briefly discussed. The LFI has beam-integrated polarisation efficiency >99% for all detectors, with uncertainties below 0.1%. Indirect assessment of polarisation position angles suggests that uncertainties are generally less than 0°.5, and this will be checked in flight using observations of the Crab nebula. Leakage of total intensity into the polarisation signal is generally well below the thermal noise level except for bright Galactic emission, where the dominant effect is likely to be spectral-dependent terms due to bandpass mismatch between the two detectors behind each feed, contributing typically 1–3% leakage of foreground total intensity. Comparable leakage from compact features occurs due to beam mismatch, but this averages to < 5 × 10^(-4) for large-scale emission. An inevitable feature of the LFI design is that the two components of the linear polarisation are recovered from elliptical beams which differ substantially in orientation. This distorts the recovered polarisation and its angular power spectrum, and several methods are being developed to correct the effect, both in the power spectrum and in the sky maps. The LFI will return a high-quality measurement of the CMB polarisation, limited mainly by thermal noise. To meet our aspiration of measuring polarisation at the 1% level, further analysis of flight and ground data is required. We are still researching the most effective techniques for correcting subtle artefacts in polarisation; in particular the correction of bandpass mismatch effects is a formidable challenge, as it requires multi-band analysis to estimate the spectral indices that control the leakage.

The intergalactic medium thermal history at redshift z = 1.7–3.2 from the Lyα forest: a comparison of measurements using wavelets and the flux distribution

We investigate the thermal history of the intergalactic medium (IGM) in the redshift interval z = 1.7–3.2 by studying the small-scale fluctuations in the Lyman α forest transmitted flux. We apply a wavelet filtering technique to 18 high-resolution quasar spectra obtained with the Ultraviolet and Visual Echelle Spectrograph, and compare these data to synthetic spectra drawn from a suite of hydrodynamical simulations in which the IGM thermal state and cosmological parameters are varied. From the wavelet analysis we obtain estimates of the IGM thermal state that are in good agreement with other recent, independent wavelet-based measurements. We also perform a reanalysis of the same data set using the Lyman α forest flux probability distribution function (PDF), which has previously been used to measure the IGM temperature– density relation. This provides an important consistency test for measurements of the IGM thermal state, as it enables a direct comparison of the constraints obtained using these two different methodologies. We find the constraints obtained from wavelets and the flux PDF are formally consistent with each other, although in agreement with previous studies, the flux PDF constraints favour an isothermal or inverted IGM temperature–density relation. We also perform a joint analysis by combining our wavelet and flux PDF measurements, constraining the IGM thermal state at z = 2.1 to have a temperature at mean density of T 0/[10 3 K] = 17.3 ± 1.9 and a power-law temperature–density relation exponent γ = 1.1 ± 0.1 (1σ ). Our results are consistent with previous observations that indicate there may be additional sources of heating in the IGM at z < 4.

Estimating the tensor-to-scalar ratio and the effect of residual foreground contamination

We consider future balloon-borne and ground-based suborbital experiments designed to search for inflationary gravitational waves, and investigate the impact of residual foregrounds that remain in the estimated cosmic microwave background maps. This is achieved by propagating foreground modelling uncertainties from the component separation, under the assumption of a spatially uniform foreground frequency scaling, through to the power spectrum estimates, and up to measurement of the tensor to scalar ratio in the parameter estimation step. We characterize the error covariance due to subtracted foregrounds, and find it to be subdominant compared to instrumental noise and sample variance in our simulated data analysis. We model the unsubtracted residual foreground contribution using a two-parameter power law and show that marginalization over these foreground parameters is effective in accounting for a bias due to excess foreground power at low l. We conclude that, at least in the suborbital experimental setups we have simulated, foreground errors may be modeled and propagated up to parameter estimation with only a slight degradation of the target sensitivity of these experiments derived neglecting the presence of the foregrounds.