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A great deal of experimental effort is currently being devoted to the precise measurements of the cosmic microwave background (CMB) sky in temperature and polarisation. Satellites, balloon-borne, and ground-based experiments scrutinize the CMB sky at multiple scales, and therefore enable to investigate not only the evolution of the early Universe, but also its late-time physics with unprecedented accuracy. The pipeline leading from time ordered data as collected by the instrument to the final product is highly structured. Moreover, it has also to provide accurate estimates of statistical and systematic uncertainties connected to the specific experiment. In this paper, we review likelihood approaches targeted to the analysis of the CMB signal at different scales, and to the estimation of key cosmological parameters. We consider methods that analyze the data in the spatial (i.e., pixel-based) or harmonic domain. We highlight the most relevant aspects of each approach and compare their performance.
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With the temperature power spectrum of the cosmic microwave background (CMB) at least four orders of magnitude larger than the B-mode polarisation power spectrum, any instrumental imperfections that couple temperature to polarisation must be carefully controlled and/or removed. Here we present two new map-making algorithms that can create polarisation maps that are clean of temperature-to-polarisation leakage systematics due to differential gain and pointing between a detector pair. Where a half wave plate is used, we show that the spin-2 systematic due to differential ellipticity can also by removed using our algorithms. The algorithms require no prior knowledge of the imperfections or temperature sky to remove the temperature leakage. Instead, they calculate the systematic and polarisation maps in one step directly from the time ordered data (TOD). The first algorithm is designed to work with scan strategies that have a good range of crossing angles for each map pixel and the second for scan strategies that have a limited range of crossing angles. The first algorithm can also be used to identify if systematic errors that have a particular spin are present in a TOD. We demonstrate the use of both algorithms and the ability to identify systematics with simulations of TOD with realistic scan strategies and instrumental noise.
Future cosmic microwave background (CMB) polarisation experiments aim to measure an unprecedentedly small signal - the primordial gravity wave component of the polarisation field B-mode. To achieve this, they will analyse huge datasets, involving years worth of time-ordered data (TOD) from massively multi-detector focal planes. This creates the need for fast and precise methods to complement the M-L approach in analysis pipelines. In this paper, we investigate fast map-making methods as applied to long duration, massively multi-detector, ground-based experiments, in the context of the search for B-modes. We focus on two alternative map-making approaches: destriping and TOD filtering, comparing their performance on simulated multi-detector polarisation data. We have written an optimised, parallel destriping code, the DEStriping CARTographer DESCART, that is generalised for massive focal planes, including the potential effect of cross-correlated TOD 1/f noise. We also determine the scaling of computing time for destriping as applied to a simulated full-season data-set for a realistic experiment. We find that destriping can out-perform filtering in estimating both the large-scale E and B-mode angular power spectra. In particular, filtering can produce significant spurious B-mode power via EB mixing. Whilst this can be removed, it contributes to the variance of B-mode bandpower estimates at scales near the primordial B-mode peak. For the experimental configuration we simulate, this has an effect on the possible detection significance for primordial B-modes. Destriping is a viable alternative fast method to the full M-L approach that does not cause the problems associated with filtering, and is flexible enough to fit into both M-L and Monte-Carlo pseudo-Cl pipelines.
We study systematic effects from half-wave plates (HWPs) for cosmic microwave background (CMB) experiments using full-sky time-domain beam convolution simulations. Using an optical model for a fiducial spaceborne two-lens refractor telescope, we investigate how different HWP configurations optimized for dichroic detectors centred at 95 and 150 GHz impact the reconstruction of primordial B-mode polarization. We pay particular attention to possible biases arising from the interaction of frequency dependent HWP non-idealities with polarized Galactic dust emission and the interaction between the HWP and the instrumental beam. To produce these simulations, we have extended the capabilities of the publicly available beamconv code. To our knowledge, we produce the first time-domain simulations that include both HWP non-idealities and realistic full-sky beam convolution. Our analysis shows how certain achromatic HWP configurations produce significant systematic polarization angle offsets that vary for sky components with different frequency dependence. Our analysis also demonstrates that once we account for interactions with HWPs, realistic beam models with non-negligible cross-polarization and sidelobes will cause significant B-mode residuals that will have to be extensively modelled in some cases.
We discuss an approach to the component separation of microwave, multi-frequency sky maps as those typically produced from Cosmic Microwave Background (CMB) Anisotropy data sets. The algorithm is based on the two step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., (2006), where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically-derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multi-dimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-square-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial-sky, total-intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by WMAP and anticipated from Planck.
We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiments beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.
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