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Register a new userBeyondPlanck II. CMB map-making through Gibbs sampling
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We present a Gibbs sampling solution to the map-making problem for CMB measurements, building on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps; noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods, and allows us for the first time to bring the destriping baseline length to a single sample. We apply the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we may compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction, and this methodology forms the conceptual basis for the map-making algorithm employed in the BeyondPlanck framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.
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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 present a new map-making method for CMB measurements. The method is based on the destriping technique, but it also utilizes information about the noise spectrum. The low-frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum-likelihood analysis, involving the covariance matrix of the amplitudes. We present simulation results with $1/f$ noise and show a reduction in the residual noise with respect to ordinary destriping. This study is related to Planck LFI activities.
We present a Bayesian calibration algorithm for CMB observations as implemented within the global end-to-end BeyondPlanck (BP) framework, and apply this to the Planck Low Frequency Instrument (LFI) data. Following the most recent Planck analysis, we decompose the full time-dependent gain into a sum of three orthogonal components: One absolute calibration term, common to all detectors; one time-independent term that can vary between detectors; and one time-dependent component that is allowed to vary between one-hour pointing periods. Each term is then sampled conditionally on all other parameters in the global signal model through Gibbs sampling. The absolute calibration is sampled using only the orbital dipole as a reference source, while the two relative gain components are sampled using the full sky signal, including the orbital and Solar CMB dipoles, CMB fluctuations, and foreground contributions. We discuss various aspects of the data that influence gain estimation, including the dipole/polarization quadrupole degeneracy and anomalous jumps in the instrumental gain. Comparing our solution to previous pipelines, we find good agreement in general, with relative deviations of -0.84% (-0.67%) for 30 GHz, -0.14% (0.02%) for 44 GHz and -0.69% (-0.08%) for 70 GHz, compared to Planck 2018 (NPIPE). The deviations we find are within expected error bounds, and we attribute them to differences in data usage and general approach between the pipelines. In particular, the BP calibration is performed globally, resulting in better inter-frequency consistency. Additionally, WMAP observations are used actively in the BP analysis, which breaks degeneracies in the Planck data set and results in better agreement with WMAP. Although our presentation and algorithm are currently oriented toward LFI processing, the procedure is fully generalizable to other experiments.
As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zeldovich (SZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB however. We develop a Bayesian formalism for rigorously characterising anisotropies that are localised on the sky, taking the TSZ and KSZ effects as an example. Using a Gibbs sampling scheme, we are able to efficiently sample from the joint posterior distribution for a multi-component model of the sky with many thousands of correlated physical parameters. The posterior can then be exactly marginalised to estimate properties of the secondary anisotropies, fully taking into account degeneracies with the other signals in the CMB map. We show that this method is computationally tractable using a simple implementation based on the existing Commander component separation code, and also discuss how other types of secondary anisotropy can be accommodated within our framework.
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