High precision simulations of weak lensing effect on Cosmic Microwave Background polarization

We study accuracy, robustness and self-consistency of pixel-domain simulations of the gravitational lensing effect on the primordial CMB anisotropies due to the large-scale structure of the Universe. In particular, we investigate dependence of the results precision on some crucial parameters of such techniques and propose a semi-analytic framework to determine their values so the required precision is a priori assured and the numerical workload simultaneously optimized. Our focus is on the B-mode signal but we discuss also other CMB observables, such as total intensity, T, and E-mode polarization, emphasizing differences and similarities between all these cases. Our semi-analytic considerations are backed up by extensive numerical results. Those are obtained using a code, nicknamed lenS2HAT -- for Lensing using Scalable Spherical Harmonic Transforms (S2HAT) -- which we have developed in the course of this work. The code implements a version of the pixel-domain approach of Lewis (2005) and permits performing the simulations at very high resolutions and data volumes, thanks to its efficient parallelization provided by the S2HAT library -- a parallel library for a calculation of the spherical harmonic transforms. The code is made publicly available.Comment: 20 pages, 14 figures, submitted to A&A, matches version accepted for publication in A&

Astrophysical foregrounds and primordial tensor-to-scalar ratio constraints from CMB B-mode polarization observations

We study the effects of astrophysical foregrounds on the ability of CMB B-mode polarization experiments to constrain the primordial tensor-to-scalar ratio, r. To clean the foreground contributions we use parametric, maximum likelihood component separation technique, and consider experimental setups optimized to render a minimal level of the foreground residuals in the recovered CMB map. We consider nearly full-sky observations, include two diffuse foreground components, dust and synchrotron, and study cases with and without calibration errors, spatial variability of the foreground properties, and partial or complete B-mode lensing signal removal. In all these cases we find that in the limit of very low noise level and in the absence of the intrumental or modeling systematic effects, the foreground residuals do not lead to a limit on the lowest detectable value of r. But the need to control the foreground residuals will play a major role in determining the minimal noise levels necessary to permit a robust detection of r < 0.1 and therefore in optimizing and forecasting the performance of the future missions. For current and proposed experiments noise levels, the foreground residuals are found non-negligible and potentially can affect our ability to set constraints on r. We also show how the constraints can be significantly improved on by restricting the post component separation processing to a smaller sky area. This procedure applied to a case of a COrE-like satellite mission is shown to result potentially in over an order of magnitude improvement in the detectable value of r. With sufficient knowledge of the experimental bandpasses as well as foreground component scaling laws, our conclusions are found to be independent on the assumed overall normalization of the foregrounds and only quantitatively depend on specific parametrizations assumed for the foreground components.Comment: 5 pages, 2 figure

Accelerating Cosmic Microwave Background map-making procedure through preconditioning

Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In this work we study new map-making solvers potentially suitable for applications to the largest anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners. We apply the proposed solvers to examples of simulated non-polarised and polarised CMB observations, and a set of idealised scanning strategies with sky coverage ranging from nearly a full sky down to small sky patches. We discuss in detail their implementation for massively parallel computational platforms and their performance for a broad range of parameters characterising the simulated data sets. We find that our best new solver can outperform carefully-optimised standard solvers used today by a factor of as much as 5 in terms of the convergence rate and a factor of up to $4$ in terms of the time to solution, and to do so without significantly increasing the memory consumption and the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable and robust, and less dependent on specific characteristics of the analysed data set. We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets.Comment: 19 pages // Final version submitted to A&

Spherical harmonic transform with GPUs

We describe an algorithm for computing an inverse spherical harmonic transform suitable for graphic processing units (GPU). We use CUDA and base our implementation on a Fortran90 routine included in a publicly available parallel package, S2HAT. We focus our attention on the two major sequential steps involved in the transforms computation, retaining the efficient parallel framework of the original code. We detail optimization techniques used to enhance the performance of the CUDA-based code and contrast them with those implemented in the Fortran90 version. We also present performance comparisons of a single CPU plus GPU unit with the S2HAT code running on either a single or 4 processors. In particular we find that use of the latest generation of GPUs, such as NVIDIA GF100 (Fermi), can accelerate the spherical harmonic transforms by as much as 18 times with respect to S2HAT executed on one core, and by as much as 5.5 with respect to S2HAT on 4 cores, with the overall performance being limited by the Fast Fourier transforms. The work presented here has been performed in the context of the Cosmic Microwave Background simulations and analysis. However, we expect that the developed software will be of more general interest and applicability

Characterising cosmic birefringence in the presence of galactic foregrounds and instrumental systematic effects

We study a possibility of constraining isotropic cosmic birefringence with help of cosmic microwave background polarisation data in the presence of polarisation angle miscalibration without relying on any assumptions about the Galactic foreground angular power spectra and in particular on their EB correlation. We propose a new analysis framework based on a generalised parametric component separation approach, which accounts simultaneously on the presence of galactic foregrounds, relevant instrumental effects and external priors. We find that upcoming multi-frequency CMB data with appropriate calibration priors will allow producing an instrumental-effect-corrected and foreground-cleaned CMB map, which can be used to estimate the isotropic birefringence angle and the tensor-to-scalar ratio, accounting on statistical and systematic uncertainties incurred during the entire procedure. In particular, in the case of a Simons Observatory-like, three Small Aperture Telescopes, we derive an uncertainty on the birefringence angle of $\sigma(\beta_{b}) = 0.07^\circ$ (0.1$^\circ$), assuming the standard cosmology and calibration priors for all (single) frequency channels with the precision of $\sigma(\alpha_i)= 0.1^\circ$ as aimed at by the near future ground-based experiments. This implies that these experiments could confirm or disprove the recently detected value of $\beta_b=0.35^\circ$ with a significance between $3$ and $5 \sigma$. [abridged version]Comment: 20 pages, 9 figure

Forecasting performance of CMB experiments in the presence of complex foreground contaminations

We present a new, semianalytic framework for estimating the level of residuals present in cosmic microwave background (CMB) maps derived from multifrequency CMB data and forecasting their impact on cosmological parameters. The data are assumed to contain non-negligible signals of astrophysical and/or Galactic origin, which we clean using a parametric component separation technique. We account for discrepancies between the foreground model assumed during the separation procedure and the true one, allowing for differences in scaling laws and/or their spatial variations. Our estimates and their uncertainties include both systematic and statistical effects and are averaged over the instrumental noise and CMB signal realizations. The framework can be further extended to account self-consistently for existing uncertainties in the foreground models. We demonstrate and validate the framework on simple study cases which aim at estimating the tensor-to-scalar ratio, r. The proposed approach is computationally efficient permitting an investigation of hundreds of setups and foreground models on a single CPU

Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments

An estimation of the sky signal from streams of Time Ordered Data (TOD) acquired by Cosmic Microwave Background (cmb) experiments is one of the most important steps in the context of cmb data analysis referred to as the map-making problem. The continuously growing cmb data sets render the cmb map-making problem more challenging in terms of computational cost and memory in particular in the context of ground based experiments. In this context, we study a novel class of the Preconditioned Conjugate Gradient (PCG) solvers which invoke two-level preconditioners. We compare them against PCG solvers commonly used in the map-making context considering their precision and time-to-solution. We compare these new methods on realistic, simulated data sets reflecting the characteristics of current and forthcoming cmb ground-based experiment. We develop an embarrassingly parallel implementation of the approach where each processor performs a sequential map-making for a subset of the TOD. We find that considering the map level residuals the new class of solvers permits achieving tolerance of up to 3 orders of magnitude better than the standard approach, where the residual level often saturates before convergence is reached. This corresponds to an important improvement in the precision of recovered power spectra in particular on the largest angular scales. The new method also typically requires fewer iterations to reach a required precision and thus shorter runtimes for a single map-making solution. However, the construction of an appropriate two-level preconditioner can be as costly as a single standard map-making run. Nevertheless, if the same problem needs to be solved multiple times, e.g., as in Monte Carlo simulations, this cost has to be incurred only once, and the method should be competitive not only as far as its precision but also its performance is concerned

Making Maps Of The Cosmic Microwave Background: The MAXIMA Example

This work describes Cosmic Microwave Background (CMB) data analysis algorithms and their implementations, developed to produce a pixelized map of the sky and a corresponding pixel-pixel noise correlation matrix from time ordered data for a CMB mapping experiment. We discuss in turn algorithms for estimating noise properties from the time ordered data, techniques for manipulating the time ordered data, and a number of variants of the maximum likelihood map-making procedure. We pay particular attention to issues pertinent to real CMB data, and present ways of incorporating them within the framework of maximum likelihood map-making. Making a map of the sky is shown to be not only an intermediate step rendering an image of the sky, but also an important diagnostic stage, when tests for and/or removal of systematic effects can efficiently be performed. The case under study is the MAXIMA data set. However, the methods discussed are expected to be applicable to the analysis of other current and forthcoming CMB experiments.Comment: Replaced to match the published version, only minor change

Separating polarized cosmological and galactic emissions for CMB B-mode polarization experiments

In this work we study the relevance of the component separation technique based on the Independent Component Analysis (ICA) and investigate its performance in the context of a limited sky coverage observation and from the viewpoint of our ability to differentiate between cosmological models with different primordial B-mode content. We focus on the low Galactic emission sky patch, corresponding to the target of several operating and planned CMB experiments and which, in many respects, adequately represents a typical "clean" high latitude sky. We consider two fiducial observations, one operating at low (40, 90 GHz) and one at high (150, 350 GHz) frequencies and thus dominated by the synchrotron and thermal dust emission, respectively. We use a parallel version of the FASTICA code to explore a substantial parameter space including Gaussian pixel noise level, observed sky area and the amplitude of the foreground emission and employ large Monte Carlo simulations to quantify errors and biases pertinent to the reconstruction for different choices of the parameter values. We identify a large subspace of the parameter space for which the quality of the CMB reconstruction is excellent. For both the cosmological models, with and without the primordial gravitational waves, we find that FASTICA performs extremely well even in the cases when the B mode CMB signal is up to a few times weaker than the foreground contamination and the noise amplitude is comparable with the total CMB polarized emission. In addition we discuss limiting cases of the noise and foreground amplitudes, for which the ICA approach fails.Comment: 19 pages, 12 figures, 5 tables, replaced to match published versio