Cosmological Parameters from CMB Maps without Likelihood Approximation

We propose an efficient Bayesian MCMC algorithm for estimating cosmological parameters from CMB data without use of likelihood approximations. It builds on a previously developed Gibbs sampling framework that allows for exploration of the joint CMB sky signal and power spectrum posterior, P(s,Cl|d), and addresses a long-standing problem of efficient parameter estimation simultaneously in high and low signal-to-noise regimes. To achieve this, our new algorithm introduces a joint Markov Chain move in which both the signal map and power spectrum are synchronously modified, by rescaling the map according to the proposed power spectrum before evaluating the Metropolis-Hastings accept probability. Such a move was already introduced by Jewell et al. (2009), who used it to explore low signal-to-noise posteriors. However, they also found that the same algorithm is inefficient in the high signal-to-noise regime, since a brute-force rescaling operation does not account for phase information. This problem is mitigated in the new algorithm by subtracting the Wiener filter mean field from the proposed map prior to rescaling, leaving high signal-to-noise information invariant in the joint step, and effectively only rescaling the low signal-to-noise component. To explore the full posterior, the new joint move is then interleaved with a standard conditional Gibbs sky map move. We apply our new algorithm to simplified simulations for which we can evaluate the exact posterior to study both its accuracy and performance, and find good agreement with the exact posterior; marginal means agree to less than 0.006 sigma, and standard deviations to better than 3%. The Markov Chain correlation length is of the same order of magnitude as those obtained by other standard samplers in the field.Comment: 9 pages, 3 figures, Published in Ap

WALOP-South: A Four Camera One Shot Imaging Polarimeter for PASIPHAE Survey. Paper I -- Optical Design

The WALOP-South instrument will be mounted on the 1 m SAAO telescope in South Africa as part of the PASIPHAE program to carry out a linear imaging polarization survey of the Galactic polar regions in the optical band. Designed to achieve polarimetric sensitivity of $0.05~\%$ across a $35\times35$ arcminute field of view, it will be capable of measuring the Stokes parameters I, q and u in a single exposure in the SDSS-r broadband and narrowband filters between $0.5~{\mu}m - 0.7~{\mu}m$. For each measurement, four images of the full field corresponding to linear polarization angles of 0 deg, 45 deg, 90 deg and 135 deg in the instrument coordinate system will be created on four detectors from which the Stokes parameters can be found using differential photometry. In designing the optical system, major challenges included correcting for the dispersion introduced by large split angle Wollaston Prisms used as analysers as well as other aberrations from the entire field to obtain imaging quality PSF at the detector. We present the optical design of the WALOP-South instrument which overcomes these challenges and delivers near seeing limited PSFs for the entire field of view.Comment: 31 pages, 18 Figures and 8 Tables. Accepted in the Journal of Astronomical Telescopes, Instruments, and System

COMAP Early Science: III. CO Data Processing

We describe the first season COMAP analysis pipeline that converts raw detector readouts to calibrated sky maps. This pipeline implements four main steps: gain calibration, filtering, data selection, and map-making. Absolute gain calibration relies on a combination of instrumental and astrophysical sources, while relative gain calibration exploits real-time total-power variations. High efficiency filtering is achieved through spectroscopic common-mode rejection within and across receivers, resulting in nearly uncorrelated white noise within single-frequency channels. Consequently, near-optimal but biased maps are produced by binning the filtered time stream into pixelized maps; the corresponding signal bias transfer function is estimated through simulations. Data selection is performed automatically through a series of goodness-of-fit statistics, including $\chi^2$ and multi-scale correlation tests. Applying this pipeline to the first-season COMAP data, we produce a dataset with very low levels of correlated noise. We find that one of our two scanning strategies (the Lissajous type) is sensitive to residual instrumental systematics. As a result, we no longer use this type of scan and exclude data taken this way from our Season 1 power spectrum estimates. We perform a careful analysis of our data processing and observing efficiencies and take account of planned improvements to estimate our future performance. Power spectrum results derived from the first-season COMAP maps are presented and discussed in companion papers.Comment: Paper 3 of 7 in series. 26 pages, 23 figures, submitted to Ap

COMAP Early Science: IV. Power Spectrum Methodology and Results

We present the power spectrum methodology used for the first-season COMAP analysis, and assess the quality of the current data set. The main results are derived through the Feed-feed Pseudo-Cross-Spectrum (FPXS) method, which is a robust estimator with respect to both noise modeling errors and experimental systematics. We use effective transfer functions to take into account the effects of instrumental beam smoothing and various filter operations applied during the low-level data processing. The power spectra estimated in this way have allowed us to identify a systematic error associated with one of our two scanning strategies, believed to be due to residual ground or atmospheric contamination. We omit these data from our analysis and no longer use this scanning technique for observations. We present the power spectra from our first season of observing and demonstrate that the uncertainties are integrating as expected for uncorrelated noise, with any residual systematics suppressed to a level below the noise. Using the FPXS method, and combining data on scales $k=0.051-0.62 \,\mathrm{Mpc}^{-1}$ we estimate $P_\mathrm{CO}(k) = -2.7 \pm 1.7 \times 10^4\mu\textrm{K}^2\mathrm{Mpc}^3$, the first direct 3D constraint on the clustering component of the CO(1-0) power spectrum in the literature.Comment: Paper 4 of 7 in series. 18 pages, 11 figures, as accepted in Ap

A CMB Gibbs sampler for localized secondary anisotropies

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-Zel'dovich (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

Planck intermediate results: XVI. Profile likelihoods for cosmological parameters

We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination. Reproduced with permission from Astronomy & Astrophysics, © ESO 201

Planck intermediate results. XIX. An overview of the polarized thermal emission from Galactic dust

This paper presents an overview of the polarized sky as seen by Planck HFI at 353 GHz, which is the most sensitive Planck channel for dust polarization. We construct and analyse maps of dust polarization fraction and polarization angle at 1° resolution, taking into account noise bias and possible systematic effects. The sensitivity of the Planck HFI polarization measurements allows for the first time a mapping of Galactic dust polarized emission on large scales, including low column density regions. We find that the maximum observed dust polarization fraction is high (pmax = 19.8%), in particular in some regions of moderate hydrogen column density (NH < 2 × 1021 cm-2). The polarization fraction displays a large scatter at NH below a few 1021 cm-2. There is a general decrease in the dust polarization fraction with increasing column density above NH ≃ 1 × 1021 cm-2 and in particular a sharp drop above NH ≃ 1.5 × 1022 cm-2. We characterize the spatial structure of the polarization angle using the angle dispersion function. We find that the polarization angle is ordered over extended areas of several square degrees, separated by filamentary structures of high angle dispersion function. These appear as interfaces where the sky projection of the magnetic field changes abruptly without variations in the column density. The polarization fraction is found to be anti-correlated with the dispersion of polarization angles. These results suggest that, at the resolution of 1°, depolarization is due mainly to fluctuations in the magnetic field orientation along the line of sight, rather than to the loss of grain alignment in shielded regions. We also compare the polarization of thermal dust emission with that of synchrotron measured with Planck, low-frequency radio data, and Faraday rotation measurements toward extragalactic sources. These components bear resemblance along the Galactic plane and in some regions such as the Fan and North Polar Spur regions. The poor match observed in other regions shows, however, that dust, cosmic-ray electrons, and thermal electrons generally sample different parts of the line of sight. Reproduced with permission, © ESO, 201

Planck intermediate results. XV. A study of anomalous microwave emission in Galactic clouds

Anomalous microwave emission (AME) is believed to be due to electric dipole radiation from small spinning dust grains. The aim of this paper is a statistical study of the basic properties of AME regions and the environment in which they emit. We used WMAP and Planck maps, combined with ancillary radio and IR data, to construct a sample of 98 candidate AME sources, assembling SEDs for each source using aperture photometry on 1°-smoothed maps from 0.408 GHz up to 3000 GHz. Each spectrum is fitted with a simple model of free-free, synchrotron (where necessary), cosmic microwave background (CMB), thermal dust, and spinning dust components. We find that 42 of the 98 sources have significant (>5σ) excess emission at frequencies between 20 and 60 GHz. An analysis of the potential contribution of optically thick free-free emission from ultra-compact H ii regions, using IR colour criteria, reduces the significant AME sample to 27 regions. The spectrum of the AME is consistent with model spectra of spinning dust. Peak frequencies are in the range 20−35 GHz except for the California nebula (NGC 1499), which appears to have a high spinning dust peak frequency of (50 ± 17) GHz. The AME regions tend to be more spatially extended than regions with little or no AME. The AME intensity is strongly correlated with the sub-millimetre/IR flux densities and comparable to previous AME detections in the literature. AME emissivity, defined as the ratio of AME to dust optical depth, varies by an order of magnitude for the AME regions. The AME regions tend to be associated with cooler dust in the range 14−20 K and an average emissivity index, βd, of +1.8, while the non-AME regions are typically warmer, at 20−27 K. In agreement with previous studies, the AME emissivity appears to decrease with increasing column density. This supports the idea of AME originating from small grains that are known to be depleted in dense regions, probably due to coagulation onto larger grains. We also find a correlation between the AME emissivity (and to a lesser degree the spinning dust peak frequency) and the intensity of the interstellar radiation field, G0. Modelling of this trend suggests that both radiative and collisional excitation are important for the spinning dust emission. The most significant AME regions tend to have relatively less ionized gas (free-free emission), although this could be a selection effect. The infrared excess, a measure of the heating of dust associated with H ii regions, is typically >4 for AME sources, indicating that the dust is not primarily heated by hot OB stars. The AME regions are associated with known dark nebulae and have higher 12 μm/25 μm ratios. The emerging picture is that the bulk of the AME is coming from the polycyclic aromatic hydrocarbons and small dust grains from the colder neutral interstellar medium phase. Reproduced with permission from Astronomy & Astrophysics, © ESO 201