HEALPix--the Hierarchical Equal Area isoLatitude Pixelization--is a versatile structure for the pixelization of data on the sphere. An associated library of computational algorithms and visualization ...software supports fast scientific applications executable directly on discretized spherical maps generated from very large volumes of astronomical data. Originally developed to address the data processing and analysis needs of the present generation of cosmic microwave background experiments (e.g., BOOMERANG, WMAP), HEALPix can be expanded to meet many of the profound challenges that will arise in confrontation with the observational output of future missions and experiments, including, e.g., Planck, Herschel, SAFIR, and the Beyond Einstein inflation probe. In this paper we consider the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere. We demonstrate how these are explicitly satisfied by HEALPix.
Background Imaging of Cosmic Extragalactic Polarization (BICEP) is a bolometric polarimeter designed to measure the inflationary B-mode polarization of the cosmic microwave background (CMB) at degree ...angular scales. During three seasons of observing at the South Pole (2006 through 2008), BICEP mapped ~2% of the sky chosen to be uniquely clean of polarized foreground emission. Here, we present initial results derived from a subset of the data acquired during the first two years. We present maps of temperature, Stokes Q and U, E and B modes, and associated angular power spectra. We demonstrate that the polarization data are self-consistent by performing a series of jackknife tests. We study potential systematic errors in detail and show that they are sub-dominant to the statistical errors. We measure the E-mode angular power spectrum with high precision at 21 <= ell <= 335, detecting for the first time the peak expected at ell ~ 140. The measured E-mode spectrum is consistent with expectations from a ΛCDM model, and the B-mode spectrum is consistent with zero. The tensor-to-scalar ratio derived from the B-mode spectrum is r = 0.02+0.31 -0.26, or r < 0.72 at 95% confidence, the first meaningful constraint on the inflationary gravitational wave background to come directly from CMB B-mode polarization.
This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, ...storing them on disk, and transmitting them between computers. While these considerations were originally motivated by the specific tasks of representing sky coverage and cross-matching catalogues of astronomical surveys, they can be profitably applied in many other situations as well.
We propose a novel approximation to the low-ℓ joint likelihood of the angular spectrum Cℓ of masked cosmic microwave background temperature maps which is both very accurate and very fast to evaluate. ...We show that, for a flat prior, the posterior distribution of each Cℓ closely follows an inverse gamma distribution even with partial sky coverage and that the posterior correlation is weak enough that a copula approximation to the joint likelihood is quite accurate. In this paper, the quantities needed to build such a copula approximation (inverse gamma parameters at each angular frequency and a correlation matrix) are computed from an exploration of the posterior using adaptive importance sampling. The accuracy of the proposed approximation is assessed using statistical criteria as well as a mock cosmological parameter fit. When applied to the Wilkinson Microwave Anisotropy Probe 5 data set, the copula approximation yields cosmological parameter estimates at the same level of accuracy as the best current techniques.
The Background Imaging of Cosmic Extragalactic Polarization (BICEP) experiment was designed specifically to search for the signature of inflationary gravitational waves in the polarization of the ...cosmic microwave background (CMB). Using a novel small-aperture refractor and 49 pairs of polarization-sensitive bolometers, BICEP has completed three years of successful observations at the South Pole beginning in 2006 February. To constrain the amplitude of the inflationary B-mode polarization, which is expected to be at least 7 orders of magnitude fainter than the 3 K CMB intensity, precise control of systematic effects is essential. This paper describes the characterization of potential systematic errors for the BICEP experiment, supplementing a companion paper on the initial cosmological results. Using the analysis pipelines for the experiment, we have simulated the impact of systematic errors on the B-mode polarization measurement. Guided by these simulations, we have established benchmarks for the characterization of critical instrumental properties including bolometer relative gains, beam mismatch, polarization orientation, telescope pointing, sidelobes, thermal stability, and timestream noise model. A comparison of the benchmarks with the measured values shows that we have characterized the instrument adequately to ensure that systematic errors do not limit BICEP's two-year results, and identifies which future refinements are likely necessary to probe inflationary B-mode polarization down to levels below a tensor-to-scalar ratio r = 0.1.
We report on observations of the cosmic microwave background (CMB) obtained during the 2003 January flight of BOOMERANG. These results are derived from 195 hr of observation with four 145 GHz ...polarization-sensitive bolometer (PSB) pairs, identical in design to the four 143 GHz Planck High Frequency Instrument (HFI) polarized pixels. The data include 75 hr of observations distributed over 1.84% of the sky with an additional 120 hr concentrated on the central portion of the field, which represents 0.22% of the full sky. From these data we derive an estimate of the angular power spectrum of temperature fluctuations of the CMB in 24 bands over the multipole range 50 ,l,1500. A series of features, consistent with those expected from acoustic oscillations in the primordial photon-baryon fluid, are clearly evident in the power spectrum, as is the exponential damping of power on scales smaller than the photon mean free path at the epoch of last scattering (l 900). As a consistency check, the collaboration has performed two fully independent analyses of the time-ordered data, which are found to be in excellent agreement.
We present the cosmological parameters from the CMB intensity and polarization power spectra of the 2003 Antarctic flight of the BOOMERANG telescope. The BOOMERANG data alone constrain the parameters ...of the CDM model remarkably well and are consistent with constraints from a multiexperiment combined CMB data set. We add LSS data from the 2dF and SDSS redshift surveys to the combined CMB data set and test several extensions to the standard model including running of the spectral index, curvature, tensor modes, the effect of massive neutrinos, and an effective equation of state for dark energy. We also include an analysis of constraints to a model that allows a CDM isocurvature admixture.
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