A. J. Banday

The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths

We present the Planck Sky Model (PSM), a parametric model for generating all-sky, few arcminute resolution maps of sky emission at submillimetre to centimetre wavelengths, in both intensity and polarisation. Several options are implemented to model the cosmic microwave background, Galactic diffuse emission (synchrotron, free-free, thermal and spinning dust, CO lines), Galactic HII regions, extragalactic radio sources, dusty galaxies, and thermal and kinetic Sunyaev-Zeldovich signals from clusters of galaxies. Each component is simulated by means of educated interpolations/extrapolations of data sets available at the time of the launch of the Planck mission, complemented by state-of-the-art models of the emission. Distinctive features of the simulations are spatially varying spectral properties of synchrotron and dust; different spectral parameters for each point source; modelling of the clustering properties of extragalactic sources and of the power spectrum of fluctuations in the cosmic infrared background. The PSM enables the production of random realisations of the sky emission, constrained to match observational data within their uncertainties. It is implemented in a software package that is regularly updated with incoming information from observations. The model is expected to serve as a useful tool for optimising planned microwave and sub-millimetre surveys and testing data processing and analysis pipelines. It is, in particular, used to develop and validate data analysis pipelines within the Planck collaboration. A version of the software that can be used for simulating the observations for a variety of experiments is made available on a dedicated website.

COBE DMR-normalized open inflation cold dark matter cosmogony

A cut-sky orthogonal mode analysis of the 2 year COBE DMR 53 and 90 GHz sky maps (in Galactic coordinates) is used to determine the normalization of an open inflation model based on the cold dark matter (CDM) scenario. The normalized model is compared to measures of large-scale structure in the universe. Although the DMR data alone does not provide sufficient discriminative power to prefer a particular value of the mass density parameter, the open model appears to be reasonably consistent with observations when Omega(sub 0) is approximately 0.3-0.4 and merits further study.

Constraints on the topology of the Universe derived from the 7-yr WMAP data

We impose constraints on the topology of the Universe determined from a search for matched circles in the temperature anisotropy patterns of the 7-year WMAP data. We pay special attention to the sensitivity of the method to residual foreground contamination of the sky maps, and show that for a full sky estimate of the CMB signal (the ILC map) such residuals introduce a non-negligible effect on the statistics of matched circles. In order to reduce this effect, we perform the analysis on maps for which the most contaminated regions have been removed. A search for pairs of matched back-to-back circles in the higher resolution WMAP W-band map allows tighter constraints to be imposed on topology. Our results rule out universes with topologies that predict pairs of such circles with radii larger than \alpha_min \approx 10 degrees. This places a lower bound on the size of the fundamental domain for a flat universe of about 27.9 Gpc. This bound is close to the upper limit on the size of Universe possible to detect by the method of matched circles, i.e. the diameter of the observable Universe is 28.3 Gpc.

Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background.

We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.

Non-Gaussian signatures in the five-year WMAP data as identified with isotropic scaling indices

We continue the analysis of non-Gaussianities in the cosmic microwave background by means of the scaling index method by applying this method on the single Q, V, W bands and the co-added VW band of the five-year data of the Wilkinson Microwave Anisotropy Probe. We compare each of the results with 1000 Monte Carlo simulations mimicking the Gaussian properties of the best fitting A cold dark matter model. Based on the scaling indices, scale-dependent empirical probability distributions, moments of these distributions and χ 2 combinations of them are calculated, obtaining similar results as in the former analysis of the three-year data: we derive evidence for non-Gaussianity with a probability of up to 97.3 per cent for the mean when regarding the KQ75-masked full sky and summing up over all considered length-scales by means of a diagonal χ 2 statistics. Looking at only the northern or southern hemisphere of the galactic coordinate system, we obtain up to 98.5 or 96.6 per cent, respectively. For the standard deviation, these results appear as 95.6 per cent for the full sky (99.7 per cent north, 89.4 per cent south) and for a χ 2 combination of both measurements as 97.4 per cent (99.1 per cent north, 95.5 per cent south). We obtain larger deviations from Gaussianity when looking at separate scale lengths. By performing an analysis of rotated hemispheres, we detect an obvious asymmetry in the data. In addition to these investigations, we present a method of filling the mask with Gaussian noise to eliminate boundary effects caused by the mask. With the help of this technique, we identify several local features on the map, of which the most significant one turns out to be the well-known cold spot. When excluding all these spots from the analysis, the deviation from Gaussianity increases, which shows that the discovered local anomalies are not the reason of the global detection of non-Gaussianity, but actually were damping the deviations on average. Our analyses per band and per year suggest, however, that it is very unlikely that the detected anomalies are due to foreground effects.

Foreground analysis using cross-correlations of external templates on the 7-year Wilkinson Microwave Anisotropy Probe data

Wilkinson Microwave Anisotropy Probe (WMAP) data when combined with ancillary data on free–free, synchrotron and dust allow an improved understanding of the spectrum of emission from each of these components. Here we examine the sky variation at intermediate and high latitudes using a cross-correlation technique. In particular, we compare the observed emission in several global partitions of the sky plus 33 selected sky regions to three ‘standard’ templates. The regions are selected using a criterion based on the morphology of these template maps. The synchrotron emission shows evidence of steepening between GHz frequencies and the WMAP bands. There are indications of spectral index variations across the sky, but the current data are not precise enough to accurately quantify this from region to region. The Hα template correlated emission derived from the global fits shows clear evidence of deviation from a free–free spectrum. If this spectrum is decomposed into a contribution from both free–free and spinning dust emission in the warm ionized medium of the Galaxy, the derived free–free emissivity corresponds to a mean electron temperature of ∼6000 K (a value critically dependent on the impact of dust absorption on the Hα intensity), and the spinning dust emission has a peak emission in intensity typically in the range 40–50 GHz. However, the analysis of the smaller regions is generally unrevealing and the analysis presented here does not unambiguously demonstrate the presence of spinning dust emission in the warm ionized medium, as advocated by Dobler & Finkbeiner. The anomalous microwave emission associated with dust is detected at high significance in most of the 33 fields studied. The anomalous emission correlates well with the Finkbeiner et al. model 8 predictions (FDS8) at 94 GHz, and is well described globally by a power-law emission model with an effective spectral index between 20 and 60 GHz of β≈−2.7. It is clear that attempts to explain the emission by spinning dust models require multiple components, which presumably relates to a complex mix of emission regions along a given line of sight. An enhancement of the thermal dust contribution over the FDS8 predictions by a factor ∼1.2 is required with such models. Furthermore, the emissivity varies by a factor of ∼50 per cent from cloud to cloud relative to the mean. The significance of these results for the correction of cosmic microwave background data for Galactic foreground emission is discussed.

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Scale-dependent non-Gaussianities in the CMB data identified with Minkowski functionals and scaling indices

We present further investigations of the Wilkinson Microwave Anisotropy Probe (WMAP) data by means of the Minkowski functionals and the scaling index method. In order to test for non-Gaussianities (NGs) with respect to scale-dependencies we use so-called surrogate maps, in which possible phase correlations of the Fourier phases of the original WMAP data and the simulations, respectively, are destroyed by applying a shuing scheme to the maps. A statistical comparison of the original maps with the surrogate maps then allows to test for the existence of higher order correlations (HOCs) in the original maps, also and especially on well-dened Fourier modes.

Scale-dependent non-Gaussianities in the WMAP data as identified by using surrogates and scaling indices

We present a model-independent investigation of the Wilkinson Microwave Anisotropy Probe (WMAP) data with respect to scale-independent and scale-dependent non-Gaussianities (NGs). To this end, we employ the method of constrained randomization. For generating so-called surrogate maps a well-specified shuffling scheme is applied to the Fourier phases of the original data, which allows us to test for the presence of higher order correlations (HOCs) also and especially on well-defined scales. Using scaling indices as test statistics for the HOCs in the maps we find highly significant signatures for NGs when considering all scales. We test for NGs in four different l-bands Δl, namely in the bands Δl=[2, 20], [20, 60], [60, 120] and [120, 300]. We find highly significant signatures for both NGs and ecliptic hemispherical asymmetries for the interval Δl=[2, 20] covering the large scales. We also obtain highly significant deviations from Gaussianity for the band Δl=[120, 300]. The result for the full l-range can then easily be interpreted as a superposition of the signatures found in the bands Δl=[2, 20] and [120, 300]. We find remarkably similar results when analysing different ILC-like maps based on the WMAP 3-, 5- and 7-year data. We perform a set of tests to investigate whether and to what extent the detected anomalies can be explained by systematics. While none of these tests can convincingly rule out the intrinsic nature of the anomalies for the low-l case, the ILC map making procedure and/or residual noise in the maps can also lead to NGs at small scales. Our investigations prove that there are phase correlations in the WMAP data of the cosmic microwave background. In the absence of an explanation in terms of Galactic foregrounds or known systematic artefacts, the signatures at low l must so far be taken to be cosmological at high significance. These findings would strongly disagree with predictions of isotropic cosmologies with single field slow roll inflation. The task is now to elucidate the origin of the phase correlations and to understand the physical processes leading to these scale-dependent NGs - if it turns out that systematics as a cause for them must be ruled out.

Comparison of the COBE DMR and Tenerife Data

We have compared the Tenerife data with the COBEDifferential Microwave Radiometer (DMR) 2 year data in the declination+40 region of the sky observed by the Tenerife experiment. Using theGalactic plane signal at 30 GHz, we show that the two data sets arecross-calibrated to within 5 percent. The high Galactic latitude datawere investigated for the presence of common structures with theproperties of cosmic microwave background (CMB) fluctuations. The mostprominent feature in the Tenerife data (AT 80 muK) appears to be presentin both the 53 and 90 GHz DMR maps and has the Planckian spectrumexpected for CMB anisotropy. The cross-correlation function of theTenerife and DMR scans is indicative of common structure and at zero laghas the value C(0)112=34+1153 muK. The combination of the spatial andspectral information from the two data sets is consistent with thepresence of cosmic microwave background anisotropies common to both. Theprobability that noise could produce the observed agreement is less than5 percent.