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1.
A number of experiments for measuring anisotropies of the cosmic microwave background (CMB) use scanning strategies in which temperature fluctuations are measured along circular scans on the sky. It is possible, from a large number of such intersecting circular scans, to build two-dimensional sky maps for subsequent analysis. However, since instrumental effects — especially the excess low-frequency 1/ f noise — project on to such two-dimensional maps in a non-trivial way, we discuss the analysis approach which focuses on information contained in the individual circular scans. This natural way of looking at CMB data from experiments scanning on the circles combines the advantages of elegant simplicity of Fourier series for the computation of statistics useful for constraining cosmological scenarios, and superior efficiency in analysing and quantifying most of the crucial instrumental effects.  相似文献   

2.
Destriping methods for constructing maps of the cosmic microwave background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates for Planck -like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. Assuming Planck -like low-frequency noise, the noise power spectrum is accurately white at high multipoles  (ℓ≳ 50)  . Destriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis of Planck data and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic '1/ f ' noise.  相似文献   

3.
Using a set of compilations of measurements for extragalactic radio sources, we construct all-sky maps of the Faraday rotation produced by the Galactic magnetic field. In order to generate the maps, we treat the radio source positions as a kind of 'mask' and construct combinations of spherical harmonic modes that are orthogonal on the masked sky. As long as relatively small multipoles are used, the resulting maps are quite stable to changes in the selection criteria for the sources, and show clearly the structure of the local Galactic magnetic field. We also suggest the use of these maps as templates for cosmic microwave background (CMB) foreground analysis, illustrating the idea with a cross-correlation analysis between the Wilkinson Microwave Anisotropy Probe ( WMAP ) data and our maps. We find a significant cross-correlation, indicating the presence of a significant residual contamination.  相似文献   

4.
We present a harmonic model for the data analysis of an all-sky cosmic microwave background survey, such as Planck , where the survey is obtained through ring-scans of the sky. In this model, resampling and pixelization of the data are avoided. The spherical transforms of the sky at each frequency, in total intensity and polarization, as well as the bright-point-source catalogue, are derived directly from the data reduced on to the rings. Formal errors and the most significant correlation coefficients for the spherical transforms of the frequency maps are preserved. A clean and transparent path from the original samplings in the time domain to the final scientific products is thus obtained. The data analysis is largely based on Fourier analysis of rings; the positional stability of the instrument's spin axis during these scans is a requirement for the data model and is investigated here for the Planck satellite. Brighter point sources are recognized and extracted as part of the ring reductions and, on the basis of accumulated data, used to build the bright-point-source catalogue. The analysis of the rings is performed in an iterative loop, involving a range of geometric and detector response calibrations. The geometric calibrations are used to reconstruct the paths of the detectors over the sky during a scan and the phase offsets between scans of different detectors; the response calibrations eliminate short- and long-term variations in detector response. Point-source information may allow the reconstruction of the beam profile. The reconstructed spherical transforms of the sky in each frequency channel form the input to the subsequent analysis stages. Although the methods in this paper were developed with the data processing for the Planck satellite in mind, there are many aspects which have wider implementation possibilities, including the construction of real-space pixelized maps.  相似文献   

5.
Using large numbers of simulations of the microwave sky, incorporating the cosmic microwave background (CMB) and the Sunyaev–Zel'dovich (SZ) effect due to clusters, we investigate the statistics of the power spectrum at microwave frequencies between spherical multipoles of 1000 and 10 000. From these virtual sky maps, we find that the spectrum of the SZ effect has a larger standard deviation by a factor of 3 than would be expected from purely Gaussian realizations, and has a distribution that is significantly skewed towards higher values, especially when small map sizes are used. The standard deviation is also increased by around 10 per cent compared to the trispectrum calculation due to the clustering of galaxy clusters. We also consider the effects of including residual point sources and uncertainties in the gas physics. This has implications for the excess power measured in the CMB power spectrum by the Cosmic Background Imager (CBI) and Berkeley–Illinois–Maryland Association (BIMA) experiments. Our results indicate that the observed excess could be explained using a lower value of σ8 than previously suggested, however the effect is not enough to match  σ8= 0.825  . The uncertainties in the gas physics could also play a substantial role. We have made our maps of the SZ effect available online.  相似文献   

6.
Polarization is the next frontier of cosmic microwave background analysis, but its signal is dominated over much of the sky by foregrounds which must be carefully removed. To determine the efficacy of this cleaning, it is necessary to have sensitive tests for residual foreground contamination in polarization sky maps. The dominant Galactic foregrounds introduce a large-scale anisotropy on to the sky, so it makes sense to use a statistic sensitive to overall directionality for this purpose. Here, we adapt the rapidly computable     statistic of Bunn and Scott to polarization data, and demonstrate its utility as a foreground monitor by applying it to the low-resolution Wilkinson Microwave Anisotropy Probe 3-yr sky maps. With a thorough simulation of the maps' noise properties, we find no evidence for contamination in the foreground cleaned sky maps.  相似文献   

7.
We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.  相似文献   

8.
Large patterns could exist on the microwave sky as a result of various non-standard possibilities for the large-scale Universe – rotation or shear, non-trivial topology, and single topological defects are specific examples. All-sky (or nearly all-sky) CMB data sets allow us, uniquely, to constrain such exotica, and it is therefore worthwhile to explore a wide range of statistical tests. We describe one such statistic here, which is based on determining gradients and is useful for assessing the level of 'preferred directionality' or 'stripiness' in the map. This method is more general than other techniques for picking out specific patterns on the sky, and it also has the advantage of being easily calculable for the mega-pixel maps which will soon be available. For the purposes of illustration, we apply this statistic to the four-year COBE DMR data. For future CMB maps, we expect this to be a useful statistical test of the large-scale structure of the Universe. In principle, the same statistic could also be applied to sky maps at other wavelengths, to CMB polarization maps, and to catalogues of discrete objects. It may also be useful as a means of checking for residual directionality (e.g. from Galactic or ecliptic signals) in maps.  相似文献   

9.
An algorithm is proposed for denoising the signal induced by cosmic strings in the cosmic microwave background. A Bayesian approach is taken, based on modelling the string signal in the wavelet domain with generalized Gaussian distributions. Good performance of the algorithm is demonstrated by simulated experiments at arcminute resolution under noise conditions including primary and secondary cosmic microwave background anisotropies, as well as instrumental noise.  相似文献   

10.
Recently, a symmetry-based method to test for statistical isotropy of the cosmic microwave background was developed. We apply the method to template-cleaned 3- and 5-years Wilkinson Microwave Anisotropy Probe - Differencing Assembly maps. We examine a wide range of angular multipoles from  2 < l < 300  . The analysis detects statistically significant signals of anisotropy inconsistent with an isotropic cosmic microwave background in some of the foreground-cleaned maps. We are unable to resolve whether the anomalies have a cosmological, local astrophysical or instrumental origin. Assuming the anisotropy arises due to residual foreground contamination, we estimate the residual foreground power in the maps. For the W -band maps, we also find a highly improbable degree of isotropy we cannot explain. We speculate that excess isotropy may be caused by faulty modelling of detector noise.  相似文献   

11.
Wilkinson Microwave Anisotropy Probe has provided cosmic microwave background (CMB) maps of the full sky. The raw data are subject to foreground contamination, in particular near to the Galactic plane. Foreground-cleaned maps have been derived, e.g. the internal linear combination map of Bennett et al., and the reduced foreground TOH map of Tegmark et al. Using S statistics, we examine whether residual foreground contamination is left over in the foreground-cleaned maps. In particular, we specify which parts of the foreground-cleaned maps are sufficiently accurate for the circle-in-the-sky signature. We generalize the S statistic, called D statistic, such that the circle test can deal with CMB maps in which the contaminated regions of the sky are excluded with masks.  相似文献   

12.
We consider wavelets as a tool to perform a variety of tasks in the context of analysing cosmic microwave background (CMB) maps. Using spherical Haar wavelets, we define a position and angular-scale-dependent measure of power that can be used to assess the existence of spatial structure. We apply planar Daubechies wavelets for the identification and removal of point sources from small sections of sky maps. Our technique can successfully identify virtually all point sources that are above 3 and more than 80 per cent of those above 1 . We discuss the trade-offs between the levels of correct and false detections. We denoise and compress a 100 000-pixel CMB map by a factor of 10 in 5 s, achieving a noise reduction of about 35 per cent. In contrast to Wiener filtering, the compression process is model-independent and very fast. We discuss the usefulness of wavelets for power spectrum and cosmological-parameter estimation. We conclude that at present wavelet functions are most suitable for identifying localized sources.  相似文献   

13.
The Planck mission is the most sensitive all-sky cosmic microwave background (CMB) experiment currently planned. The High-Frequency Instrument (HFI) will be especially suited for observing clusters of galaxies by their thermal Sunyaev–Zel'dovich (SZ) effect. In order to assess Planck 's SZ capabilities in the presence of spurious signals, a simulation is presented that combines maps of the thermal and kinetic SZ effects with a realization of the CMB, in addition to Galactic foregrounds (synchrotron emission, free–free emission, thermal emission from dust, CO-line radiation) as well as the submillimetric emission from celestial bodies of our Solar system. Additionally, observational issues such as the finite angular resolution and spatially non-uniform instrumental noise of Planck 's sky maps are taken into account, yielding a set of all-sky flux maps, the autocorrelation and cross-correlation properties of which are examined in detail. In the second part of the paper, filtering schemes based on scale-adaptive and matched filtering are extended to spherical data sets, that enable the amplification of the weak SZ signal in the presence of all contaminations stated above. The theory of scale-adaptive and matched filtering in the framework of spherical maps is developed, the resulting filter kernel shapes are discussed and their functionality is verified.  相似文献   

14.
The map-making step of cosmic microwave background (CMB) data analysis involves linear inversion problems that cannot be performed by a brute-force approach for the large time-lines of today. In this paper we present optimal vector-only map-making methods, which are an iterative COBE method, a Wiener direct filter and a Wiener iterative method. We apply these methods on diverse simulated data, and we show that they produce very well restored maps, by removing nearly completely the correlated noise that appears as intense stripes on the simply pixel-averaged maps. The COBE iterative method can be applied to any signals, assuming the stationarity of the noise in the time-line. The Wiener methods assume both the stationarity of the noise and the sky, which is the case for CMB-only data. We apply the methods to Galactic signals too, and test them on balloon-borne experiment strategies and on a satellite whole-sky survey.  相似文献   

15.
We present a new method for analysing multidetector maps containing several astrophysical components. Our method, based on matching the data to a model in the spectral domain, permits us to estimate jointly the spatial power spectra of the components and of the noise, as well as their mixing coefficients. It is of particular relevance for analysis of millimetre-wave maps of cosmic microwave background (CMB) anisotropies.  相似文献   

16.
We present a new technique for constraining the topology of the Universe. The method exploits the existence of correlations in the phases of the spherical harmonic coefficients of the cosmic microwave background (CMB) temperature pattern associated with matched pairs of circles seen in the sky in universes with non-trivial topology. The method is computationally faster than all other statistics developed to hunt for these matched circles. We applied the method to a range of simulations with topologies of various forms and on different scales. A characteristic form of phase correlation is found in the simulations. We also applied the method to preliminary CMB maps derived from WMAP , but the separation of topological effects from e.g. foregrounds is not straightforward.  相似文献   

17.
I present results of new statistical techniques for the interpretation of the temperature and polarization maps and power spectra of the cosmic microwave background. We show that the power deficit at low ℓ in the WMAP1 data is consistent with a statistical fluctuation at the 10% level; that future high S/N maps of the temperature and polarization anisotropies can be combined into a reconstruction of the metric perturbations imprinted during inflation; and that machine learning techniques can accelerate cosmological parameter estimation by orders of magnitude while being highly accurate and robust.  相似文献   

18.
We introduce new symmetry-based methods to test for isotropy in cosmic microwave background (CMB) radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide two new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated Galactic plane contamination is readily identified. The ILC– WMAP data maps show seven axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5 per cent probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9 per cent, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.  相似文献   

19.
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20.
A directional spherical wavelet analysis is performed to examine the Gaussianity of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 1-yr data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows us to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark, de Oliveira-Costa & Hamilton foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9 per cent significance level is only made at the 95.3 per cent significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of ∼26° and an internal size of ∼3°) at an azimuthal orientation of 72°, are made at the 98.3 per cent significance level, using the same conservative method. The wavelet analysis inherently allows us to localize on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.  相似文献   

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