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1.
We implement an independent component analysis (ICA) algorithm to separate signals of different origin in sky maps at several frequencies. Owing to its self-organizing capability, it works without prior assumptions on either the frequency dependence or the angular power spectrum of the various signals; rather, it learns directly from the input data how to identify the statistically independent components, on the assumption that all but, at most, one of the components have non-Gaussian distributions.
We have applied the ICA algorithm to simulated patches of the sky at the four frequencies (30, 44, 70 and 100 GHz) used by the Low Frequency Instrument of the European Space Agency's Planck satellite. Simulations include the cosmic microwave background (CMB), the synchrotron and thermal dust emissions, and extragalactic radio sources. The effects of the angular response functions of the detectors and of instrumental noise have been ignored in this first exploratory study. The ICA algorithm reconstructs the spatial distribution of each component with rms errors of about 1 per cent for the CMB, and 10 per cent for the much weaker Galactic components. Radio sources are almost completely recovered down to a flux limit corresponding to ≃0.7 σ CMB, where σ CMB is the rms level of the CMB fluctuations. The signal recovered has equal quality on all scales larger than the pixel size. In addition, we show that for the strongest components (CMB and radio sources) the frequency scaling is recovered with per cent precision. Thus, algorithms of the type presented here appear to be very promising tools for component separation. On the other hand, we have been dealing here with a highly idealized situation. Work to include instrumental noise, the effect of different resolving powers at different frequencies and a more complete and realistic characterization of astrophysical foregrounds is in progress.  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.
Given a set of images, whose pixel values can be considered as the components of a vector, it is interesting to estimate the modulus of such a vector in some localized areas corresponding to a compact signal. For instance, the detection/estimation of a polarized signal in compact sources immersed in a background is relevant in some fields like astrophysics. We develop two different techniques, one based on the Neyman–Pearson lemma, the Neyman–Pearson filter (NPF), and another based on pre-filtering before fusion, the filtered fusion (FF), to deal with the problem of detection of the source and estimation of the polarization given two or three images corresponding to the different components of polarization (two for linear polarization, three including circular polarization). For the case of linear polarization, we have performed numerical simulations on two-dimensional patches to test these filters following two different approaches (a blind and a non-blind detection), considering extragalactic point sources immersed in cosmic microwave background (CMB) and non-stationary noise with the conditions of the 70 GHz Planck channel. The FF outperforms the NPF, especially for low fluxes. We can detect with the FF extragalactic sources in a high noise zone with fluxes      Jy for (blind/non-blind) detection and in a low noise zone with fluxes      Jy for (blind/non-blind) detection with low errors in the estimated flux and position.  相似文献   

4.
It is the aim of this paper to introduce the use of isotropic wavelets to detect and determine the flux of point sources appearing in cosmic microwave background (CMB) maps. The most suitable wavelet to detect point sources filtered with a Gaussian beam is the 'Mexican Hat'. An analytical expression of the wavelet coefficient obtained in the presence of a point source is provided and used in the detection and flux estimation methods presented. For illustration the method is applied to two simulations (assuming Planck mission characteristics) dominated by CMB (100 GHz) and dust (857 GHz), as these will be the two signals dominating at low and high frequencies respectively in the Planck channels. We are able to detect bright sources above 1.58 Jy at 857 GHz (82 per cent of all sources) and above 0.36 Jy at 100 GHz (100 per cent of all), with errors in the flux estimation below 25 per cent. The main advantage of this method is that nothing has to be assumed about the underlying field, i.e. about the nature and properties of the signal plus noise present in the maps. This is not the case in the detection method presented by Tegmark & Oliveira-Costa. Both methods are compared, producing similar results.  相似文献   

5.
We examine the ability of the future Planck mission to provide a catalogue of galaxy clusters observed via their Sunyaev–Zel'dovich (SZ) distortion in the cosmic microwave background (CMB). For this purpose we produce full-sky SZ maps based on N -body simulations and scaling relations between cluster properties for several cosmological models. We extrapolate the N -body simulations by a mass function to high redshifts in order to obtain a realistic SZ background. The simulated Planck observations include, besides the thermal and kinematic SZ effects, contributions from the primordial CMB, extragalactic point sources as well as Galactic dust, free–free and synchrotron emission. A harmonic-space maximum-entropy method is used to separate the SZ signal from contaminating components in combination with a cluster detection algorithm based on thresholding and flux integration to identify clusters and to obtain their fluxes. We estimate a survey sensitivity limit (depending on the quality of the recovered cluster flux) and provide cluster survey completeness and purity estimates. We find that, given our modelling and detection algorithm, Planck will reliably detect at least several thousands of clusters over the full sky. The exact number depends on the particular cosmological model (up to 10 000 cluster detections in a concordance ΛCDM model with  σ8= 0.9  ). We show that the Galaxy does not significantly affect the cluster detection. Furthermore, the dependence of the thermal SZ power spectrum on the matter variance on scales of  8 h −1  Mpc and the quality of its reconstruction by the employed method are investigated. Our simulations suggest that the Planck cluster sample will not only be useful as a basis for follow-up observations, but also will have the ability to provide constraints on cosmological parameters.  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 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   

8.
One of the main obstacles for extracting the Cosmic Microwave Background (CMB) signal from observations in the mm-submm range is the foreground contamination by emission from Galactic components: mainly synchrotron, free-free and thermal dust emission. Due to the statistical nature of the intrinsic CMB signal it is essential to minimize the systematic errors in the CMB temperature determinations. Following the available knowledge of the spectral behavior of the Galactic foregrounds simple power law-like spectra have been assumed. The feasibility of using a simple neural network for extracting the CMB temperature signal from the combined signal CMB and the foregrounds has been investigated. As a specific example, we have analysed simulated data, as expected from the ESA Planck CMB mission. A simple multilayer perceptron neural network with 2 hidden layers can provide temperature estimates over more than 80 per cent of the sky that are to a high degree uncorrelated with the foreground signals. A single network will be able to cover the dynamic range of the Planck noise level over the entire sky.  相似文献   

9.
We present the first tests of a new method, the correlated component analysis (CCA) based on second-order statistics, to estimate the mixing matrix, a key ingredient to separate astrophysical foregrounds superimposed to the Cosmic Microwave Background (CMB). In the present application, the mixing matrix is parametrized in terms of the spectral indices of Galactic synchrotron and thermal dust emissions, while the free–free spectral index is prescribed by basic physics, and is thus assumed to be known. We consider simulated observations of the microwave sky with angular resolution and white stationary noise at the nominal levels for the Planck satellite, and realistic foreground emissions, with a position-dependent synchrotron spectral index. We work with two sets of Planck frequency channels: the low-frequency set, from 30 to 143 GHz, complemented with the Haslam 408 MHz map, and the high-frequency set, from 217 to 545 GHz. The concentration of intense free–free emission on the Galactic plane introduces a steep dependence of the spectral index of the global Galactic emission with Galactic latitude, close to the Galactic equator. This feature makes difficult for the CCA to recover the synchrotron spectral index in this region, given the limited angular resolution of Planck , especially at low frequencies. A cut of a narrow strip around the Galactic equator  (| b | < 3°)  , however, allows us to overcome this problem. We show that, once this strip is removed, the CCA allows an effective foreground subtraction, with residual uncertainties inducing a minor contribution to errors on the recovered CMB power spectrum.  相似文献   

10.
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   

11.
One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free‐free and thermal dust emission. The feasibility of using simple neural networks to extract CMB has been demonstrated on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto‐correlation and cross‐correlation power spectra within a mask covering about 63 % of the sky have been used together with a “high pass filter” in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron neural networks. This spectrum contains a bright feature with signal to noise ratios 4.5 within 200 ≪ l ≪ 250. The spectrum is significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour quite different from the “canonical” models (weak lensing plus B‐modes spectra with different tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

12.
Significant alignment and signed-intensity anomalies of local features of the cosmic microwave background (CMB) are detected on the three-year Wilkinson Microwave Anisotropy Probe data, through a decomposition of the signal with steerable wavelets on the sphere. In addition to identifying local features of a signal at specific scales, steerable wavelets allow one to determine their local orientation and signed intensity. First, an alignment analysis identifies two mean preferred planes in the sky, both with normal axes close to the CMB dipole axis. The first plane is defined by the directions towards which local CMB features are anomalously aligned. A mean preferred axis is also identified in this plane, located very close to the ecliptic poles axis. The second plane is defined by the directions anomalously avoided by local CMB features. This alignment anomaly provides further insight on recent results. Secondly, a signed-intensity analysis identifies three mean preferred directions in the southern Galactic hemisphere with anomalously high or low temperature of local CMB features: a cold spot essentially identified with a known cold spot, a second cold spot lying very close to the southern end of the CMB dipole axis, and a hotspot lying close to the southern end of the ecliptic poles axis. In both analyses, the anomalies are observed at wavelet scales corresponding to angular sizes around 10° on the celestial sphere, with global significance levels around 1 per cent. Further investigation reveals that the alignment and signed-intensity anomalies are only very partially related. Instrumental noise, foreground emissions and some form of other systematics are strongly rejected as possible origins of the detections. An explanation might still be envisaged in terms of a global violation of the isotropy of the Universe, inducing an intrinsic statistical anisotropy of the CMB.  相似文献   

13.
Despite the fact that the physics of the cosmic microwave background anisotropies is most naturally expressed in Fourier space, pixelized maps are almost always used in the analysis and simulation of microwave data. A complementary approach is investigated here, in which maps are used only in the visualization of the data, and the temperature anisotropies and polarization are only ever expressed in terms of their spherical multipoles. This approach has a number of advantages: there is no information loss (assuming a band-limited observation); deconvolution of asymmetric beam profiles and the temporal response of the instrument are naturally included; correlated noise can easily be taken into account, removing the need for additional 'destriping'; polarization is also analysed in the same framework; and reliable estimates of the spherical multipoles of the sky and their errors are obtained directly for subsequent component separation and power spectrum estimation. The formalism required to analyse experiments which survey the full sky by scanning on circles is derived here, with particular emphasis on the Planck mission. A number of analytical results are obtained in the limit of simple scanning strategies. Although there are non-trivial computational obstacles to be overcome before the techniques described here can be implemented at high resolution, if these can be overcome the method should allow for a more robust return from the next generation of full-sky microwave background experiments.  相似文献   

14.
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   

15.
The SCUBA instrument on the James Clerk Maxwell Telescope has already had an impact on cosmology by detecting relatively large numbers of dusty galaxies at high redshift. Apart from identifying well-detected sources, such data can also be mined for information about fainter sources and their correlations, as revealed through low-level fluctuations in SCUBA maps. As a first step in this direction, we analyse a small SCUBA data set as if it were obtained from a cosmic microwave background (CMB) differencing experiment. This enables us to place limits on CMB anisotropy at 850 m. Expressed as Q flat, the quadrupole expectation value for a flat power spectrum, the limit is 152 K at 95 per cent confidence, corresponding to     (or T T <14105) for a Gaussian autocorrelation function, with a coherence angle of about 2025 arcsec. These results could easily be reinterpreted in terms of any other fluctuating sky signal. This is currently the best limit for these scales at high frequency, and comparable to limits at similar angular scales in the radio. Even with such a modest data set, it is possible to put a constraint on the slope of the SCUBA counts at the faint end, since even randomly distributed sources would lead to fluctuations. Future analysis of sky correlations in more extensive data sets ought to yield detections, and hence additional information on source counts and clustering.  相似文献   

16.
We investigate the power of geometrical estimators on detecting non-Gaussianity in the cosmic microwave background (CMB). In particular the number, eccentricity and Gaussian curvature of excursion sets above (and below) a threshold are studied. We compare their different performance when applied to non-Gaussian simulated maps of small patches of the sky, which take into account the angular resolution and instrumental noise of the Planck satellite. These non-Gaussian simulations are obtained as perturbations of a Gaussian field in two different ways which introduce a small level of skewness or kurtosis in the distribution. A comparison with a classical estimator, the genus, is also shown. We find that the Gaussian curvature is the best of our estimators in all the considered cases. Therefore we propose the use of this quantity as a particularly useful test to look for non-Gaussianity in the CMB.  相似文献   

17.
We present a new map-making method for cosmic microwave background (CMB) measurements. The method is based on the destriping technique, but it also utilizes information about the noise spectrum. The low-frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum-likelihood analysis, involving the covariance matrix of the amplitudes. We present simulation results with  1/ f   noise and show a reduction in the residual noise with respect to ordinary destriping. This study is related to Planck Low Frequency Instrument (LFI) activities.  相似文献   

18.
In this paper, I investigate the family of mixed three-point correlation functions  〈τ q γ3− q 〉, q = 0, 1, 2  , between the integrated Sachs–Wolfe (iSW) temperature perturbation τ and the galaxy overdensity γ as a tool for detecting the gravitational interaction of cosmic microwave background (CMB) photons with the potentials of non-linearly evolving cosmological structures. Both the iSW-effect and the galaxy overdensity are derived in hyperextended perturbation theory to second order and I emphasize the different parameter sensitivities of the linear and non-linear iSW-effect. I examine the configuration dependence of the relevant bispectra, quantify their sensitivities and discuss their degeneracies with respect to the cosmological parameters  Ωm, σ8, h   and the dark energy equation of state parameter w . I give detection significances for combining Planck CMB data and galaxy sample of a survey like Dark UNiverse Explorer (DUNE) by using a quadratic approximation for the likelihood with Λ cold dark matter (ΛCDM) as the fiducial cosmology: the combination of Planck with DUNE should be able to reach a cumulative signal-to-noise ratio of ≃0.6 for the bispectrum  〈τγ2〉  up to ℓ= 2000, which is too weak to be detected. The most important noise source is the primary CMB fluctuations as the Poisson noise in the galaxy number density is almost negligible for a survey like DUNE.  相似文献   

19.
The High Frequency Instrument (HFI) of Planck is the most sensitive CMB experiment ever planned. Statistical fluctuations (photon noise) of the CMB itself will be the major limitation to the sensitivity of the CMB channels. Higher frequency channels will measure galactic foregrounds. Together with the Low Frequency Instrument, this will make a unique tool to measure the full sky and to separate the various components of its spectrum. Measurement of the polarization of these various components will give a new picture of the CMB. In addition, HFI will provide the scientific community with new full sky maps of intensity and polarization at six frequencies, with unprecedented angular resolution and sensitivity. This paper describes the logics that prevailed to define the HFI and the performances expected from this instrument. It details several features of the HFI design that has not been published up to now.  相似文献   

20.
We propose a new method for measuring the possible large-scale bulk flows in the universe from the cosmic microwave background (CMB) maps from the upcoming missions of the Microwave Anistropy Probe (MAP) and Planck. This can be done by studying the statistical properties of the CMB temperature field at many X-ray cluster positions. At each cluster position, the CMB temperature fluctuation will be a combination of the Sunyaev-Zeldovich (SZ) kinematic and thermal components, the cosmological fluctuations, and the instrument noise term. When averaged over many such clusters, the last three will integrate down, whereas the first one will be dominated by a possible bulk flow component. In particular, we propose to use all-sky X-ray cluster catalogs that should (or could) be available soon from X-ray satellites and then to evaluate the dipole component of the CMB field at the cluster positions. We show that for the MAP and Planck mission parameters, the dominant contributions to the dipole will be from the terms that are due to the SZ kinematic effect produced by the bulk flow (the signal we seek) and the instrument noise (the noise in our signal). Then, by computing the expected signal-to-noise ratio for such measurement, we find that at the 95% confidence level, the bulk flows on scales >/=100 h(-1) Mpc can be probed down to the amplitude of less than 200 km s(-1) with the MAP data and down to only approximately 30 km s(-1) with the Planck mission.  相似文献   

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