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1.
We study the power of several scalar quantities constructed on the sphere (presented in Monteserín et al.) to detect non-Gaussianity in the temperature distribution of the cosmic microwave background (CMB). The test has been performed using non-Gaussian CMB simulations with injected skewness or kurtosis generated through the Edgeworth expansion. We have also taken into account in the analysis the effect of anisotropic noise and the presence of a Galactic mask. We find that the best scalars to detect an excess of skewness in the simulations are the derivative of the gradient, the fractional isotropy, the Laplacian and the shape index. For the kurtosis case, the fractional anisotropy, the Laplacian and the determinant are the quantities that perform better.  相似文献   

2.
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   

3.
We present a method, based on the correlation function of excursion sets above a given threshold, to test the Gaussianity of the cosmic microwave background (CMB) temperature fluctuations in the sky. In particular, this method can be applied to discriminate between standard inflationary scenarios and those producing non-Gaussianity such as topological defects. We have obtained the normalized correlation of excursion sets, including different levels of noise, for two-point probability density functions constructed from the Gaussian, χ2 n and Laplace one-point probability density functions in two different ways. Considering subdegree angular scales, we find that this method can distinguish between different distributions even if the corresponding marginal probability density functions and/or the radiation power spectra are the same.  相似文献   

4.
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   

5.
The identification of non-Gaussian signatures in cosmic microwave background (CMB) temperature maps is one of the main cosmological challenges today. We propose and investigate alternative methods to analyse CMB maps. Using the technique of constrained randomization, we construct surrogate maps which mimic both the power spectrum and the amplitude distribution of simulated CMB maps containing non-Gaussian signals. Analysing the maps with weighted scaling indices and Minkowski functionals yields in both cases statistically significant identification of the primordial non-Gaussianities. We demonstrate that the method is very robust with respect to noise. We also show that Minkowski functionals are able to account for non-linearities at higher noise level when applied in combination with surrogates than when only applied to noise added CMB maps and phase randomized versions of them, which only reproduce the power spectrum.  相似文献   

6.
We present ray tracing simulations combined with sets of large N -body simulations. Experiments were performed to explore, for the first time, the statistical properties of fluctuations in angular separation of nearby light-ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian, but has an exponential tail. It is found, however, that the tail, or more generally the non-Gaussian nature of the PDF has no significant impact on the weak lensing of the cosmic microwave background (CMB). Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate the validity of using the power spectrum approach to compute lensing effects on the CMB.  相似文献   

7.
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   

8.
We investigate the number density of maxima in the cosmological galaxy density field smoothed with a filter as a probe of clustering. In previous work it has been shown that this statistic is closely related to the slope of the linear power spectrum, even when the directly measured power spectrum is non-linear. In the present paper we investigate the sensitivity of the peak number density to various models with differing power spectra, including rolling index models, cosmologies with massive neutrinos and different baryon densities. We find that rolling index models which have given an improved fit to CMB/LSS (cosmic microwave background/large scale structure) data yield a ∼10 per cent difference in peak density compared to the scale invariant case. Models with 0.3 eV neutrinos have effects of similar magnitude and it should be possible to constrain them with data from current galaxy redshift surveys. Baryon oscillations in the power spectrum also give rise to distinctive features in the peak density. These are preserved without modification when measured from the peak density in fully non-linear N -body simulations. Using the simulations, we also investigate how the peak density is modified in the presence of redshift distortions. Redshift distortions cause a suppression of the number of peaks, largely due to fingers of God overlapping in redshift space. We find that this effect can be modelled by using a modification of the input power spectrum. We also study the results when the simulation density field is traced by galaxies obtained by populating haloes with a halo occupation distribution consistent with observations. The peak number density is consistent with that in the dark matter for filter scales  >4  h −1 Mpc  , for which we find good agreement with the linear theory predictions. In a companion paper we analyse data from the 2dF Galaxy Redshift Survey.  相似文献   

9.
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   

10.
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   

11.
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   

12.
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   

13.
We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ2  analysis. The  χ2  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f nl parameter is constrained to  −8 < f nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.  相似文献   

14.
We have estimated the cosmic microwave background (CMB) variance from the three-year Wilkinson Microwave Anisotropy Probe ( WMAP ) data, finding a value which is significantly lower than the one expected from Gaussian simulations using the WMAP best-fitting cosmological model, at a significance level of 98.7 per cent. This result is even more prominent if we consider only the North ecliptic hemisphere (99.8 per cent). Different analyses have been performed in order to identify a possible origin for this anomaly. In particular, we have studied the behaviour of single-radiometer and single-year data as well as the effect of residual foregrounds and 1/f noise, finding that none of these possibilities can explain the low value of the variance. We have also tested the effect of varying the cosmological parameters, finding that the estimated CMB variance tends to favour higher values of n s than the one of the WMAP best-fitting model. In addition, we have also tested the consistency between the estimated CMB variance and the actual measured CMB power spectrum of the WMAP data, finding a strong discrepancy. A possible interpretation of this result could be a deviation from Gaussianity and/or isotropy of the CMB.  相似文献   

15.
We compare simulations of the Lyman α forest performed with two different hydrodynamical codes, gadget-2 and enzo . A comparison of the dark matter power spectrum for simulations run with identical initial conditions show differences of 1–3 per cent at the scales relevant for quantitative studies of the Lyman α forest. This allows a meaningful comparison of the effect of the different implementations of the hydrodynamic part of the two codes. Using the same cooling and heating algorithm in both codes, the differences in the temperature and the density probability distribution function are of the order of 10 per cent. The differences are comparable to the effects of box size and resolution on these statistics. When self-converged results for each code are taken into account, the differences in the flux power spectrum – the statistics most widely used for estimating the matter power spectrum and cosmological parameters from Lyman α forest data – are about 5 per cent. This is again comparable to the effects of box size and resolution. Numerical uncertainties due to a particular implementation of solving the hydrodynamic or gravitational equations appear therefore to contribute only moderately to the error budget in estimates of the flux power spectrum from numerical simulations. We further find that the differences in the flux power spectrum for enzo simulations run with and without adaptive mesh refinement are also of the order of 5 per cent or smaller. The latter require 10 times less CPU time making the CPU time requirement similar to that of a version of gadget-2 that is optimized for Lyman α forest simulations.  相似文献   

16.
Weak gravitational lensing surveys have the potential to probe mass density fluctuation in the Universe directly. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by modelling the statistics of the underlying density field in the highly non-linear regime. We propose a new method to model the complete probability distribution function of the convergence field as a function of smoothing angle and source redshift. The model relies on a hierarchical ansatz for the behaviour of higher order correlations of the density field. We compare our results with ray-tracing simulations and find very good agreement over a range of smoothing angles. Whereas the density probability distribution function is not sensitive to the cosmological model, the probability distribution function for the convergence can be used to constrain both the power spectrum and cosmological parameters.  相似文献   

17.
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   

18.
Map making presents a significant computational challenge to the next generation of kilopixel cosmic microwave background polarization experiments. Years worth of time ordered data (TOD) from thousands of detectors will need to be compressed into maps of the T , Q and U Stokes parameters. Fundamental to the science goal of these experiments, the observation of B modes, is the ability to control noise and systematics. In this paper, we consider an alternative to the maximum likelihood method, called destriping , where the noise is modelled as a set of discrete offset functions and then subtracted from the time stream. We compare our destriping code (Descart: the DEStriping CARTographer) to a full maximum likelihood mapmaker, applying them to 200 Monte Carlo simulations of TOD from a ground-based, partial-sky polarization modulation experiment. In these simulations, the noise is dominated by either detector or atmospheric  1/ f   noise. Using prior information of the power spectrum of this noise, we produce destriped maps of T , Q and U which are negligibly different from optimal. The method does not filter the signal or bias the E- or B-mode power spectra. Depending on the length of the destriping baseline, the method delivers between five and 22 times improvement in computation time over the maximum likelihood algorithm. We find that, for the specific case of single detector maps, it is essential to destripe the atmospheric  1/ f   in order to detect B modes, even though the Q and U signals are modulated by a half-wave plate spinning at 5 Hz.  相似文献   

19.
We investigate a spatially flat cold dark matter model (with the matter density parameter     with a primordial feature in the initial power spectrum. We assume that there is a bump in the power spectrum of density fluctuations at wavelengths     , which corresponds to the scale of superclusters of galaxies . There are indications for such a feature in the power spectra derived from redshift surveys and also in the power spectra derived from peculiar velocities of galaxies. We study the mass function of clusters of galaxies, the power spectrum of the cosmic microwave background (CMB) temperature fluctuations, the rms bulk velocity and the rms peculiar velocity of clusters of galaxies. The baryon density is assumed to be consistent with the big bang nucleosynthesis value. We show that with an appropriately chosen feature in the power spectrum of density fluctuations at the scale of superclusters, the mass function of clusters, the CMB power spectrum, the rms bulk velocity and the rms peculiar velocity of clusters are in good agreement with the observed data.  相似文献   

20.
We address the problem of encoding and compressing data dominated by noise. Information is decomposed into 'reference' sequences plus arrays containing noisy differences susceptible to being described by a known probability distribution. One can then give reliable estimates of the optimal compression rates by estimating the corresponding Shannon entropy. As a working example, this idea is applied to an idealized model of the cosmic microwave background (CMB) data on board the Planck satellite. Data reduction is a critical issue in space missions because the total information that can be downloaded to Earth is sometimes limited by telemetry allocation. Similar limitations might arise in remotely operated ground based telescopes. This download-rate limitation could reduce the amount of diagnostics sent on the stability of the instruments and, as a consequence, curb the final sensitivity of the scientific signal. Our proposal for Planck consists of taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences could be made independent of the external signal, so that they are dominated by thermal (white) instrumental noise, which is simpler to model than the sky signal. Similar approaches can be found in other individual applications. Generic simulations and analytical predictions show that high compression rates,     can be obtained with minor or zero loss of sensitivity. Possible effects of digital distortion are also analysed. The proposed scheme is flexible and reliable enough to be optimized in relation to other critical aspects of the corresponding application. For Planck , this study constitutes an important step towards a more realistic modelling of the final sensitivity of the CMB temperature anisotropy maps.  相似文献   

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