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1.
Higher Criticism (HC) has been proposed by Donoho & Jin as an effective statistic to detect deviations from Gaussianity. Motivated by the success of the Bianchi VIIh model in addressing many of the anomalies observed in the Wilkinson Microwave Anisotropy Probe ( WMAP ) data (Jaffe et al.), we present calculations in real and in wavelet space of the HC statistic of the Bianchi-corrected WMAP first-year data. At the wavelet scale of 5°, the HC of the WMAP map drops from a value above the 99 per cent confidence level (c.l.) to a value below the 68 per cent CL when corrected by the Bianchi template. An important property of the HC statistic is its ability to locate the pixels that account for the deviation from Gaussianity. The analysis of the uncorrected WMAP data pointed to a cold spot in the Southern hemisphere, centred at   l ∼ 209°, b ∼−57°  . The HC of the Bianchi-corrected map indicates that this spot remains prominent, albeit at a level completely consistent with Gaussian statistics. Consequently, it is debatable how much emphasis should be placed on this residual feature, but we consider the effect of modestly increasing the scaling of the template. A factor of only 1.2 renders the spot indistinguishable from the background level, with no noticeable impact on the results published in Jaffe et al. for the low- l anomalies, large-scale power asymmetry or wavelet kurtosis. A trivial interpretation would be that the Bianchi template may require a small enhancement of power on scales corresponding to the wavelet scale of 5°.  相似文献   

2.
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   

3.
We repeat the directional spherical real Morlet wavelet analysis, used previously to detect non-Gaussianity in the Wilkinson Microwave Anisotropy Probe ( WMAP ) 1- and 3-yr data, on the WMAP 5-yr data. The non-Gaussian signal detected previously is present in the 5-yr data at a slightly increased statistical significance of approximately 99 per cent. Localized regions that contribute most strongly to the non-Gaussian signal are found to be very similar to those detected in the previous releases of the WMAP data. When the localized regions detected in the 5-yr data are excluded from the analysis, the non-Gaussian signal is eliminated.  相似文献   

4.
We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang, using a technique based on the discrete wavelet transform. Their analysis was performed on the two DMR faces centred on the North and South Galactic poles, respectively, using the Daubechies 4 wavelet basis. We show that these results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations of the data, we calculate estimates of the skewness, kurtosis and scale–scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity in the DMR-DSMB map at greater than the 99 per cent confidence level, but most of these occur on pixel–pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond ℓ=40 from the COBE maps, only one robust detection remains. Moreover, using Monte Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. We repeat the analysis for the 53+90 GHz coadded COBE map. In this case, after removing ℓ>40 multipoles, two non-Gaussian detections at the 99 per cent level remain. Nevertheless, again using Monte Carlo simulations, we find that the probability of obtaining two such detections by chance is 0.28. Thus, we conclude the wavelet technique does not yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE data.  相似文献   

5.
We investigate the Gaussianity of the 4-yr COBE DMR data (in HEALPix pixelization) using an analysis based on spherical Haar wavelets. We use all the pixels lying outside the Galactic cut and compute the skewness, kurtosis and scale–scale correlation spectra for the wavelet coefficients at each scale. We also take into account the sensitivity of the method to the orientation of the input signal. We find a detection of non-Gaussianity at >99 per cent level in just one of our statistics. Taking into account the total number of statistics computed, we estimate that the probability of obtaining such a detection by chance for an underlying Gaussian field is 0.69. Therefore, we conclude that the spherical wavelet technique shows no strong evidence of non-Gaussianity in the COBE DMR data.  相似文献   

6.
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   

7.
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8.
We study the non-Gaussianity induced by the Sunyaev–Zel'dovich (SZ) effect in cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features to the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalogue, we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the fourth-order cross-correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the fourth-order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high-order autocorrelation of the WMAP . This is because the SZ signals in the autocorrelations of the WMAP data generally are weaker than the WMAP –2MASS cross-correlations by a factor f 2, which is the ratio between the powers of the SZ-effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high-order autocorrelations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of the SZ effect on various scales.  相似文献   

9.
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   

10.
We present an extensive frequentist analysis of the one-point statistics (number, mean, variance, skewness and kurtosis) and two-point correlation functions determined for the local extrema of the cosmic microwave background temperature field observed in five-years of Wilkinson Microwave Anisotropy Probe ( WMAP ) data. Application of a hypothesis test on the one-point statistics indicates a low variance of hot and cold spots in all frequency bands of the WMAP data. The consistency of the observations with Gaussian simulations of the best-fitting cosmological model is rejected at the 95 per cent confidence level outside the WMAP KQ75 mask and the Northern hemispheres in the Galactic and ecliptic coordinate frames. We demonstrate that it is unlikely that residual Galactic foreground emission contributes to the observed non-Gaussianities. However, the application of a high-pass filter that removes large angular scale power does improve the consistency with the best-fitting cosmological model.
Two-point correlation functions of the local extrema are calculated for both the temperature pair product [temperature–temperature (T–T)] and spatial pair-counting [point–point (P–P)]. The T–T observations demonstrate weak correlation on scales below  20°  and lie completely below the lower 3σ confidence region once various temperature thresholds are applied to the extrema determined for the KQ75 mask and northern sky partitions. The P–P correlation structure corresponds to the clustering properties of the temperature extrema, and provides evidence that it is the large angular-scale structures, and some unusual properties thereof, that are intimately connected to the properties of the hot and cold spots observed in the WMAP five-year data.  相似文献   

11.
Using local morphological measures on the sphere defined through a steerable wavelet analysis, we examine the three-year Wilkinson Microwave Anisotropy Probe WMAP and the NRAO VLA Sky Survey (NVSS) data for correlation induced by the integrated Sachs–Wolfe (ISW) effect. The steerable wavelet constructed from the second derivative of a Gaussian allows one to define three local morphological measures, namely the signed-intensity, orientation and elongation of local features. Detections of correlation between the WMAP and NVSS data are made with each of these morphological measures. The most significant detection is obtained in the correlation of the signed-intensity of local features at a significance of 99.9 per cent. By inspecting signed-intensity sky maps, it is possible for the first time to see the correlation between the WMAP and NVSS data by eye. Foreground contamination and instrumental systematics in the WMAP data are ruled out as the source of all significant detections of correlation. Our results provide new insight on the ISW effect by probing the morphological nature of the correlation induced between the cosmic microwave background and large-scale structure of the Universe. Given the current constraints on the flatness of the Universe, our detection of the ISW effect again provides direct and independent evidence for dark energy. Moreover, this new morphological analysis may be used in future to help us to better understand the nature of dark energy.  相似文献   

12.
We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB) temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable  σ,  S =σ2−〈σ2〉  , can give the same signal-to-noise ratio as   f NL= 30  even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum α. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction  α < 0.070  (95 per cent CL) for a scale-invariant spectrum which is comparable to the limit obtained from the power spectrum.  相似文献   

13.
We look for a non-Gaussian signal in the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year temperature anisotropy maps by performing a needlet-based data analysis. We use the foreground-reduced maps obtained by the WMAP team through the optimal combination of the W, V and Q channels, and perform realistic non-Gaussian simulations in order to constrain the non-linear coupling parameter f NL. We apply a third-order estimator of the needlet coefficients skewness and compute the  χ2  statistics of its distribution. We obtain  −80 < f NL < 120  at 95 per cent confidence level, which is consistent with a Gaussian distribution and comparable to previous constraints on the non-linear coupling. We then develop an estimator of f NL based on the same simulations and we find consistent constraints on primordial non-Gaussianity. We finally compute the three-point correlation function in needlet space: the constraints on f NL improve to  −50 < f NL < 110  at 95 per cent confidence level.  相似文献   

14.
A remarkable similarity between the large-scale non-Gaussian pattern of cosmic microwave background (CMB) temperatures obtained by the Wilkinson Microwave Anisotropy Probe ( WMAP ) mission and the distribution features of observation numbers is noted. Motivated by such a similarity, in this work we check the WMAP data for the correlation between pixel temperature t and observation number N . Systematic effects of imbalance in the differential observations and significant t – N correlations in magnitude, distribution of non-Gaussianity and north–south asymmetry are found. Our results indicate that, for precision cosmology studies based on WMAP observations, the observation effect on released WMAP temperature maps requires further careful study.  相似文献   

15.
We describe different methods for estimating the bispectrum of cosmic microwave background data. In particular, we construct a minimum-variance estimator for the flat-sky limit and compare results with previously studied frequentist methods. Application to the MAXIMA data set shows consistency with primordial Gaussianity. Weak quadratic non-Gaussianity is characterized by a tunable parameter   f NL  , corresponding to non-Gaussianity at a level of  ∼10−5 f NL  (the ratio of non-Gaussian to Gaussian terms), and we find limits of   f NL= 1500 ± 950  for the minimum-variance estimator and   f NL= 2700 ± 1650  for the usual frequentist estimator. These are the tightest limits on primordial non-Gaussianity, which include the full effects of the radiation transfer function.  相似文献   

16.
We investigate the effect of primordial non-Gaussianity of the local f NL type on the auto- and cross-power spectra of dark matter haloes using simulations of the Λ cold dark matter cosmology. We perform a series of large N -body simulations of both positive and negative f NL, spanning the range between 10 and 100. Theoretical models predict a scale-dependent bias correction  Δ b ( k , f NL)  that depends on the linear halo bias   b ( M )  . We measure the power spectra for a range of halo mass and redshifts covering the relevant range of existing galaxy and quasar populations. We show that auto- and cross-correlation analyses of bias are consistent with each other. We find that for low wavenumbers with   k < 0.03  h  Mpc−1  the theory and the simulations agree well with each other for biased haloes with   b ( M ) > 1.5  . We show that a scale-independent bias correction improves the comparison between theory and simulations on smaller scales, where the scale-dependent effect rapidly becomes negligible. The current limits on f NL from Slosar et al. come mostly from very large scales   k < 0.01  h  Mpc−1  and, therefore, remain valid. For the halo samples with   b ( M ) < 1.5 − 2  , we find that the scale-dependent bias from non-Gaussianity actually exceeds the theoretical predictions. Our results are consistent with the bias correction scaling linearly with f NL.  相似文献   

17.
Submillimetre mapping observations of the active edge-on spiral galaxy NGC 3079 are presented. These maps at 850 and 450 μm were made with the Submillimetre Common User Bolometer Array (SCUBA) at the James Clerk Maxwell Telescope (JCMT).
The source structure at these wavelengths consists of a central unresolved source embedded in diffuse disc emission, similar to that displayed at 1.2 mm. The disc emission is fitted with two optically thin, isothermal dust models which give temperatures of 12 and 31 K, similar to those derived previously by Braine et al. The core component is well described by a single-temperature fit (∼32 K). The combined dust mass from these observations, using the same mass absorption coefficient as Devereux & Young (1990) is 3.5×108 M⊙, of which ∼90 per cent resides in the cold component of the galactic disc. The effect of the cold dust component detected by SCUBA is thus to reduce the global gas-to-dust mass ratio from ∼1400 found in the above study to 85, very similar to the Galactic level. Calculations using the models of Draine & Lee and/or alternative molecular gas mass estimates yield gas-to-dust mass ratios in the range 60–190.
The data presented here, together with previously published 1.2-mm mapping observations and IRAS data, are inconsistent with detections made with the Infrared Space Observatory ( ISO ). In particular, the latter give an excess of flux at 200 and 180 μm relative to that predicted by our simple model fits (approximately a factor of 2–3).  相似文献   

18.
We present a careful analysis of the point-source detection limit of the AKARI All-Sky Survey in the WIDE-S 90-μm band near the North Ecliptic Pole (NEP). Timeline analysis is used to detect IRAS ( Infrared Astronomy Satellite ) sources and then a conversion factor is derived to transform the peak timeline signal to the interpolated 90-μm flux of a source. Combined with a robust noise measurement, the point-source flux detection limit at signal-to-noise ratio  (S/N) > 5  for a single detector row is  1.1 ± 0.1 Jy  which corresponds to a point-source detection limit of the survey of ∼0.4 Jy.
Wavelet transform offers a multiscale representation of the Time Series Data ( tsd ). We calculate the continuous wavelet transform of the tsd and then search for significant wavelet coefficients considered as potential source detections. To discriminate real sources from spurious or moving objects, only sources with confirmation are selected. In our multiscale analysis, IRAS sources selected above 4σ can be identified as the only real sources at the Point Source Scales. We also investigate the correlation between the non- IRAS sources detected in timeline analysis and cirrus emission using wavelet transform and contour plots of wavelet power spectrum. It is shown that the non- IRAS sources are most likely to be caused by excessive noise over a large range of spatial scales rather than real extended structures such as cirrus clouds.  相似文献   

19.
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   

20.
We report the results of a spectroscopic and polarimetric study of the massive, hydrogen-rich WN6h stars R144 (HD 38282 = BAT99-118 = Brey 89) and R145 (HDE 269928 = BAT99-119 = Brey 90) in the Large Magellanic Cloud. Both stars have been suspected to be binaries by previous studies (R144: Schnurr et al.; R145: Moffat). We have combined radial-velocity (RV) data from these two studies with previously unpublished polarimetric data. For R145, we were able to establish, for the first time, an orbital period of 158.8 d, along with the full set of orbital parameters, including the inclination angle i , which was found to be   i = 38°± 9°  . By applying a modified version of the shift-and-add method developed by Demers et al., we were able to isolate the spectral signature of the very faint line companion star. With the RV amplitudes of both components in R145, we were thus able to estimate their absolute masses. We find minimum masses   M WRsin3 i = 116 ± 33 M⊙  and   M Osin3 i = 48 ± 20 M⊙  for the WR and the O component, respectively. Thus, if the low-inclination angle were correct, resulting absolute masses of the components would be at least 300 and  125 M⊙  , respectively. However, such high masses are not supported by brightness considerations when R145 is compared to systems with known very high masses such as NGC 3603-A1 or WR20a. An inclination angle close to  90°  would remedy the situation, but is excluded by the currently available data. More and better data are thus required to firmly establish the nature of this puzzling, yet potentially very massive and important system. As to R144, however, the combined data sets are not sufficient to find any periodicity.  相似文献   

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