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Register a new userThe integrated bispectrum as a test of CMB non-Gaussianity: detection power and limits on f_NL with WMAP data
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We propose a fast and efficient bispectrum statistic for Cosmic Microwave Background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter f_NL. We show how the method can achieve a remarkable computational advantage by focussing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test, increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales as l_{max}^3 instead of l_{max}^5 for the full bispectrum which for Planck resolution l_{max} sim 3000 means an improvement in speed of a factor 10^7 compared to the full bispectrum analysis with minor loss in precision. We find that the introduction of a galactic cut partially destroys the optimality of the configuration, which will then need to be dealt with in the future. We find for an ideal experiment with l_{max}=2000 that upper limits of f_{NL}<8 can be obtained at 1 sigma. For the case of the WMAP experiment, we would be able to put limits of |f_{NL}|<40 if no galactic cut were present. Using the real data with galactic cut, we obtain an estimate of -80<f_{NL}<80 and -160<f_{NL}<160 at 1 and 2 sigma respectively.
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We present skeleton studies of non-Gaussianity in the CMB temperature anisotropy observed in the WMAP5 data. The local skeleton is traced on the 2D sphere by cubic spline interpolation which leads to more accurate estimation of the intersection positions between the skeleton and the secondary pixels than conventional linear interpolation. We demonstrate that the skeleton-based estimator of non-Gaussianity of the local type (f_NL) - the departure of the length distribution from the corresponding Gaussian expectation - yields an unbiased and sufficiently converged f_NL-likelihood. We analyse the skeleton statistics in the WMAP5 combined V- and W-band data outside the Galactic base-mask determined from the KQ75 sky-coverage. The results are consistent with Gaussian simulations of the the best-fitting cosmological model, but deviate from the previous results determined using the WMAP1 data. We show that it is unlikely that the improved skeleton tracing method, the omission of Q-band data, the modification of the foreground-template fitting method or the absence of 6 extended regions in the new mask contribute to such a deviation. However, the application of the Kp0 base-mask in data processing does improve the consistency with the WMAP1 results. The f_NL-likelihoods of the data are estimated at 9 different smoothing levels. It is unexpected that the best-fit values show positive correlation with the smoothing scales. Further investigation argues against a point-source or goodness-of-fit explanation but finds that about 30% of either Gaussian or f_NL samples having better goodness-of-fit than the WMAP5 show a similar correlation. We present the estimate f_NL=47.3+/-34.9 (1sigma error) determined from the first four smoothing angles and f_NL=76.8+/-43.1 for the combination of all nine. The former result may be overestimated at the 0.21sigma-level because of point sources.
We test the consistency of estimates of the non-linear coupling constant f_{NL} using non-Gaussian CMB maps generated by the method described in (Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on estimation of f_{NL}. Nevertheless, using spherical wavelets, we find results in very good agreement with (Mukherjee and Wang 2004), showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f_{NL}, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate f_{NL}=-10^{+270}_{-260} at the 2sigma level (Bayesian) and f_{NL}=-10^{+310}_{-270} (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of f_{NL} and therefore, as advocated in (Cabella et al. 2004), the estimates may be combined to reduce the error bars. In this way, we obtain f_{NL}=-5pm 85 and f_{NL}=-5pm 175 at the 1sigma and 2sigma level respectively using the frequentist approach.
Two of the most commonly used tools to constrain the primordial non-Gaussianity are the bispectrum and the Minkowski functionals of CMB temperature anisotropies. These two measures of non-Gaussianity in principle provide distinct (though correlated) information, but in the past constraints from them have only been loosely compared, and not statistically combined. In this work we evaluate, for the first time, the covariance matrix between the local non-Gaussianity coefficient fnl estimated through the bispectrum and Minkowski functionals. We find that the estimators are positively correlated, with corerlation coefficient r ~ 0.3. Using the WMAP7 data to combine the two measures and accounting for the point-source systematics, we find the combined constraint fnl=37+/-28, which has a ~20% smaller error than either of the individual constraints.
We investigate the power of geometrical estimators on detecting non-Gaussianity in the cosmic microwave background. 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.
We describe the details of the binned bispectrum estimator as used for the official 2013 and 2015 analyses of the temperature and polarization CMB maps from the ESA Planck satellite. The defining aspect of this estimator is the determination of a map bispectrum (3-point correlator) that has been binned in harmonic space. For a parametric determination of the non-Gaussianity in the map (the so-called fNL parameters), one takes the inner product of this binned bispectrum with theoretically motivated templates. However, as a complementary approach one can also smooth the binned bispectrum using a variable smoothing scale in order to suppress noise and make coherent features stand out above the noise. This allows one to look in a model-independent way for any statistically significant bispectral signal. This approach is useful for characterizing the bispectral shape of the galactic foreground emission, for which a theoretical prediction of the bispectral anisotropy is lacking, and for detecting a serendipitous primordial signal, for which a theoretical template has not yet been put forth. Both the template-based and the non-parametric approaches are described in this paper.
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