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Register a new userThe primordial non-Gaussianity of local type (f_NL) in the WMAP 5-year data: the length distribution of CMB skeleton
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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.
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We constrain the amplitude of primordial non-Gaussianity in the CMB data taking into account the presence of foreground residuals in the maps. We generalise the needlet bispectrum estimator marginalizing over the amplitudes of thermal dust, free-free and synchrotron templates. We apply our procedure to WMAP 5 year data, finding fNL= 38pm 47 (1 sigma), while the analysis without marginalization provides fNL= 35pm 42. Splitting the marginalization over each foreground separately, we found that the estimates of fNL are positively cross correlated of 17%, 12% with the dust and synchrotron respectively, while a negative cross correlation of about -10% is found for the free-free component.
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.
A well-tested and validated Gibbs sampling code, that performs component separation and CMB power spectrum estimation, was applied to the {it WMAP} 5-yr data. Using a simple model consisting of CMB, noise, monopoles and dipoles, a ``per pixel low-frequency power-law (fitting for both amplitude and spectral index), and a thermal dust template with fixed spectral index, we found that the low-$ell$ ($ell < 50$) CMB power spectrum is in good agreement with the published {it WMAP}5 results. Residual monopoles and dipoles were found to be small ($lesssim 3 mu$K) or negligible in the 5-yr data. We comprehensively tested the assumptions that were made about the foregrounds (e.g. dust spectral index, power-law spectral index prior, templates), and found that the CMB power spectrum was insensitive to these choices. We confirm the asymmetry of power between the north and south ecliptic hemispheres, which appears to be robust against foreground modeling. The map of low frequency spectral indices indicates a steeper spectrum on average ($beta=-2.97pm0.21$) relative to those found at low ($sim$GHz) frequencies.
We present evidence for the detection of primordial non-Gaussianity of the local type (fNL), using the temperature information of the Cosmic Microwave Background (CMB) from the WMAP 3-year data. We employ the bispectrum estimator of non-Gaussianity described in (Yadav et al. 2007) which allows us to analyze the entirety of the WMAP data without an arbitrary cut-off in angular scale. Using the combined information from WMAPs two main science channels up to lmax=750 and the conservative Kp0 foreground mask we find 27 < fNL < 147 at 95% C.L., with a central value of fNL=87. This corresponds to a rejection of fNL=0 at more than 99.5% significance. We find that this detection is robust to variations in lmax, frequency and masks, and that no known foreground, instrument systematic, or secondary anisotropy explains our signal while passing our suite of tests. We explore the impact of several analysis choices on the stated significance and find 2.5 sigma for the most conservative view. We conclude that the WMAP 3-year data disfavors canonical single field slow-roll inflation.
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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