First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity, E. Komatsu, et al., 2003ApJS..148..119K, reprint / preprint (392 Kb) / individual figures / ADS / astro-ph

WMAP First-year Paper Figures, E. Komatsu, et al.

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Fig.1 Nonlinear coupling parameter ƒ_{NL} as a function of the maximum multipole l_{max}, measured from the Q+V+W co-added map using the cubic (bispectrum) estimator (eq. [8]). The best constraint is obtained from l_{max} = 265. The distribution is cumulative, so that the error bars at each l_{max} are not independent.

Fig.2 Left panels show the Minkowski functionals for WMAP data ( filled circles) at nside = 128 (28' pixels). The gray band shows the 68% confidence interval for the Gaussian Monte Carlo simulations. The right panels show the residuals between the mean of the Gaussian simulations and the WMAP data. The WMAP data are in excellent agreement with the Gaussian simulations.

Fig.3 Limits to ƒ_{NL} from &chi^{2} fit of the WMAP data to the non- Gaussian models (eq. [1]). The fit is a joint analysis of the three Minkowski functionals at 28' pixel resolution. There are 44 degrees of freedom. The Minkowski functionals show no evidence for non-Gaussian signals in the WMAP data.

Fig.4 Limits to the effect of the primordial non-Gaussianity on the dark-matter halo mass function dn/dM as a function of z. The shaded area represents the 95% constraint on the ratio of the non-Gaussian dn/dM to the Gaussian one.

Fig.6 Point-source angular bispectrum b_{src} and power spectrum c_{src}. The left panels show b_{src} in the Q (top panel) and V bands (bottom panel). The shaded areas show measurements from the WMAP sky maps with the standard source cut, while the filled circles show those with flux thresholds S_{c} defined at 4.85 GHz. The dashed lines show predictions from eq. (17) with N(> S) modeled by Toffolatti et al. (1998), while the solid lines are those multiplied by 0.65 to match the WMAP measurements. The right panels show c_{src}. The filled circles are computed from the measured b_{src} substituted into eq. (19). The lines are from eq. (18). The error bars are not independent, because the distribution is cumulative.

Fig.7 One-point PDF of temperature fluctuations measured from simulated non-Gaussian maps (noise and beam smearing are not included). From the top left to the bottom right panel the solid lines show the PDF for ƒ_{NL} = 100, 500, 1000, and 3000, while the dashed lines enclose the rms scatter of Gaussian realizations (i.e., ƒ_{NL} = 0).

Fig.8 Distribution of the nonlinear coupling parameter ƒ_{NL} (left panel) and the point-source bispectrum b_{src} (right panel) measured from 300 simulated realizations of non-Gaussian maps for ƒ_{NL} = 100 (solid line) and ƒ_{NL} = 0 (dashed line). The simulations include noise properties and window functions of the WMAP 1 yr data but do not include point sources.

Fig.9 Testing the estimator for the reduced point-source bispectrum b_{src} (eq. [22]). The left panel shows b_{src} measured from a simulated map including point sources and properties of the WMAP sky map at the Q band, as a function of flux cut S_{c} ( filled circles). Black, dark gray, and light gray indicate three different realizations of point sources. The solid line is the expectation from the input source number counts in the point-source simulation. The right panel compares the power spectrum c_{src} estimated from b_{src} with the expectation. The error bars are not independent, because the distribution is cumulative. The behavior for S_{c} > 2 Jy shows the cumulative effect of sources with brightness comparable to the instrument noise (see text in Appendix B).