On the Non-Gaussianity Observed in the COBE-DMR Sky Maps

In this paper we pursue the origin of the non-Gaussianity determined by a bispectrum analysis of the COBE-DMR 4-year sky maps. The robustness of the statistic is demonstrated by the rebinning of the data into 12 coordinate systems. By computing the bispectrum statistic as a function of various data partitions - by channel, frequency, and time interval, we show that the observed non-Gaussian signal is driven by the 53 GHz data. This frequency dependence strongly rejects the hypothesis that the signal is cosmological in origin. A jack-knife analysis of the coadded 53 and 90 GHz sky maps reveals those sky pixels to which the bispectrum statistic is particularly sensitive. We find that by removing data from the 53 GHz sky maps for periods of time during which a known systematic effect perturbs the 31 GHz channels, the amplitudes of the bispectrum coefficients become completely consistent with that expected for a Gaussian sky. We conclude that the non-Gaussian signal detected by the normalised bispectrum statistic in the publicly available DMR sky maps is due to a systematic artifact. The impact of removing the affected data on estimates of the normalisation of simple models of cosmological anisotropy is negligible.Comment: 14 pages, plus 8 Postscript and 3 GIF figures. LaTeX2e document using AASTeX v5.0 macros. Revised version accepted for publication in the Astrophysical Journal: small changes to the text, minor modifications to figures 1 and

Topology of the Galaxy Distribution in the Hubble Deep Fields

We have studied topology of the distribution of the high redshift galaxies identified in the Hubble Deep Field (HDF) North and South. The two-dimensional genus is measured from the projected distributions of the HDF galaxies at angular scales from $3.8''$ to $6.1''$. We have also divided the samples into three redshift slices with roughly equal number of galaxies using photometric redshifts to see possible evolutionary effects on the topology. The genus curve of the HDF North clearly indicates clustering of galaxies over the Poisson distribution while the clustering is somewhat weaker in the HDF South. This clustering is mainly due to the nearer galaxies in the samples. We have also found that the genus curve of galaxies in the HDF is consistent with the Gaussian random phase distribution with no significant redshift dependence.Comment: 14 pages, 4 figures, submitted to Ap

Genus Topology of the Cosmic Microwave Background from the WMAP 3-Year Data

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen in the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data. A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation. We set 95% confidence limits on non-linearities of -101 < f_{nl} < 107. We also find that the observed low l (l <= 8) modes show a slight anti-correlation with the Galactic foreground, but not exceeding 95% confidence, and that the topology defined by these modes is consistent with that of a Gaussian random-phase distribution (within 95% confidence).Comment: MNRAS LaTeX style (mn2e.cls), EPS and JPEG figure

Towards Locating the Brightest Microlensing Events on the Sky

It is estimated that a star brighter than visual magnitude 17 is undergoing a detectable gravitational microlensing event, somewhere on the sky, at any given time. It is assumed that both lenses and sources are normal stars drawn from a standard Bahcall-Soneira model of our Galaxy. Furthermore, over the time scale of a year, a star 15th magnitude or brighter should undergo a detectable gravitational lens amplification. Detecting and studying the microlensing event rate among the brightest 10$^8$ stars could yield a better understanding of Galactic stellar and dark matter distributions. Diligent tracking of bright microlensing events with even small telescopes might detect planets orbiting these stellar lenses.Comment: 19 pages, 4 figures, accepted by Ap

Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy

We use simulated maps of the cosmic microwave background anisotropy to quantify the ability of different statistical tests to discriminate between Gaussian and non-Gaussian models. Despite the central limit theorem on large angular scales, both the genus and extrema correlation are able to discriminate between Gaussian models and a semi-analytic texture model selected as a physically motivated non-Gaussian model. When run on the COBE 4-year CMB maps, both tests prefer the Gaussian model. Although the bispectrum has comparable statistical power when computed on the full sky, once a Galactic cut is imposed on the data the bispectrum loses the ability to discriminate between models. Off-diagonal elements of the bispectrum are comparable to the diagonal elements for the non-Gaussian texture model and must be included to obtain maximum statistical power.Comment: Accepted for publication in ApJ; 20 pages, 6 figures, uses AASTeX v5.

Effects of Foreground Contamination on the Cosmic Microwave Background Anisotropy Measured by MAP

We study the effects of diffuse Galactic, far-infrared extragalactic source, and radio point source emission on the cosmic microwave background (CMB) anisotropy data anticipated from the MAP experiment. We focus on the correlation function and genus statistics measured from mock MAP foreground-contaminated CMB anisotropy maps generated in a spatially-flat cosmological constant dominated cosmological model. Analyses of the simulated MAP data at 90 GHz (0.3 deg FWHM resolution smoothed) show that foreground effects on the correlation function are small compared with cosmic variance. However, the Galactic emission, even just from the region with |b| > 20 deg, significantly affects the topology of CMB anisotropy, causing a negative genus shift non-Gaussianity signal. Given the expected level of cosmic variance, this effect can be effectively reduced by subtracting existing Galactic foreground emission models from the observed data. IRAS and DIRBE far-infrared extragalactic sources have little effect on the CMB anisotropy. Radio point sources raise the amplitude of the correlation function considerably on scales below 0.5 deg. Removal of bright radio sources above a 5 \sigma detection limit effectively eliminates this effect. Radio sources also result in a positive genus curve asymmetry (significant at 2 \sigma) on 0.5 deg scales. Accurate radio point source data is essential for an unambiguous detection of CMB anisotropy non-Gaussianity on these scales. Non-Gaussianity of cosmological origin can be detected from the foreground-subtracted CMB anisotropy map at the 2 \sigma level if the measured genus shift parameter |\Delta\nu| >= 0.02 (0.04) or if the measured genus asymmetry parameter |\Delta g| >= 0.03 (0.08) on a 0.3 (1.0) deg FWHM scale.Comment: 26 pages, 7 figures, Accepted for Publication in Astrophysical Journal (Some sentences and figures modified

Two-Dimensional Topology of the 2dF Galaxy Redshift Survey

We study the topology of the publicly available data released by the 2dFGRS. The 2dFGRS data contains over 100,000 galaxy redshifts with a magnitude limit of b_J=19.45 and is the largest such survey to date. The data lie over a wide range of right ascension (75 degree strips) but only within a narrow range of declination (10 degree and 15 degree strips). This allows measurements of the two-dimensional genus to be made. The NGP displays a slight meatball shift topology, whereas the SGP displays a bubble like topology. The current SGP data also have a slightly higher genus amplitude. In both cases, a slight excess of overdense regions are found over underdense regions. We assess the significance of these features using mock catalogs drawn from the Virgo Consortium's Hubble Volume LCDM z=0 simulation. We find that differences between the NGP and SGP genus curves are only significant at the 1 sigma level. The average genus curve of the 2dFGRS agrees well with that extracted from the LCDM mock catalogs. We compare the amplitude of the 2dFGRS genus curve to the amplitude of a Gaussian random field with the same power spectrum as the 2dFGRS and find, contradictory to results for the 3D genus of other samples, that the amplitude of the GRF genus curve is slightly lower than that of the 2dFGRS. This could be due to a a feature in the current data set or the 2D genus may not be as sensitive as the 3D genus to non-linear clustering due to the averaging over the thickness of the slice in 2D. (Abridged)Comment: Submitted to ApJ A version with Figure 1 in higher resolution can be obtained from http://www.physics.drexel.edu/~hoyle