Professor Pedro Ferreira

Abstract:

A simple method is presented for the rapid simulation of statistically-isotropic non-Gaussian maps of CMB temperature fluctuations with a given power spectrum and analytically-calculable bispectrum and higher-order polyspectra. The $n$th-order correlators of the pixel values may also be calculated analytically. The cumulants of the simulated map may be used to obtain an expression for the probability density function of the pixel temperatures. The statistical properties of the simulated map are determined by the univariate non-Gaussian distribution from which pixel values are drawn independently in the first stage of the simulation process. We illustrate the method using a non-Gaussian distribution derived from the wavefunctions of the harmonic oscillator. The basic simulation method is easily extended to produce non-Gaussian maps with a given power spectrum and diagonal bispectrum.

Abstract:

We cross-correlate the cosmic microwave background (CMB) temperature anisotropy maps from the Wilkinson Microwave Anisotropy Probe (WMAP), MAXIMA-1, and MAXIMA-2 experiments. We use the cross spectrum, which is the spherical harmonic transform of the angular two-point correlation function, to quantify the correlation as a function of angular scale. We find that the three possible pairs of cross spectra are in close agreement with each other and with the power spectra of the individual maps. The probability that there is no correlation between the maps is smaller than 1 × 10^-8. We also calculate power spectra for maps made of differences between pairs of maps and show that they are consistent with no signal. The results conclusively show that the three experiments not only display the same statistical properties of the CMB anisotropy, but also detect the same features wherever the observed sky areas overlap. We conclude that the contribution of systematic errors to these maps is negligible and that MAXIMA and WMAP have accurately mapped the CMB anisotropy.

Abstract:

We measure the angular power spectrum of radio galaxies in the NRAO VLA Sky Survey (NVSS) using two independent methods: direct spherical harmonic analysis and maximum likelihood estimation. The results are consistent and can be understood using models for the spatial matter power spectrum and for the redshift distribution of radio galaxies at mJy flux-density levels. A good fit to the angular power spectrum can only be achieved if radio galaxies possess high bias with respect to mass fluctuations; by marginalizing over the other parameters of the model we derive a 68% confidence interval 1.53 < b_0 sigma_8 < 1.87, where b_0 is the linear bias factor for radio galaxies and sigma_8 describes the normalization of the matter power spectrum. Our models indicate that the majority of the signal in the NVSS angular power spectrum is generated at low redshifts. Individual redshifts for the NVSS sources are thus required to alleviate projection effects and probe directly the matter power spectrum on large scales.