Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLooking for non-Gaussianity in the COBE-DMR data with spherical wavelets
75
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present an analysis of the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) based on spherical wavelets. The skewness, kurtosis and scale-scale correlation spectra are computed from the detail wavelet coefficients at each scale. The sensitivity of the method to the orientation of the data is also taken into account. We find a single detection of non-Gaussianity at the $>99%$ confidence level in one of our statistics. We use Monte-Carlo simulations to assess the statistical significance of this detection and find that the probability of obtaining such a detection by chance for an underlying Gaussian field is as high as 0.69. Therefore, our analysis does not show evidence of non-Gaussianity in the COBE-DMR data.
rate research
Read More
We investigate the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) using an analysis based on spherical Haar wavelets. We use all the pixels lying outside the Galactic cut and compute the skewness, kurtosis and scale-scale correlation spectra for the wavelet coefficients at each scale. We also take into account the sensitivity of the method to the orientation of the input signal. We find a detection of non-Gaussianity at $> 99$ per cent level in just one of our statistics. Taking into account the total number of statistics computed, we estimate that the probability of obtaining such a detection by chance for an underlying Gaussian field is 0.69. Therefore, we conclude that the spherical wavelet technique shows no strong evidence of non-Gaussianity in the COBE-DMR data.
We derive an optimal linear filter to suppress the noise from the COBE DMR sky maps for a given power spectrum. We then apply the filter to the first-year DMR data, after removing pixels within $20^circ$ of the Galactic plane from the data. The filtered data have uncertainties 12 times smaller than the noise level of the raw data. We use the formalism of constrained realizations of Gaussian random fields to assess the uncertainty in the filtered sky maps. In addition to improving the signal-to-noise ratio of the map as a whole, these techniques allow us to recover some information about the CMB anisotropy in the missing Galactic plane region. From these maps we are able to determine which hot and cold spots in the data are statistically significant, and which may have been produced by noise. In addition, the filtered maps can be used for comparison with other experiments on similar angular scales.
We present an application of the fast Independent Component Analysis method to the COBE-DMR 4yr data. Although the signal-to-noise ratio in the COBE-DMR data is typically $sim 1$, the approach is able to extract the CMB signal with high confidence when working at high galactic latitudes. The reconstructed CMB map shows the expected frequency scaling of the CMB. We fit the resulting CMB component for the rms quadrupole normalisation Qrms and primordial spectral index n and find results in excellent agreement with those derived from the minimum-noise combination of the 90 and 53 GHz DMR channels without galactic emission correction. Including additional channels (priors) such as the Haslam map of radio emission at 408 MHz and the DIRBE 140um map of galactic infra-red emission, the FastICA algorithm is able to both detect galactic foreground emission and separate it from the dominant CMB signal. Fitting the resulting CMB component for Qrms and n we find good agreement with the results from Gorski et al.(1996) in which the galactic emission has been taken into account by subtracting that part of the DMR signal observed to be correlated with these galactic template maps. We further investigate the ability of FastICA to evaluate the extent of foreground contamination in the COBE-DMR data. We include an all-sky Halpha survey (Dickinson, Davies & Davis 2003) to determine a reliable free-free template. In particular we find that, after subtraction of the thermal dust emission predicted by the Finkbeiner, Davis & Schlegel (1999) model 7, this component is the dominant foreground emission at 31.5 GHz. This indicates the presence of an anomalous dust correlated component which is well fitted by a power law spectral shape $ u^{-beta}$ with $beta sim 2.5$ in agreement with Banday et al. (2003).
More than a dozen papers analyzing the COBE data have now appeared. We review the different techniques and compare them to a ``brute force likelihood analysis where we invert the full 4038 x 4038 Galaxy-cut pixel covariance matrix. This method is optimal in the sense of producing minimal error bars, and is a useful reference point for comparing other analysis techniques. Our maximum-likelihood estimate of the spectral index and normalization are n=1.15 (0.95) and Q=18.2 (21.3) micro-Kelvin including (excluding) the quadrupole. Marginalizing over the normalization C_9, we obtain n=1.10 +/- 0.29 (n=0.90 +/- 0.32). When we compare these results with those of the various techniques that involve a linear ``compression of the data, we find that the latter are all consistent with the brute-force analysis and have error bars that are nearly as small as the minimal error bars. We therefore conclude that the data compressions involved in these techniques do indeed retain most of the useful cosmological information.
We investigate the power of wavelet techniques in detecting non-Gaussianity in the cosmic microwave background (CMB). We use the method to discriminate between an inflationary and a cosmic strings model using small simulated patches of the sky. We show the importance of the choice of a good test statistic in order to optimise the discriminating power of the wavelet technique. In particular, we construct the Fisher discriminant function, which combines all the information available in the different wavelet scales. We also compare the performance of different decomposition schemes and wavelet bases. For our case, we find that the Mallat and {it `a trous} algorithms are superior to the 2D-tensor wavelets. Using this technique, the inflationary and strings models are clearly distinguished even in the presence of a superposed Gaussian component with twice the rms amplitude of the original cosmic string map.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
