arXiv subjects

K. M. Gorski

Publications and source records attributed to K. M. Gorski.

At least 91 records · Page 5Linked to original sources

arXiv2004

Estimating N-Point Correlation Functions from Pixelized Sky Maps

We develop, implement and test a set of algorithms for estimating N-point correlation functions from pixelized sky maps. These algorithms are slow, in the sense that they do not break the O(N_pix^N) barrier, and yet, they are fast enough for efficient analysis of data sets up to several hundred thousand pixels. The typical application of these methods is Monte Carlo analysis using several thousand realizations, and therefore we organize our programs so that the initialization cost is paid only once. The effective cost is then reduced to a few additions per pixel multiplet (pair, triplet etc.). Further, the algorithms waste no CPU time on computing undesired geometric configurations, and, finally, the computations are naturally divided into independent parts, allowing for trivial (i.e., optimal) parallelization.

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arXiv2003

Reappraising foreground contamination in the COBE-DMR data

With the advent of all-sky H-Alpha surveys it is possible to determine a reliable free-free template of the diffuse interstellar medium (Dickinson, Davies & Davis 2003) which can be used in conjunction with the synchrotron and dust templates to correct CMB observations for diffuse Galactic foregrounds. We have used the COBE-DMR data at 31.5, 53 and 90 GHz and employed cross- correlation techniques to re-evaluate the foreground contributions, particularly that due to dust which is known to be correlated with H-Alpha (and free-free) emission.The DMR microwave maps are found to contain, as well as the expected synchrotron and free-free components, a component tightly correlated to the 140 micron dust maps of DIRBE. At 31.5, 53 and 90 GHz this emission is 6.3 +/- 0.6, 2.4 +/- 0.4 and 2.2 +/- 0.4 microK/(MJy/sr) at 140 microns respectively. When corrected for the contribution from thermal dust following model 7 of Finkbeiner, Davis & Schlegel (1999), a strong anomalous dust emission component remains, which is well-fitted by a frequency spectrum of the form $ν^{-β}$ where beta ~ 2.5 in the DMR frequency range; this is the dominant foreground at 31.5 GHz. The result implies the presence of an emission component with a dust-like morphology but a synchrotron-like spectrum. We discuss the possible origins of this component and compare it with the recent WMAP interpretation. The better knowledge of the individual foregrounds provided by the present study enables a larger area of the sky (|b|>15) to be used to re-appraise the CMB quadrupole normalisation, Qrms-PS, and the scalar perturbations spectral index, n. We find Qrms-PS=15.2^{+2.8}_{-2.3} with a power-law spectral index of n=1.2 +/- 0.2. These values are consistent with previous COBE-DMR analyses and the WMAP 1-year analysis.

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arXiv2003

Astrophysical components separation of COBE-DMR 4yr data with FastICA

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 $ν^{-β}$ with $β\sim 2.5$ in agreement with Banday et al. (2003).

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arXiv2002

COBE-DMR constraints on the nonlinear coupling parameter: a wavelet based method

Nonlinearity introduced in slow-roll inflation will produce weakly non-Gaussian CMB temperature fluctuations. We have simulated non-Gaussian large scale CMB maps (including COBE-DMR constraints) introducing an additional quadratic term in the gravitational potential.The amount of nonlinearity being controlled by the so called nonlinear coupling parameter f_{nl}. An analysis based on the Spherical Mexican Hat wavelet was applied to these and to the COBE-DMR maps. Skewness values obtained at several scales were combined into a Fisher discriminant. Comparison of the Fisher discriminant distributions obtained for different nonlinear coupling parameters with the COBE-DMR values, sets a constraint of abs(f_{nl})<1100 at the 68% confidence level. This new constraint being tighter than the one previously obtained by using the bispectrum by Komatsu et al. (2002).

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arXiv2002

The N-point correlation functions of the COBE-DMR maps revisited

We calculate the two-, three- and (for the first time) four-point correlation functions of the COBE-DMR 4-year sky maps, and search for evidence of non-Gaussianity by comparing the data to Monte Carlo-simulations of the functions. The analysis is performed for the 53 and 90 GHz channels, and five linear combinations thereof. For each map, we simulate an ensemble of 10,000 Gaussian realisations based on an a priori best-fit scale-invariant cosmological power spectrum, the DMR beam pattern and instrument-specific noise properties. Each observed COBE-DMR map is compared to the ensemble using a simple chi^2 statistic, itself calibrated by simulations. In addition, under the assumption of Gaussian fluctuations, we find explicit expressions for the expected values of the four-point functions in terms of combinations of products of the two-point functions, then compare the observed four-point statistics to those predicted by the observed two-point function, using a redefined chi^2 statistic. Both tests accept the hypothesis that the DMR maps are consistent with Gaussian initial perturbations.

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arXiv2002

Topology of the universe from COBE-DMR; a wavelet approach

In this paper we pursue a new technique to search for evidence of a finite Universe, making use of a spherical mexican-hat wavelet decomposition of the microwave background fluctuations. Using the information provided by the wavelet coefficients at several scales we test whether compact orientable flat topologies are consistent with the COBE-DMR data. We consider topological sizes ranging from half to twice the horizon size. A scale-scale correlation test indicates that non-trivial topologies with appropriate topological sizes are as consistent with the COBE-DMR data as an infinite universe. Among the finite models the data seems to prefer a Universe which is about the size of the horizon for all but the hypertorus and the triple-twist torus. For the latter the wavelet technique does not seem a good discriminator of scales for the range of topological sizes considered here, while a hypertorus has a preferred size which is 80% of the horizon. This analysis allows us to find a best fit topological size for each model, although cosmic variance might limit our ability to distinguish some of the topologies.

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arXiv2002

Towards a model of full-sky Galactic synchrotron intensity and linear polarisation: a re-analysis of the Parkes data

We have analysed the angular power spectra of the Parkes radio continuum and polarisation survey of the Southern galactic plane at 2.4 GHz. We have found that in the multipole range l=40-250 the angular power spectrum of the polarised intensity is well described by a power-law spectrum with fitted spectral index alpha_L = 2.37 +- 0.21. In the same multipole range the angular power spectra of the E and B components of the polarised signal are significantly flatter, with fitted spectral indices respectively of alpha_E = 1.57 +- 0.12 and alpha_B = 1.45 +- 0.12. Temperature fluctuations in the E and B components are mostly determined by variations in polarisation angle. We have combined these results with other data from available radio surveys in order to produce a full-sky toy model of Galactic synchrotron intensity and linear polarisation at high frequencies (> 10 GHz). This can be used to study the feasibility of measuring the Cosmic Microwave Background polarisation with forthcoming experiments and satellite missions.

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arXiv2002

Removing 1/f noise stripes in cosmic microwave background anisotropy observations

Removal of systematic effects is crucial in present and future CMB experiments mapping large fraction of the sky. Accurate CMB measurements ask for multi-feed array instruments observing the sky with a redundant scanning strategy covering the same region of the sky on different time scales and with different detectors for a better control of systematic effects. We investigate here the capability to suppress 1/f noise features in Time Ordered Data (TOD) by using the destriping technique described in Maino et al. (1999), under realistic assumptions for crossing condition between different scan circles and sky signal fluctuations on small angular scales. We consider as working case, Planck-LFI simulated observations with few arminutes pixel size convolved with LFI beam resolutions. We also extend the analysis to high values of the knee-frequency and found a residual additional noise rms ~31% larger than the pure white noise rms at fk=1 Hz which could be a critical issue in the extraction of the CMB angular power spectrum. Furthermore we verified that destriping quality does not significantly depend on the receiver sensitivity whereas it improves proportionally to the improvement of sampling rate. Therefore given a noise level, the higher the sampling rate, the better the destriping quality.

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arXiv2002

The Trispectrum of the 4 Year COBE-DMR data

We propose an estimator for the trispectrum of a scalar random field on a sphere, discuss its geometrical and statistical properties, and outline its implementation. By estimating the trispectrum of the 4 year COBE-DMR data (in HEALPix pixelization) we find new evidence of a non-Gaussian signal associated with a known systematic effect. We find that by removing data from the sky maps for those periods of time perturbed by this effect, the amplitudes of the trispectrum coefficients become completely consistent with predictions for a Gaussian sky. These results reinforce the importance of statistical methods based in harmonic space for quantifying non-Gaussianity.

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arXiv2001

All-sky astrophysical component separation with Fast Independent Component Analysis (FastICA)

We present a new, fast, algorithm for the separation of astrophysical components superposed in maps of the sky, based on the fast Independent Component Analysis technique (FastICA). It allows to recover both the spatial pattern and the frequency scalings of the emissions from statistically independent astrophysical processes, present along the line-of-sight, from multi-frequency observations. We apply FastICA to simulated observations of the microwave sky with angular resolution and instrumental noise at the mean nominal levels for the Planck satellite, containing the most important known diffuse signals: the Cosmic Microwave Background (CMB), Galactic synchrotron, dust and free-free emissions. A method for calibrating the reconstructed maps of each component at each frequency has been devised. The spatial pattern of all the components have been recovered on all scales probed by the instrument. In particular, the CMB angular power spectra is recovered at the percent level up to $\ell_{max}\simeq 2000$. Frequency scalings and normalization have been recovered with better than percent precision for all the components at frequencies and in sky regions where their signal-to-noise ratio exceeds 1.5; the error increases at ten percent level for signal-to-noise ratios about 1. Runs have been performed on a Pentium III 600 MHz computer; FastICA typically took a time of the order of 10 minutes for all-sky simulations with 3.5 arcminutes pixel size. We conclude that FastICA is an extremly promising technique for analyzing the maps that will be obtained by the forthcoming high resolution CMB experiments.

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arXiv2001

Resolving gravitational microlensing events with long-baseline optical interferometry. Prospects for the ESO Very Large Telescope Interferometer

Until now, the detailed interpretation of the observed microlensing events has suffered from the fact that the physical parameters of the phenomenon cannot be uniquely determined from the available astronomical measurements, i.e. the photometric lightcurves. The situation will change in the near-future with the availability of long-baseline, sensitive optical interferometers, which should be able to resolve the images of the lensed objects into their components. For this, it will be necessary to achieve a milliarcsecond resolution on sources with typical magnitudes K $\ga 12$. Indeed, brighter events have never been observed up to now by micro-lensing surveys. We discuss the possibilities opened by the use of long baseline interferometry in general, and in particular for one such facility, the ESO VLT Interferometer, which will attain the required performance. We discuss the expected accuracy and limiting magnitude of such measurements. On the basis of the database of the events detected by the OGLE experiment, we estimate the number of microlenses that could be available for measurements by the VLTI. We find that at least several tens of events could be observed each year. In conjunction with the photometric data, our ability to measure the angular separation between the microlensed images will enable a direct and unambiguous determination of both their masses and locations.

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arXiv2001

MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets

We describe a fast and accurate method for estimation of the cosmic microwave background (CMB) anisotropy angular power spectrum --- Monte Carlo Apodised Spherical Transform EstimatoR. Originally devised for use in the interpretation of the Boomerang experimental data, MASTER is both a computationally efficient method suitable for use with the currently available CMB data sets (already large in size, despite covering small fractions of the sky, and affected by inhomogeneous and correlated noise), and a very promising application for the analysis of very large future CMB satellite mission products.

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arXiv2001

Spherical Mexican Hat wavelet: an application to detect non-Gaussianity in the COBE-DMR maps

The spherical Mexican Hat wavelet is introduced in this paper, with the aim of testing the Gaussianity of the Cosmic Microwave Background temperature fluctuations. Using the information given by the wavelet coefficients at several scales, we have performed several statistical tests on the COBE-DMR maps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale-scale correlations (for two and three scales) and Kolmogorov-Smirnov tests indicate that the COBE-DMR data are consistent with a Gaussian distribution. We have extended the analysis to compare temperature values provided by COBE-DMR data with distributions (obtained from Gaussian simulations) at each pixel and at each scale. The number of pixels with temperature values outside the 95% and the 99% is consistent with that obtained from Gaussian simulations, at all scales. Moreover, the extrema values for COBE-DMR data (maximum and minimum temperatures in the map) are also consistent with those obtained from Gaussian simulations.

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arXiv2001

The angular power spectrum of radio emission at 2.3 GHz

We have analysed the Rhodes/HartRAO survey at 2326 MHz and derived the global angular power spectrum of Galactic continuum emission. In order to measure the angular power spectrum of the diffuse component, point sources were removed from the map by median filtering. A least-square fit to the angular power spectrum of the entire survey with a power law spectrum C_l proportional to l^{-alpha}, gives alpha = 2.43 +/- 0.01 for l = 2-100. The angular power spectrum of radio emission appears to steepen at high Galactic latitudes and for observed regions with |b| > 20 deg, the fitted spectral index is alpha = 2.92 +/- 0.07. We have extrapolated this result to 30 GHz (the lowest frequency channel of Planck) and estimate that no significant contribution to the sky temperature fluctuation is likely to come from synchrotron at degree-angular scales

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arXiv2000

Analysis of CMB foregrounds using a database for Planck

Within the scope of the Planck IDIS (Integrated Data Information System) project we have started to develop the data model for time-ordered data and full-sky maps. The data model is part of the Data Management Component (DMC), a software system designed according to a three-tier architecture which allows complete separation between data storage and processing. The DMC is already being used for simulation activities and the modeling of some foreground components. We have ingested several Galactic surveys into the database and used the science data-access interface to process the data. The data structure for full-sky maps utilises the HEALPix tessellation of the sphere. We have been able to obtain consistent measures of the angular power spectrum of the Galactic radio continuum emission between 408 MHz and 2417 MHz.

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arXiv2000

Looking for non-Gaussianity in the COBE-DMR data with spherical wavelets

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.

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arXiv2000

Testing the Gaussianity of the COBE-DMR data with spherical wavelets

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.

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arXiv1999

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.

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