arXiv subjects

K. M. Gorski

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

At least 73 records · Page 4Linked to original sources

arXiv2006

No Higher Criticism of the Bianchi Corrected WMAP Data

Motivated by the success of the Bianchi VII_h model in addressing many of the anomalies observed in the WMAP data (Jaffe et al.), we present calculations in real and in wavelet space of the Higher Criticism statistic of the Bianchi corrected Wilkinson Microwave Anisotropy Probe (WMAP) first year data. At the wavelet scale of 5 degrees the Higher Criticism of the WMAP map drops from a value above the 99% c.l. to a value below the 68% c.l. when corrected by the Bianchi template. An important property of the Higher Criticism statistic is its ability to locate the pixels that account for the deviation from Gaussianity. The analysis of the uncorrected WMAP data pointed to a cold spot in the southern hemisphere centered at (l,b)~ (209, -57). The Higher Criticism of the Bianchi corrected map indicates that this spot remains prominent, albeit at a level completely consistent with Gaussian statistics. Consequently, it is debatable how much emphasis should be placed on this residual feature, but we consider the effect of modestly increasing the scaling of the template. A factor of only 1.2 renders the spot indistinguishable from the background level, with no noticeable impact on the results published in Jaffe et al. for the low-l anomalies, large-scale power asymmetry or wavelet kurtosis. A trivial interpretation would be that the Bianchi template may require a small enhancement of power on scales corresponding to the wavelet scale of 5 degrees.

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arXiv2005

On the Viability of Bianchi Type VIIh Models with Dark Energy

We generalize the predictions for the CMB anisotropy patterns arising in Bianchi type VIIh universes to include a dark energy component. We consider these models in light of the result of Jaffe et al. (2005a,b) in which a correlation was found on large angular scales between the WMAP data and the anisotropy structure in a low density Bianchi universe. We find that by including a term Omega_L > 0, the same best-fit anisotropy pattern is reproduced by several combinations of cosmological parameters. This sub-set of models can then be further constrained by current observations that limit the values of various cosmological parameters. In particular, we consider the so-called geometric degeneracy in these parameters imposed by the peak structure of the WMAP data itself. Apparently, despite the additional freedom allowed by the dark energy component, the modified Bianchi models are ruled out at high significance.

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arXiv2005

Evidence of vorticity and shear at large angular scales in the WMAP data: a violation of cosmological isotropy?

Motivated by the large-scale asymmetry observed in the cosmic microwave background sky, we consider a specific class of anisotropic cosmological models -- Bianchi type VII_h -- and compare them to the WMAP first-year data on large angular scales. Remarkably, we find evidence of a correlation which is ruled out as a chance alignment at the 3sigma level. The best fit Bianchi model corresponds to x=0.55, Omega_0=0.5, a rotation axis in the direction (l,b)=(222degr,-62degr), shear (sigma/H)_0=2.4e-10 and a right--handed vorticity (omega/H)_0=6.1e-10. Correcting for this component greatly reduces the significance of the large-scale power asymmetry, resolves several anomalies detected on large angular scales (ie. the low quadrupole amplitude and quadrupole/octopole planarity and alignment), and can account for a non--Gaussian "cold spot" on the sky. Despite the apparent inconsistency with the best-fit parameters required in inflationary models to account for the acoustic peaks, we consider the results sufficiently provocative to merit further consideration.

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arXiv2005

Multipole vector anomalies in the first-year WMAP data: a cut-sky analysis

We apply the recently defined multipole vector framework to the frequency-specific first-year WMAP sky maps, estimating the low-l multipole coefficients from the high-latitude sky by means of a power equalization filter. While most previous analyses of this type have considered only heavily processed (and foreground-contaminated) full-sky maps, the present approach allows for greater control of residual foregrounds, and therefore potentially also for cosmologically important conclusions. The low-l spherical harmonics coefficients and corresponding multipole vectors are tabulated for easy reference. Using this formalism, we re-assess a set of earlier claims of both cosmological and non-cosmological low-l correlations based on multipole vectors. First, we show that the apparent l=3 and 8 correlation claimed by Copi et al. (2004) is present only in the heavily processed map produced by Tegmark et al. (2003), and must therefore be considered an artifact of that map. Second, the well-known quadrupole-octopole correlation is confirmed at the 99% significance level, and shown to be robust with respect to frequency and sky cut. Previous claims are thus supported by our analysis. Finally, the low-l alignment with respect to the ecliptic claimed by Schwarz et al. (2004) is nominally confirmed in this analysis, but also shown to be very dependent on severe a-posteriori choices. Indeed, we show that given the peculiar quadrupole-octopole arrangement, finding such a strong alignment with the ecliptic is not unusual.

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arXiv2005

CMB component separation by parameter estimation

We propose a solution to the CMB component separation problem based on standard parameter estimation techniques. We assume a parametric spectral model for each signal component, and fit the corresponding parameters pixel by pixel in a two-stage process. First we fit for the full parameter set (e.g., component amplitudes and spectral indices) in low-resolution and high signal-to-noise ratio maps using MCMC, obtaining both best-fit values for each parameter, and the associated uncertainty. The goodness-of-fit is evaluated by a chi^2 statistic. Then we fix all non-linear parameters at their low-resolution best-fit values, and solve analytically for high-resolution component amplitude maps. This likelihood approach has many advantages: The fitted model may be chosen freely, and the method is therefore completely general; all assumptions are transparent; no restrictions on spatial variations of foreground properties are imposed; the results may be rigorously monitored by goodness-of-fit tests; and, most importantly, we obtain reliable error estimates on all estimated quantities. We apply the method to simulated Planck and six-year WMAP data based on realistic models, and show that separation at the muK level is indeed possible in these cases. We also outline how the foreground uncertainties may be rigorously propagated through to the CMB power spectrum and cosmological parameters using a Gibbs sampling technique.

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arXiv2005

Astro-ph communication: Simulations of the WMAP Internal Linear Combination sky map

Following this astro-ph communication, we release a set of 10,000 WMAP ILC simulations, produced as described by Eriksen et al. (2004). We strongly encourage that an analysis of these simulations accompanies any scientific analysis of the observed ILC map, in order to assess the stability of the results. For examples of such analyses, we refer the reader to our original paper. In particular, Figure 1c) and d) show the bias and uncertainty induced by the ILC method, and Figure 7 shows a sobering examples of a low-l analysis; the reconstructed quadrupole-octopole alignment is plotted against the true input alignment, and the correlation is underwhelming. It can hardly be emphasized too strongly -- the heavily processed full-sky WMAP maps are not reliable for quantitative analysis, neither at large nor small scales, and they should only, at best, be used as supportive evidence. We hope that these simulations will reduce some of the confusion regarding these maps that currently exists in the community.

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arXiv2004

Low-order multipole maps of CMB anisotropy derived from WMAP

Recent analyses of the WMAP data have suggested that the low-order multipoles of the CMB anisotropy distribution show cosmologically interesting and unexpected morphologies and amplitudes. In this paper, we apply a power equalization (PE) filter to the high-latitude WMAP data in order to reconstruct these low-l multipoles free from the largest Galactic foreground modelling uncertainties in the Galactic plane. The characteristic spatial distributions of the modes of order l=2,3,4,5 have been determined as a function of frequency, sky coverage and two methods for foreground correction: using the template fitting results of Bennett et al. (2003) and by a simple linear projection scheme assuming the spectral dependence of the foreground components. Our analyses suggest that the K and Ka frequency bands remain significantly contaminated by residual foreground emission for the WMAP Kp2 mask. However, the l=3,4,5 multipole maps for the Q, V and W channels indicate that, after foreground cleaning, these multipoles are dominated by the CMB anisotropy component. We confirm the Tegmark et al. (2003) result that the octopole does indeed show structure in which its hot and cold spots are centred on a single plane in the sky, and show further that this is very stable with respect to the applied mask and foreground correction. The estimated quadrupole is much less stable showing non-negligible dependence on the Galactic foreground correction. Including these uncertainties is likely to weaken the statistical significance of the claimed alignment between the quadrupole and octopole. Nevertheless, these anisotropy patterns are also present for in COBE-DMR data, and are unlikely to be associated with instrumental systematic artifacts.

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arXiv2004

Bayesian Power Spectrum Analysis of the First-Year WMAP data

We present the first results from a Bayesian analysis of the WMAP first year data using a Gibbs sampling technique. Using two independent, parallel supercomputer codes we analyze the WMAP Q, V and W bands. The analysis results in a full probabilistic description of the information the WMAP data set contains about the power spectrum and the all-sky map of the cosmic microwave background anisotropies. We present the complete probability distributions for each C_l including any non-Gaussianities of the power spectrum likelihood. While we find good overall agreement with the previously published WMAP spectrum, our analysis uncovers discrepancies in the power spectrum estimates at low l multipoles. For example we claim the best-fit Lambda-CDM model is consistent with the C_2 inferred from our combined Q+V+W analysis with a 10% probability of an even larger theoretical C_2. Based on our exact analysis we can therefore attribute the "low quadrupole issue" to a statistical fluctuation.

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arXiv2004

The N-point correlation functions of the first-year Wilkinson Microwave Anisotropy Probe sky maps

We compute the two-, three- and four-point correlation functions from the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data, and compare these to a Monte Carlo ensemble of 5000 realizations, based on the best-fit WMAP running-index spectrum of Gaussian fluctuations. The analysis is carried out in three steps, covering small (< 72'), intermediate (< 5 degrees) and large scales (up to 180 degrees). On the largest scales our results are consistent with the previously reported hemisphere power asymmetries: the northern ecliptic hemisphere is practically devoid of large scale fluctuations, while the southern hemisphere show relatively strong fluctuations. We also detect excess correlations in W-band difference maps as compared to the detailed noise simulations produced by the WMAP team, possibly indicative of unknown systematics. While unlikely to affect any temperature based results, this effect could potentially be important for the upcoming polarization data. On intermediate angular scales we find hints of a similar anisotropic distribution of power as seen on the very largest scales, but not to the same extent. In general the model is accepted on these scales. Finally, the same is also true on the smallest scales probed in this paper.

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arXiv2004

Cosmological Parameter Constraints as Derived from the Wilkinson Microwave Anisotropy Probe Data via Gibbs Sampling and the Blackwell-Rao Estimator

We study the Blackwell-Rao (BR) estimator of the probability distribution of the angular power spectrum, P(C_l|d), by applying it to samples of full-sky no-noise CMB maps generated via Gibbs sampling. We find the estimator, given a set of samples, to be very fast and also highly accurate, as determined by tests with simulated data. We also find that the number of samples required for convergence of the BR estimate rises rapidly with increasing l, at least at low l. Our existing sample chains are only long enough to achieve convergence at l less than about 40. In comparison with P(C_l|d) as reported by the WMAP team we find significant differences at these low l values. These differences lead to up to approximately 0.5 sigma shifts in the estimates of parameters in a 7-parameter Lambda CDM model with non-zero dn_s/dln(k). Fixing dn_s/dln(k)= 0 makes these shifts much less significant. Unlike existing analytic approximations, the BR estimator can be straightforwardly extended for the case of power spectra from correlated fields, such as temperature and polarization. We discuss challenges to extending the procedure to higher l and provide some solutions.

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arXiv2004

HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere

HEALPix -- the Hierarchical Equal Area iso-Latitude Pixelization -- is a versatile data structure with an associated library of computational algorithms and visualization software that supports fast scientific applications executable directly on very large volumes of astronomical data and large area surveys in the form of discretized spherical maps. Originally developed to address the data processing and analysis needs of the present generation of cosmic microwave background (CMB) experiments (e.g. BOOMERanG, WMAP), HEALPix can be expanded to meet many of the profound challenges that will arise in confrontation with the observational output of future missions and experiments, including e.g. Planck, Herschel, SAFIR, and the Beyond Einstein CMB polarization probe. In this paper we consider the requirements and constraints to be met in order to implement a sufficient framework for the efficient discretization and fast analysis/synthesis of functions defined on the sphere, and summarise how they are satisfied by HEALPix.

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arXiv2004

Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton

The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a chi^2 that is large at the 95% level for all scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 sigma. On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data.

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arXiv2004

On Foreground Removal from the Wilkinson Microwave Anisotropy Probe Data by an Internal Linear Combination Method: Limitations and Implications

We study the Internal Linear Combination (ILC) method presented by the Wilkinson Microwave Anisotropy Probe (WMAP) science team, with the goal of determining whether it may be used for cosmological purposes, as a template-free alternative to existing foreground correction methods. We conclude that the method does have the potential to do just that, but great care must be taken both in implementation, and in a detailed understanding of limitations caused by residual foregrounds which can still affect cosmological results. As a first step we demonstrate how to compute the ILC weights both accurately and efficiently by means of Lagrange multipliers, and apply this method to the observed data to produce a new version of the ILC map. Next we describe how to generate Monte Carlo simulations of the ILC map, and find that these agree well with the observed map on angular scales up to l~200. Finally we make two comments to the on-going debates concerning the large-scale properties of the WMAP data. First, we note that the Galactic south-eastern quadrant is associated with notably different ILC weights than the other three quadrants, possibly indicating a foreground related anisotropy. Second, we study the properties of the quadrupole and octopole (amplitude, alignment and planarity), and confirm the previously reported anomalies. Even more interestingly, we find that the l=5 mode is spherically symmetric at about 3 sigma, and that the l=6 mode is planar at the 2 sigma level. However, we also assess the impact of residual foregrounds on these statistics, and find that the ILC map is not clean enough to allow for cosmological conclusions. Alternative methods must be developed to study these issues further.

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arXiv2004

Power spectrum estimation from high-resolution maps by Gibbs sampling

We revisit a recently introduced power spectrum estimation technique based on Gibbs sampling, with the goal of applying it to the high-resolution WMAP data. In order to facilitate this analysis, a number of sophistications have to be introduced, each of which is discussed in detail. We have implemented two independent versions of the algorithm to cross-check the computer codes, and to verify that a particular solution to any given problem does not affect the scientific results. We then apply these programs to simulated data with known properties at intermediate (N_side = 128) and high (N_side = 512) resolutions, to study effects such as incomplete sky coverage and white vs. correlated noise. From these simulations we also establish the Markov chain correlation length as a function of signal-to-noise ratio, and give a few comments on the properties of the correlation matrices involved. Parallelization issues are also discussed, with emphasis on real-world limitations imposed by current super-computer facilities. The scientific results from the analysis of the first-year WMAP data are presented in a companion letter.

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arXiv2004

Cosmological parameters and the WMAP data revisited

Several recent papers have made claims about the detection of an asymmetric distribution of large scale power in the cosmic microwave background anisotropy as measured by the WMAP satellite. In this paper, we investigate how the estimates of particular cosmological parameters vary when inferred from power spectra computed separately on the northern and southern hemispheres in three frames of reference. We focus our investigation on the three specific parameters to which the analysis is most sensitive, the spectral index n, the amplitude of fluctuations A and the optical depth tau. When using a gaussian prior on the spectral index n centred at n=1 with a flat prior on the optical depth tau, the preferred value for the optical depth (derived in the reference frame of maximum asymmetry) in the north is tau=0 with upper limit tau<0.08, whereas in the south we find tau=0.24 +0.06/-0.07 (68% confidence level). The latter result is inconsistent with tau=0 at the 2 sigma level. The estimated optical depth of tau=0.17 on the (nearly) full sky found by the WMAP collaboration and confirmed independently here, could thus in large part originate in structure associated with the southern hemisphere. Furthermore, putting a prior on tau, we find values of the spectral index which are inconsistent between the opposite hemispheres. The exact values depend on the prior on tau. While our results should not be considered more than suggestive, the significance of the parameter differences in the two hemispheres being typically of order 2 sigma, if they are confirmed with the higher sensitivity WMAP 2-year data then it may be necessary to question the assumption of cosmological isotropy and the conceptual framework within which studies of the CMB anisotropy are made.

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arXiv2004

Foreground separation using a flexible maximum-entropy algorithm: an application to COBE data

A flexible maximum-entropy component separation algorithm is presented that accommodates anisotropic noise, incomplete sky-coverage and uncertainties in the spectral parameters of foregrounds. The capabilities of the method are determined by first applying it to simulated spherical microwave data sets emulating the COBE-DMR, COBE-DIRBE and Haslam surveys. Using these simulations we find that is very difficult to determine unambiguously the spectral parameters of the galactic components for this data set due to their high level of noise. Nevertheless, we show that is possible to find a robust CMB reconstruction, especially at the high galactic latitude. The method is then applied to these real data sets to obtain reconstructions of the CMB component and galactic foreground emission over the whole sky. The best reconstructions are found for values of the spectral parameters: T_d=19 K, alpha_d=2, beta_ff=-0.19 and beta_syn=-0.8. The CMB map has been recovered with an estimated statistical error of \sim 22 muK on an angular scale of 7 degrees outside the galactic cut whereas the low galactic latitude region presents contamination from the foreground emissions.

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arXiv2004

Testing the cosmological principle of isotropy: local power spectrum estimates of the WMAP data

We apply the Gabor transform methodology proposed in (Hansen et al. 2002, 2003) to the WMAP data in order to test the statistical properties of the CMB fluctuation field and specifically to evaluate the fundamental assumption of cosmological isotropy. We estimate the angular power spectrum locally in discs of various sizes positioned in different directions. We determine whether the spatial position of a few outliers in the angular power spectrum could suggest the presence of residual foregrounds or systematic effects. For multipoles close to the first peak, the most deviant local estimates from the best fit WMAP model are associated with a few particular areas close to the Galactic plane. Such deviations also include the ``dent'' in the spectrum just shortward of the first peak which was remarked upon by the WMAP team. Estimating the angular power spectrum excluding these areas gives a slightly higher first Doppler peak amplitude. Finally, we probe the isotropy of the largest angular scales by estimating the power spectrum on hemispheres and reconfirm strong indications of a north-south asymmetry previously reported by other authors. We find tentative evidence for residual foregrounds in the range l=2-4, which could be associated with the low measured quadrupole amplitudes and other anomalies on these angular scales. However, over the range l=5-40 the observed asymmetry is much harder to explain in terms of residual foregrounds and known systematic effects. Such asymmetric distributions of power on the sky provide a serious test for the cosmological principle of isotropy.

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arXiv2004

Asymmetries in the CMB anisotropy field

We report on the results from two independent but complementary statistical analyses of the WMAP first-year data, based on the power spectrum and N-point correlation functions. We focus on large and intermediate scales (larger than about 3 degrees) and compare the observed data against Monte Carlo ensembles with WMAP-like properties. In both analyses, we measure the amplitudes of the large-scale fluctuations on opposing hemispheres and study the ratio of the two amplitudes. The power-spectrum analysis shows that this ratio for WMAP, as measured along the axis of maximum asymmetry, is high at the 95%-99% level (depending on the particular multipole range included). The axis of maximum asymmetry of the WMAP data is weakly dependent on the multipole range under consideration but tends to lie close to the ecliptic axis. In the N-point correlation function analysis we focus on the northern and southern hemispheres defined in ecliptic coordinates, and we find that the ratio of the large-scale fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results are stable with respect to choice of Galactic cut and also with respect to frequency band. A similar asymmetry is found in the COBE-DMR map, and the axis of maximum asymmetry is close to the one found in the WMAP data.

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