Internal Linear Combination Map Research Articles

Bayesian analysis of anisotropic cosmologies: Bianchi VIIh and WMAP

We perform a definitive analysis of Bianchi VII_h cosmologies with WMAP observations of the cosmic microwave background (CMB) temperature anisotropies. Bayesian analysis techniques are developed to study anisotropic cosmologies using full-sky and partial-sky, masked CMB temperature data. We apply these techniques to analyse the full-sky internal linear combination (ILC) map and a partial-sky, masked W-band map of WMAP 9-year observations. In addition to the physically motivated Bianchi VII_h model, we examine phenomenological models considered in previous studies, in which the Bianchi VII_h parameters are decoupled from the standard cosmological parameters. In the two phenomenological models considered, Bayes factors of 1.7 and 1.1 units of log-evidence favouring a Bianchi component are found in full-sky ILC data. The corresponding best-fit Bianchi maps recovered are similar for both phenomenological models and are very close to those found in previous studies using earlier WMAP data releases. However, no evidence for a phenomenological Bianchi component is found in the partial-sky W-band data. In the physical Bianchi VII_h model we find no evidence for a Bianchi component: WMAP data thus do not favour Bianchi VII_h cosmologies over the standard Lambda Cold Dark Matter (LCDM) cosmology. It is not possible to discount Bianchi VII_h cosmologies in favour of LCDM completely, but we are able to constrain the vorticity of physical Bianchi VII_h cosmologies at $(\omega/H)_0 < 8.6 \times 10^{-10}$ with 95% confidence.

INTERACTING GALACTIC NEUTRAL HYDROGEN FILAMENTS AND ASSOCIATED HIGH-FREQUENCY CONTINUUM EMISSION

Galactic HI emission profiles in an area where several large-scale filaments at velocities ranging from -46 km/s to 0 km/s overlap were decomposed into Gaussian components. Eighteen families of components defined by similarities of center velocity and line width were identified and related to small-scale structure in the high-frequency continuum emission observed by the WMAP spacecraft, as evidenced in the Internal Linear Combination (ILC) map of Hinshaw et al. (2007). When the center velocities of the Gaussian families, which summarize the properties of all the HI along the lines-of-sight in a given area, are used to focus on HI channel maps the phenomenon of close associations between HI and ILC peaks reported in previous papers is dramatically highlighted. Of particular interest, each of two pairs of HI peaks straddles a continuum peak. The previously hypothesized model for producing the continuum radiation (Verschuur, 2010) involving free-free emission from electrons is re-examined in the light of the new data. By choosing reasonable values for the parameters required to evaluate the model, the distance for associated HI-ILC features is of order 30 to 100 pc. No associated H-alpha radiation is expected because the electrons involved exist throughout the Milky Way. The mechanism for clumping and separation of neutrals and electrons needs to be explored.

Searching for hidden mirror symmetries in CMB fluctuations from WMAP 7 year maps

We search for hidden mirror symmetriesat large angular scales in the WMAP 7 year Internal LinearCombination map of CMB temperature anisotropies using global pixel based estimatorsintroduced for this aim. Two different axes are found for whichthe CMB intensity pattern is anomalously symmetric (oranti-symmetric) under reflection with respect to orthogonal planesat the 99.84(99.96)% CL (confidence level), if compared to a result for an arbitrary axis in simulations withoutthe symmetry. We have verified that our results are robust to the introduction ofthe galactic mask.The direction of such axes is close to the CMB kinematic dipole and nearly orthogonalto the ecliptic plane, respectively.If instead the real data are compared to those in simulations taken with respect to planes for which the maximal mirror symmetry is generatedby chance, the confidence level decreases to 92.39(76.65)%. But when theeffect in question translates into the anomalous alignment betweennormals to planes of maximal mirror (anti)-symmetry and these natural axesmentioned.We also introduce the representation of the above estimators in the harmonic domain, confirming the results obtained in the pixel one.The symmetry anomaly is shown to be almost entirely due to lowmultipoles, so it may have a cosmological and even primordialorigin. Contrary, the anti-symmetry one is mainly due tointermediate multipoles that probably suggests its non-fundamentalnature. We have demonstrated that these anomalies are not connected to the known issue of the low variance in WMAP observationsand we have checked that axially symmetric parts of theseanomalies are small, so that the axes are not the symmetry ones.

Searching for non-Gaussianity in the WMAP data

Some analyses of recent cosmic microwave background (CMB) data have provided hints that there are deviations from Gaussianity in the WMAP CMB temperature fluctuations. Given the far-reaching consequences of such a non-Gaussianity for our understanding of the physics of the early universe, it is important to employ alternative indicators in order to determine whether the reported non-Gaussianity is of cosmological origin, and/or extract further information that may be helpful for identifying its causes. We propose two new non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, which provide a measure of departure from Gaussianity on large angular scales. A distinctive feature of these indicators is that they provide sky maps of non-Gaussianity of the CMB temperature data, thus allowing a possible additional window into their origins. Using these indicators, we find no significant deviation from Gaussianity in the three and five-year WMAP Internal Linear Combination (ILC) map with KQ75 mask, while the ILC unmasked map exhibits deviation from Gaussianity, quantifying therefore the WMAP team recommendation to employ the new mask KQ75 for tests of Gaussianity. We also use our indicators to test for Gaussianity the single frequency foreground unremoved WMAP three and five-year maps, and show that the K and Ka maps exhibit a clear indication of deviation from Gaussianity even with the KQ75 mask. We show that our findings are robust with respect to the details of the method.

COSMIC COVARIANCE AND THE LOW QUADRUPOLE ANISOTROPY OF THEWILKINSON MICROWAVE ANISOTROPY PROBE(WMAP) DATA

The quadrupole power of microwave background (CMB) temperature anisotropies seen in the Wilkinson Microwave Anisotropy Probe (WMAP) data is puzzlingly low. In this paper, we demonstrate that Minimum Variance Optimization (MVO), a technique used by many authors (including the WMAP science team) to separate the CMB from contaminating foregrounds, has the effect of forcing the extracted CMB map to have zero statistical correlation with the foreground emission. Over an ensemble of universes the true CMB and foreground are indeed expected to be uncorrelated, but any particular sky pattern (such as the one we happen to observe) will generate nonzero measured correlations simply by chance. We call this effect cosmic and it is a possible source of bias in the CMB maps cleaned using the MVO technique. We show that the presence of covariance is expected to artificially suppress the variance of the Internal Linear Combination (ILC) map obtained via MVO. It also propagates into the multipole expansion of the ILC map, generating a quadrupole deficit with more than 90% confidence. Since we do not know the CMB and the foregrounds a priori, there is therefore an unknown contribution to the uncertainty in the measured quadrupole power, over and above the usual variance contribution.

EXTRAGALACTIC POINT SOURCE SEARCH IN FIVE-YEARWMAP41, 61, AND 94 GHz MAPS

We present the results of an extragalactic point source search using the five-year WMAP 41, 61 and 94 GHz (Q-, V- and W-band) temperature maps. This work is an extension of our point source search in the WMAP maps applying a CMB-free technique. An internal linear combination (ILC) map has been formed from the three-band maps, with the weights chosen to remove the CMB anisotropy signal as well as to favor a selection of flat-spectrum sources. We find 381 sources at the > 5 sigma level outside the WMAP point source detection mask in the ILC map, among which 89 are "new" (i.e., not present in the WMAP catalog). Source fluxes have been calculated and corrected for the Eddington bias. We have solidly identified 367 (96.3%) of our sources. The 1 sigma positional uncertainty is estimated to be 2'. The 14 unidentified sources could be either extended radio structure or obscured by Galactic emission. We have also applied the same detection process on simulated maps and found 364+/-21 detections on average. The recovered source distribution N(>S) agrees well with the simulation input, which proves the reliability of this method.

CMB map derived from the WMAP data through harmonic internal linear combination

We are presenting an internal linear combination CMB map, in which the foreground is reduced through harmonic variance minimization. We have derived our method by converting a general form of pixel-space approach into spherical harmonic space, maintaining full correspondence. By working in spherical harmonic space, spatial variability of linear weights is incorporated in a self-contained manner and our linear weights are continuous functions of position over the entire sky. The full correspondence to pixel-space approach enables straightforward physical interpretation on our approach. In variance minimization of a linear combination map, the existence of a cross term between residual foregrounds and CMB makes the linear combination of minimum variance differ from that of minimum foreground. We have developed an iterative foreground reduction method, where perturbative correction is made for the cross term. Our CMB map derived from the WMAP data is in better agreement with the WMAP best-fit $\ensuremath{\Lambda}\mathrm{CDM}$ model than the WMAP team's internal linear combination map. We find that our method's capacity to clean foreground is limited by the availability of enough spherical harmonic coefficients of good signal-to-noise ratio.

PECULIARITIES OF PHASES OF THE WMAP QUADRUPOLE

We present the analysis of the quadrupole phases of the Internal Linear Combination map, ILC(I) and (III), derived by the WMAP team (one- and three-year data release). This approach allows us to see the global trend of non-Gaussianity of the quadrupoles for the ILC(III) map through phase correlations with the foregrounds. Significant phase correlations are found between the ILC(III) quadrupole and the WMAP foreground phases for the K-W band: the phases of the ILC(III) quadrupole ξ2,1, ξ2,2 and those of the foregrounds at K–W bands Φ2,1, Φ2,2 display significant symmetry: ξ2,1 + Φ2,1 ≃ ξ2,2 + Φ2,2, which is a strong indication that the morphology of the ILC(III) quadrupole is a mere reflection of that the foreground quadrupole through coupling. To clarify this issue we exploit the symmetry of the CMB power, which is invariant under permutation of the index m = 1 ⇔ 2. By simple rotation of the ILC(III) phases with the same angle we reach the phases of the foreground quadrupole. We discuss possible sources of phase correlation and come to the conclusion that the phases of the ILC(III) quadrupole reflect most likely systematic effects such as changing of the gain factor for the three-year data release with respect to the one-year, rather than manifestation of the primordial non-Gaussianity.

High Galactic Latitude Interstellar Neutral Hydrogen Structure and Associated (WMAP) High‐Frequency Continuum Emission

Spatial associations have been found between interstellar neutral hydrogen (H I) emission morphology and small-scale structure observed by the Wilkinson Microwave Anisotropy Probe (WMAP) in an area bounded by l = 60°, 180° and b = 30°, 70°, which was the primary target for this study. This area is marked by the presence of highly disturbed local H I and a preponderance of intermediate- and high-velocity gas. The H I distribution toward the brightest peaks in the WMAP Internal Linear Combination (ILC) map for this area is examined, and by comparing with a second area on the sky it is demonstrated that the associations do not appear to be the result of chance coincidence. Close examination of several of the associations reveals important new properties of diffuse interstellar neutral hydrogen structure. In the case of the high-velocity cloud MI, the H I and WMAP ILC morphologies are similar, and an excess of soft X-ray emission and Hα emission have been reported for this feature. It is suggested that the small angular scale, high-frequency continuum emission observed by WMAP may be produced at the surfaces of H I features interacting one another, or at the interface between moving H I structures and regions of enhanced plasma density in the surrounding interstellar medium. It is possible that dust grains play a role in producing the emission. However, the primary purpose of this report is to draw attention to these apparent associations, without offering an unambiguous explanation as to the relevant emission mechanism(s).

LARGE-SCALE MODES OF CLEANED THREE-YEAR WMAP CMB MAP

We have produced a cleaned map of the WMAP three-year data using an improved version of an internal linear combination (ILC) method to subtract the Galactic foreground emission. We divide the whole sky into hundreds of pixel groups with similar foreground spectral indices over a range of WMAP frequencies, apply the ILC for each group, and obtain a CMB map with foreground emission effectively reduced. With the resulting foreground-reduced ILC map, we have investigated the known anomalies in CMB maps at large scales, and confirmed that the quadrupole power is low and the quadrupole and the octopole are strongly aligned and are planar. Although our estimates are consistent with the previous measurements, ILC simulation implies that the observed low quadrupole power and the alignment between the quadrupole and the octopole are marginally statistically significant, and the observed planarity is not statistically significant.

Departure from Gaussianity of the Cosmic Microwave Background Temperature Anisotropies in the Three‐YearWMAPData

We test the hypothesis that the temperature of the cosmic microwave background is consistent with a Gaussian random field defined on the celestial sphere, using de-biased internal linear combination (DILC) map produced from the 3-year WMAP data. We test the phases for spherical harmonic modes with l <= 10 (which should be the cleanest) for their uniformity, randomness, and correlation with those of the foreground templates. The phases themselves are consistent with a uniform distribution, but not for l <= 5, and the differences between phases are not consistent with uniformity. For l=3 and l=6, the phases of the CMB maps cross-correlate with the foregrounds, suggestion the presence of residual contamination in the DLC map even on these large scales. We also use a one-dimensional Fourier representation to assemble a_lm into the \Delta T_l(\phi) for each l mode, and test the positions of the resulting maxima and minima for consistency with uniformity randomness on the unit circle. The results show significant departures at the 0.5% level, with the one-dimensional peaks being concentrated around \phi=180 degs. This strongly significant alignment with the Galactic meridian, together with the cross-correlation of DILC phases with the foreground maps, strongly suggests that even the lowest spherical harmonic modes in the map are significantly contaminated with foreground radiation.

Broken Isotropy from a Linear Modulation of the Primordial Perturbations

A linear modulation of the primordial perturbations is proposed as an explanation for the observed asymmetry between the northern and southern hemispheres of the Wilkinson Microwave Anisotropy Probe (WMAP) data. A cut sky, reduced-resolution third-year internal linear combination (ILC) map was used to estimate the modulation parameters. A foreground template and a modulated plus unmodulated monopole and dipole were projected out of the likelihood. The effective χ2 was reduced by 9 for three extra parameters. The mean Galactic colatitude and longitude of the modulation, with 68%, 95%, and 99.7% confidence intervals were 56 and 63. The mean percentage change of the variance across the poles of the modulation was 62. Implications of these results and possible generating mechanisms are discussed.

Uncorrelated universe: Statistical anisotropy and the vanishing angular correlation function in WMAP years 1–3

The large-angle (low-l) correlations of the cosmic microwave background (CMB) as reported by the Wilkinson Microwave Anisotropy Probe (WMAP) after their first year of observations exhibited statistically significant anomalies compared to the predictions of the standard inflationary big-bang model. We suggested then that these implied the presence of a solar system foreground, a systematic correlated with solar system geometry, or both. We reexamine these anomalies for the data from the first three years of WMAP's operation. We show that, despite the identification by the WMAP team of a systematic correlated with the equinoxes and the ecliptic, the anomalies in the first-year internal linear combination (ILC) map persist in the three-year ILC map, in all-but-one case at similar statistical significance. The three-year ILC quadrupole and octopole therefore remain inconsistent with statistical isotropy - they are correlated with each other (99.6% C.L.), and there are statistically significant correlations with local geometry, especially that of the solar system. The angular two-point correlation function at scales > 60 deg in the regions outside the (kp0) galactic cut, where it is most reliably determined, is approximately zero in all wavebands and is even more discrepant with the best-fit Lambda CDM inflationary model than in the first-year data - 99.97% C.L. for the new ILC map. The full-sky ILC map, on the other hand, has a nonvanishing angular two-point correlation function, apparently driven by the region inside the cut, but which does not agree better with Lambda CDM. The role of the newly-identified low-l systematics is more puzzling than reassuring.

The one-dimensional Fourier representation and large angular scale foregroundcontamination in the three-year Wilkinson Microwave Anisotropy Probe data

We employ the one-dimensional Fourier representation (1DFR) to analyse the three-yearWMAP de-biased internal linear combination (DILC) map and its possible contaminationwith galactic foregrounds. The 1DFR is a representation of the spherical harmoniccoefficients for each ℓ mode using an inverse Fourier transform into one-dimensional curves. On the basis ofthe a priori assumption that the cosmic microwave background signal shouldbe statistically independent of, and consequently have no significant correlationwith, any foregrounds, we cross correlate the 1DFR curves of 2 ≤ ℓ ≤ 10 modes, which are claimed by the WMAP team to be free of contamination and suitablefor whole-sky analysis. We find that eight out of the nine modes are negatively crosscorrelated with the foreground maps, an event which has a probability of only 9/512 ≃ 0.0176 for uncorrelated signals. Furthermore, the local extrema of the 1DFR curves between theDILC and those of the foregrounds for ℓ = 2 and 6 are correlated with significance level below 0.04. We also discuss the minimumvariance optimization method and use the properties of the measured cross correlation toestimate the possible level of contamination present in the DILC map.

Testing global isotropy of three-year Wilkinson Microwave Anisotropy Probe (WMAP) data: Temperature analysis

We examine statistical isotropy of large scale anisotropies of the Internal Linear Combination (ILC) map, based on 3 yr WMAP data. Our study reveals no significant deviation from statistical isotropy on large angular scales of the 3 yr ILC map. Comparing statistical isotropy of the 3 yr ILC map and 1 yr ILC map, we find a significant improvement in the 3 yr ILC map which can be due to the gain model, improved ILC map processing, and foreground minimization.

Foreground contamination of the WMAP CMB maps from the perspective of the matched circle test

WMAP has provided CMB maps of the full sky. The raw data is subject to foreground contamination, in particular near to the Galactic plane. Foreground cleaned maps have been derived, e.g., the internal linear combination (ILC) map of Bennett et al. and the reduced foreground TOH map of Tegmark et al. Using S statistics we examine whether residual foreground contamination is left over in the foreground cleaned maps. In particular, we specify which parts of the foreground cleaned maps are sufficiently accurate for the circle-in-the-sky signature. We generalise the S statistic, called D statistic, such that the circle test can deal with CMB maps in which the contaminated regions of the sky are excluded with masks.

AUTO- AND CROSS-CORRELATION OF PHASES OF THE WHOLE-SKY CMB AND FOREGROUND MAPS FROM THE 1-YEAR WMAP DATA

The issue of non-Gaussianity is not only related to distinguishing the theories of the origin of primordial fluctuations, but also crucial for the determination of cosmological parameters in the framework of inflation paradigm. We present a method for testing non-Gaussianity on the whole-sky cosmic microwave background (CMB) anisotropies. This method is based on the Kuiper's statistic to probe the two-dimensional uniformity on a periodic mapping square associating phases: return mapping of phases of the derived CMB (similar to auto-correlation) and cross-correlations between phases of the derived CMB and foregrounds. Since phases reflect morphology, detection of cross-correlation of phases signifies the contamination of foreground signals in the derived CMB map. The advantage of this method is that one can cross-check the auto- and cross-correlation of phases of the derived maps and foregrounds, and mark off those multipoles in which the non-Gaussianity results from the foreground contaminations. We apply this statistic on the derived signals from the 1-year WMAP data. The auto-correlations of phases from the internal linear combination map show the significance above 95% C.L. against the random phase hypothesis on 17 spherical harmonic multipoles, among which some have pronounced cross-correlations with the foreground maps. We find that most of the non-Gaussianity found in the derived maps are from foreground contaminations. With this method we are better equipped to approach the issue of non-Gaussianity of primordial origin for the upcoming Planck mission.

Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Temperature Analysis

We present new full-sky temperature maps in five frequency bands from 23 to 94 GHz, based on data from the first 3 years of the WMAP sky survey. The new maps are consistent with the first-year maps and are more sensitive. The 3 year maps incorporate several improvements in data processing made possible by the additional years of data and by a more complete analysis of the polarization signal. These include several new consistency tests as well as refinements in the gain calibration and beam response models. We employ two forms of multifrequency analysis to separate astrophysical foreground signals from the CMB, each of which improves on our first-year analyses. First, we form an improved Internal Linear Combination (ILC) map, based solely on WMAP data, by adding a bias-correction step and by quantifying residual uncertainties in the resulting map. Second, we fit and subtract new spatial templates that trace Galactic emission; in particular, we now use low-frequency WMAP data to trace synchrotron emission instead of the 408 MHz sky survey. The WMAP point source catalog is updated to include 115 new sources whose detection is made possible by the improved sky map sensitivity. We derive the angular power spectrum of the temperature anisotropy using a hybrid approach that combines a maximum likelihood estimate at low l (large angular scales) with a quadratic cross-power estimate for l > 30. The resulting multifrequency spectra are analyzed for residual point source contamination. At 94 GHz the unmasked sources contribute 128 ± 27 μK2 to l(l + 1)Cl/2π at l = 1000. After subtracting this contribution, our best estimate of the CMB power spectrum is derived by averaging cross-power spectra from 153 statistically independent channel pairs. The combined spectrum is cosmic variance limited to l = 400, and the signal-to-noise ratio per l-mode exceeds unity up to l = 850. For bins of width Δl/l = 3%, the signal-to-noise ratio exceeds unity up to l = 1000. The first two acoustic peaks are seen at l = 220.8 ± 0.7 and l = 530.9 ± 3.8, respectively, while the first two troughs are seen at l = 412.4 ± 1.9 and l = 675.2 ± 11.1. The rise to the third peak is unambiguous; when the WMAP data are combined with higher resolution CMB measurements, the existence of a third acoustic peak is well established. Spergel et al. use the 3 year temperature and polarization data to constrain cosmological model parameters. A simple six-parameter ΛCDM model continues to fit CMB data and other measures of large-scale structure remarkably well. The new polarization data produce a better measurement of the optical depth to reionization, τ = 0.089 ± 0.03. This new and tighter constraint on τ helps break a degeneracy with the scalar spectral index, which is now found to be ns = 0.960 ± 0.016. If additional cosmological data sets are included in the analysis, the spectral index is found to be ns = 0.947 ± 0.015.

Assessing the effects of foregrounds and sky removal in WMAP

Many recent analyses have indicated that large scale Wilkinson Microwave Anisotropy Probe (WMAP) data display anomalies that appear inconsistent with the standard cosmological paradigm. However, the effects of foreground contamination, which require elimination of some fraction of the data, have not been fully investigated due to the complexity in the analysis. Here we develop a general formalism of how to incorporate these effects into any analysis of this type. Our approach is to compute the full multidimensional probability distribution function of all possible sky realizations that are consistent with the data and with the allowed level of contamination. Any statistic can be integrated over this probability distribution to assess its significance. As an example we apply this method to compute the joint probability distribution function for the possible realizations of quadrupole and octopole using the WMAP data. This 12 dimensional distribution function is explored using the Markov Chain Monte Carlo technique. The resulting chains are used to assess the statistical significance of the low quadrupole using frequentist methods, which we find to be 3-4%. Octopole is normal and the probability of it being anomalously low or as low as WMAP reported value is very small. We address the quadrupole-octopole alignmentmore » using several methods that have been recently used to argue for anomalies, such as angular momentum dispersion, multipole vectors and a new method based on feature matching. While we confirm that the full-sky map Internal Linear Combination Map (ILC) suggest an alignment, we find that removing the most contaminated part of the data also removes any evidence of alignment: the probability distributions strongly disfavor the alignment. This suggests that most of the evidence for it comes from non-Gaussian features in the part of the data most contaminated by the foregrounds. We also present an example, that of octopole alignment with the ecliptic, where the statistical significance can be enhanced by removing the contamination.« less

On Foreground Removal from theWilkinson Microwave Anisotropy ProbeData 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 we apply this method to the observed data to produce a new version of the ILC map. This map has 12% lower variance than the ILC map of the WMAP team, primarily because of less noise. 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, using a conservative sky cut. Finally we make two comments to the ongoing debates concerning the large-scale properties of the WMAP data. First, we note that the Galactic southeastern 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 reproduce the previously reported results that the quadrupole and octopole are strongly aligned and that the octopole is moderately planar. Even more interestingly, we find that the l = 5 mode is spherically symmetric at about 3 σ, and that the l = 6 mode is planar at the 2 σ 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.