arXiv subjects

F. K. Hansen

Publications and source records attributed to F. K. Hansen.

At least 163 records · Page 9Linked to original sources

arXiv2008

WMAP 5-year constraints on fnl with wavelets

We present a Gaussianity analysis of the WMAP 5-year Cosmic Microwave Background (CMB) temperature anisotropy data maps. We use several third order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter fnl using well motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q, V, and W frequency bands. We use the KQ75 mask recommended by the WMAP team which masks out 28% of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients we compute the third order estimators which are used to perform a chi-squared analysis. The chi-squared statistic is used to test the Gaussianity of the WMAP data as well as to constrain the fnl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the fnl parameter is constrained to -8 < fnl < +111 at 95% CL for the combined V+W map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of Delta_fnl = 3+-5 in the V+W map. Our results are very similar to those obtained by Komatsu et al (2008) using the bispectrum.

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arXiv2008

Constraints on the non-linear coupling parameter fnl with the Archeops data

We present a Gaussianity analysis of the Archeops Cosmic Microwave Background (CMB) temperature anisotropy data maps at high resolution to constrain the non-linear coupling parameter fnl characterising well motivated non-Gaussian CMB models. We used the data collected by the most sensitive Archeops bolometer at 143 GHz. The instrumental noise was carefully characterised for this bolometer, and for another Archeops bolometer at 143 GHz used for comparison. Angular scales from 27 arcmin to 1.8 degrees and a large fraction of the sky, 21 %, covering both hemispheres (avoiding pixels with Galactic latitude |b| < 15 degrees) were considered. The three Minkowski functionals on the sphere evaluated at different thresholds were used to construct a chi-squared statistics for both the Gaussian and the non-Gaussian CMB models. The Archeops maps were produced with the Mirage optimal map-making procedure from processed time ordered data. The analysis is based on simulations of signal (Gaussian and non-Gaussian fnl CMB models) and noise which were processed in the time domain using the Archeops pipeline and projected on the sky using the Mirage optimal map-making procedure. The Archeops data were found to be compatible with Gaussianity after removal of highly noisy pixels at high resolution. The non-linear coupling parameter was constrained to -400 < fnl < 590 at 68% CL and -920 < fnl < 1075 at 95% CL, for realistic non-Gaussian CMB simulations.

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arXiv2007

The scalar perturbation spectral index n_s: WMAP sensitivity to unresolved point sources

Precision measurement of the scalar perturbation spectral index, n_s, from the Wilkinson Microwave Anisotropy Probe temperature angular power spectrum requires the subtraction of unresolved point source power. Here we reconsider this issue. First, we note a peculiarity in the WMAP temperature likelihood's response to the source correction: Cosmological parameters do not respond to increased source errors. An alternative and more direct method for treating this error term acts more sensibly, and also shifts n_s by ~0.3 sigma closer to unity. Second, we re-examine the source fit used to correct the power spectrum. This fit depends strongly on the galactic cut and the weighting of the map, indicating that either the source population or masking procedure is not isotropic. Jackknife tests appear inconsistent, causing us to assign large uncertainties to account for possible systematics. Third, we note that the WMAP team's spectrum was computed with two different weighting schemes: uniform weights transition to inverse noise variance weights at l = 500. The fit depends on such weighting schemes, so different corrections apply to each multipole range. For the Kp2 mask used in cosmological analysis, we prefer source corrections A = 0.012 +/- 0.005 muK^2 for uniform weighting and A = 0.015 +/- 0.005 muK^2 for N_obs weighting. Correcting WMAP's spectrum correspondingly, we compute cosmological parameters with our alternative likelihood, finding n_s = 0.970 +/- 0.017 and sigma_8 = 0.778 +/- 0.045 . This n_s is only 1.8 sigma from unity, compared to the ~2.6 sigma WMAP 3-year result. Finally, an anomalous feature in the source spectrum at l<200 remains, most strongly associated with W-band.

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arXiv2007

Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps

We consider the issue of hemispherical power asymmetry in the three-year WMAP data, adopting a previously introduced modulation framework. Computing both frequentist probabilities and Bayesian evidences, we find that the model consisiting of an isotropic CMB sky modulated by a dipole field, gives a substantially better fit to the observations than the purely isotropic model, even when accounting for the larger prior volume. For the ILC map, the Bayesian log-evidence difference is ~1.8 in favour of the modulated model, and the raw improvement in maximum log-likelihood is 6.1. The best-fit modulation dipole axis points toward (l,b) = (225 deg,-27 deg), and the modulation amplitude is 0.114, in excellent agreement with the results from the first-year analyses. The frequentist probability of obtaining such a high modulation amplitude in an isotropic universe is ~1%. These results are not sensitive to data set or sky cut. Thus, the statistical evidence for a power asymmetry anomaly is both substantial and robust, although not decisive, for the currently available data. Increased sky coverage through better foreground handling and full-sky and high-sensitivity polarization maps may shed further light on this issue.

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arXiv2007

Point-Source Power in 3 Year Wilkinson Microwave Anisotropy Probe Data

Using a set of multifrequency cross spectra computed from the 3 year WMAP sky maps, we fit for the unresolved point-source contribution. For a white-noise power spectrum, we find a Q-band amplitude of A=0.011 +/- 0.001 muK^2 sr (antenna temperature), significantly smaller than the value of 0.017 +/- 0.002 muK^2 sr used to correct the spectra in the WMAP release. Modifying the point-source correction in this way largely resolves the discrepancy that Eriksen et al. found between the WMAP V- and W-band power spectra. Correcting the co-added WMAP spectrum for both the low-l power excess due to a suboptimal likelihood approximation--also reported by Eriksen et al.--and the high-l power deficit due to oversubtracted point sources--presented in this Letter--we find that the net effect in terms of cosmological parameters is an \~0.7 sigma shift in n_s to larger values. For the combination of WMAP, BOOMERANG, and ACBAR data, we find n_s=0.969 +/- 0.016, lowering the significance of n_s not equal to 1 from ~2.7 sigma to ~2.0 sigma.

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arXiv2006

A re-analysis of the three-year WMAP temperature power spectrum and likelihood

We analyze the three-year WMAP temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations to the parameter estimation. Our single most important result is that we broadly confirm the WMAP power spectrum and analysis. Still, we do find two small but potentially important discrepancies: On large angular scales there is a small power excess in the WMAP spectrum (5-10% at l<~30) primarily due to likelihood approximation issues between 13 <= l <~30. On small angular scales there is a systematic difference between the V- and W-band spectra (few percent at l>~300). Recently, the latter discrepancy was explained by Huffenberger et al. (2006) in terms of over-subtraction of unresolved point sources. As far as the low-l bias is concerned, most parameters are affected by a few tenths of a sigma. The most important effect is seen in n_s. For the combination of WMAP, Acbar and BOOMERanG, the significance of n_s =/ 1 drops from ~2.7 sigma to ~2.3 sigma when correcting for this bias. We propose a few simple improvements to the low-l WMAP likelihood code, and introduce two important extensions to the Gibbs sampling method that allows for proper sampling of the low signal-to-noise regime. Finally, we make the products from the Gibbs sampling analysis publically available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.

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arXiv2006

Bianchi Type VII_h Models and the WMAP 3-year Data

Context. A specific example of Bianchi Type VIIh models, i.e. those including universal rotation (vorticity) and differential expansion (shear), has been shown in Jaffe et al. (2005) to correlate unexpectedly with the WMAP first-year data. Aims. We re-assess the signature of this model in the WMAP 3-year data. Methods. The cross-correlation methods are described in Jaffe et al. (2006a). We use the WMAP 3-year data release, including maps for individual years, and perform additional comparisons to assess the influence of both noise and residual foregrounds and eliminate potential non-cosmological sources for the correlation. Results. We confirm that the signal is detected in both the combined 3-year data and the individual yearly sky maps at a level consistent with our original analysis. The significance of the correlation is not affected by either noise or foreground residuals. Conclusions. The results of our previous study are unchanged.

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arXiv2006

Bayesian foreground analysis with CMB data

The quality of CMB observations has improved dramatically in the last few years, and will continue to do so in the coming decade. Over a wide range of angular scales, the uncertainty due to instrumental noise is now small compared to the cosmic variance. One may claim with some justification that we have entered the era of precision CMB cosmology. However, some caution is still warranted: The errors due to residual foreground contamination in the CMB power spectrum and cosmological parameters remain largely unquantified, and the effect of these errors on important cosmological parameters such as the optical depth tau and spectral index n_s is not obvious. A major goal for current CMB analysis efforts must therefore be to develop methods that allows us to propagate such uncertainties from the raw data through to the final products. Here we review a recently proposed method that may be a first step towards that goal.

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arXiv2006

Fast and Efficient Template Fitting of Deterministic Anisotropic Cosmological Models Applied to WMAP Data

We explore methods of fitting templates to cosmic microwave background (CMB) data, and in particular demonstrate the application of the total convolver algorithm as a fast method of performing a search over all possible locations and orientations of the template relative to the sky. This analysis includes investigation of issues such as chance alignments and foreground residuals. We apply these methods to compare Bianchi models of type VII_h to WMAP first year data and confirm the basic result of our 2005 paper.

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arXiv2006

Foreground Subtraction of Cosmic Microwave Background Maps using WI-FIT (Wavelet based hIgh resolution Fitting of Internal Templates)

We present a new approach to foreground removal for Cosmic Microwave Background (CMB) maps. Rather than relying on prior knowledge about the foreground components, we first extract the necessary information about them directly from the microwave sky maps by taking differences of temperature maps at different frequencies. These difference maps, which we refer to as internal templates, consist only of linear combinations of galactic foregrounds and noise, with no CMB component. We obtain the foreground cleaned maps by fitting these internal templates to, and subsequently subtracting the appropriately scaled contributions of them from, the CMB dominated channels. The fitting operation is performed in wavelet space, making the analysis feasible at high resolution with only a minor loss of precision. Applying this procedure to the WMAP data, we obtain a power spectrum that matches the spectrum obtained by the WMAP team at the signal dominated scales. Finally, we have revisited previous claims about a north-south power asymmetry on large angular scales, and confirm that these remain unchanged with this completely different approach to foreground separation. This also holds when fitting the foreground contribution independently to the northern and southern hemisphere indicating that the asymmetry is unlikely to have its origin in different foreground properties of the hemispheres. This conclusion is further strengthened by the lack of any observed frequency dependence.

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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

The integrated bispectrum as a test of CMB non-Gaussianity: detection power and limits on f_NL with WMAP data

We propose a fast and efficient bispectrum statistic for Cosmic Microwave Background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter f_NL. We show how the method can achieve a remarkable computational advantage by focussing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test, increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales as l_{max}^3 instead of l_{max}^5 for the full bispectrum which for Planck resolution l_{max} \sim 3000 means an improvement in speed of a factor 10^7 compared to the full bispectrum analysis with minor loss in precision. We find that the introduction of a galactic cut partially destroys the optimality of the configuration, which will then need to be dealt with in the future. We find for an ideal experiment with l_{max}=2000 that upper limits of f_{NL}<8 can be obtained at 1 sigma. For the case of the WMAP experiment, we would be able to put limits of |f_{NL}|<40 if no galactic cut were present. Using the real data with galactic cut, we obtain an estimate of -80<f_{NL}<80 and -160<f_{NL}<160 at 1 and 2 sigma respectively.

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arXiv2005

Testing Primordial Non-Gaussianity in CMB Anisotropies

Recent second-order perturbation computations have provided an accurate prediction for the primordial gravitational potential $Φ(x)$ in scenarios in which cosmological perturbations are generated either during or after inflation. This enables us to make realistic predictions for a non-Gaussian part of $Φ(x)$, which is generically written in momentum space as a double convolution of its Gaussian part with a suitable kernel, f_NL(k1,k2). This kernel defines the amplitude and angular structure of the non-Gaussian signals and originates from the evolution of second-order perturbations after the generation of the curvature perturbation. We derive a generic formula for the CMB angular bispectrum with arbitrary f_NL(k1,k2) and examine the detectability of the primordial non-Gaussian signals from various scenarios such as single-field inflation, inhomogeneous reheating, and curvaton scenarios. Our results show that in the standard slow-roll inflation scenario the signal actually comes from the momentum-dependent part of f_NL(k1,k2), and thus it is important to include the momentum dependence in the data analysis. In the other scenarios the primordial non-Gaussianity is comparable to or larger than these post-inflationary effects. We find that WMAP cannot detect non-Gaussian signals generated by these models. Numerical calculations for l>500 are still computationally expensive, and we are not yet able to extend our calculations to Planck's angular resolution; however, there is an encouraging trend which shows that Planck may be able to detect these non-Gaussian signals.

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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

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

The imprints of local superclusters on the Sunyaev-Zel'dovich signals and their detectability with Planck

We use high-resolution hydrodynamical simulations of large-scale structure formation to study the imprints of the local superclusters onto the full-sky Sunyaev-Zel'dovich (SZ) signals. Following (Mathis et al. 2002), the initial conditions have been statistically constrained to reproduce the density field within a sphere of 110 Mpc around the Milky Way, as observed in the IRAS 1.2-Jy all-sky redshift survey. As a result, the positions and masses of prominent galaxy clusters and superclusters in our simulations coincide closely with their real counterparts in the local universe. We present the results of two different runs, one with adiabatic gas physics only, and one also including cooling, star formation and feedback. By analysing the full-sky maps for the thermal and kinetic SZ signals extracted from these simulations, we find that for multipoles with l<100 the power spectrum is dominated by the prominent local superclusters, and its amplitude at these scales is a factor of two higher than that obtained from unconstrained simulations; at lower multipoles (l<20) this factor can even reach one order of magnitude. We check the influence of the SZ effect from local superclusters on the cosmic microwave background (CMB) power spectrum at small multipoles and find it negligible and with no signs of quadrupole-octopole alignment. However, performing simulations of the CMB radiation including the experimental noise at the frequencies which will be observed by the Planck satellite, we find results suggesting that an estimate of the SZ power spectrum at large scales can be extracted.

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arXiv2005

A full sky prediction of the SZ effect from diffuse hot gas in the local universe and the upper limit from the WMAP data

We use the PSCz galaxy redshift catalogue combined with constrained simulations based on the IRAS 1.2 Jy galaxy density field to estimate the contribution of hot gas in the local universe to the SZ-effect on large scales. We produce a full sky Healpix map predicting the SZ-effect from clusters as well as diffuse hot gas within 80Mpc/h. Performing cross-correlation tests between this map and the WMAP data in pixel, harmonic and wavelet space we can put an upper limit on the effect. We conclude that the SZ effect from diffuse gas in the local universe cannot be detected in current CMB data and is not a contaminating factor on large scales (l<60) in studies of the CMB angular anisotropies. However, for future high sensitivity experiments observing at a wider range of frequencies, the predicted large scale SZ effect could be of importance.

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arXiv2005

Primordial non-Gaussianity: local curvature method and statistical significance of constraints on f_NL from WMAP data

We test the consistency of estimates of the non-linear coupling constant f_{NL} using non-Gaussian CMB maps generated by the method described in (Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on estimation of f_{NL}. Nevertheless, using spherical wavelets, we find results in very good agreement with (Mukherjee and Wang 2004), showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f_{NL}, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate f_{NL}=-10^{+270}_{-260} at the 2σlevel (Bayesian) and f_{NL}=-10^{+310}_{-270} (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of f_{NL} and therefore, as advocated in (Cabella et al. 2004), the estimates may be combined to reduce the error bars. In this way, we obtain f_{NL}=-5\pm 85 and f_{NL}=-5\pm 175 at the 1σand 2σlevel respectively using the frequentist approach.

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