arXiv subjects

H. K. Eriksen

Publications and source records attributed to H. K. Eriksen.

At least 271 records · Page 15Linked to original sources

arXiv2008

Power Asymmetry in Cosmic Microwave Background Fluctuations from Full Sky to Sub-degree Scales: Is the Universe Isotropic?

We repeat and extend the analysis of Eriksen et al 2004 and Hansen et al 2004 testing the isotropy of the Cosmic Microwave Background (CMB) fluctuations. We find that the hemispherical power asymmetry previously reported for the largest scales l=2-40 extend to much smaller scales. In fact, for the full multipole range l=2-600, significantly more power is found in the hemisphere centered at (theta=107 deg., phi=226 deg.) in galactic co-latitude and longitude than in the opposite hemisphere consistent with the previously detected direction of asymmetry for l=2-40. We adopt a model selection test where the direction and amplitude of asymmetry as well as the multipole range are free parameters. A model with an asymmetric distribution of power for l=2-600 is found to be preferred over the isotropic model at the 0.4% significance level taking into account the additional parameters required to describe it. A similar direction of asymmetry is found independently in all six subranges of 100 multipoles between l=2-600 and none of our 9800 isotropic simulated maps show a similarly consistent direction of asymmetry over such a large multipole range. No known systematic effects or foregrounds are found to be able to explain the asymmetry.

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arXiv2008

Component separation methods for the Planck mission

The Planck satellite will map the full sky at nine frequencies from 30 to 857 GHz. The CMB intensity and polarization that are its prime targets are contaminated by foreground emission. The goal of this paper is to compare proposed methods for separating CMB from foregrounds based on their different spectral and spatial characteristics, and to separate the foregrounds into components of different physical origin. A component separation challenge has been organized, based on a set of realistically complex simulations of sky emission. Several methods including those based on internal template subtraction, maximum entropy method, parametric method, spatial and harmonic cross correlation methods, and independent component analysis have been tested. Different methods proved to be effective in cleaning the CMB maps from foreground contamination, in reconstructing maps of diffuse Galactic emissions, and in detecting point sources and thermal Sunyaev-Zeldovich signals. The power spectrum of the residuals is, on the largest scales, four orders of magnitude lower than that of the input Galaxy power spectrum at the foreground minimum. The CMB power spectrum was accurately recovered up to the sixth acoustic peak. The point source detection limit reaches 100 mJy, and about 2300 clusters are detected via the thermal SZ effect on two thirds of the sky. We have found that no single method performs best for all scientific objectives. We foresee that the final component separation pipeline for Planck will involve a combination of methods and iterations between processing steps targeted at different objectives such as diffuse component separation, spectral estimation and compact source extraction.

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arXiv2008

CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell}$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.

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arXiv2008

Velocity dispersions in a cluster of stars: How fast could Usain Bolt have run?

Since that very memorable day at the Beijing 2008 Olympics, a big question on every sports commentator's mind has been "What would the 100 meter dash world record have been, had Usain Bolt not celebrated at the end of his race?" Glen Mills, Bolt's coach suggested at a recent press conference that the time could have been 9.52 seconds or better. We revisit this question by measuring Bolt's position as a function of time using footage of the run, and then extrapolate into the last two seconds based on two different assumptions. First, we conservatively assume that Bolt could have maintained Richard Thompson's, the runner-up, acceleration during the end of the race. Second, based on the race development prior to the celebration, we assume that he could also have kept an acceleration of 0.5 m/s^2 higher than Thompson. In these two cases, we find that the new world record would have been 9.61 +/- 0.04 and 9.55 +/- 0.04 seconds, respectively, where the uncertainties denote 95% statistical errors.

physics.pop-ph↗

arXiv2008

A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data

We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C_l, followed by a particular deterministic rescaling operation of the sky signal. The acceptance probability for this joint move depends on the sky map only through the difference of chi-squared between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.

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arXiv2007

Joint Bayesian component separation and CMB power spectrum estimation

We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are 1) conditional sampling of foreground spectral parameters, and 2) joint sampling of all amplitude-type degrees of freedom (e.g., CMB, foreground pixel amplitudes, and global template amplitudes) given spectral parameters. Given a parametric model of the foreground signals, we estimate efficiently and accurately the exact joint foreground-CMB posterior distribution, and therefore all marginal distributions such as the CMB power spectrum or foreground spectral index posteriors. The main limitation of the current implementation is the requirement of identical beam responses at all frequencies, which restricts the analysis to the lowest resolution of a given experiment. We outline a future generalization to multi-resolution observations. To verify the method, we analyse simple models and compare the results to analytical predictions. We then analyze a realistic simulation with properties similar to the 3-yr WMAP data, downgraded to a common resolution of 3 degree FWHM. The results from the actual 3-yr WMAP temperature analysis are presented in a companion Letter.

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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

The joint large-scale foreground-CMB posteriors of the 3-year WMAP data

Using a Gibbs sampling algorithm for joint CMB estimation and component separation, we compute the large-scale CMB and foreground posteriors of the 3-yr WMAP temperature data. Our parametric data model includes the cosmological CMB signal and instrumental noise, a single power law foreground component with free amplitude and spectral index for each pixel, a thermal dust template with a single free overall amplitude, and free monopoles and dipoles at each frequency. This simple model yields a surprisingly good fit to the data over the full frequency range from 23 to 94 GHz. We obtain a new estimate of the CMB sky signal and power spectrum, and a new foreground model, including a measurement of the effective spectral index over the high-latitude sky. A particularly significant result is the detection of a common spurious offset in all frequency bands of ~ -13muK, as well as a dipole in the V-band data. Correcting for these is essential when determining the effective spectral index of the foregrounds. We find that our new foreground model is in good agreement with template-based model presented by the WMAP team, but not with their MEM reconstruction. We believe the latter may be at least partially compromised by the residual offsets and dipoles in the data. Fortunately, the CMB power spectrum is not significantly affected by these issues, as our new spectrum is in excellent agreement with that published by the WMAP team. The corresponding cosmological parameters are also virtually unchanged.

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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

Bayesian analysis of the low-resolution polarized 3-year WMAP sky maps

We apply a previously developed Gibbs sampling framework to the foreground corrected 3-yr WMAP polarization data and compute the power spectrum and residual foreground template amplitude posterior distributions. We first analyze the co-added Q- and V-band data, and compare our results to the likelihood code published by the WMAP team. We find good agreement, and thus verify the numerics and data processing steps of both approaches. However, we also analyze the Q- and V-bands separately, allowing for non-zero EB cross-correlations and including two individual foreground template amplitudes tracing synchrotron and dust emission. In these analyses, we find tentative evidence of systematics: The foreground tracers correlate with each of the Q- and V-band sky maps individually, although not with the co-added QV map; there is a noticeable negative EB cross-correlation at l <~ 16 in the V-band map; and finally, when relaxing the constraints on EB and BB, noticeable differences are observed between the marginalized band powers in the Q- and V-bands. Further studies of these features are imperative, given the importance of the low-l EE spectrum on the optical depth of reionization tau and the spectral index of scalar perturbations n_s.

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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

Estimation of Polarized Power Spectra by Gibbs sampling

Earlier papers introduced a method of accurately estimating the angular cosmic microwave background (CMB) temperature power spectrum based on Gibbs sampling. Here we extend this framework to polarized data. All advantages of the Gibbs sampler still apply, and exact analysis of mega-pixel polarized data sets is thus feasible. These advantages may be even more important for polarization measurements than for temperature measurements. While approximate methods can alias power from the larger E-mode spectrum into the weaker B-mode spectrum, the Gibbs sampler (or equivalently, exact likelihood evaluations) allows for a statistically optimal separation of these modes in terms of power spectra. To demonstrate the method, we analyze two simulated data sets: 1) a hypothetical future CMBPol mission, with the focus on B-mode estimation; and 2) a Planck-like mission, to highlight the computational feasibility of the method.

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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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