arXiv subjects

F. K. Hansen

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

167 records · Page 10Linked to original sources

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 the isotropy of the Cosmic Microwave Backround

There have recently been several claims of an asymmetric distribution of large scale fluctuations in the WMAP data. I review some recent results from a test of isotropy of the power spectrum at all scales and show how the power is asymmetrically distributed for the multipole range l=5-40 in three WMAP frequency channels. I compare this to a recent detection of a non-Gaussian signal in one part of the sky using the local curvature properties of the cosmic microwave background fluctuation field. I find that there may be a common origin of these two findings due to a similar direction and frequency independence of the results.

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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

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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