A preferred-direction statistic for sky maps

Large patterns could exist on the microwave sky as a result of various non-standard possibilities for the large-scale Universe – rotation or shear, non-trivial topology, and single topological defects are specific examples. All-sky (or nearly all-sky) CMB data sets allow us, uniquely, to constrain such exotica, and it is therefore worthwhile to explore a wide range of statistical tests. We describe one such statistic here, which is based on determining gradients and is useful for assessing the level of 'preferred directionality' or 'stripiness' in the map. This method is more general than other techniques for picking out specific patterns on the sky, and it also has the advantage of being easily calculable for the mega-pixel maps which will soon be available. For the purposes of illustration, we apply this statistic to the four-year COBE DMR data. For future CMB maps, we expect this to be a useful statistical test of the large-scale structure of the Universe. In principle, the same statistic could also be applied to sky maps at other wavelengths, to CMB polarization maps, and to catalogues of discrete objects. It may also be useful as a means of checking for residual directionality (e.g. from Galactic or ecliptic signals) in maps.     

Analysing large-scale structure – II. Testing for primordial non-Gaussianity in CMB maps using surrogates

The identification of non-Gaussian signatures in cosmic microwave background (CMB) temperature maps is one of the main cosmological challenges today. We propose and investigate alternative methods to analyse CMB maps. Using the technique of constrained randomization, we construct surrogate maps which mimic both the power spectrum and the amplitude distribution of simulated CMB maps containing non-Gaussian signals. Analysing the maps with weighted scaling indices and Minkowski functionals yields in both cases statistically significant identification of the primordial non-Gaussianities. We demonstrate that the method is very robust with respect to noise. We also show that Minkowski functionals are able to account for non-linearities at higher noise level when applied in combination with surrogates than when only applied to noise added CMB maps and phase randomized versions of them, which only reproduce the power spectrum.     

Processing and compression of noise-dominated data: application to the cosmic microwave background data on board the Planck satellite

We address the problem of encoding and compressing data dominated by noise. Information is decomposed into 'reference' sequences plus arrays containing noisy differences susceptible to being described by a known probability distribution. One can then give reliable estimates of the optimal compression rates by estimating the corresponding Shannon entropy. As a working example, this idea is applied to an idealized model of the cosmic microwave background (CMB) data on board the Planck satellite. Data reduction is a critical issue in space missions because the total information that can be downloaded to Earth is sometimes limited by telemetry allocation. Similar limitations might arise in remotely operated ground based telescopes. This download-rate limitation could reduce the amount of diagnostics sent on the stability of the instruments and, as a consequence, curb the final sensitivity of the scientific signal. Our proposal for Planck consists of taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences could be made independent of the external signal, so that they are dominated by thermal (white) instrumental noise, which is simpler to model than the sky signal. Similar approaches can be found in other individual applications. Generic simulations and analytical predictions show that high compression rates,     can be obtained with minor or zero loss of sensitivity. Possible effects of digital distortion are also analysed. The proposed scheme is flexible and reliable enough to be optimized in relation to other critical aspects of the corresponding application. For Planck , this study constitutes an important step towards a more realistic modelling of the final sensitivity of the CMB temperature anisotropy maps.     

Gravitational wave background from neutrino-driven gamma-ray bursts

We study cosmic microwave background (CMB) secondary anisotropies produced by inhomogeneous reionization by means of cosmological simulations coupled with the radiative transfer code crash . The reionization history is consistent with the Wilkinson Microwave Anisotropy Probe Thomson optical depth determination. We find that the signal arising from this process dominates over the primary CMB component for   l ≳ 4000  and reaches a maximum amplitude of   l ( l + 1) C_l /2π≃ 1.6 × 10⁻¹³  on arcmin scales (i.e. l as large as several thousands). We then cross-correlate secondary CMB anisotropy maps with neutral hydrogen 21-cm line emission fluctuations obtained from the same simulations. The two signals are highly anticorrelated on angular scales corresponding to the typical size of H  ii regions (including overlapping) at the 21-cm map redshift. We show how the CMB/21-cm cross-correlation can be used: (i) to study the nature of the reionization sources; (ii) to reconstruct the cosmic reionization history; (iii) to infer the mean cosmic ionization level at any redshift. We discuss the feasibility of the proposed experiment with forthcoming facilities.     

Scalar statistics on the sphere: application to the cosmic microwave background

A method to compute several scalar quantities of cosmic microwave background (CMB) maps on the sphere is presented. We consider here four type of scalars: the Hessian matrix scalars, the distortion scalars, the gradient-related scalars and the curvature scalars. Such quantities are obtained directly from the spherical harmonic coefficients   a _{ℓ m}   of the map. We also study the probability density function of these quantities for the case of a homogeneous and isotropic Gaussian field, which are functions of the power spectrum of the initial field. From these scalars it is possible to construct a new set of scalars which are independent of the power spectrum of the field. We test our results using simulations and find good agreement between the theoretical probability density functions and those obtained from simulations. Therefore, these quantities are proposed to investigate the presence of non-Gaussian features in CMB maps. Finally, we show how to compute the scalars in the presence of anisotropic noise and realistic masks.     

Geometrical estimators as a test of Gaussianity in the cosmic microwave background

We investigate the power of geometrical estimators on detecting non-Gaussianity in the cosmic microwave background (CMB). In particular the number, eccentricity and Gaussian curvature of excursion sets above (and below) a threshold are studied. We compare their different performance when applied to non-Gaussian simulated maps of small patches of the sky, which take into account the angular resolution and instrumental noise of the Planck satellite. These non-Gaussian simulations are obtained as perturbations of a Gaussian field in two different ways which introduce a small level of skewness or kurtosis in the distribution. A comparison with a classical estimator, the genus, is also shown. We find that the Gaussian curvature is the best of our estimators in all the considered cases. Therefore we propose the use of this quantity as a particularly useful test to look for non-Gaussianity in the CMB.     

Sunyaev–Zel'dovich cluster survey simulations for Planck

We examine the ability of the future Planck mission to provide a catalogue of galaxy clusters observed via their Sunyaev–Zel'dovich (SZ) distortion in the cosmic microwave background (CMB). For this purpose we produce full-sky SZ maps based on N -body simulations and scaling relations between cluster properties for several cosmological models. We extrapolate the N -body simulations by a mass function to high redshifts in order to obtain a realistic SZ background. The simulated Planck observations include, besides the thermal and kinematic SZ effects, contributions from the primordial CMB, extragalactic point sources as well as Galactic dust, free–free and synchrotron emission. A harmonic-space maximum-entropy method is used to separate the SZ signal from contaminating components in combination with a cluster detection algorithm based on thresholding and flux integration to identify clusters and to obtain their fluxes. We estimate a survey sensitivity limit (depending on the quality of the recovered cluster flux) and provide cluster survey completeness and purity estimates. We find that, given our modelling and detection algorithm, Planck will reliably detect at least several thousands of clusters over the full sky. The exact number depends on the particular cosmological model (up to 10 000 cluster detections in a concordance ΛCDM model with  σ₈= 0.9  ). We show that the Galaxy does not significantly affect the cluster detection. Furthermore, the dependence of the thermal SZ power spectrum on the matter variance on scales of  8 h ⁻¹  Mpc and the quality of its reconstruction by the employed method are investigated. Our simulations suggest that the Planck cluster sample will not only be useful as a basis for follow-up observations, but also will have the ability to provide constraints on cosmological parameters.     

Gaussianity of the cosmic microwave background: smooth goodness-of-fit tests applied to interferometric data

We adapt the smooth tests of goodness-of-fit developed by Rayner and Best to the study of the non-Gaussianity of interferometric observations of the cosmic microwave background (CMB). The interferometric measurements (visibilities) are transformed into signal-to-noise ratio eigenmodes, and then the method is applied directly in Fourier space. This transformation allows us to perform the analysis in different subsets of eigenmodes according to their signal-to-noise ratio level. The method can also deal with non-uniform or incomplete coverage of the UV plane. We explore here two possibilities: we analyse either the real and imaginary parts of the complex visibilities (Gaussianly distributed under the Gaussianity hypothesis) or their phases (uniformly distributed under the Gaussianity hypothesis). The power of the method in discriminating between Gaussian and non-Gaussian distributions is studied by using several kinds of non-Gaussian simulations. On the one hand, we introduce a certain degree of non-Gaussianity directly into the Fourier space using the Edgeworth expansion, and afterwards the desired correlation is introduced. On the other hand, we consider interferometric observations of a map with topological defects (cosmic strings). To these previous non-Gaussian simulations we add different noise levels and quantify the required signal-to-noise ratio necessary to achieve a detection of these non-Gaussian features. Finally, we have also studied the ability of the method to constrain the so-called non-linear coupling constant f _NL using χ² simulations. The whole method is illustrated here by application to simulated data from the Very Small Array interferometer.     

A low cosmic microwave background variance in the Wilkinson Microwave Anisotropy Probe data

We have estimated the cosmic microwave background (CMB) variance from the three-year Wilkinson Microwave Anisotropy Probe ( WMAP ) data, finding a value which is significantly lower than the one expected from Gaussian simulations using the WMAP best-fitting cosmological model, at a significance level of 98.7 per cent. This result is even more prominent if we consider only the North ecliptic hemisphere (99.8 per cent). Different analyses have been performed in order to identify a possible origin for this anomaly. In particular, we have studied the behaviour of single-radiometer and single-year data as well as the effect of residual foregrounds and 1/f noise, finding that none of these possibilities can explain the low value of the variance. We have also tested the effect of varying the cosmological parameters, finding that the estimated CMB variance tends to favour higher values of n _s than the one of the WMAP best-fitting model. In addition, we have also tested the consistency between the estimated CMB variance and the actual measured CMB power spectrum of the WMAP data, finding a strong discrepancy. A possible interpretation of this result could be a deviation from Gaussianity and/or isotropy of the CMB.     

Scalar quantities as detectors of non-Gaussianity in cosmic microwave background maps

We study the power of several scalar quantities constructed on the sphere (presented in Monteserín et al.) to detect non-Gaussianity in the temperature distribution of the cosmic microwave background (CMB). The test has been performed using non-Gaussian CMB simulations with injected skewness or kurtosis generated through the Edgeworth expansion. We have also taken into account in the analysis the effect of anisotropic noise and the presence of a Galactic mask. We find that the best scalars to detect an excess of skewness in the simulations are the derivative of the gradient, the fractional isotropy, the Laplacian and the shape index. For the kurtosis case, the fractional anisotropy, the Laplacian and the determinant are the quantities that perform better.     

Circular scans for cosmic microwave background anisotropy observation and analysis

A number of experiments for measuring anisotropies of the cosmic microwave background (CMB) use scanning strategies in which temperature fluctuations are measured along circular scans on the sky. It is possible, from a large number of such intersecting circular scans, to build two-dimensional sky maps for subsequent analysis. However, since instrumental effects — especially the excess low-frequency 1/ f noise — project on to such two-dimensional maps in a non-trivial way, we discuss the analysis approach which focuses on information contained in the individual circular scans. This natural way of looking at CMB data from experiments scanning on the circles combines the advantages of elegant simplicity of Fourier series for the computation of statistics useful for constraining cosmological scenarios, and superior efficiency in analysing and quantifying most of the crucial instrumental effects.     

X-ray polarization in relativistic jets

We investigate the polarization properties of Comptonized X-rays from relativistic jets in active galactic nuclei (AGN) using Monte Carlo simulations. We consider three scenarios commonly proposed for the observed X-ray emission in AGN: Compton scattering of blackbody photons emitted from an accretion disc; scattering of cosmic microwave background (CMB) photons and self-Comptonization of intrinsically polarized synchrotron photons emitted by jet electrons. Our simulations show that for Comptonization of disc and CMB photons, the degree of polarization of the scattered photons increases with the viewing inclination angle with respect to the jet axis. In both cases, the maximum linear polarization is  ≈20 per cent  . In the case of synchrotron self-Comptonization (SSC), we find that the resulting X-ray polarization depends strongly on the seed synchrotron photon injection site, with typical fractional polarizations   P ≈ 10–20 per cent  when synchrotron emission is localized near the jet base, while   P ≈ 20–70 per cent  for the case of uniform emission throughout the jet. These results indicate that X-ray polarimetry may be capable of providing unique clues to identify the location of particle acceleration sites in relativistic jets. In particular, if synchrotron photons are emitted quasi-uniformly throughout a jet, then the observed degree of X-ray polarization may be sufficiently different for each of the competing X-ray emission mechanisms (synchrotron, SSC or external Comptonization) to determine which is the dominant process. However, X-ray polarimetry alone is unlikely to be able to distinguish between disc and CMB Comptonization.     

Isotropic wavelets: a powerful tool to extract point sources from cosmic microwave background maps

It is the aim of this paper to introduce the use of isotropic wavelets to detect and determine the flux of point sources appearing in cosmic microwave background (CMB) maps. The most suitable wavelet to detect point sources filtered with a Gaussian beam is the 'Mexican Hat'. An analytical expression of the wavelet coefficient obtained in the presence of a point source is provided and used in the detection and flux estimation methods presented. For illustration the method is applied to two simulations (assuming Planck mission characteristics) dominated by CMB (100 GHz) and dust (857 GHz), as these will be the two signals dominating at low and high frequencies respectively in the Planck channels. We are able to detect bright sources above 1.58 Jy at 857 GHz (82 per cent of all sources) and above 0.36 Jy at 100 GHz (100 per cent of all), with errors in the flux estimation below 25 per cent. The main advantage of this method is that nothing has to be assumed about the underlying field, i.e. about the nature and properties of the signal plus noise present in the maps. This is not the case in the detection method presented by Tegmark & Oliveira-Costa. Both methods are compared, producing similar results.     

A full-sky prediction of the Sunyaev–Zeldovich effect from diffuse hot gas in the local universe and the upper limit from the WMAP data

We use the Point Source Catalogue Redshift Survey 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 Sunyaev–Zeldovich (SZ) effect on a large scale. We produce a full-sky healpix map predicting the SZ effect from clusters as well as diffuse hot gas within  80  h ⁻¹ Mpc  . 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 cosmic microwave background (CMB) data and is not a large-scale contaminating factor  (ℓ < 60)  in studies of CMB angular anisotropies. We derive an upper limit for the mean temperature decrement of  Δ T < 0.33 μK  at the 2σ confidence level for the 61-GHz frequency channel. However, for future high-sensitivity experiments observing at a wider range of frequencies, the predicted large-scale SZ effect could be of importance.     

COBE and global topology: an example of the application of the identified circles principle

The significance to which the cosmic microwave background (CMB) observations by the satellite COBE can be used to refute a specific observationally based hypothesis for the global topology (3-manifold) of the Universe is investigated, by a new method of applying the principle of matched circle pairs.
Moreover, it is shown that this can be done without assuming Gaussian distributions for the density perturbation spectrum.
The Universe is assumed to correspond to a flat Friedmann–Lemaître model with a zero value of the cosmological constant. The 3-manifold is hypothesized to be a 2-torus in two directions, with a third axis larger than the horizon diameter. The positions and lengths of the axes are determined by the relative positions of the galaxy clusters Coma, RX J1347.5−1145 and CL 09104+4109, assumed to be multiple topological images of a single, physical cluster.
If the following two assumptions are valid: (i) that the error estimates in the COBE DMR data are accurate estimates of the total random plus systematic error; and (ii) that the temperature fluctuations are dominated by the naı¨ve Sachs–Wolfe effect; then the distribution of the temperature differences between multiply imaged pixels is significantly wider than the uncertainty in the differences, and the candidate is rejected at the 94 per cent level.
This result is valid for either the 'subtracted' or 'combined' Analysed Science Data Sets, for either 10° or 20° smoothing, and is slightly strengthened if suspected contaminated regions from the galactic centre and the Ophiuchus and Orion complexes are removed.     

Numerical study of the statistical properties of the lensing excursion angles

We present ray tracing simulations combined with sets of large N -body simulations. Experiments were performed to explore, for the first time, the statistical properties of fluctuations in angular separation of nearby light-ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian, but has an exponential tail. It is found, however, that the tail, or more generally the non-Gaussian nature of the PDF has no significant impact on the weak lensing of the cosmic microwave background (CMB). Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate the validity of using the power spectrum approach to compute lensing effects on the CMB.     

Camouflaged Galactic cosmic microwave background polarization foregrounds: total and polarized contributions of the kinetic Sunyaev–Zeldovich effect

We consider the role of the Galactic kinetic Sunyaev–Zeldovich (SZ) effect as a cosmic microwave background (CMB) polarization foreground. While the Galactic thermal SZ effect has previously been studied and discarded as a potential CMB foreground, we find that the kinetic SZ effect is dominant in the Galactic case. We analyse the detectability of the kinetic SZ effect by means of an optimally matched filter technique applied to a simulation of an ideal observation. We obtain no detection, getting a signal-to-noise ratio of 0.1, thereby demonstrating that the kinetic SZ effect can also safely be ignored as a CMB foreground. However, we provide maps of the expected signal for inclusion in future high-precision data processing. Furthermore, we rule out the significant contamination of the polarized CMB signal by second scattering of Galactic kinetic SZ photons, since we show that the scattering of the CMB quadrupole photons by Galactic electrons is a stronger effect than the SZ second scattering, and has already been shown to produce no significant polarized contamination.     

Ironing out primordial temperature fluctuations with polarization: optimal detection of cosmic structure imprints

Secondary anisotropies of the cosmic microwave background (CMB) can be detected by using the cross-correlation between the large-scale structure (LSS) and the CMB temperature fluctuations. In such studies, chance correlations of primordial CMB fluctuations with the LSS are the main source of uncertainty. We present a method for reducing this noise by exploiting information contained in the polarization of CMB photons. The method is described in general terms and then applied to our recently proposed optimal method for measuring the integrated Sachs–Wolfe (ISW) effect. We obtain an expected signal-to-noise ratio of up to 8.5. This corresponds to an enhancement of the signal-to-noise ratio by 23 per cent as compared to the standard method for ISW detection, and by 16 per cent w.r.t. our recently proposed method, both for the best-case scenario of having perfect (noiseless) CMB and LSS data.     

Current models of the observable consequences of cosmic reionization and their detectability

A number of large current experiments aim to detect the signatures of the cosmic reionization at redshifts z > 6. Their success depends crucially on understanding the character of the reionization process and its observable consequences and designing the best strategies to use. We use large-scale simulations of cosmic reionization to evaluate the reionization signatures at redshifted 21-cm and small-scale cosmic microwave background (CMB) anisotropies in the best current model for the background universe, with fundamental cosmological parameters given by Wilkinson Microwave Anisotropy Probe three-year results. We find that the optimal frequency range for observing the 'global step' of the 21-cm emission is 120–150 MHz, while statistical studies should aim at 140–160 MHz, observable by GMRT. Some strongly non-Gaussian brightness features should be detectable at frequencies up to ∼190 MHz. In terms of sensitivity-signal trade-off relatively low resolutions, corresponding to beams of at least a few arcminutes, are preferable. The CMB anisotropy signal from the kinetic Sunyaev–Zel'dovich effect from reionized patches peaks at tens of μK at arcminute scales and has an rms of ∼1 μK, and should be observable by the Atacama Cosmology Telescope and the South Pole Telescope. We discuss the various observational issues and the uncertainties involved, mostly related to the poorly known reionization parameters and, to a lesser extend, to the uncertainties in the background cosmology.     

Phase shift sequences for an adding interferometer

Cosmic microwave background (CMB) polarimetry has the potential to provide revolutionary advances in cosmology. Future experiments to detect the very weak B-mode signal in CMB polarization maps will require unprecedented sensitivity and control of systematic errors. Bolometric interferometry may provide a way to achieve these goals. In a bolometric interferometer (or other adding interferometer), phase shift sequences are applied to the inputs in order to recover the visibilities. Noise is minimized when the phase shift sequences corresponding to all visibilities are orthogonal. We present a systematic method for finding sequences that produce this orthogonality, approximately minimizing both the length of the time sequence and the number of discrete phase shift values required. When some baselines are geometrically equivalent, we can choose sequences that read out those baselines simultaneously, which has been shown to improve the signal-to-noise ratio.