Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.     

In-Flight Main Beam Reconstruction for Planck-LFI

In-flight measurements of the shape of the antenna main beam is a crucial input to the data analysis pipeline of each high resolution Cosmic Microwave Background (CMB) anisotropy experiment. We study the main beam reconstruction achievable by the PLANCK Low Frequency Instrument (LFI) through the observation of external planets. Although were strict our analysis to the 30 GHz LFI channel, the method can be easily extended to all the PLANCK frequency channels and to other CMB anisotropy experiments. We show that it is possible to fit the time ordered data from the external planets (mainly Jupiter and Saturn) to obtain an accurate, robust, simple and fast reconstruction of the main beam properties under very general conditions, almost independently of the calibration accuracy. In addition, we find that a bivariate Gaussian approximation of main beam shapes represents a significant improvement with respect to asymmetric representation. The impact of the most relevant systematic effects is also addressed. We demonstrate that by combining the recovery of the maximum signal at the planet transit with accurate in-flight calibration, it is possible to measure the intrinsic planet temperatures at millimetric wavelengths with < 1% accuracy. This work is based on PLANCK-LFI activities. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Separation of instrumental and astrophysical foregrounds for mapping cosmic microwave background anisotropies

For the most sensitive present and future experiments dedicated to cosmic microwave background (CMB) anisotropy observations, the identification and separation of signals coming from different sources is an important step in the data analysis. This problem of the restitution of signals from the observation of their mixture is classically called 'component separation' in CMB mapping. In this paper, we address the general problem of separating, for millimetre-wave sky-mapping applications, components which include not only astrophysical emissions in two-dimensional maps, but also one-dimensional instrumental effects in the data streams. We show that component separation methods can be adapted to separate simultaneously both astrophysical emissions and components coming from time-dependent foreground signals which originate from the instrument itself. Such general methods can be used for the optimal processing of low-redundancy observations where multi-channel observations are a precious tool to remove systematic effects, as may be the case for the Planck mission.     

MAXIPOL: a balloon-borne experiment for measuring the polarization anisotropy of the cosmic microwave background radiation

We discuss MAXIPOL, a bolometric balloon-borne experiment designed to measure the E-mode polarization anisotropy of the cosmic microwave background radiation (CMB) on angular scales of 10^′ to 2°. MAXIPOL is the first CMB experiment to collect data with a polarimeter that utilizes a rotating half-wave plate and fixed wire-grid polarizer. We present the instrument design, elaborate on the polarimeter strategy and show the instrument performance during flight with some time domain data. Our primary dataset was collected during a 26 h turnaround flight that was launched from the National Scientific Ballooning Facility in Ft. Sumner, New Mexico in May 2003. During this flight five regions of the sky were mapped. Data analysis is in progress.     

Testing isotropy of cosmic microwave background radiation

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background (CMB) radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide two new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated Galactic plane contamination is readily identified. The ILC– WMAP data maps show seven axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5 per cent probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9 per cent, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.     

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.     

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.     

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.     

Exact shearing box solutions of magnetohydrodynamic flows with resistivity, viscosity and cooling

Axisymmetric incompressible modes of the magnetorotational instability (MRI) with a vertical wavenumber are exact solutions of the non-linear local equations of motion for a disc (shearing box). They are referred to as 'channel solutions'. Here, we generalize a class of these solutions to include energy losses, viscous, and resistive effects. In the limit of zero shear, we recover the result that torsional Alfvén waves are exact solutions of the non-linear equations. Our method allows the extension of these solutions into the dissipative regime.
These new solutions serve as benchmarks for simulations including dissipation and energy loss, and to calibrate numerical viscosity and resistivity in the zeus3d code. We quantify the anisotropy of numerical dissipation and compute its scaling with time and space resolution. We find a strong dependence of the dissipation on the mean magnetic field that may affect the saturation state of the MRI as computed with zeus3d . It is also shown that elongated grid cells generally preclude isotropic dissipation and that a Courant time-step smaller than that which is commonly used should be taken to avoid spurious anti-diffusion of magnetic field.     

Bianchi model CMB polarization and its implications for CMB anomalies

We derive the cosmic microwave background (CMB) radiative transfer equation in the form of a multipole hierarchy in the nearly Friedmann–Robertson–Walker limit of homogeneous, but anisotropic, universes classified via their Bianchi type. Compared with previous calculations, this allows a more sophisticated treatment of recombination, produces predictions for the polarization of the radiation and allows for reionization. Our derivation is independent of any assumptions about the dynamical behaviour of the field equations, except that it requires anisotropies to be small back to recombination; this is already demanded by observations.
We calculate the polarization signal in the Bianchi VII _h case, with the parameters recently advocated to mimic the several large-angle anomalous features observed in the CMB. We find that the peak polarization signal is  ∼1.2 μK  for the best-fitting model to the temperature anisotropies, and is mostly confined to multipoles   l < 10  . Remarkably, the predicted large-angle EE and TE power spectra in the Bianchi model are consistent with Wilkinson Microwave Anisotropy Probe ( WMAP ) observations that are usually interpreted as evidence of early reionization. However, the power in B-mode polarization is predicted to be similar to the E-mode power and parity-violating correlations are also predicted by the model; the WMAP non-detection of either of these signals casts further strong doubts on the veracity of attempts to explain the large-angle anomalies with global anisotropy. On the other hand, given that there exist further dynamical degrees of freedom in the VII _h universes that are yet to be compared with CMB observations, we cannot at this time definitively reject the anisotropy explanation.     

Alignment and signed-intensity anomalies in Wilkinson Microwave Anisotropy Probe data

Significant alignment and signed-intensity anomalies of local features of the cosmic microwave background (CMB) are detected on the three-year Wilkinson Microwave Anisotropy Probe data, through a decomposition of the signal with steerable wavelets on the sphere. In addition to identifying local features of a signal at specific scales, steerable wavelets allow one to determine their local orientation and signed intensity. First, an alignment analysis identifies two mean preferred planes in the sky, both with normal axes close to the CMB dipole axis. The first plane is defined by the directions towards which local CMB features are anomalously aligned. A mean preferred axis is also identified in this plane, located very close to the ecliptic poles axis. The second plane is defined by the directions anomalously avoided by local CMB features. This alignment anomaly provides further insight on recent results. Secondly, a signed-intensity analysis identifies three mean preferred directions in the southern Galactic hemisphere with anomalously high or low temperature of local CMB features: a cold spot essentially identified with a known cold spot, a second cold spot lying very close to the southern end of the CMB dipole axis, and a hotspot lying close to the southern end of the ecliptic poles axis. In both analyses, the anomalies are observed at wavelet scales corresponding to angular sizes around 10° on the celestial sphere, with global significance levels around 1 per cent. Further investigation reveals that the alignment and signed-intensity anomalies are only very partially related. Instrumental noise, foreground emissions and some form of other systematics are strongly rejected as possible origins of the detections. An explanation might still be envisaged in terms of a global violation of the isotropy of the Universe, inducing an intrinsic statistical anisotropy of the CMB.     

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.     

Observations of the Sunyaev–Zel''dovich effect at high angular resolution towards the galaxy clusters A665, A2163 and CL0016+16

We report on the first observation of the Sunyaev–Zel'dovich (SZ) effect, a distortion of the Cosmic Microwave Background radiation (CMB) by hot electrons in clusters of galaxies, with the Diabolo experiment at the IRAM 30 m telescope. Diabolo is a dual-channel 0.1 K bolometer photometer dedicated to the observation of CMB anisotropies at 2.1 and 1.2 mm. A significant brightness decrement in the 2.1 mm channel is detected in the direction of three clusters (Abell 665, Abell 2163 and CL0016+16). With a 30 arcsec beam and 3 arcmin beamthrow, this is the highest angular resolution observation to date of the SZ effect. Interleaving integrations on targets and on nearby blank fields have been performed in order to check and correct for systematic effects. Gas masses can be directly inferred from these observations.     

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.     

Wilkinson Microwave Anisotropy Probe 5-yr constraints on fnl with wavelets

We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr 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 f _nl 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 KQ 75 mask recommended by the WMAP team which masks out 28 per cent 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  χ²  analysis. The  χ²  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f _nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f _nl parameter is constrained to  −8 < f _nl < +111  at 95 per cent confidence level (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  Δ f _nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.     

Constraints on structure formation models from the Sunyaev–Zel'dovich effect

In the context of cold dark matter (CDM) cosmological models, we have simulated images of the brightness temperature fluctuations in the cosmic microwave background (CMB) sky owing to the Sunyaev–Zel'dovich (S–Z) effect in a cosmological distribution of clusters. We compare the image statistics with recent ATCA limits on arcmin-scale CMB anisotropy. The S–Z effect produces a generically non-Gaussian field and we compute the variance in the simulated temperature-anisotropy images, after convolution with the ATCA beam pattern, for different cosmological models. All the models are normalized to the 4-yr COBE data. We find an increase in the simulated-sky temperature variance with increase in the cosmological density parameter Ω₀. A comparison with the upper limits on the sky variance set by the ATCA appears to rule out our closed-universe model: low-Ω₀ open-universe models are preferred. The result is independent of any present day observations of σ ₈.     

Using SCUBA to place upper limits on arcsecond-scale cosmic microwave background anisotropies at 850 m

The SCUBA instrument on the James Clerk Maxwell Telescope has already had an impact on cosmology by detecting relatively large numbers of dusty galaxies at high redshift. Apart from identifying well-detected sources, such data can also be mined for information about fainter sources and their correlations, as revealed through low-level fluctuations in SCUBA maps. As a first step in this direction, we analyse a small SCUBA data set as if it were obtained from a cosmic microwave background (CMB) differencing experiment. This enables us to place limits on CMB anisotropy at 850 m. Expressed as Q _flat, the quadrupole expectation value for a flat power spectrum, the limit is 152 K at 95 per cent confidence, corresponding to     (or T T <1410⁵) for a Gaussian autocorrelation function, with a coherence angle of about 2025 arcsec. These results could easily be reinterpreted in terms of any other fluctuating sky signal. This is currently the best limit for these scales at high frequency, and comparable to limits at similar angular scales in the radio. Even with such a modest data set, it is possible to put a constraint on the slope of the SCUBA counts at the faint end, since even randomly distributed sources would lead to fluctuations. Future analysis of sky correlations in more extensive data sets ought to yield detections, and hence additional information on source counts and clustering.