Foreground removal from Planck Sky Model temperature maps using a MLP neural network

Unfortunately, the Cosmic Microwave Background (CMB) radiation is contaminated by emission originating in the Milky Way (synchrotron, free‐free and dust emission). Since the cosmological information is statistically in nature, it is essential to remove this foreground emission and leave the CMB with no systematic errors. To demonstrate the feasibility of a simple multilayer perceptron (MLP) neural network for extracting the CMB temperature signal, we have analyzed a specific data set, namely the Planck Sky Model maps, developed for evaluation of different component separation methods before including them in the Planck data analysis pipeline. It is found that a MLP neural network can provide a CMB map of about 80 % of the sky to a very high degree uncorrelated with the foreground components. Also the derived power spectrum shows little evidence for systematic errors (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Foreground removal from CMB temperature maps using an MLP neural network

One of the main obstacles for extracting the Cosmic Microwave Background (CMB) signal from observations in the mm-submm range is the foreground contamination by emission from Galactic components: mainly synchrotron, free-free and thermal dust emission. Due to the statistical nature of the intrinsic CMB signal it is essential to minimize the systematic errors in the CMB temperature determinations. Following the available knowledge of the spectral behavior of the Galactic foregrounds simple power law-like spectra have been assumed. The feasibility of using a simple neural network for extracting the CMB temperature signal from the combined signal CMB and the foregrounds has been investigated. As a specific example, we have analysed simulated data, as expected from the ESA Planck CMB mission. A simple multilayer perceptron neural network with 2 hidden layers can provide temperature estimates over more than 80 per cent of the sky that are to a high degree uncorrelated with the foreground signals. A single network will be able to cover the dynamic range of the Planck noise level over the entire sky.     

Effects of destriping errors on estimates of the CMB power spectrum

Destriping methods for constructing maps of the cosmic microwave background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates for Planck -like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. Assuming Planck -like low-frequency noise, the noise power spectrum is accurately white at high multipoles  (ℓ≳ 50)  . Destriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis of Planck data and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic '1/ f ' noise.     

Foreground removal from WMAP 7 yr polarization maps using an MLP neural network

One of the fundamental problems in extracting the cosmic microwave background signal (CMB) from millimeter/submillimeter observations is the pollution by emission from the Milky Way: synchrotron, free-free, and thermal dust emission. To extract the fundamental cosmological parameters from CMB signal, it is mandatory to minimize this pollution since it will create systematic errors in the CMB power spectra. In previous investigations, it has been demonstrated that the neural network method provide high quality CMB maps from temperature data. Here the analysis is extended to polarization maps. As a concrete example, the WMAP 7-year polarization data, the most reliable determination of the polarization properties of the CMB, has been analyzed. The analysis has adopted the frequency maps, noise models, window functions and the foreground models as provided by the WMAP Team, and no auxiliary data is included. Within this framework it is demonstrated that the network can extract the CMB polarization signal with no sign of pollution by the polarized foregrounds. The errors in the derived polarization power spectra are improved compared to the errors derived by the WMAP Team.     

Trans‐Planckian signatures in the cosmic microwave background?

With the increasingly precise measurement of the cosmic microwave background (CMB), cosmology has entered an era where a model's predictions become testable to percent‐level accuracy. In particular, the CMB spectrum has so far provided impressive support for the scenario of inflation, first invented to solve outstanding problems of standard cosmology. While current data (COBE, WMAP etc.) have already constrained cosmological parameters like Ω₀ to high precision, next generation instruments such as the PLANCK satellite should give access to specific characteristics of the inflationary mechanism itself. Another tantalizing idea has been discussed in this context: Given the enormous expansion of the Universe during the phase of inflation, could it be that even Planck scale physics has been stretched to observable distances and is therefore within grasp in the CMB observations? In this contribution, I discuss the possibility of carrying through the calculation of the perturbation spectrum from an ansatz for short distance physics right to its imprint in the CMB. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wavelet analysis of non-Gaussian anisotropies from primordial voids in simulated maps of the Cosmic Microwave Background

Phase transitions taking place during the inflationary epoch give rise to bubbles of true vacuum embedded in the false vacuum. These bubbles can imprint a distinctive signal on the Cosmic Microwave Background (CMB). We evaluate the feasibility of detecting these signatures with wavelets in CMB maps, such as those that will be made available by the European Space Agency’s (ESA) Planck mission.     

The Planck High Frequency Instrument, a third generation CMB experiment, and a full sky submillimeter survey

The High Frequency Instrument (HFI) of Planck is the most sensitive CMB experiment ever planned. Statistical fluctuations (photon noise) of the CMB itself will be the major limitation to the sensitivity of the CMB channels. Higher frequency channels will measure galactic foregrounds. Together with the Low Frequency Instrument, this will make a unique tool to measure the full sky and to separate the various components of its spectrum. Measurement of the polarization of these various components will give a new picture of the CMB. In addition, HFI will provide the scientific community with new full sky maps of intensity and polarization at six frequencies, with unprecedented angular resolution and sensitivity. This paper describes the logics that prevailed to define the HFI and the performances expected from this instrument. It details several features of the HFI design that has not been published up to now.     

Statistical properties of polarized radio continuum emission and effects of data processing

Polarized intensity and polarization angles are calculated from Stokes parameters Q and U in a nonlinear way. The statistical properties of polarized emission hold information about the structure of magnetic fields in a large range of scales, but the contributions of different stages of data processing to the statistical properties should first be understood. We use 1.4 GHz polarization data from the Effelsberg 100‐m telescope of emission in the Galactic plane, near the plane and far out of the plane. We analyze the probability distribution function and the wavelet spectrum of the original maps in Stokes parameters Q, U and corresponding PI. Then we apply absolute calibration (i.e. adding the large‐scale emission to the maps in Q and U), subtraction of polarized sources and subtraction of the positive bias in PI due to noise (“denoising”). We show how each procedure affects the statistical properties of the data. We find a complex behavior of the statistical properties for the different regions analyzed which depends largely on the intensity level of polarized emission. Absolute calibration changes the morphology of the polarized structures. The statistical properties change in a complex way: Compact sources in the field flatten the wavelet spectrum over a substantial range. Adding large‐scale emission does not change the spectral slopes in Q and U at small scales, but changes the PI spectrum in a complex way. “Denoising” significantly changes the p.d.f. of PI and raises the entire spectrum. The final spectra are flat in the Galactic plane due to magnetic structures in the ISM, but steeper at high Galactic latitude and in the anticenter. For a reliable study of the statistical properties of magnetic fields and turbulence in the ISM based on radio polarization observations, absolute calibration and source subtraction are required. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detecting Sunyaev–Zel'dovich clusters with Planck– II. Foreground components and optimized filtering schemes

The Planck mission is the most sensitive all-sky cosmic microwave background (CMB) experiment currently planned. The High-Frequency Instrument (HFI) will be especially suited for observing clusters of galaxies by their thermal Sunyaev–Zel'dovich (SZ) effect. In order to assess Planck 's SZ capabilities in the presence of spurious signals, a simulation is presented that combines maps of the thermal and kinetic SZ effects with a realization of the CMB, in addition to Galactic foregrounds (synchrotron emission, free–free emission, thermal emission from dust, CO-line radiation) as well as the submillimetric emission from celestial bodies of our Solar system. Additionally, observational issues such as the finite angular resolution and spatially non-uniform instrumental noise of Planck 's sky maps are taken into account, yielding a set of all-sky flux maps, the autocorrelation and cross-correlation properties of which are examined in detail. In the second part of the paper, filtering schemes based on scale-adaptive and matched filtering are extended to spherical data sets, that enable the amplification of the weak SZ signal in the presence of all contaminations stated above. The theory of scale-adaptive and matched filtering in the framework of spherical maps is developed, the resulting filter kernel shapes are discussed and their functionality is verified.     

A comparison of anisotropic statistical properties of CMB maps based on the WMAP and planck space mission data

We compare the anisotropic properties of the cosmic microwave background (CMB) maps constructed based on the data of NASA’s WMAP (9th year of observations) and ESA’s Planck (2015 release) space missions. In our analysis, we use two two-dimensional estimators of the scatter of the signal on a sphere, which amount to algorithms of mapping the ratio of the scatter in the Northern and Southern hemispheres depending on the method of dividing (specifically, rotating and cutting) the sky into hemispheres. The scatter is computed either as a standard deviation σ, or as the difference between the minimum and maximum values on a given hemisphere. Applying both estimators to the CMB anisotropy datameasured by two spacemissions, Planck and WMAP, we compared the variations of the background at different angular scales.Maps with a resolution of l ≤ 100 show that the division into regions with different levels of statistical anisotropy lies close to the ecliptic plane, and after preliminary removal of the l ≤ 20 harmonics from the CMB data, the anisotropic signal related to the Galaxy begins to dominate.     

Impact of Galactic polarized emission on B-mode detection at low multipoles

We use a model of polarized Galactic emission developed by the Planck collaboration to assess the impact of foregrounds on B -mode detection at low multipoles. Our main interest is in applications of noisy polarization data and in particular in assessing the feasibility of B -mode detection by Planck . This limits the complexity of foreground subtraction techniques that can be applied to the data. We analyse internal linear combination techniques and show that the offset caused by the dominant E -mode polarization pattern leads to a fundamental limit of   r ∼ 0.1  for the tensor–scalar ratio even in the absence of instrumental noise. We devise a simple, robust, template fitting technique using multifrequency polarization maps. We show that template fitting using Planck data alone offers a feasible way of recovering primordial B -modes from dominant foreground contamination, even in the presence of noise on the data and templates. We implement and test a pixel-based scheme for computing the likelihood function of cosmological parameters at low multipoles that incorporates foreground subtraction of noisy data.     

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.     

Measuring statistical isotropy of CMB anisotropy

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson microwave anisotropy probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian and Souradeep [Hajian, A., Souradeep, T. (2003) Astrophys. J. Lett. 597, L5] for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian and Souradeep [Basak, S., Hajian, A., Souradeep, T. (2006) Phys. Rev. D74, 02130(R)]. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released first WMAP polarization maps, however, indicate significant violation of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.     

Weak lensing of the CMB: extraction of lensing information from the trispectrum

We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-Gaussian noise contributions, beyond the previously discussed dominant Gaussian noise. Non-Gaussian noise contributions are generated by lensing itself and by the correlation between the lensing effect and other foreground secondary anisotropies in the CMB such as the Sunyaev–Zel’dovich (SZ) effect. When the SZ effect is removed from temperature maps using its spectral dependence, we find these additional non-Gaussian noise contributions to be an order of magnitude lower than the dominant Gaussian noise. If the noise-bias due to the dominant Gaussian part of the temperature squared power spectrum is removed, then these additional non-Gaussian contributions provide the limiting noise level for the lensing reconstruction. The temperature squared power spectrum allows a high signal-to-noise extraction of the lensing deflections and a confusion-free separation of the curl (or B-mode) polarization due to inflationary gravitational waves from that due to lensed gradient (or E-mode) polarization. The small angular scale temperature and polarization anisotropy measurements provide a novel approach to weak lensing studies, complementing the approach based on galaxy ellipticities.     

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.     

Angular power spectrum of CMB anisotropy from WMAP

The remarkable improvement in the estimates of different cosmological parameters in recent years has been largely spearheaded by accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum from multi-frequency observations has been proposed and implemented on the first year WMAP (WMAP-1) data by Saha et al. [Saha, R., Jain, P., Souradeep, T., 2006. ApJL, 645, L89]. We review the results from WMAP-1 and also present the new angular power spectrum based on three years of the WMAP data (WMAP-3). Previous estimates have depended on foreground templates built using extraneous observational input to remove foreground contamination. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. The primary product of WMAP are the observations of CMB in 10 independent difference assemblies (DA) distributed over five frequency bands that have uncorrelated noise. Our method utilizes maximum information available within WMAP data by linearly combining DA maps from different frequencies to remove foregrounds and estimating the power spectrum from the 24 cross-power spectra of clean maps that have independent noise. An important merit of the method is that the expected residual power from unresolved point sources is significantly tempered to a constant offset at large multipoles (in contrast to the l² contribution expected from a Poisson distribution) leading to a small correction at large multipoles. Hence, the power spectrum estimates are less susceptible to uncertainties in the model of point sources.     

Measurements of the Matter Density Perturbation Amplitude from Cosmological Data

The various measurements of the linear matter density perturbation amplitude obtained from the observations of the cosmic microwave background (CMB) anisotropy, weak gravitational lensing, galaxy cluster mass function, matter power spectrum, and redshift space distortions are compared. The Planck data on the CMB temperature anisotropy spectrum at high multipoles, ? > 1000 (where the effect of gravitational lensing is most significant), are shown to give a measurement of the matter density perturbation amplitude that contradicts all other measurements of this quantity from both Planck CMB anisotropy data and other data at a significance level of about 3.7σ. Thus, at present these data should not be combined together for the calculations of constraints on cosmological parameters. Except for the Planck data on the CMB temperature anisotropy spectrum at high multipoles, all the remaining measurements of the density perturbation amplitude agree well between themselves and give the following constraints: σ₈ = 0.792± 0.006 on the linear matter density perturbation amplitude, Ω_m = 0.287± 0.007 on the matter density parameter, and H₀ = 69.4 ± 0.6 km s^?1 Mpc^?1 on the Hubble constant. Various constraints on the sum of neutrino masses and the number of neutrino flavors can be obtained by additionally taking into account the data on baryon acoustic oscillations and (or) direct Hubble constant measurements in the local Universe.     

Signals from the epoch of cosmological recombination – Karl Schwarzschild Award Lecture 2008

The physical ingredients to describe the epoch of cosmological recombination are amazingly simple and well‐understood. This fact allows us to take into account a very large variety of physical processes, still finding potentially measurable consequences for the energy spectrum and temperature anisotropies of the Cosmic Microwave Background (CMB). In this contribution we provide a short historical overview in connection with the cosmological recombination epoch and its connection to the CMB. Also we highlight some of the detailed physics that were studied over the past few years in the context of the cosmological recombination of hydrogen and helium. The impact of these considerations is two‐fold: (i) The associated release of photons during this epoch leads to interesting and unique deviations of the CosmicMicrowave Background (CMB) energy spectrum from a perfect blackbody, which, in particular at decimeter wavelength and the Wien part of the CMB spectrum, may become observable in the near future. Despite the fact that the abundance of helium is rather small, it still contributes a sizeable amount of photons to the full recombination spectrum, leading to additional distinct spectral features. Observing the spectral distortions from the epochs of hydrogen and helium recombination, in principle would provide an additional way to determine some of the key parameters of the Universe (e.g. the specific entropy, the CMB monopole temperature and the pre‐stellar abundance of helium). Also it permits us to confront our detailed understanding of the recombination process with direct observational evidence. In this contribution we illustrate how the theoretical spectral template of the cosmological recombination spectrum may be utilized for this purpose. We also show that because hydrogen and helium recombine at very different epochs it is possible to address questions related to the thermal history of our Universe. In particular the cosmological recombination radiation may allow us to distinguish between Compton y ‐distortions that were created by energy release before or after the recombination of the Universe finished. (ii) With the advent of high precision CMB data, e.g. as will be available using the PLANCK Surveyor or CMBPOL, a very accurate theoretical understanding of the ionization history of the Universe becomes necessary for the interpretation of the CMB temperature and polarization anisotropies. Here we show that the uncertainty in the ionization history due to several processes, which until now were not taken in to account in the standard recombination code RECFAST, reaches the percent level. In particular He II → He I recombination occurs significantly faster because of the presence of a tiny fraction of neutral hydrogen at z ∼ 2400. Also recently it was demonstrated that in the case of H I Lyman α photons the timedependence of the emission process and the asymmetry between the emission and absorption profile cannot be ignored. However, it is indeed surprising how inert the cosmological recombination history is even at percent‐level accuracy. Observing the cosmological recombination spectrum should in principle allow us to directly check this conclusion, which until now is purely theoretical. Also it may allow to reconstruct the ionization history using observational data (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fast parameter estimation from the cosmic microwave background power spectrum

The statistical properties of a map of the primary fluctuations in the cosmic microwave background (CMB) may be specified to high accuracy by a few thousand power spectra measurements, provided the fluctuations are Gaussian, yet the number of parameters relevant for the CMB is probably no more than ∼10–20. Consequently, there is a large degree of redundancy in the power spectrum data. In this paper, we show that the moped data compression technique can reduce the CMB power spectrum measurements to ∼10–20 numbers (one for each parameter), from which the cosmological parameters can be estimated virtually as accurately as from the complete power spectrum. Combined with recent advances in the speed of generation of theoretical power spectra, this offers opportunities for very fast parameter estimation from real and simulated CMB skies. The evaluation of the likelihood itself, at Planck resolution, is speeded up by factors up to ∼10⁸, ensuring that this step will not be the dominant part of the data analysis pipeline.     

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.