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.     

Amplifier arrays for CMB polarization

Cryogenic low noise amplifier technology has been successfully used in the study of the cosmic microwave background (CMB). Monolithic millimeter wave integrated circuit (MMIC) technology makes the mass production of coherent detection receivers feasible. We have produced large numbers of MMIC amplifiers for CMB measurements. We have also demonstrated the viability of multi-function multi-chip modules as sensitive receiver front-ends. MMIC integration makes it possible to realize massive arrays of receivers suitable for measurements of the polarization of the CMB. We describe the development of the unit cell of such an array and the development plans for implementation.     

Detection/estimation of the modulus of a vector. Application to point-source detection in polarization data

Given a set of images, whose pixel values can be considered as the components of a vector, it is interesting to estimate the modulus of such a vector in some localized areas corresponding to a compact signal. For instance, the detection/estimation of a polarized signal in compact sources immersed in a background is relevant in some fields like astrophysics. We develop two different techniques, one based on the Neyman–Pearson lemma, the Neyman–Pearson filter (NPF), and another based on pre-filtering before fusion, the filtered fusion (FF), to deal with the problem of detection of the source and estimation of the polarization given two or three images corresponding to the different components of polarization (two for linear polarization, three including circular polarization). For the case of linear polarization, we have performed numerical simulations on two-dimensional patches to test these filters following two different approaches (a blind and a non-blind detection), considering extragalactic point sources immersed in cosmic microwave background (CMB) and non-stationary noise with the conditions of the 70 GHz Planck channel. The FF outperforms the NPF, especially for low fluxes. We can detect with the FF extragalactic sources in a high noise zone with fluxes      Jy for (blind/non-blind) detection and in a low noise zone with fluxes      Jy for (blind/non-blind) detection with low errors in the estimated flux and position.     

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.     

Separation of foreground and background signals in single frequency measurements of the CMB polarization

The polarization of the Cosmic Microwave Background (CMB) is a powerful observational tool at hand for modern cosmology. It allows to break the degeneracy of fundamental cosmological parameters one cannot obtain using only anisotropy data and provides new insight into conditions existing in the very early Universe. Many experiments are now in progress whose aim is detecting anisotropy and polarization of the CMB. Measurements of the CMB polarization are however hampered by the presence of polarized foregrounds, above all the synchrotron emission of our Galaxy, whose importance increases as frequency decreases and dominates the polarized diffuse radiation at frequencies below ≃50 GHz. In the past the separation of CMB and synchrotron was made combining observations of the same area of sky at different frequencies. In this paper, we show that the statistical properties of the polarized components of the synchrotron and dust foregrounds are different from the statistical properties of the polarized component of the CMB, therefore one can build a statistical estimator which allows to extract the polarized component of the CMB from single frequency data also when the polarized CMB signal is just a fraction of the total polarized signal. Our estimator improves the signal/noise ratio for the polarized component of the CMB and reduces from ≃50 to ≃20 GHz, the frequency above which the polarized component of the CMB can be extracted from single frequency maps of the diffuse radiation.     

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.     

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.     

Excess B‐modes extracted from the Planck polarization maps

One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free‐free and thermal dust emission. The feasibility of using simple neural networks to extract CMB has been demonstrated on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto‐correlation and cross‐correlation power spectra within a mask covering about 63 % of the sky have been used together with a “high pass filter” in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron neural networks. This spectrum contains a bright feature with signal to noise ratios 4.5 within 200 ≪ l ≪ 250. The spectrum is significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour quite different from the “canonical” models (weak lensing plus B‐modes spectra with different tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the influence of resonant scattering on cosmic microwave background polarization anisotropies

We implement the theory of resonant scattering in the context of cosmic microwave background (CMB) polarization anisotropies. We compute the changes in the E-mode polarization (EE) and temperature E-mode (TE) CMB power spectra introduced by the scattering on a resonant transition with a given optical depth τ_X and polarization coefficient E ₁. The latter parameter, accounting for how anisotropic the scattering is, depends on the exchange of angular momentum in the transition, enabling observational discrimination between different resonances. We use this formalism in two different scenarios: cosmological recombination and cosmological re-ionization. In the context of cosmological recombination, we compute predictions in frequency and multipole space for the change in the TE and EE power spectra introduced by scattering on the Hα and Pα lines of hydrogen. This constitutes a fundamental test of the standard model of recombination, and the sensitivity it requires is comparable to that needed in measuring the primordial CMB B-mode polarization component. In the context of re-ionization, we study the scattering off metals and ions produced by the first stars, and find that polarization anisotropies, apart from providing a consistency test for intensity measurements, give some insight on how re-ionization evolved. Since polarization anisotropies have memory of how anisotropic the line scattering is, they should be able to discern the O  i 63.2-μm transition from other possible transitions associated to O  iii , N  ii , N  iii , etc. The amplitude of these signals are, however, between 10 and 100 times below the (already challenging) level of CMB B-mode polarization anisotropies.     

Predicting the polarization of the microwave background from the WMAP temperature maps

In this paper, we study how to predict the polarization of the Cosmic Microwave Background (CMB) using knowledge of only the temperature (intensity) and the cross-correlation between temperature and polarization. We derive a “Wiener prediction” method and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) all-sky CMB temperature maps and to the MAXIMA field.     

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.     

Microwave polarization in the direction of galaxy clusters induced by the CMB quadrupole anisotropy

Electron scattering induces a polarization in the cosmic microwave background (CMB) signal measured in the direction of a galaxy cluster owing to the presence of a quadrupole component in the CMB temperature distribution. Measuring the polarization towards distant clusters provides the unique opportunity to observe the evolution of the CMB quadrupole at moderate redshifts, z ∼0.5–3. We demonstrate that for the local cluster population the polarization degree will depend on the cluster celestial position. There are two extended regions in the sky, which are opposite to each other, where the polarization is maximal, ∼0.1( τ /0.02) μK in the Rayleigh–Jeans part of the CMB spectrum ( τ being the Thomson optical depth across the cluster). This value exceeds the polarization introduced by the cluster transverse peculiar motion if v _t<1300 km s⁻¹. One can hope to detect this small signal by measuring a large number of clusters, thereby effectively removing the systematic contribution from other polarization components produced in clusters. These polarization effects, which are of the order of ( v _t c )² τ , ( v _t c ) τ ² and ( kT _e m _e c ²) τ ², as well as the polarization owing to the CMB quadrupole, were previously given by Sunyaev and Zel'dovich for the Rayleigh–Jeans part of the spectrum. We fully confirm their earlier results and present exact frequency dependences for all these effects. The polarization degree is considerably higher in the Wien region.     

Reionization and the large-scale 21-cm cosmic microwave background cross-correlation

Of the many probes of reionization, the 21-cm line and the cosmic microwave background (CMB) are among the most effective. We examine how the cross-correlation of the 21-cm brightness and the CMB Doppler fluctuations on large angular scales can be used to study this epoch. We employ a new model of the growth of large-scale fluctuations of the ionized fraction as reionization proceeds. We take into account the peculiar velocity field of baryons and show that its effect on the cross-correlation can be interpreted as a mixing of Fourier modes. We find that the cross-correlation signal is strongly peaked towards the end of reionization and that the sign of the correlation should be positive because of the inhomogeneity inherent to reionization. The signal peaks at degree scales (ℓ∼ 100) and comes almost entirely from large physical scales ( k ∼ 10⁻² Mpc). Since many of the foregrounds and noise that plague low-frequency radio observations will not correlate with CMB measurements, the cross-correlation might appear to provide a robust diagnostic of the cosmological origin of the 21-cm radiation around the epoch of reionization. Unfortunately, we show that these signals are actually only weakly correlated and that cosmic variance dominates the error budget of any attempted detection. We conclude that the detection of a cross-correlation peak at degree-size angular scales is unlikely even with ideal experiments.     

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.     

Power spectra of CMB polarization by scattering in clusters

Mapping cosmic microwave background (CMB) polarization is an essential ingredient of current cosmological research. Particularly challenging is the measurement of an extremely weak B-mode polarization that can potentially yield unique insight on inflation. Achieving this objective requires very precise measurements of the secondary polarization components on both large and small angular scales. Scattering of the CMB in galaxy clusters induces several polarization effects whose measurements can probe cluster properties. Perhaps more important are levels of the statistical polarization signals from the population of clusters. Power spectra of five of these polarization components are calculated and compared with the primary polarization spectra. These spectra peak at multipoles  ℓ≥ 3000  , and attain levels that are unlikely to appreciably contaminate the primordial polarization signals.     

The cross-correlation of the CMB polarization and the 21-cm line fluctuations from cosmic reionization

The cosmic microwave background (CMB) polarization and the 21-cm line fluctuations are powerful probes of cosmological reionization. We study how the cross-correlation between the CMB polarization ( E modes) and the 21-cm line fluctuations can be used to gain further understanding of the reionization history, within the framework of inhomogeneous reionization. Since the E -mode polarization reflects the amplitude of the quadrupole component of the CMB temperature fluctuations, the angular power spectrum of the cross-correlation exhibits oscillations at all multipoles. The first peak of the power spectrum appears at the scale corresponding to the quadrupole at the redshift, which is probed by the 21-cm line fluctuations. The peak reaches its maximum value in redshift when the average ionization fraction of the universe is about half. On the other hand, on small scales, there is a damping that depends on the duration of reionization. Thus, the cross-correlation between the CMB polarization and the 21-cm line fluctuations has the potential to accurately constrain the epoch and the duration of reionization.     

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.     

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.     

Gravitational waves as a source for the polarization of the Cosmic Microwave Background

The polarization of the Cosmic Microwave Background (CMB) induced by gravitational waves (GWs) is studied by solving in a semi-analytical way the Chandrasekhar radiative transfer equation; following the Polnarev approach, the equation is written as a second-kind Volterra integral equation and its kernel is handled by performing a series expansion of the trigonometric functions it contains. In this way, a recursive calculation of the Volterra equation gets possible and the polarizing effect of the gravitational waves can be brought out.The polarization degree of the CMB coming from this analysis shows a peak for a wavenumber corresponding to GWs re-entering the horizon at the end of the recombination epoch: the position and the size of the maximum are in agreement with the results of other works, based on a totally numerical calculation. However, a difference quite relevant can be remarked when one looks at the shape of the polarization plot: a semi-analytical calculation of the solution of the Volterra integral equation gives a sharp peak due to the fact that the contribution of each packet of GWs of fixed wavenumberk is strongly singled out when one substitutes the integrals with series and sums.As a consequence, this solution method may have some usefulness when one wants to point out the contributions really dominating in producing a polarization for the CMB.From this analysis one can also infer that the best angular scales to test in order to detect a polarization for the CMB are 2°–3°, smaller than those investigated by COBE.