Implementation of a Fourier Matched Filter in CMB Analyses. Application to ISW Studies

Aims: Implement a matched filter (MF) cross-correlation algorithm in multipole space and compare it to the standard Angular Cross Power Spectrum (ACPS) method. Apply both methods on a Integrated Sachs Wolfe (ISW) - Large Scale Structure (LSS) cross correlation scenario and study how sky masks influence the multipole range where signal arises and its comparison to theoretical predictions. Methods: The MF requires the inversion of a multipole covariance matrix that if $f_{sky} \lt 1$ is generally non-diagonal and singular. We use a SVD approach that focuses on those modes carrying most of the information. We compare the MF to the ACPS in ISW-LSS Monte Carlo simulations, paying attention on the effect that a limited sky coverage has on the cross-correlation results. Results: Within the linear data model for which the MF is defined, the MF performs comparatively better than the ACPS for smaller values of $f_{sky}$ and scale dependent (non-Poissonian) noise fields. In the context of ISW studies both methods are comparable, although the MF performs slightly more sensitively under more restrictive masks. A preliminary study predicts that most of the ISW--LSS cross correlation S/N ratio should be found in the very large scales (50% of the S/N at $l\lt 10$, 90% at $l\lt 40-50$), and this is confirmed by Monte Carlo simulations. The statistical significance of our cross-correlation statistics reaches its maximum when considering $l\in [2,l_{max}]$, with $l_{max} \in[5,40]$ for all values of $f_{sky}$ observed, despite of the smoothing and power aliasing that aggressive masks introduce in Fourier space. This $l$-confinement of the ISW-LSS cross correlation should enable a safe distinction from other secondary effects arising at smaller angular scales.Comment: 9 pages, 5 figures, submitted to A&

Intracluster Medium through three years of WMAP

Wilkinson Microwave Anisotropy Probe (WMAP) has provided us with the yet highest resolution all-sky maps of the Cosmic Microwave Background. As a result of thermal Sunyaev-Zel'dovich effect, clusters of galaxies are imprinted as tiny, poorly resolved dips on top of primary CMB anisotropies in these maps. Here, I describe different efforts to extract the physics of Intracluster Medium (ICM) from the sea of primary CMB, through combining WMAP with low-redshift galaxy or X-ray cluster surveys. This finally culminates at a mean (universal) ICM pressure profile, which is for the first time directly constrained from WMAP 3yr maps, and leads to interesting constraints on the ICM baryonic budget.Comment: 9 pages and 4 figures; Proceedings of the Fundamental Physics With CMB workshop, UC Irvine, March 23-25, 2006, to be published in New Astronomy Review

Missing baryons, bulk flows and the E-mode polarization of the Cosmic Microwave Background

If the peculiar motion of galaxy groups and clusters indeed resembles that of the surrounding baryons, then the kinetic Sunyaev-Zel'dovich (kSZ) pattern of those massive halos should be closely correlated to the kSZ pattern of all surrounding electrons. Likewise, it should also be correlated to the CMB E-mode polarization field generated via Thomson scattering after reionization. We explore the cross-correlation of the kSZ generated in groups and clusters to the all sky E-mode polarization in the context of upcoming CMB experiments like Planck, ACT, SPT or APEX. We find that this cross-correlation is effectively probing redshifts below $z=3-4$ (where most of baryons cannot be seen), and that it arises in the very large scales ($l<10$). The significance with which this cross-correlation can be measured depends on the Poissonian uncertainty associated to the number of halos where the kSZ is measured and on the accuracy of the kSZ estimations themselves. Assuming that Planck can provide a cosmic variance limited E-mode polarization map at $l<20$ and S/N $\sim 1$ kSZ estimates can be gathered for all clusters more massive than $10^{14} M_{\odot}$, then this cross-correlation should be measured at the 2--3 $\sigma$ level. Further, if an all-sky ACT or SPT type CMB experiment provides similar kSZ measurements for all halos above $10^{13} M_{\odot}$, then the cross-correlation total signal to noise (S/N) ratio should be at the level of 4--5. A detection of this cross-correlation would provide direct and definite evidence of bulk flows and missing baryons simultaneously.Comment: 6 pages, 2 figures, submitted to A&

Determining cosmic microwave background structure from its peak distribution

We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic describing their angular clustering - analogously to galaxies, the 2-point angular correlation function, $\xi_\nu(\theta)$. We show that for increasing peak threshold, $\nu$, the $\xi_\nu(\theta)$ is strongly amplified and becomes measurable for $\nu\geq$1 on angular scales $\leq 10^\circ$. Its amplitude at every scale depends uniquely on the CMB temperature correlation function, $C(\theta)$, and thus the measured $\xi_\nu$ can be uniquely inverted to obtain $C(\theta)$ and its Legendre transform, the power spectrum of the CMB field. Because in this method the CMB power spectrum is deduced from high peaks/troughs of the CMB field, the procedure takes only $[f(\nu)]^2N^2$ operations where $f(\nu)$ is the fraction of pixels with $|\delta T|\geq\nu$ standard deviations in the map of $N$ pixels and is e.g. 0.045 and 0.01 for $\nu$=2 and 2.5 respectively. We develop theoretical formalism for the method and show with detailed simulations, using MAP mission parameters, that this method allows to determine very accurately the CMB power spectrum from the upcoming CMB maps in only $\sim(10^{-4}-10^{-3})\times N^2$ operations.Comment: To be published in Ap.J. Letters. Minor changes to match the journal versio

Revisiting the WMAP - NVSS angular cross correlation. A skeptic's view

In the context of the study of the ISW, we revisit the angular cross correlation of WMAP CMB data with the NVSS radio survey. We compute 2-point cross functions between the two surveys in real and in Fourier space, paying particular attention on the dependence of results on the flux of NVSS radio sources, the angular scales where correlations arise and the comparison with theoretical expectations. We reproduce previous results that claim an excess of correlation in the angular correlation function (ACF), and we also find some (low significance) similarity between the CMB and radio galaxy data in the multipole range \el \in [10, 25]. However, the S/N in the ACFs increases with higher flux thresholds for NVSS sources, but drops a $\sim$ 30 - 50% in separations of the order of a pixel size, suggesting some residual point source contribution. When restricting our analyses to multipoles \el \gt 60, we fail to find any evidence for cross correlation in the range \el \in [2,10], where according to the model predictions and our simulations $\sim$ 50% of the S/N is supposed to arise. Also, the accumulated S/N for \el \lt 60 is below 1, far from the theoretical expectation of S/N$\sim 5$. Part of this disagreement may be caused by an inaccurate modeling of the NVSS source population: as in previous works, we find a level of large scale (\el \lt 70) clustering in the NVSS catalog that seems incompatible with a high redshift population. This is unlikely to be caused by contaminants or systematics, since it is independent of flux threshold, and hence present for the brightest ($\gt 30 \sigma$) NVSS sources. Either our NVSS catalogs are not probing the high redshift, large scale gravitational potential wells, or there is a clear mismatch between the ISW component present in WMAP data and theoretical expectations.Comment: 16 pages, one extra figure (13 total), matches accepted version in A&

The ISW-tSZ cross correlation: ISW extraction out of pure CMB data

If Dark Energy introduces an acceleration in the universal expansion then large scale gravitational potential wells should be shrinking, causing a blueshift in the CMB photons that cross such structures (Integrated Sachs-Wolfe effect, [ISW]). Galaxy clusters are known to probe those potential wells. In these objects, CMB photons also experience inverse Compton scattering off the hot electrons of the intra-cluster medium, and this results in a distortion with a characteristic spectral signature of the CMB spectrum (the so-called thermal Sunyaev-Zel'dovich effect, [tSZ]). Since both the ISW and the tSZ effects take place in the same potential wells, they must be spatially correlated. We present how this cross ISW-tSZ signal can be detected in a CMB-data contained way by using the frequency dependence of the tSZ effect in multi frequency CMB experiments like {\it Planck}, {\em without} requiring the use of external large scale structure tracers data. We find that by masking low redshift clusters, the shot noise level decreases significantly, boosting the signal to noise ratio of the ISW--tSZ cross correlation. We also find that galactic and extragalactic dust residuals must be kept at or below the level of ~0.04 muK^2 at l=10, a limit that is a factor of a few below {\it Planck}'s expectations for foreground subtraction. If this is achieved, CMB observations of the ISW-tSZ cross correlation should also provide an independent probe for the existence of Dark Energy and the amplitude of density perturbations.Comment: submitted to MNRA

Evidence of the missing baryons from the kinematic Sunyaev-Zeldovich effect in Planck data

Under the terms of the Creative Commons Attribution license.-- et al.We estimate the amount of the missing baryons detected by the Planck measurements of the cosmic microwave background in the direction of central galaxies (CGs) identified in the Sloan galaxy survey. The peculiar motion of the gas inside and around the CGs unveils values of the Thomson optical depth τT in the range 0.2-2×10-4, indicating that the regions probed around CGs contain roughly half of the total amount of baryons in the Universe at the epoch where the CGs are found. If baryons follow dark matter, the measured τT's are compatible with the detection of all of the baryons existing inside and around the CGs.C. H.-M. acknowledges the support of Ramón y Cajal Fellowship No. RyC-2011-08262, Marie Curie Career Integration Grant No. 294183, and Spanish Ministerio de Economía y Competitividad Project No. AYA2012-30789. Y.-Z. M thanks ERC for its support through Starting Grant No. 307209.Peer Reviewe

On the Number Density of Sunyaev-Zel'dovich Clusters of Galaxies

If the mean properties of clusters of galaxies are well described by the entropy-driven model, the distortion induced by the cluster population on the blackbody spectrum of the Cosmic Microwave Background radiation is proportional to the total amount of intracluster gas while temperature anisotropies are dominated by the contribution of clusters of about 10^{14} solar masses. This result depends marginally on cluster parameters and it can be used to estimate the number density of clusters with enough hot gas to produce a detectable Sunyaev-Zel'dovich effect. Comparing different cosmological models, the relation depends mainly on the density parameter Omega_m. If the number density of clusters could be estimated by a different method, then this dependence could be used to constrain Omega_m.Comment: 8 pages, 3 figures, submitted to ApJ Letter