The Sunyaev-Zeldovich effect in CMB-calibrated theories applied to the Cosmic Background Imager anisotropy power at l > 2000

TL;DR

This study investigates whether the observed high-$\ell$ excess in the CBI power spectrum can be attributed to the Sunyaev-Zeldovich effect from hot cluster gas within $\Lambda$CDM. It combines CMB-driven constraints on $\sigma_8$ and the shape parameter with two independent hydrodynamical simulations and halo-model analytic SZ calculations to predict the SZ contribution, propagating simulated SZ maps through the CBI pipeline and with Wiener-filtering to isolate SZ signatures. The results show a strong $\sigma_8$ dependence of the SZ signal, with $\mathcal{C}_\ell^{SZ} \propto (\Omega_b h)^2 \sigma_8^7$; for $\sigma_8$ near unity, SZ can plausibly account for the excess, though non-Gaussian sample variance and astrophysical uncertainties can shift this conclusion. The work demonstrates that SZ is a viable explanation for the CBI excess within certain parameter ranges and highlights SZ power as a powerful probe of $\sigma_8$ when combining CMB data with SZ modeling and robust component separation techniques.

Abstract

We discuss the nature of the possible high-l excess in the Cosmic Microwave Background (CMB) anisotropy power spectrum observed by the Cosmic Background Imager (CBI). We probe the angular structure of the excess in the CBI deep fields and investigate whether it could be due to the scattering of CMB photons by hot electrons within clusters, the Sunyaev-Zeldovich (SZ) effect. We estimate the density fluctuation parameters for amplitude, sigma_8, and shape, Gamma, from CMB primary anisotropy data and other cosmological data. We use the results of two separate hydrodynamical codes for Lambda-CDM cosmologies, consistent with the allowed sigma_8 and Gamma values, to quantify the expected contribution from the SZ effect to the bandpowers of the CBI experiment and pass simulated SZ effect maps through our CBI analysis pipeline. The result is very sensitive to the value of sigma_8, and is roughly consistent with the observed power if sigma_8 ~ 1. We conclude that the CBI anomaly could be a result of the SZ effect for the class of Lambda-CDM concordance models if sigma_8 is in the upper range of values allowed by current CMB and Large Scale Structure (LSS) data.

Figures (12)

• Figure 1: One-dimensional projected likelihood functions of $\sigma_8$ calculated for the CMB data with three prior probability restrictions on the cosmological parameters are contrasted with estimates from other datasets. The curves shown used 'all-data' for the CMB available for Paper V, namely DMR, DASI DASI, BOOMERANG (for the Ruhl02 cut), MAXIMA Lee01, VSA VSA02 and the CBI mosaic data for the odd $\Delta L$=140 binning. The marginalization has been performed over seven cosmological variables and all of the relevant calibration and beam uncertainty variables associated with the experiments, seven in this case. Application of the weak-h prior is long-dashed blue, of the flat weak-h prior is solid black and of the LSS flat weak-h prior is dotted black. Adding TOCOTOCO, the Boomerang test flight and 17 other experiments predating April 1999 (hereafter 'April 99') as well gives very similar results. The Bayesian 50% and associated 16% and 84% error bars are shown as data points in blue for these and other priors, in particular those with the stronger HST measurement of $h$ included and with SN data included. The magenta data points with smaller errors are those determined with 'all-data' to March 2003, including WMAP, as described in broysoc03. The original LSS prior was constructed based on the cluster abundance data bh95Bond99Lange01. An SZ estimate of $\sigma_8$ from Goldstein02 that simultaneously determines amplitudes for a best-fit primordial spectrum and an SZ spectrum for our CBI deep field data in conjunction with ACBAR Kuo02 and BIMA BIMA02 data is shown at the top. Estimates of $\sigma_8$ from cluster abundance data and from weak lensing data are also shown. These results have invariably had more restrictive priors imposed than those for the CMB, and so are not always applicable, but the overall level of agreement in the various approaches is encouraging. From top to bottom, the sample cluster values are from Eke96Carlberg97Fan98Pen98cPierpaoli01Reiprich01Seljak01Viana01Borgani01, then two estimates from Pierpaoli03, then from SBCG03Allen03VV03. From top to bottom, the weak lensing estimates are from Hoekstra02Ludo02Refregier02Bacon02Jarvis03Hamana03Brown03Heymans03.
• Figure 2: The weak prior we use for LSS in $\sigma_8\Omega_m^{0.56}$ is compared with estimates from SZ, cluster abundances, weak lensing and from the CMB data shown in Fig. \ref{['fig:priors8']}, appropriately scaled. The blue error bars are for 'all-data' to June 2002, and the magenta are for 'all-data' to March 2003. The prior used in past work was shifted up in central value from 0.47 to 0.55, but was otherwise the same. We have also considered the LSS(low-$\sigma_8$) case (dashed green), with the prior shifted downward to be centered on 0.40 to accommodate better the low cluster abundance estimates, with results shown in Tables \ref{['tab:lss']}, \ref{['tab:lss1']}.
• Figure 3: The prior probability used for the shape parameter $\Gamma_{\rm eff}$ is shown as solid green. (This is to be contrasted with the more skewed one used in Lange01, etc., shown as light dashed-dotted green.) The $\Gamma$-prior was designed to encompass the range indicated by the APM data, vintage 1992, but estimates from the 2dFRS and SDSS shown below are quite compatible. The CMB results for $\Gamma_{\rm eff}$ are shown with various choices for priors for comparison. Solid blue is for 'all-data' as of June 2002, as described in Sievers02, and magenta is for the data as of March 2003, as described in broysoc03. $\Gamma_{\rm eff}$ includes corrections for $\omega_b$, $h$, and the tilt. The related values of $\Omega_m h$ are shown at the bottom to show the effect of these corrections.
• Figure 4: One and two sigma contours of 2D projected likelihood functions show how various cosmological parameters correlate with $\sigma_8$. For this case, 'all--data' from the June 2002 compilation was used: DASI+MAXIMA+BOOMERANG+VSA plus the CBI mosaic data for the odd $\Delta L$=140 binning. The $\Omega_k-\sigma_8$ panel shows the weak-$h$ prior (magenta) and LSS+weak-$h$ prior (solid black). For the other 3 panels the flat constraint was added to these two priors as well. Note the positive correlation with $n_s$, but little correlation in the other variables.
• Figure 5: One and two sigma contours of 2D projected likelihood functions for $\omega_b$ and $\tau_C$ for 'all-data' of Sievers02. The flat+weak-$h$ prior (magenta) and flat+LSS+weak-$h$ prior (solid black) cases are shown. The significant $\sigma_8$--$\tau_C$ correlation is evident, which results in a higher $\sigma_8$ for higher $\tau_C$. One could impose a stronger prior than $\tau_C < 0.7$ (as is done here) based on astrophysical arguments. This is fraught with uncertainty since it involves the first objects collapsing on small scales in the universe and their efficiency in generating stars that produce ionizing radiation. However, $\tau_C$ has apparently been detected by WMAP at the $0.16 \pm 0.04$ level Kogut03, and results with a prior encompassing this detection on the March 2003 compilation of the data are given in Table \ref{['tab:lss1']}.