Sunyaev-Zeldovich effect in WMAP and its effect on cosmological parameters

We use multifrequency information in first year Wilkinson microwave anisotropy probe (WMAP) data to search for the Sunyaev-Zeldovich (SZ) effect. WMAP has sufficiently broad frequency coverage to constrain the SZ effect without the addition of higher frequency data: the SZ power spectrum amplitude is expected to increase 50% from W to Q frequency band. This, in combination with the low noise in WMAP, allows us to strongly constrain the SZ contribution. We derive an optimal frequency combination of WMAP cross-spectra to extract the SZ effect in the presence of noise, cosmic microwave background (CMB), and radio point sources, which are marginalized over. We find that the SZ contribution is less than 2% (95% C.L.) at the first acoustic peak in W band. Under the assumption that the removed radio point sources are not correlated with the SZ effect this limit implies ${\sigma }_8<1.07$ at 95% C.L. We investigate the effect on the cosmological parameters of allowing an SZ component. We run Monte Carlo Markov chains with and without an SZ component and find that the addition of the SZ effect does not affect any of the cosmological conclusions. We conclude that the SZ effect does not contaminate the WMAP CMB or change cosmological parameters, refuting the recent claims that they may be corrupted.

Figure 1

Reconstruction of the SZ power spectrum in the RJ regime, in bins of $\Delta l=40$. There is no visible SZ detection, which would have been positive for this combination. The SZ error bars are correlated at less than the 1%–15% level. For comparison, we have included the WMAP combined temperature power spectrum, binned the same way, the WMAP best-fit theoretical CMB power spectrum, and a theoretical prediction of the SZ power in the RJ regime for ${\sigma }_8=0.9$ calculated from a halo model (thick dotted), which is barely distinguishable from zero (thin dotted) on this plot.

Figure 2

The contribution to the SZ amplitude estimator $\overline{B}$ from the cross-spectra. The horizontal axis is the multipole $l$. The vertical axis show the weight of each spectrum in $\mu {\mathrm{K}}^{\mathrm{-}\mathrm{2}}$. We have grouped the cross-spectra by band as noted. Within each group, we have summed the weights of the individual spectra. In the top frame, we have included the CMB power spectrum (arbitrary units) to give scale for $l$.

Figure 3

Limit on SZ power spectrum. We present a 95% upper limit on the amplitude of the SZ power spectrum from a combination of WMAP band cross-spectra. We show the temperature fluctuation in the Rayleigh-Jeans regime. For comparison we display the WMAP best-fit power spectrum and SZ power spectra from a halo model calculation using ${\sigma }_8=0.9,1,1.1$.

Figure 4

A joint estimation of the SZ power spectrum amplitude and the point source spectrum amplitude. The ellipse encloses 68% of the likelihood. The best-fit point is shown by a “$+$”. The vertical line at $\mathrm{B}=1$ shows the theoretically predicted SZ amplitude. The horizontal line shows WMAP’s value for point sources, which does not take into account SZ. Because the power spectrum is a positive quantity, note that portions of the plane where either axis is negative are unphysical.

Figure 5

We show two-dimensional contours of 68% and 95% confidence levels in $({\omega }_b,B)$ plane. The larger contours show the degeneracy using the WMAP combined temperature power spectrum without any prior on the SZ amplitude. The smaller contours include our multifrequency cross-spectrum analysis as a prior. $\mathrm{B}=1$ is expected from halo models for the SZ effect when ${\sigma }_8=0.9$.