The CMB anisotropy from spatial correlations between clusters of galaxies

Eiichiro Komatsu1,2,3, Tetsu Kitayama4, Alexandre Refregier5, David N. Spergel1,6 and Ue-Li Pen7

1. Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
2. School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton, NJ 08540, USA
3. Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
4. Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
5. Institute of Astronomy, Madingley Road, University of Cambridge, Cambridge CB3 OHA, England
6. Keck Distinguished Visiting Professor, School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
7. Canadian Institute of Theoretical Astrophysics, University of Toronto, 60 St. George St., Toronto, Canada


The Sunyaev-Zel'dovich (SZ) effect from clusters of galaxies is a dominant source of secondary cosmic microwave background (CMB) anisotropy in the low-redshift universe. We present analytic predictions for the CMB power spectrum from massive halos arising from the SZ effect. Since halos are discrete, the power spectrum consists of a Poisson and a correlation term. The latter is always smaller than the former, which is entirely dominated by nearby bright massive halos, i.e., by rich clusters. In practice however, those bright clusters are easy to indentify and can thus be subtracted from the map. After this subtraction, the correlation term dominates degree-scale fluctuations over the Poisson term, as the main contribution to the correlation term comes from distant clusters. We compare the signal of the correlation term to the expected sensitivity for the Planck experiment for the SZ effect, and find that the correlation term is detectable. Since the degree scale spectrum is quite insensitive to the highly uncertain core structures of halos, our predictions are robust on these scales. Measuring the correlation term on degree scales thus cleanly probes the clustering of distant halos. This has not been measured yet, mainly because optical and X-ray surveys are not sufficiently sensitive to include such distant clusters and groups. Our analytic predictions are also compared to adiabatic hydrodynamic simulations. The agreement is remarkably good, down to ten arcminutes scales, indicating that our predictions are robust for the Planck experiment. Below ten arcminute scales, where the details of the core structure dominates the power spectrum, our analytic and simulated predictions might fail. In the near future, interferometer and bolometer array experiments will measure the SZ power spectrum down to arcminutes scales, and yield new insight into the physics of the intrahalo medium.


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