The Standard Cosmological Model and CMB Anisotropies

This is a course on cosmic microwave background (CMB) anisotropies in the standard cosmological model, designed for beginning graduate students and advanced undergraduates. ``Standard cosmological model'' in this context means a Universe dominated by some form of cold dark matter (CDM) with adiabatic perturbations generated at some initial epoch, e.g., Inflation, and left to evolve under gravity alone (which distinguishes it from defect models). The course is primarily theoretical and concerned with the physics of CMB anisotropies in this context and their relation to structure formation. Brief presentations of the uniform Big Bang model and of the observed large--scale structure of the Universe are given. The bulk of the course then focuses on the evolution of small perturbations to the uniform model and on the generation of temperature anisotropies in the CMB. The theoretical development is performed in the (pseudo--)Newtonian gauge because it aids intuitive understanding by providing a quick reference to classical (Newtonian) concepts. The fundamental goal of the course is not to arrive at a highly exact nor exhaustive calculation of the anisotropies, but rather to a good understanding of the basic physics that goes into such calculations.Comment: Course given at the International School of Space Science: 3K Cosmology, held in L'Aquila, Italy, September 1998. 44 pages with 4 figure

Measuring cluster masses with CMB lensing: a statistical approach

We present a method for measuring the masses of galaxy clusters using the imprint of their gravitational lensing signal on the cosmic microwave background (CMB) temperature anisotropies. The method first reconstructs the projected gravitational potential with a quadratic estimator and then applies a matched filter to extract cluster mass. The approach is well-suited for statistical analyses that bin clusters according to other mass proxies. We find that current experiments, such as Planck, the South Pole Telescope and the Atacama Cosmology Telescope, can practically implement such a statistical methodology, and that future experiments will reach sensitivities sufficient for individual measurements of massive systems. As illustration, we use simulations of Planck observations to demonstrate that it is possible to constrain the mass scale of a set of 62 massive clusters with prior information from X-ray observations, similar to the published Planck ESZ-XMM sample. We examine the effect of the thermal (tSZ) and kinetic (kSZ) Sunyaev-Zeldovich (SZ) signals, finding that the impact of the kSZ remains small in this context. The stronger tSZ signal, however, must be actively removed from the CMB maps by component separation techniques prior to reconstruction of the gravitational potential. Our study of two such methods highlights the importance of broad frequency coverage for this purpose. A companion paper presents application to the Planck data on the ESZ-XMM sample.Comment: 9 pages, 5 figures, version accepted for publication in A&

Point Source Confusion in SZ Cluster Surveys

We examine the effect of point source confusion on cluster detection in Sunyaev-Zel'dovich (SZ) surveys. A filter matched to the spatial and spectral characteristics of the SZ signal optimally extracts clusters from the astrophysical backgrounds. We calculate the expected confusion (point source and primary cosmic microwave background [CMB]) noise through this filter and quantify its effect on the detection threshold for both single and multiple frequency surveys. Extrapolating current radio counts, we estimate that confusion from sources below 100 microJy limits single-frequency surveys to 1-sigma detection thresholds of Y 3.10^{-6} arcmin^2 at 30 GHz and Y 10^{-5} arcmin^2 at 15 GHz (for unresolved clusters in a 2 arcmin beam); these numbers are highly uncertain, and an extrapolation with flatter counts leads to much lower confusion limits. Bolometer surveys must contend with an important population of infrared point sources. We find that a three-band matched filter with 1 arcminute resolution (in each band) efficiently reduces confusion, but does not eliminate it: residual point source and CMB fluctuations contribute significantly the total filter noise. In this light, we find that a 3-band filter with a low-frequency channel (e.g, 90+150+220 GHz) extracts clusters more effectively than one with a high frequency channel (e.g, 150+220+300 GHz).Comment: Accepted for publication in Astronomy & Astrophysics; Updated grant information in acknowledgement

SZ Surveys are Coming: What should we do?

Galaxy clusters furnish extremely rich information on the contents and structure of our universe. The potential of galaxy cluster studies to constrain dark energy, for example, motivates a number of ambitious cluster surveys. Among these, surveys based on the Sunyaev-Zel'dovich (SZ) effect are particularly powerful for their ability to cleanly select clusters out to redshifts z>1. Now poised to begin surveying substantial areas of sky, dedicated interferometers, bolometer cameras and the Planck satellite will soon produce large cluster catalogs that will provide a precise measure of the cosmic expansion rate over a range of redshifts and precipitate a new understanding of structure and galaxy formation. I review the science potential of these surveys and examine some issues of SZ cluster catalog construction.Comment: Review talk given at the Rencontres de Moriond, "Contents and Structures of the Universe", La Thuile, Italy, March 18-25, 200

redMaPPer III: A Detailed Comparison of the Planck 2013 and SDSS DR8 RedMaPPer Cluster Catalogs

We compare the Planck Sunyaev-Zeldovich (SZ) cluster sample (PSZ1) to the Sloan Digital Sky Survey (SDSS) redMaPPer catalog, finding that all Planck clusters within the redMaPPer mask and within the redshift range probed by redMaPPer are contained in the redMaPPer cluster catalog. These common clusters define a tight scaling relation in the richness-SZ mass ($\lambda$--$M_{SZ}$) plane, with an intrinsic scatter in richness of $\sigma_{\lambda|M_{SZ}} = 0.266 \pm 0.017$. The corresponding intrinsic scatter in true cluster halo mass at fixed richness is $\approx 21\%$. The regularity of this scaling relation is used to identify failures in both the redMaPPer and Planck cluster catalogs. Of the 245 galaxy clusters in common, we identify three failures in redMaPPer and 36 failures in the PSZ1. Of these, at least 12 are due to clusters whose optical counterpart was correctly identified in the PSZ1, but where the quoted redshift for the optical counterpart in the external data base used in the PSZ1 was incorrect. The failure rates for redMaPPer and the PSZ1 are $1.2\%$ and $14.7\%$ respectively, or 9.8% in the PSZ1 after subtracting the external data base errors. We have further identified 5 PSZ1 sources that suffer from projection effects (multiple rich systems along the line-of-sight of the SZ detection) and 17 new high redshift ($z\gtrsim 0.6$) cluster candidates of varying degrees of confidence. Should all of the high-redshift cluster candidates identified here be confirmed, we will have tripled the number of high redshift Planck clusters in the SDSS region. Our results highlight the power of multi-wavelength observations to identify and characterize systematic errors in galaxy cluster data sets, and clearly establish photometric data both as a robust cluster finding method, and as an important part of defining clean galaxy cluster samples.Comment: comments welcom