On the Angular Correlation Function of SZ Clusters : Extracting cosmological information from a 2D catalog

We discuss the angular correlation function of Sunyaev-Zel'dovich (SZ)-detected galaxy clusters as a cosmological probe. As a projection of the real-space cluster correlation function, the angular function samples the underlying SZ catalog redshift distribution. It offers a way to study cosmology and cluster evolution directly with the two-dimensional catalog, even before extensive follow-up observations, thereby facilitating the immediate scientific return from SZ surveys. As a simple illustration of the information content of the angular function, we examine its dependence on the parameter pair Om_m, sigma_8 in flat cosmologies. We discuss sources of modeling uncertainty and consider application to the future Planck SZ catalog, showing how these two parameters and the normalization of the SZ flux-mass relation can be simultaneously found when the local X-ray cluster abundance constraint is included.Comment: 11 pages, 5 figures. A&A, 410, 767; corrected typo, published versio

Cosmological constraints from a 2D SZ catalog

We perform a Fisher matrix analysis to quantify cosmological constraints obtainable from a 2-dimensional Sunyaev-Zel'dovich (SZ) cluster catalog using the counts and the angular correlation function. Three kinds of SZ survey are considered: the almost all-sky Planck survey and two deeper ground-based surveys, one with 10% sky coverage, the other one with a coverage of 250 square degrees. With the counts and angular function, and adding the constraint from the local X-ray cluster temperature function, joint 10% to 30% errors (1 sigma) are achievable on the cosmological parameter pair (sigma_8, Omega_m) in the flat concordance model. Constraints from a 2D distribution remain relatively robust to uncertainties in possible cluster gas evolution for the case of Planck. Alternatively, we examine constraints on cluster gas physics when assuming priors on the cosmological parameters (e.g., from cosmic microwave background anisotropies and SNIa data), finding a poor ability to constrain gas evolution with the 2-dimensional catalog. From just the SZ counts and angular correlation function we obtain, however, a constraint on the product between the present-day cluster gas mass fraction and the normalization of the mass-temperature relation, T_*, with a precision of 15%. This is particularly interesting because it would be based on a very large catalog and is independent of any X-ray data.Comment: 9 pages, 4 figures, A&A in pres

Catalog Extraction in SZ Cluster Surveys: a matched filter approach

We present a method based on matched multifrequency filters for extracting cluster catalogs from Sunyaev-Zel'dovich (SZ) surveys. We evaluate its performance in terms of completeness, contamination rate and photometric recovery for three representative types of SZ survey: a high resolution single frequency radio survey (AMI), a high resolution ground-based multiband survey (SPT), and the Planck all-sky survey. These surveys are not purely flux limited, and they loose completeness significantly before their point-source detection thresholds. Contamination remains relatively low at <5% (less than 30%) for a detection threshold set at S/N=5 (S/N=3). We identify photometric recovery as an important source of catalog uncertainty: dispersion in recovered flux from multiband surveys is larger than the intrinsic scatter in the Y-M relation predicted from hydrodynamical simulations, while photometry in the single frequency survey is seriously compromised by confusion with primary cosmic microwave background anisotropy. The latter effect implies that follow-up observations in other wavebands (e.g., 90 GHz, X-ray) of single frequency surveys will be required. Cluster morphology can cause a bias in the recovered Y-M relation, but has little effect on the scatter; the bias would be removed during calibration of the relation. Point source confusion only slightly decreases multiband survey completeness; single frequency survey completeness could be significantly reduced by radio point source confusion, but this remains highly uncertain because we do not know the radio counts at the relevant flux levels.Comment: 14 pages, 13 figures, replaced to match version accepted for publication in A&

The Selection Function of SZ Cluster Surveys

We study the nature of cluster selection in Sunyaev-Zel'dovich (SZ) surveys, focusing on single frequency observations and using Monte Carlo simulations incorporating instrumental effects, primary cosmic microwave background (CMB) anisotropies and extragalactic point sources. Clusters are extracted from simulated maps with an optimal, multi-scale matched filter. We introduce a general definition for the survey selection function that provides a useful link between an observational catalog and theoretical predictions. The selection function defined over the observed quantities of flux and angular size is independent of cluster physics and cosmology, and thus provides a useful characterization of a survey. Selection expressed in terms of cluster mass and redshift, on the other hand, depends on both cosmology and cluster physics. We demonstrate that SZ catalogs are not simply flux limited, and illustrate how incorrect modeling of the selection function leads to biased estimates of cosmological parameters. The fact that SZ catalogs are not flux limited complicates survey ``calibration'' by requiring more detailed information on the relation between cluster observables and cluster mass.Comment: Accepted for publication in Astronomy & Astrophysics, 11 pages, 7 figure

Spacetime algebraic skeleton

The cosmological constant Lambda, which has seemingly dominated the primaeval Universe evolution and to which recent data attribute a significant present-time value, is shown to have an algebraic content: it is essentially an eigenvalue of a Casimir invariant of the Lorentz group which acts on every tangent space. This is found in the context of de Sitter spacetimes but, as every spacetime is a 4-manifold with Minkowski tangent spaces, the result suggests the existence of a "skeleton" algebraic structure underlying the geometry of general physical spacetimes. Different spacetimes come from the "fleshening" of that structure by different tetrad fields. Tetrad fields, which provide the interface between spacetime proper and its tangent spaces, exhibit to the most the fundamental role of the Lorentz group in Riemannian spacetimes, a role which is obscured in the more usual metric formalism.Comment: 13 page

An Approximation to the Likelihood Function for Band-Power Estimates of CMB Anisotropies

Band-power estimates of cosmic microwave background fluctuations are now routinely used to place constraints on cosmological parameters. For this to be done in a rigorous fashion, the full likelihood function of band-power estimates must be employed. Even for Gaussian theories, this likelihood function is not itself Gaussian, for the simple reason that band-powers measure the {\em variance} of the random sky fluctuations. In the context of Gaussian sky fluctuations, we use an ideal situation to motivate a general form for the full likelihood function from a given experiment. This form contains only two free parameters, which can be determined if the 68% and 95% confidence intervals of the true likelihood function are known. The ansatz works remarkably well when compared to the complete likelihood function for a number of experiments. For application of this kind of approach, we suggest that in the future both 68% and 95% (and perhaps also the 99.7%) confidence intervals be given when reporting experimental results.Comment: Published versio