Volume 536, December 2011
|Number of page(s)||36|
|Section||Cosmology (including clusters of galaxies)|
|Published online||16 December 2011|
Covariance matrices for halo number counts and correlation functions⋆
1 Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France
2 Laboratoire AIM, CEA/DSM/IRFU/Sap, CEA Saclay, 91191 Gif-sur-Yvette, France
3 Argelander-Institut für Astronomie, University of Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
Received: 20 April 2011
Accepted: 20 September 2011
Aims. We study the mean number counts and two-point correlation functions, along with their covariance matrices, of cosmological surveys such as for clusters. In particular, we consider correlation functions averaged over finite redshift intervals, which are well suited to cluster surveys or populations of rare objects, where one needs to integrate over nonzero redshift bins to accumulate enough statistics.
Methods. We develop an analytical formalism to obtain explicit expressions of all contributions to these means and covariance matrices, taking into account both shot-noise and sample-variance effects. We compute low-order as well as high-order (including non-Gaussian) terms.
Results. We derive expressions for the number counts per redshift bins both for the general case and for the small window approximation. We estimate the range of validity of Limber’s approximation and the amount of correlation between different redshift bins. We also obtain explicit expressions for the integrated 3D correlation function and the 2D angular correlation. We compare the relative importance of shot-noise and sample-variance contributions, and of low-order and high-order terms. We check the validity of our analytical results through a comparison with the Horizon full-sky numerical simulations, and we obtain forecasts for several future cluster surveys.
Key words: cosmology: observations / large-scale structure of Universe / galaxies: clusters: general
Appendices are only available in electronic form at http://www.aanda.org
© ESO, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.