Likelihood Functions for Galaxy Cluster Surveys

TL;DR

This paper develops nearly exact likelihood functions for galaxy cluster surveys, leveraging their sparse sampling to improve cosmological parameter estimation, and validates these methods with simulation data.

Contribution

It introduces a novel approach to constructing likelihood functions for galaxy cluster surveys, simplifying analysis by exploiting their sparse sampling nature.

Findings

Likelihood functions are highly accurate for clusters above 10^{14}h^{-1} solar masses.

Method is validated with numerical simulations, showing precise probability distributions.

Applicable across different redshifts with adjustments for mass thresholds.

Abstract

Galaxy cluster surveys offer great promise for measuring cosmological parameters, but survey analysis methods have not been widely studied. Using methods developed decades ago for galaxy clustering studies, it is shown that nearly exact likelihood functions can be written down for galaxy cluster surveys. The sparse sampling of the density field by galaxy clusters allows simplifications that are not possible for galaxy surveys. An application to counts in cells is explicitly tested using cluster catalogs from numerical simulations and it is found that the calculated probability distributions are very accurate at masses above several times 10^{14}h^{-1} solar masses at z=0 and lower masses at higher redshift.