Effects of Selection and Covariance on X-ray Scaling Relations of Galaxy Clusters

TL;DR

This paper investigates how selection biases and intrinsic covariance influence X-ray scaling relations in galaxy clusters, revealing that observed relations can be biased or degenerate with true evolution, especially in flux-limited samples.

Contribution

It develops models to quantify the effects of selection biases and covariance on galaxy cluster scaling relations, providing analytical expressions and insights into their impact.

Findings

Flux-limited samples can mimic evolution in scaling relations.

Deep surveys yield unbiased relations above certain mass thresholds.

Covariance affects the observed slope, scatter, and redshift evolution of relations.

Abstract

We explore how the behavior of galaxy cluster scaling relations are affected by flux-limited selection biases and intrinsic covariance among observable properties. Our models presume log-normal covariance between luminosity (L) and temperature (T) at fixed mass (M), centered on evolving, power-law mean relations as a function of host halo mass. Selection can mimic evolution; the \lm and \lt relations from shallow X-ray flux-limited samples will deviate from mass-limited expectations at nearly all scales while the relations from deep surveys ($10^{-14} \cgsflux$) become complete, and therefore unbiased, at masses above $\sims 2 \times 10^{14} \hinv \msol$. We derive expressions for low-order moments of the luminosity distribution at fixed temperature, and show that the slope and scatter of the \lt relation observed in flux-limited samples is sensitive to the assumed \lt correlation coefficient. In addition, \lt covariance affects the redshift behavior of halo counts and mean luminosity in a manner that is nearly degenerate with intrinsic population evolution.