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

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.