Effects of selection and covariance on X-ray scaling relations of galaxy clusters

We explore how the behaviour 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), centred on evolving, power-law mean relations as a function of host halo mass. Selection can mimic evolution; the L–M and L–T 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 erg s−1 cm−2) become complete, and therefore unbiased, at masses above ∼2 × 1014 h−1 M . We derive expressions for low-order moments of the luminosity distribution at fixed temperature, and show that the slope and scatter of the L–T relation observed in flux-limited samples is sensitive to the assumed L–T correlation coefficient. In addition, L–T covariance affects the redshift behaviour of halo counts and mean luminosity in a manner that is nearly degenerate with intrinsic population evolution.