  X-ray selected samples are known to miss galaxy clusters that are gas poor
and have a low surface brightness. This is different for the optically selected
samples such as the X-ray Unbiased Selected Sample (XUCS). We characterise the
origin of galaxy clusters that are gas poor and have a low surface-brightness
by studying covariances between various cluster properties at fixed mass using
hydrodynamic cosmological simulations. We extracted approx. 1800 galaxy
clusters from a high-resolution Magneticum hydrodynamic cosmological simulation
and computed covariances at fixed mass of the following properties:
core-excised X-ray luminosity, gas fraction, hot gas temperature, formation
redshift, concentration, galaxy richness, fossilness parameter, and stellar
mass of the bright central galaxy. We also compared the correlation between
concentration and gas fractions in non-radiative simulations, and we followed
the trajectories of particles inside galaxy clusters to assess the role of AGN
depletion on the gas fraction. In simulations and in observational data,
differences in surface brightness are related to differences in gas fraction.
Simulations show that the gas fraction strongly correlates with assembly time,
in the sense that older clusters are gas poor. Clusters that formed earlier
have lower gas fractions because the feedback of the active galactic nucleus
ejected a significant amount of gas from the halo. When the X-ray luminosity is
corrected for the gas fraction, it shows little or no covariance with other
quantities. Older galaxy clusters tend to be gas poor and possess a low X-ray
surface brightness because the feedback mechanism removes a significant
fraction of gas from these objects. Moreover, we found that most of the $L_X$
covariance with the other quantities is explained by differences in the gas
fraction.
