Variegate galaxy cluster gas content: Mean fraction, scatter, selection
  effects and covariance with X-ray luminosity
  We use a cluster sample selected independently of the intracluster medium
content with reliable masses to measure the mean gas mass fraction and its
scatter, the biases of the X-ray selection on gas mass fraction, and the
covariance between the X-ray luminosity and gas mass. The sample is formed by
34 galaxy clusters in the nearby ($0.050<z<0.135$) Universe, mostly with
$14<\log M_{500}/M_\odot \lesssim 14.5$, and with masses calculated with the
caustic technique. First, we found that integrated gas density profiles have
similar shapes, extending earlier results based on subpopulations of clusters
such as those that are relaxed or X-ray bright for their mass. Second, the
X-ray unbiased selection of our sample allows us to unveil a variegate
population of clusters; the gas mass fraction shows a scatter of $0.17\pm0.04$
dex, possibly indicating a quite variable amount of feedback from cluster to
cluster, which is larger than is found in previous samples targeting
subpopulations of galaxy clusters, such as relaxed or X-ray bright clusters.
The similarity of the gas density profiles induces an almost scatterless
relation between X-ray luminosity, gas mass, and halo mass, and modulates
selection effects in the halo gas mass fraction: gas-rich clusters are
preferentially included in X-ray selected samples. The almost scatterless
relation also fixes the relative scatters and slopes of the $L_X-M$ and
$M_{gas}-M$ relations and makes core-excised X-ray luminosities and gas masses
fully covariant. Therefore, cosmological or astrophysical studies involving
X-ray or SZ selected samples need to account for both selection effects and
covariance of the studied quantities with X-ray luminosity/SZ strength.
