Low X-ray surface brightness clusters: Implications on the scatter of
  the $M-T$ and $L-T$ relations
  We aim at studying scaling relations of a small but well defined sample of
galaxy clusters that includes the recently discovered class of objects that are
X-ray faint for their mass. These clusters have an average low X-ray surface
brightness, a low gas fraction and are under-represented (by a factor of 10) in
X-ray surveys or entirely absent in SZ surveys. With the inclusion of these
objects, we find that the temperature-mass relation has an unprecedented large
scatter, 0.20+-0.03 dex at fixed mass, as wide as allowed by the temperature
range, and the location of a cluster in this plane depends on its surface
brightness. Clusters obey a relatively tight luminosity-temperature relation
independently of the their brightness. We interpret the wide difference in
scatter around the two relations as due to the fact that X-ray luminosity and
temperature are dominated by photons coming from small radii (in particular for
T we used a 300 kpc aperture radius) and strongly affected by gas
thermodynamics (e.g. shocks, cool-cores), whereas mass is dominated by dark
matter at large radii. We measure a slope of 2.0+-0.2 for the L500-T relation.
Given the characteristics of our sample, this value is free from the
collinearity (degeneracy) between evolution and slope and from hypothesis on
the undetected population, that both affect the analysis of X-ray selected
samples, and can therefore be profitably used both as reference and to break
the above degeneracy of X-ray selected-samples.
