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We aim at studying scaling relations of a small but well defined sample ofgalaxy clusters that includes the recently discovered class of objects that areX-ray faint for their mass. These clusters have an average low X-ray surfacebrightness, a low gas fraction and are under-represented (by a factor of 10) inX-ray surveys or entirely absent in SZ surveys. With the inclusion of theseobjects, we find that the temperature-mass relation has an unprecedented largescatter, 0.20+-0.03 dex at fixed mass, as wide as allowed by the temperaturerange, and the location of a cluster in this plane depends on its surfacebrightness. Clusters obey a relatively tight luminosity-temperature relationindependently of the their brightness. We interpret the wide difference inscatter around the two relations as due to the fact that X-ray luminosity andtemperature are dominated by photons coming from small radii (in particular forT we used a 300 kpc aperture radius) and strongly affected by gasthermodynamics (e.g. shocks, cool-cores), whereas mass is dominated by darkmatter 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 thecollinearity (degeneracy) between evolution and slope and from hypothesis onthe undetected population, that both affect the analysis of X-ray selectedsamples, and can therefore be profitably used both as reference and to breakthe above degeneracy of X-ray selected-samples.

Low X-ray surface brightness clusters: Implications on the scatter of the $M-T$ and $L-T$ relations