The generalized scaling relations for X-ray galaxy clusters: the most
  powerful mass proxy
  The application to observational data of the generalized scaling relations
(gSR) presented in Ettori et al. (2012) is here discussed. We extend further
the formalism of the gSR in the self-similar model for X-ray galaxy clusters,
showing that for a generic relation M_tot ~ L^a M_g^b T^c, where L, M_g and T
are the gas luminosity, mass and temperature, respectively, the values of the
slopes lay in the plane 4*a+3*b+2*c=3. Using published dataset, we show that
some projections of the gSR are the most efficient relations, holding among
observed physical X-ray quantities, to recover the cluster mass. This
conclusion is based on the evidence that they provide the lowest chi^2, the
lowest total scatter and the lowest intrinsic scatter among the studied scaling
laws on both galaxy group and cluster mass scales. By the application of the
gSR, the intrinsic scatter is reduced in all the cases down to a relative error
on M_tot below 16 per cent. The best-fit relations are: M_tot ~ M_g^a
T^{1.5-1.5a}, with a~0.4, and M_tot ~ L^a T^{1.5-2a}, with a~0.15. As a by
product of this study, we provide the estimates of the gravitating mass at
Delta=500 for 120 objects (50 from the Mahdavi et al. 2013 sample, 16 from
Maughan 2012; 31 from Pratt et al. 2009; 23 from Sun et al. 2009), 114 of which
are unique entries. The typical relative error in the mass provided from the
gSR only (i.e. not propagating any uncertainty associated with the observed
quantities) ranges between 3-5 per cent on cluster scale and is about 10 per
cent for galaxy groups. With respect to the hydrostatic values used to
calibrate the gSR, the masses are recovered with deviations in the order of 10
per cent due to the different mix of relaxed/disturbed objects present in the
considered samples. In the extreme case of a gSR calibrated with relaxed
systems, the hydrostatic mass in disturbed objects is over-estimated by about
20 per cent.
