SIMBAD references

The application to observational data of the generalized scaling relations (gSRs) 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^α M_g^β T^γ, where L, Mg and T are the gas luminosity, mass and temperature, respectively, the values of the slopes lay in the plane 4α + 3β + 2γ = 3. Using published data set, we show that some projections of the gSR are the most efficient relations, holding among observed physical quantities in the X-ray band, to recover the cluster gravitating mass. This conclusion is based on the evidence that they provide the lowest χ2, 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 the reconstructed mass below 16 percent. The best-fitting relations are M_tot ∝M_g^a T^1.5-1.5 a, with a ~ 0.4, and Mtot ∝ LaT1.5 - 2a, with a ~ 0.15. As by-product of this study, we provide the estimates of the gravitating mass at Δ = 500 for 120 objects (50 from the Mahdavi et al. sample, 16 from Maughan sample; 31 from Pratt et al. sample; 23 from Sun et al. sample), 114 of which are unique entries. The typical relative error on the mass provided from the gSR only (i.e. not propagating any uncertainty associated with the observed quantities) ranges between 3 and 5 percent on cluster scale and is about 10 percent for galaxy groups. With respect to the hydrostatic values used to calibrate the gSR, the masses are recovered with deviations of the order of 10 percent 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 overestimated by about 20 percent.