Scaling laws in X-ray galaxy clusters at redshift between 0.4 and 1.3

We present a study of the integrated physical properties of a sample of 28 X-ray galaxy clusters observed with Chandra  at a redshift between 0.4 and 1.3. In particular, we have twelve objects in the redshift range 0.4–0.6, five between 0.6 and 0.8, seven between 0.8 and 1 and four at $z>1.0$, compounding the largest sample available for such a study. We focus particularly on the properties and evolution of the X-ray scaling laws. We fit both a single and a double $\beta-$model with the former which provides a good representation of the observed surface brightness profiles, indicating that these clusters do not show any significant excess in their central brightness. By using the best-fit parameters of the $\beta-$model together with the measured emission-weighted temperature (in the range 3–11 keV), we recover gas luminosity, gas mass and total gravitating mass out to  R 500 . We observe scaling relations steeper than expected from the self-similar model by a significant (>$3 \sigma$) amount in the $L-T$ and $M_{\rm gas}-T$ relations and by a marginal value in the $M_{\rm tot}-T$ and $L-M_{\rm tot}$ relations. The degree of evolution of the $M_{\rm tot}-T$ relation is found to be consistent with the expectation based on the hydrostatic equilibrium for gas within virialized dark matter halos. We detect hints of negative evolution in the $L-T$, $M_{\rm gas}-T$ and $L-M_{\rm tot}$ relations, thus suggesting that systems at higher redshift have lower X-ray luminosity and gas mass for fixed temperature. In particular, when the 16 clusters at $z>0.6$ are considered, the evolution becomes more evident and its power-law modelization is a statistically good description of the data. In this subsample, we also find significant evidence for positive evolution, such as $(1\,+\,z)^{0.3}$, in the $E_z^{4/3} S - T$ relation, where the entropy  S is defined as $T/n_{\rm gas}^{2/3}$ and is measured at 0.1$\,R_{200}$. Such results point toward a scenario in which a relatively lower gas density is present in high-redshift objects, thus implying a suppressed X-ray emission, a smaller amount of gas mass and a higher entropy level. This represents a non-trivial constraint for models aiming at explaining the thermal history of the intra-cluster medium out to the highest redshift reached so far.