The Halo Mass-Temperature Relation for Clusters, Groups, and Galaxies

The halo mass-temperature relation for a sample of 216 galaxy clusters, groups, and individual galaxies observed by $Chandra$ X-ray Observatory is presented. Using accurate spectral measurements of their hot atmospheres, we derive the $M-T$ relation for systems with temperatures ranging between 0.4-15.0 keV. We measure the total mass of clusters, groups, and galaxies at radius $R_{2500}$, finding that the $M_{2500} \propto T^{\alpha}$ relation follows a power-law with $\alpha$ = 1.65$\pm$0.06. Our relation agrees with recent lensing studies of the $M-T$ relation at $R_{200}$ and is consistent with self-similar theoretical prediction and recent simulations. This agreement indicates that the $M-T$ relation is weakly affected by non-gravitational heating processes. Using lensing masses within $R_{200}$ we find $M_{200}-T$ follows a power-law with slope 1.61$\pm$0.19, consistent with the $M_{2500}-T$ relation. No evidence for a break or slope change is found in either relation. Potential biases associated with sample selection, evolution, and the assumption of hydrostatic equilibrium that may affect the scaling are examined. No significant impacts attributable to these biases are found. Non-cool-core clusters and early spirals produce higher scatter in the $M-T$ relation than cool-core clusters and elliptical galaxies.