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An X-ray survey with the XMM-Newton telescope, XMM-XXL, has identifiedhundreds of galaxy groups and clusters in two 25 deg$^2$ fields. Combiningspectroscopic and X-ray observations in one field, we determine how the kineticenergy of galaxies scales with hot gas temperature and also, by imposing priorconstraints on the relative energies of galaxies and dark matter, infer apower-law scaling of total mass with temperature. Our goals are: i) todetermine parameters of the scaling between galaxy velocity dispersion andX-ray temperature, $T_{\rm 300kpc}$, for the halos hosting XXL-selectedclusters, and; ii) to infer the log-mean scaling of total halo mass withtemperature, $\langle \ln M_{200} \, | \, T, z \rangle$. We apply an ensemblevelocity likelihood to a sample of $> 1500$ spectroscopic redshifts within$132$ spectroscopically confirmed clusters with redshifts $z < 0.6$ to model,$\langle \ln \sigma_{\rm gal}\,|\,T,z\rangle$, where $\sigma_{\rm gal}$ is thevelocity dispersion of XXL cluster member galaxies and $T$ is a 300 kpcaperture temperature. To infer total halo mass we use a precise virial relationfor massive halos calibrated by N-body simulations along with a single degreeof freedom summarizing galaxy velocity bias with respect to dark matter. Forthe XXL-N cluster sample, we find $\sigma_{\rm gal} \propto T^{0.63\pm0.05}$, aslope significantly steeper than the self-similar expectation of $0.5$.Assuming scale-independent galaxy velocity bias, we infer a mean logarithmicmass at a given X-ray temperature and redshift, $\langle\ln (E(z)M_{200}/10^{14}\,{\rm M}_{\odot})|T,z\rangle=\pi+\alpha \ln(T/T_p )+\beta\ln(E(z)/E(z_p) )$ using pivot values ${\rm k}T_{p}=2.2\,{\rm keV}$ and$z_p=0.25$, with normalization $\pi=0.45\pm0.24$ and slope$\alpha=1.89\pm0.15$. We obtain only weak constraints on redshift evolution,$\beta=-1.29\pm1.14$.

The XXL Survey: XXIII. The Mass Scale of XXL Clusters from Ensemble Spectroscopy