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

Context. An X-ray survey with the XMM-Newton telescope, XMM-XXL, has identified hundreds of galaxy groups and clusters in two 25 deg² fields. Combining spectroscopic and X-ray observations in one field, we determine how the kinetic energy of galaxies scales with hot gas temperature and also, by imposing prior constraints on the relative energies of galaxies and dark matter, infer a power-law scaling of total mass with temperature.
Aims: Our goals are: i) to determine parameters of the scaling between galaxy velocity dispersion and X-ray temperature, T_{300 kpc}, for the halos hosting XXL-selected clusters, and; ii) to infer the log-mean scaling of total halo mass with temperature, ⟨lnM₂₀₀ | T_{300 kpc}, z⟩.
Methods: We applied an ensemble velocity likelihood to a sample of >1500 spectroscopic redshifts within 132 spectroscopically confirmed clusters with redshifts z < 0.6 to model, ⟨lnσ_gal | T_{300 kpc}, z⟩, where σ_gal is the velocity dispersion of XXL cluster member galaxies and T_{300 kpc} is a 300 kpc aperture temperature. To infer total halo mass we used a precise virial relation for massive halos calibrated by N-body simulations along with a single degree of freedom summarising galaxy velocity bias with respect to dark matter.
Results: For the XXL-N cluster sample, we find σ_gal ∝ T_{300 kpc}^0.63±0.05, a slope significantly steeper than the self-similar expectation of 0.5. Assuming scale-independent galaxy velocity bias, we infer a mean logarithmic mass at a given X-ray temperature and redshift, <ln(E(z)M₂₀₀/10¹⁴ M_⊙)|T₃₀₀ kpc, z> = π_T + α_T ln (T₃₀₀ kpc/T_p) + β_T ln (E(z)/E(z_p)) using pivot values kT_p = 2.2 keV and z_p = 0.25, with normalization π_T = 0.45 ± 0.24 and slope α_T = 1.89 ± 0.15. We obtain only weak constraints on redshift evolution, β_T = -1.29 ± 1.14.
Conclusions: The ratio of specific energies in hot gas and galaxies is scale dependent. Ensemble spectroscopic analysis is a viable method to infer mean scaling relations, particularly for the numerous low mass systems with small numbers of spectroscopic members per system. Galaxy velocity bias is the dominant systematic uncertainty in dynamical mass estimates.

Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.