Galaxy cluster virial quantities from extrapolating strong lensing mass profiles

We study the radial total mass profiles of nine massive galaxy clusters ($M_\mathrm{200c}>5\times10^{14}$ M$_\odot$) in the redshift range $0.2 < z < 0.9$. These clusters were observed as part of the CLASH, HFF, BUFFALO, and CLASH-VLT programs, that provided high-quality photometric and spectroscopic data. Additional high-resolution spectroscopic data were obtained with MUSE at the VLT. Our research is based on strong lensing analyses that rely on these measurements. From these data, we measure the projected total mass profiles of each galaxy cluster in our sample. We fit these mass profiles with one-component, spherically symmetric mass models including the Navarro-Frenk-White (NFW), non-singular isothermal sphere, beta model, and Hernquist profiles. We perform a Bayesian analysis to sample the posterior probability distributions of the free parameters of the models. We find that the NFW, Hernquist, and beta models are the most suitable profiles to fit the measured projected cluster total mass profiles. Moreover, we test the robustness of our results in a twofold way: we slightly modify the center of the projected mass profiles and the radial range of the considered region. We employ the results obtained with the Hernquist profile to compare our total mass estimates ($M_\mathrm{H}^\mathrm{tot} = M_\mathrm{H} (r\rightarrow + \infty)$), with the $M_\mathrm{200c}$ values from weak lensing studies. Through this analysis, we find scaling relations between $M_\mathrm{H}^\mathrm{tot}$ and $M_\mathrm{200c}$ and the value of the scale radius, $r_\mathrm{S}$, and $R_\mathrm{200c}$. Interestingly, we also find that the $M_\mathrm{200c}$ values, obtained by extrapolating the fitted total mass profiles, are very close to the weak lensing results. This feature can be exploited in future studies on clusters and cosmology, as it provides an easy way to infer galaxy cluster virial masses.