Dynamical mass estimation of a galaxy cluster using the Virial Theorem and emerging techniques

Abstract

We estimate the dynamical mass of a Sloan Digital Sky Survey cluster using three techniques: (i) the classical virial theorem, (ii) a recent velocity–dispersion–mass scaling relation, and (iii) the caustic estimator based on the escape envelope in phase space. From a sample of 92 galaxies, we computed line-of-sight velocities and projected distances. Bootstrap resampling was implemented to assess stability, bias, and variance, and performance was quantified using mean absolute error, root-mean-square error, and confusion matrices. The virial approach yields ∼ 3.6 × 10¹⁵, M_⊙; the scaling relation predicts ∼ 8.6 × 10¹⁵, M_⊙; the caustic method gives ∼ 8.9 × 10¹⁴, M_⊙. The metrics indicate that the caustic shows smaller relative deviations from the virial, although all approaches exhibit substantial dispersion and sensitivity to sample size. The physical implications of the discrepancies, potential sources of bias (anisotropies, interlopers, non-equilibrium), and the need for cross-calibration with weak lenses and X-rays are discussed. We conclude that combining classical and emerging estimators improves robustness and delineates a path to hierarchical Bayesian inference in forthcoming spectroscopic catalogs based on SDSS and complementary next-generation surveys in the optical and near-infrared bands, enabling tighter scaling-relation calibrations and reducing systematic mass-bias uncertainties overall.