= Solution
The three probes constrain the same deep gravitational potential by different observations. A large member-galaxy <velocity dispersion> requires a large binding mass. Applying the <virial theorem>, with a gravitational scale radius $R$ and approximately isotropic orbits, gives a <cluster velocity-dispersion mass estimate> of order $M\sim R\sigma_v^2/G$, with a profile-dependent numerical coefficient. The inferred <mass-to-light ratio> is much larger than the stellar value. Membership, orbital anisotropy and equilibrium assumptions affect the precision.
The hot <intracluster medium> radiates through <thermal bremsstrahlung> and line emission. Its X-ray spectrum measures <temperature>, while its surface brightness constrains gas density. Confining this gas requires a potential with characteristic $GM/R\sim k_BT/(\mu m_p)$. Combining resolved profiles through the <cluster hydrostatic mass estimator> gives the total mass, not just the gas mass. The detected gas contributes substantial baryonic mass but does not normally account for the full gravitating mass. Nonthermal pressure or a merging cluster can invalidate a purely thermal <hydrostatic equilibrium> estimate.
Finally, <gravitational lensing> measures mass through light deflection. <Strong gravitational lensing> supplies multiple images and arcs; <weak gravitational lensing> measures coherent background-image distortion over larger radii. The <lensing convergence> is projected <surface mass density> divided by the critical surface density, irrespective of whether the material emits light. <Cluster gravitational-lensing mass estimates> agree broadly with the high masses implied by galaxy motions and hot gas, while having different equilibrium assumptions. Together these observations support a dominant nonluminous component in <galaxy clusters>, after accounting for their stars and observed gas.
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