Comparisons of Cluster Mass Determinations by X-ray Observations and Gravitational Lensing

Gravitational lensing by clusters of galaxies has been detected on scales ranging from $\sim10^{-1}$ Mpc to $\sim10$ Mpc, namely, arcs/arclets, weak lensing and quasar-cluster associations. This allows us to derive an overall radius matter distribution of clusters of galaxies. While the dynamical analysis of the X-ray observations has yielded a great number of data for the virial cluster masses, it becomes possible to statistically compare the cluster mass determinations by these two independent methods. In this letter we show that as compared with gravitational lensing, the dynamical analysis under the assumption of isothermal and hydrostatic equilibrium has systematically underestimated the cluster masses inside the Abell radius by a factor of $\sim2$ with scatter between $0.7$ and $5$. Because the same correction factor should be applicable to the gas baryon fraction of clusters of galaxies obtained from the X-ray data, it is probably too premature to claim a baryon crisis in today's cosmology.