Mass Estimation of Clusters with Unseen Mass

Abstract

Unseen mass can bias cluster mass estimates using the virial theorem, as implied by Limber’s (1959) modification of the virial theorem and confirmed by the author (Smith 1980) using N-body experiments. The virial mass M_V becomes

$$\text{M}_\text{v} \text{ = M}_\text{G} \left( {\text{1 + K}_\text{2} \frac{{\text{M}_\text{B} }}{{\text{M}_\text{G} }}} \right)$$

where M_G is the mass of visible matter (e.g., galaxies) and M_B is the mass of background (unseen) matter. The factor K₂ depends on the distributions of galaxies and background; if they are the same K₂ has the value unity, whereas if the background is more centrally concentrated than the galaxies K₂>1.