The Hubble Constant and X-rays from Galaxy Clusters

Abstract

X-RAY measurements and limits on the Coma and Virgo clusters of galaxies have been said to limit the mass of hot gas in them to 2% of the amount required for stabilization according to the virial theorem¹. Such a conclusion is strongly dependent on the value of the Hubble constant H₀. The linear diameter of the cluster D and the cluster mass M, estimated by the virial theorem, each vary as H₀⁻¹. Therefore, the density ρ has the dependence ρ∼H₀². The predicted X-ray flux F from this gas is ∼ρM/R², where R is the distance to the cluster. R varies as H₀⁻¹. We therefore have the relation Meekins et al.¹ appear to have used the value H₀ = 95 km s⁻¹ Mpc⁻¹ found by van den Bergh², because they took R= 70 Mpc. If Abell's value³H₀ = 47 is used, the predicted flux is reduced by a factor of 0.12. A reduction of H₀ to a value as low as 20 is not inconceivable. Although clumpiness increases F/M², the presence of helium as a mass fraction f reduces F for fixed M in the ratio (1–½f).