Measures of Galactic and Intergalactic Mass in Clusters

Abstract

If a galaxy cluster's X-ray gas distribution follows an isothermal polytropic β model, we may write the electron radial density distribution as; ne = ne0(1 + r2/rc2)–3/2β, rc being the core radius and ne0 the central electron density. This may be related to both an X-ray surface brightness distribution and a Sunyaev-Zel'dovich effect distribution (Sarazin 1986). Fitting to observational data then enables us to constrain the value of β. The normalisation value, ne0, to obtain a total mass estimate is calculated via the relationship between the X-ray and S-Z distribution normalisation constants, and the gas temperature and spectral emissivity parameters from fits to the X-ray spectrum. We are then in a position to evaluate ne(r) and its integral; the total electron gas mass. If we can further assume that there exists a simple ratio between the electron and proton number densities within the gas, we may straightforwardly posit a value for the total gas mass. An additional method of determining the polytropic gas index exists, with optical constraints on the galactic velocity dispersion, through the relation; β = μmHσz2/kBTe. Studies at optical, as well as X-ray and radio wavelengths are thus useful as a corroborative measure in determining the total gas mass.