1. The problem statement, all variables and given/known data Determine the radial dependence of gas density for an isothermal cluster of galaxies with temperature T that has a total mass density profile given by the Navarro, Frenk, & White form: ρ(r) = ρcδc , (r/rs)(1 + r/rs)2 where ρc is the critical density, rs is a characteristic radius and δc is a dimensionless parameter. You should assume that the cluster is in hydrostatic equilibrium. 2. Relevant equations ρc = 3H2/8πG 3. The attempt at a solution I am a bit confused at how to start this problem. I am thinking that I need to take an integral where the bounds refer to the size of the radius of the cluster. However, I am not sure where to take this integral. I thought maybe I should use ρ=m/V and do m = ∫ 4∏r^2ρ(r) dr, but I am not sure why I would do that. It is more of a guess to get myself started. I am also confused where T comes in since it is mentioned in the problem. Any hints to get me started in the right direction wold be very much appreciated.