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Homework Statement
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.
Homework Equations
ρc = 3H2/8πG
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.