Mass constraints from multiphase cooling flow models

I review the multiphase cooling flow equations that reduce to a relatively simple form for a wide class of self-similar density distributions described by the single parameter, k , first introduced by Nulsen. It is shown that steady-state cooling flows are not consistent with all possible emissivity profiles, which can therefore be used as a test of the theory. In combination, they provide strong constraints on the temperature profile and mass distribution within the cooling radius. The model is applied to ROSAT HRI data for three rich clusters. At one extreme ( K  ∼ 1) these show evidence for cores in the mass distribution of size 110–140 h ⁻¹₅₀ kpc and have temperatures that decline towards the flow centre. At the other ( k ∈ ∞), the mass density and gas temperature both rise sharply towards the flow centre. The former are more consistent with observations which usually show a lower emission-weighted temperature within the cooling flow than from the cluster as a whole. The requirement that the solutions have a temperature gradient that is non-increasing towards the cluster centre limits the matter density gradient to be shallower than ρ_grav ∝∼  r ^−1.2 in the cluster core.