Isothermal cooling flows

Details of the solution are derived for a steady, self‐similar, comoving, isothermal cooling flow. The distribution of gas phases can be expressed in terms of the mass flow function, Ṁ( r, T ), which gives the mass per unit time of gas hotter than temperature T flowing into a sphere of radius r . Self‐similarity allows this to be separated as Ṁ( r, T ) =Ṁ (r) g (T) , where Ṁ (r) is the usual mass flow rate and g(T) is a dimensionless function expressing the distribution of the phases. It is shown that, for Ṁ (r)∝r η , where T m is the maximum temperature of the hot gas. In the units used here, the corresponding solution for the differential emission measure from within a sphere of radius r is where Ṁ=Ṁ (r) is the total mass flow rate into the sphere.