In this section I will outline the method which is used to calculate the Hubble constant from radio and x-ray data. The above image illustrates the combination of radio and x-ray data. Countours indicate the negative intensity of the radio signal.
Colors indicate the x-ray intensity.
The radio data was obtained by Carlstrom and collaborators at BIMA . First, we will calculate the Compton y-parameter. We can do the line integral because of the assumptions we've made about the density and temperature profiles. We find that y only depends on n e,o r c , where n e,o is the central number density of the electron gas and r c is the core radius of the cluster. We can see from the figure in the derivation section of this site that the temperature decrement is roughly constant at low frequencies.