electron density as a function of pressure and entropy can be expressed as $$n_\rmn{e} = (P_\rmn{e}/S_\rmn{e})^{3/5}.$$ The pressure as a function of radius can then be derived by substituting the above expression for $n_\rmn{e}$ into Equation\[equation:HE\] and rearranging to give $$\label{equation:pressure}
  P_\rmn{e}(r) = \left[P_\rmn{e0}^{2/5} - {2\over5}G\mu m_\rmn{p}\int_0^{r}{Mdr'\over
      S_\rmn{e}^{3/5}r'^2}\right]^{5/2},$$ where the central pressure, $P_\rmn{e0}$, is equal to the product of the central density and temperature. The integral in the above expression can be solved numerically so that the electron pressure is calculated as a function of radius. The total mass is calculated by summing the enclosed DM and baryonic masses (note that the fraction of mass contained in stellar material is considered insignificant) at each radius out from the centre of the cluster. A value of 1.16 is assumed for the ratio of baryons to electrons, in order to calculate the baryonic mass. The pressure is then integrated in shells from the cluster centre to the required radius.

SZ and X-ray Observables
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The SZ signal is a measure of the integrated line-of-sight electron pressure, and when integrated over the whole cluster is a measure of the total thermal energy. The observed change in CMB temperature as a result of the 