temperature. The observed X-ray surface brightness per unit energy $\rmn{d}E$ is given by the following expression $${\rmn{d}S_\rmn{X}\over \rmn{d}E} = {1\over 4\pi(1+z)^{3}}\int{n_\rmn{e}^{2}\tilde{\Lambda}(E',T_\rmn{e})\rmn{d}l},$$ where $z$ is the cluster redshift and $\tilde{\Lambda}(E',T_\rmn{e})$ is the X-ray spectral emissivity as a function of temperature and emitted energy, $E' = E(1+z)$. The surface brightness for a particular observer-frame energy band is then given by the equation $$\label{equation:xray_sb}
  S_\rmn{X}  = {1\over 4\pi(1+z)^{4}}\int{n_\rmn{e}^{2}\Lambda(T_\rmn{e})\rmn{d}l},$$ where $$\Lambda(T_\rmn{e}) = \int{\tilde{\Lambda}(E',T_\rmn{e})\rmn{d}E}.$$ In this work the emissivity values for every radial position in the cluster volume are interpolated from a look-up table of values, as a function of temperature and redshift, based upon the Raymond-Smith plasma model [@Raymond:1977] for an observer-frame energy range 0.5-2keV and a metallicity of $Z = 0.3\,Z_{\odot}$.

Combined observations of the SZ and X-ray surface brightness constrain the pressure and electron density of the ICM and hence provide constraints on all of the model parameters. The physical properties of the cluster, including the total mass and electron temperature, as a function of radius are constrained by the 6 parameters defined by this model: $c_\rmn{DM}$, $r_\rmn{DM}$, $n_\rmn{e0}$, $T_{e0}$, $r_\rmn{core}$ and $\alpha$.

Model Fitting {#section:model_fitting}
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Bayesian inference of the parameter values
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We fit parameterized models to the SZ and 