also take into account the contribution from the gas when calculating the total mass. It is related to the scale radius by $$r_{\rmn{s}} = {r_\rmn{DM}\over c_\rmn{DM}},$$ where $c_\rmn{DM}$ is known as the DM concentration parameter. This is related to the DM density contrast [@Navarro:1996] by $$\delta_{\rmn{c}} = {200\over3}{c_\rmn{DM}^3\over[\ln(1 + c_\rmn{DM}) -
    c_\rmn{DM}/(1 + c_\rmn{DM})]}.$$ The DM density becomes increasingly large at small radii, and is unbounded at the centre of the cluster. However the enclosed DM mass is calculated by integrating this density over volume and this converges at the origin. The enclosed DM mass is given by the following expression $$M_\rmn{DM}(<r) =
  4\pi\delta_{\rmn{c}}\rho_{\rmn{crit}}r_\rmn{s}^3\left[\ln\left({r_\rmn{s}
        + r\over r_\rmn{s}}\right) - \left({r\over r_\rmn{s} +
        r}\right)\right].$$ Therefore the DM mass distribution in the cluster is defined by the two parameters $c_\rmn{DM}$ and $r_\rmn{DM}$.

### The Entropy

In order to derive the electron pressure, and hence the thermal SZ decrement, a physical quantity is required that describes the gaseous properties in a similar way for all clusters. The cluster entropy is expected to behave in a self-similar way for reasonably massive clusters, differing primarily in the cluster cores due to the injection of non-gravitational thermal energy. The electron pressure and entropy observable [@Ponman:1999; @Lloyd-Davies:2000] are 