Models {#sec:dm}
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The determination of the gamma-ray flux from dark matter annihilation in clusters depends on both the dark matter density distribution in the specific object under consideration and on assumptions on the dark matter particle model. For definiteness, we again consider here the case of the Coma cluster, for which a detailed study of the dark matter density distribution was carried out in [@Colafrancesco:2005ji].

As far as the dark matter density distribution is concerned, we assume a Navarro, Frenk and White (NFW) profile [@nfw] for both the smooth component (with a scale radius $a$, to be defined in the Equations below) and for the radial distribution of substructure (with a biased scaling parameter $a^\prime\simeq7a$, as inferred from numerical simulations of e.g. [@Nagai:2004ac; @Diemand:2004kx][^2]. We adopt here the semi-analytic approach outlined in [@Colafrancesco:2005ji] to evaluate the contribution from the smooth host halo and from substructures. The relevant quantity for the computation of the dark matter annihilation signal is a number density of particle dark matter pairs, defined as: $$\label{eq:npair}
{\mathcal N}_{\rm pairs}(r) =\frac{\rho_{\rm m}^2}{2m^2_{\rm WIMP}}\Big(\frac{\left[\rho^\prime\  g(r/a)-f_s\ \tilde\rho_s\  g(r/a^\prime)\right]^2}{\rho_{\rm m}^2}+f_s\ \Delta^2 \frac{\tilde\rho_s\  g(r/a^\prime)}{\rho_{\rm m}}\Big).$$ In the Equation above, the first line represents the contribution from the smooth part of the 