,$$

where the cutoff parameter $\beta=0.5$ serves to insure that no subhalo was larger than half the present mass of the parent (otherwise it would, by definition, be the parent). The slope $\alpha=1.9$ is set to the same value as is generally found for the present day subhalo mass function in simulations (e.g., @gao [@jochen; @vdbshmf; @zentner; @laurie]). The normalization $A(M)=1/\beta[\Gamma(2-\alpha)-\Gamma(2-\alpha,1)]$ is set so that the total mass originally in subhaloes corresponds to the present day mass (where the integration is done to an upper limit of $0.5M$). This approximation potentially ignores the problem of total disruption of some of the merged subhaloes, as can occur for example in the case of major mergers, by assuming that all of these subhaloes are still present and that therefore the total fraction of mass originally in subhaloes is one. In @paper2, we showed that as long as this fraction is close to one, then the resulting mass luminosity relation is similar, with both number of satellites in a halo and their total luminosity decreasing slightly. From the study of simulation results it is still not completely clear how to treat this complex issue, and no simple analytical models are available, so we 