addition to tidal destruction, to get the correct number of luminous satellites.

In our model, the solution to the aforementioned problems is connected to the complex interaction between DM and baryons mediated by DF. Our study is similar to those of El-Zant et al. (2001, 2004), Romano-Diaz et al. (2008), Cole et al. (2011), in the sense that DF plays an important role. However, while previous studies considered one effect at a time (e.g., random angular momentum, angular momentum generated by tidal torques, adiabatic contraction, cooling, star formation), we consider the joint effect of all of them.

Indeed, here the dynamics of the satellites (i.e., the TBP model in Appendix \[Dynamics of the satellites\]) proceeds from two competing mechanisms: dynamical friction, inducing a decay of the satellites orbits, and tidal stripping and heating, reducing the bound mass of the satellite. This reduction causes a decrease in the frictional force, which produces in turn a slowing down of the orbital collapse. Massive and dense satellite are more subject to DF and sink fast towards the centre of the potential. Low-density satellites are more subject to stripping and fall slowly towards the centre. Mass loss and tidal heating depend primarily on the 