shocking, as discussed in the introduction.These effects, properly taken into account in our model, explain the different results we obtain.

Equation \[eq:mia\], generated from our semi-analytical model, gives the difference between the equivalent of DM and enhanced SPH runs, and therefore the corrections to apply to satellites in N-body simulations to take account of the missing piece of baryonic physics.

In the case of $v_{infall}={\rm 30km/s}$, the Z12 correction gives $\Delta(v_{1kpc})=5.74$, while ours gives $\Delta(v_{1kpc})=8.7$. The difference between the two $\Delta(v_{1kpc})$ is due to the different models used to produce the pre-infall flattening of the satellites density profile and the tidal heating of subhaloes (Gnedin et al. 1999; Mayer et al. 2001; D’Onghia et al. 2010b; Kazantzidis et al. 2011).

Indeed, as stated, in Z12 the pre-infall flattening is due to SF, while in our case it is connected to DF. As shown by Cole et al. (2011), DF on infalling clumps is a very efficient mechanism in flattening the DM profile. On one hand, a clump having a mass of 1% of the halo mass can give rise to a core from a cuspy profile, removing twice its mass from the inner part of the halo. On another hand, 