agrees with the results of Inoue & Saitoh (2012). There, the addition of SF does not alter the outcome significantly. This phase is originally described in DP09.

2.  Then comes the second phase, when the satellite, no longer considered isolated, is now subject to the tidal field of the host halo, and finally accreted to it. The total central mass is further reduced by tidal stripping and heating. This can be expressed in terms of changes in the circular velocity, $v_{c}$, also proportional to the density. More precisely, we calculate the difference in circular velocity, at 1 kpc, between the DM-only (hereafter DMO) satellites and those containing also baryons (hereafter DMB satellites), $\Delta v_{{\rm c,1kpc}}=v_{{\rm c,DMO}}-v_{{\rm c,DMB}}$, and starting with the same DM content in our semi-analytical model.

    Then, the effects of baryon physics, that are not taken into account in N-body simulations and responsible of the flattening of the profile, are introduced in the VL2 simulation by correcting the central circular velocity of the satellites, calculating their mass loss and ascribing them stellar masses and luminosities.

In other words, we obtain an analytical correction, along a similar idea to Z12 but with a semi-analytical model, using tidal stripping and 