Fig. 2 in P10, that cored satellites, having $v_{{\rm infall}}>30$ km/s, are disrupted if they loose $>90\%$ of their mass after infall and pass at a distance $<20$ kpc from the host galaxy centre. In the cases $v_{{\rm infall}}<30$ km/s (cuspy satellite), or cored satellites with pericenters $>20$ kpc, the halo is fully stripped off only if it loose 97% of its mass (Wetzel & White 2010).

Summarising, all the VL2 satellites loosing more than 97% mass ($x=0.03$), or loosing more than 90% mass, combined with $v_{{\rm infall}}>30$ km/s and a pericentric passages $<20 kpc$, are considered to be destroyed.

The second correction is the suppression of star formation by photo-heating, obtained from the Okamoto et al. (2008) results. In their paper, a uniform ionising background is assumed, for which He II reionization happens at $z=3.5$, while it occurs at $z=9$ for H and He I. They found the value of the typical halo mass retaining 50% of $f_{b}$: $M_{t}(z)$. This mass can be converted into a typical velocity, $v_{t}(z)$[^9]. Thus, if a VL2 subhalo has a larger peak velocity, $v_{{\rm peak}}>v_{t}$[^10], it is considered to contain enough baryons to make it luminous.

The last step consists in assigning a 