luminosity to the surviving satellites. We first need to allocate stellar masses to VL2 satellites via a relation between their $v_{\rm infall}$ and the stellar mass $M_\ast$.

To do so, we recycled the pairs of satellites considered in the determination of $\Delta v_{\rm c, 1kpc}$. DM-only subhaloes are usually associated with their DMB satellites at formation or accretion time (Bullock et al. 2000; Kravtsov et al. 2004; Strigari et al. 2007; Bovill & Ricotti 2011; Simha et al. 2012). Our semi analytical model simply creates a series of DMO, and a series of corresponding DMB haloes.

Fig. \[fig:vmax-M\] plots $v_{\rm infall}$ in terms of the stellar mass, $M_\ast$. The $v_{\rm infall}$-$M_\ast$ relation is obtained by fitting the data, yielding the relation[^11]

$$\frac{M_{\ast}}{M_{\odot}}=0.1 (\frac{v_{\rm infall}}{\rm kms^{-1}})^{5.5}.$$

Finally, we need to relate $M_\ast$ and the V-band magnitude, $M_{\rm V}$. We apply the relation from B13, extracted from Z12 simulations, $$\log_{10}(\frac{M_{\ast}}{M_{\odot}})=2.37-0.38 M_{\rm V}.$$

Results and discussion
======================

The result of the corrections discussed above are plotted in Fig. \[fig:correction\]. The top panel represents the raw results from VL2 at $z=0$. The bottom panel presents the results of applying the corrections discussed (heating, destruction, and velocity corrections) on the same satellites. The objects considered 