that are tidally disrupted by fixing a destruction criterion (e.g., mass lost). For satellites from N-body simulations, such as the VL2, inner slopes are expected at $\gamma\simeq1$, as found in B13. Consequently, we fix for them $\zeta=0.40$ and $\eta=0.30$ in Eq. (\[eq:pe\]). The fit (\[eq:pe\]) enables to calculate the mass loss from VL2 satellites’ velocities at infall and z=0 together with the infall mass. The velocity of VL2 satellites in the simulation at infall time, $v_{\rm c,VL2,infall}$, is modified with Phase 1 correction, $\Delta v_{{\rm c,infall}}$, to account for baryon flattening, yielding $v_{{\rm max,infall}}=v_{\rm c,VL2,infall}+\Delta v_{{\rm c,infall}}$. Using the correction from Eq. \[eq:mia\], the velocity of VL2 satellites in the simulation at present $v_{\rm c,VL2,z0}$ is modified into $v_{{\rm max,z0}}=v_{\rm c,VL2,z0}+\Delta v_{{\rm c}}$. The infall mass is directly obtained from the simulation $M_{\rm vir,infall}=M_{\rm sat,VL2}$.

As for the destruction criteria, we fix it similarly to B13, as follows. Tides affect much more cored, for which $\gamma=0$, than cuspy satellites (with $\gamma=1$). Governato et al. (2012) found that satellites having a stellar mass $>10^{7}M_{\odot}$, corresponding to $v_{{\rm infall}}>30$ km/s, are cored, the opposite denoting a cusp. Here we assume, as B13 for our cuspy host with a disk and based on 