circular velocity, $\Delta(v_{1kpc})$, is larger in our model compared to Z12 and B13. In addition, in our case, some satellites are “overcorrected”: their corrected velocities are negative.

Similarly to B13, overcorrected haloes are part of a population that lost a great part of their mass after infall. At $z=0$, their circular velocity at 1 kpc, $v_{1kpc}$, is very low so the correction $\Delta(v_{1kpc})$ brings them to negative values. After infall, that population suffers mass loss larger than 99.9% and exhibit tidal radii $<1$ kpc. It can therefore be considered as a population of destroyed subhaloes.

It is interesting to note from Fig. \[fig:correction\] that the model obtains not only a reduction of the number of satellites, solving the MSP, but also a reduction of their central velocity, clearing up the TBTF problem.

In analogy with B13, UV heating and tidal destruction are necessary to reconcile the total number of luminous satellites with observations, while the Z12-type correction is necessary to reconcile the masses of the subhaloes with observations.

If the baryonic effects were not taken into account, a population would exist of satellites significantly more massive than those of the MW.

Finally, the effect of UV heating is required, in 