The characteristic velocities are measured inside ($\sigma_*$) and around ($v_{rot}$) the half-mass radius, which is defined for the whole 3D mass distribution.

Our classification scheme to decide whether or not the final remnant is a dSph is more stringent than the one used in ([@2011ApJ...726...98K];[@2013ApJ...764L..29K]). There two criteria were used simultaneously, namely that the object had to have $c/a > 0.5$ and $v_{rot} / \sigma_*  < 1$. With the latter criterion outliers from the typical structural properties of dSphs, such as the Tucana dSph, which has $v_{rot}/\sigma_* \sim 1$, would be included. Here instead we use only the criterion $v_{rot}/\sigma_* < 0.5$, which is indeed the case for nearly all observed dSphs and that, as we will see, automatically guarantees also that $c/a < 0.5$ in our simulated remnants at $z=0$. Finally, for brevity we will refer to “cored models” when we talk about the models with inner slope of the dark halo $\gamma=0.6$, and to “cuspy models” when we discuss models with an NFW profile.

Dimensions along the principal axes
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With the object aligned and principal axes identified three maps of the projected stellar mass corresponding to the three pairs of principal axes can be generated. Perpendicular to 