the $(l,b)$-$r_{GC}$ plane with the LMCa debris. For the latter, the black histograms in Fig. \[fig:r\_vr\_each\_nov\] show their expected radial velocities for a Magellanic origin. We summarize these predictions in Table \[TabPropMot2\], together with uncertainties derived from the interquartile velocity range of the histograms in Fig. \[fig:r\_vr\_each\_nov\].

Probability of LMC association {#SecLMCProb}
------------------------------

The discussion of Figs.  \[fig:r\_vr\_each\_wv\] and  \[fig:r\_vr\_each\_nov\] suggests that, for each dwarf, the probability of prior LMC association scales with the total number of LMCa particles that match its sky position, distance, and radial velocity. We emphasize that these are not probabilities in the statistical “likelihood” sense, but nevertheless provide a simple way to rank order the dwarfs in terms of their potential association with the LMC and to weed out unrelated systems.

We adopt the following procedure, which attempts to quantify how likely the observed position (and velocity, when available) of a dwarf is, assuming LMCa membership. To this aim, we first compute, for each LMCa particle, the radius of a sphere, $r_{100p}$, that contains the $100$ nearest debris particles, and rank them by this metric[^3]. The smaller $r_{100p}$ the more closely associated a particle is to the stream, which suggests that we may use $r_{100p}$ 