in the notation of @Springel2008a, which has a mass per particle $m_p=4.9 \times 10^4 M_\odot$. We identify and follow all particles that were associated with the LMCa friends-of-friends group at the time of infall, and evaluate their positions and velocities at the time of first and second pericenter passages.

Using [subfind]{} [@Springel2001a], we have identified more than 200 subhalos associated with LMCa at infall time (see Fig. 1 in S11 for their individual orbits), suggesting that a large satellite such as the LMC should bring along its own population of satellites [@Springel2008b]. We use for our analysis [*all*]{} particles (and not just the subhalos) initially bound to LMCa in order to provide a more complete sampling of the positions and velocities of any potential companion associated with the LMC.

LMCa in Galactic coordinates {#SecLMCaCoord}
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We transform the coordinate system of the simulation into “Galactic coordinates” by requiring that the orientation of the orbital angular momentum of LMCa coincides with that measured for the LMC’s orbit, and that its position on the sky coincides with the LMC. For consistency with S11, we use throughout this paper the LMC proper motion as given by K06[^2]. After the rotation, we also rescale 