of the FOF group). A Type 1 galaxy sits at the centre of one of the smaller non-dominant subhalos associated with a FOF group. Finally, a Type 2 galaxy is associated to a specific particle and no longer has an associated subhalo because the object within which it formed was tidally disrupted after accretion onto a larger halo. Such galaxies merge with the central galaxy of their new halo after waiting for a dynamical friction time.

Each galaxy in the catalogue has an associated “rotation velocity” $V_{max}$. This is the maximum of the circular velocity $V_c(r) =
(GM(r)/r)^{1/2}$ of its subhalo for Types 0 and 1; for Type 2 objects $V_{max}$ is frozen to its value at the latest time when the galaxy still occupied a subhalo. Type 0 and 1 galaxies also have an associated mass $M_{halo}$ which is the mass of the self-bound subhalo which surrounds them. Finally, halos of Type 0 galaxies have a conventional “virial mass” $M_{200}$, defined as the total mass within the largest sphere surrounding them with an enclosed mean density exceeding 200 times the critical value. Below we will consider both $M_{halo}$ and $M_{200}$ as possible definitions for the “true” masses of M31 