  The connection between galaxies and their dark matter haloes is often
described with the Stellar-to-Halo Mass relation (SHMR). Satellite galaxies in
clusters have been shown to follow a SHMR distinct from central galaxies
because of the environmental processes that they are subject to. In addition,
the variety of accretion histories leads to an important scatter in this
relation, even more for satellites than for central galaxies. In this work, we
use the hydrodynamical simulation IllustrisTNG to study the scatter in the
satellite galaxy SHMR, and extract the parameters that can best allow to
understand it. Active galaxies, that represent a very small fraction of cluster
galaxies, follow a very different relation than their passive counterparts,
mainly because they were accreted much more recently. For this latter
population, we find that the distance to the cluster centre is a good predictor
of variations in the SHMR, but some information on the galaxy orbital history,
such as the distance of closest approach to the host centre, is an even better
one, although it is in practice more difficult to measure. In addition, we
found that galaxy compactness is also correlated with the SHMR, while the host
cluster properties (mass and concentration, formation redshift, mass and size
of BCG) do not play a significant role. We provide accurate fitting functions
and scaling relations to the scientific community, useful to predict the
subhalo mass given a set of observable parameters. Finally, we connect the
scatter in the SHMR to the physical processes affecting galaxies in clusters,
and how they impact the different satellite sub-populations.
