Tracking the orbit of unresolved subhaloes for semi-analytic models

We present a model to track the orbital evolution of 'unresolved subhaloes' (USHs) in cosmological simulations. USHs are subhaloes that are no longer distinguished by halo finders as self-bound overdensities within their larger host system due to limited mass resolution. These subhaloes would host 'orphan galaxies' in semi-analytic models of galaxy formation and evolution (SAMs). Predicting the evolution of the phase-space components of USHs is crucial for the adequate modelling of environmental processes, interactions, and mergers implemented in SAMs that affect the baryonic properties of orphan satellites. Our model takes into account dynamical friction drag, mass-loss by tidal stripping and merger with the host halo, involving three free parameters. To calibrate this model, we consider two DM-only simulations of different mass resolution (MultiDark simulations). The simulation with higher mass resolution (smdpl; $m_{\rm DM} = 9.6 \times 10^7\, h^{-1}\, \mathrm{M_{\odot }}$) provides information about subhaloes that are not resolved in the lower mass resolution one (mdpl2; $m_{\rm DM} = 1.5 \times 10^9\, h^{-1}\, \mathrm{M_{\odot }}$); the orbit of those USHs is tracked by our model. We use as constraining functions the subhalo mass function (SHMF) and the two-point correlation function (2PCF) obtained from smdpl, being the latter a novel aspect of our approach. While the SHMF fails to put tight constraints on the efficiency of dynamical friction and the merger condition, the addition of clustering information helps us to specify the parameters of the model related to the spatial distribution of subhaloes. Our model allows to achieve good convergence between the results of simulations of different mass resolution, with a precision better than 10 per cent for both SHMF and 2PCF.