Tracking the orbit of unresolved subhalos 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
({\sc 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 ({\sc 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 {\sc 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 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.
