Mapping substructure in the HST Frontier Fields cluster lenses and in
  cosmological simulations
  We map the lensing-inferred substructure in the first three clusters observed
by the Hubble Space Telescope Frontier Fields Initiative (HSTFF): Abell 2744 (z
= 0.308), MACSJ0416, (z = 0.396) and MACSJ1149 (z = 0.543). Statistically
resolving dark-matter subhaloes down to ~10^{9.5} solar masses, we compare the
derived subhalo mass functions (SHMFs) to theoretical predictions from
analytical models and with numerical simulations in a Lambda Cold Dark Matter
(LCDM) cosmology. Mimicking our observational cluster member selection criteria
in the HSTFF, we report excellent agreement in both amplitude and shape of the
SHMF over four decades in subhalo mass (10^{9-13} solar masses). Projection
effects do not appear to introduce significant errors in the determination of
SHMFs from simulations. We do not find evidence for a substructure crisis,
analogous to the missing satellite problem in the Local Group, on cluster
scales, but rather excellent agreement of the count-matched HSTFF SHMF down to
M_{sub halo}/M_{halo} ~ 10^{-5}. However, we do find discrepancies in the
radial distribution of sub haloes inferred from HSTFF cluster lenses compared
to determinations from simulated clusters. This suggests that although the
selected simulated clusters match the HSTFF sample in mass, they do not
adequately capture the dynamical properties and complex merging morphologies of
these observed cluster lenses. Therefore, HSTFF clusters are likely observed in
a transient evolutionary stage that is presently insufficiently sampled in
cosmological simulations. The abundance and mass function of dark matter
substructure in cluster lenses continues to offer an important test of the LCDM
paradigm, and at present we find no tension between model predictions and
observations.
