The Contribution of Halos with Different Mass Ratios to the Overall
  Growth of Cluster-Sized Halos
  We provide a new observational test for a key prediction of the \Lambda CDM
cosmological model: the contributions of mergers with different
halo-to-main-cluster mass ratios to cluster-sized halo growth. We perform this
test by dynamically analyzing seven galaxy clusters, spanning the redshift
range $0.13 < z_c < 0.45$ and caustic mass range $0.4-1.5$ $10^{15}
h_{0.73}^{-1}$ M$_{\odot}$, with an average of 293 spectroscopically-confirmed
bound galaxies to each cluster. The large radial coverage (a few virial radii),
which covers the whole infall region, with a high number of spectroscopically
identified galaxies enables this new study. For each cluster, we identify bound
galaxies. Out of these galaxies, we identify infalling and accreted halos and
estimate their masses and their dynamical states. Using the estimated masses,
we derive the contribution of different mass ratios to cluster-sized halo
growth. For mass ratios between ~0.2 and ~0.7, we find a ~1 $\sigma$ agreement
with \Lambda CDM expectations based on the Millennium simulations I and II. At
low mass ratios, $\lesssim 0.2$, our derived contribution is underestimated
since the detection efficiency decreases at low masses, $\sim 2 \times 10^{14}$
$h_{0.73}^{-1}$ M$_{\odot}$. At large mass ratios, $\gtrsim 0.7$, we do not
detect halos probably because our sample, which was chosen to be quite X-ray
relaxed, is biased against large mass ratios. Therefore, at large mass ratios,
the derived contribution is also underestimated.
