The Effects of $\Lambda$CDM Dark Matter Substructure on the Orbital
  Evolution of Star Clusters
  We present a comprehensive study on how perturbations due to a distribution
of $\Lambda$CDM dark matter subhalos can lead to star clusters deviating from
their orbits. Through a large suite of massless test particle simulations, we
find that (1) subhalos with masses less than $10^8 M_{\odot}$ negligibly affect
test particle orbits, (2) perturbations lead to orbital deviations only in
environments with substructure fractions $f_{sub} \geq 1\%$, (3) perturbations
from denser subhalos produce larger orbital deviations, and (4) subhalo
perturbations that are strong relative to the background tidal field lead to
larger orbital deviations. To predict how the variation in test particle
orbital energy $\sigma_e(t)$ increases with time, we test the applicability of
theory derived from single-mass subhalo populations to populations where
subhalos have a mass spectrum. We find $\sigma_e(t)$ can be predicted for test
particle evolution within a mass spectrum of subhalos by assuming subhalos all
have masses equal to the mean subhalo mass and by using the local mean subhalo
separation to estimate the change in test particle velocities due to subhalo
interactions. Furthermore, the orbital distance variation at an orbital
distance $r$ can be calculated via $\sigma_r=2.98 \times 10^{-5} \pm 8 \times
10^{-8} (\rm kpc^{-1} km^{-2} s^{2}) \times r \times \sigma_e$ with a
dispersion about the line of best fit equalling 0.08 kpc. Finally, we conclude
that clusters that orbit within 100 kpc of Milky Way-like galaxies experience a
change no greater than $2\%$ in their dissolution times.
