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.