On the reliability of simulations of collisional stellar systems
  It is well known that numerical errors grow exponentially in $N$-body
simulations of gravitational bound stellar systems, but it is not well
understood how the accuracy parameters of algorithms affect the physical
evolution in simulations. By using the hybrid $N$-body code, PeTar, we
investigate how escapers and the structure evolution of collisional stellar
systems (e.g., star clusters) depend on the accuracy of long-range and
short-range interactions. We study a group of simulations of ideal low-mass
star clusters in which the accuracy parameters are varied. We find that
although the number of escapers is different in individual simulations, its
distribution from all simulations can be described by Poisson statistics. The
density profile also has a similar feature. By using a self-consistent set-up
of the accuracy parameters for long- and short-range interactions, such that
orbits are resolved well enough, the physical evolution of the models is
identical. But when the short-range accuracy is too low, a nonphysical
dynamical evolution can easily occur; this is not the case for long-range
interactions. This strengthens the need to include a proper algorithm (e.g.
regularization methods) in the realistic modelling of collisional stellar
systems. We also demonstrate that energy-conservation is not a good indicator
to monitor the quality of the simulations. The energy error of the system is
controlled by the hardest binary, and thus, it may not reflect the ensemble
error of the global system.
