MSTAR - a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates

We present the novel algorithmically regularized integration method MSTAR for high-accuracy (|ΔE/E| ≳ 10^-14) integrations of N-body systems using minimum spanning tree coordinates. The twofold parallelization of the O(N_part^2) force loops and the substep divisions of the extrapolation method allow for a parallel scaling up to N_CPU = 0.2 × N_part. The efficient parallel scaling of MSTAR makes the accurate integration of much larger particle numbers possible compared to the traditional algorithmic regularization chain (AR-CHAIN) methods, e.g. N_part = 5000 particles on 400 CPUs for 1 Gyr in a few weeks of wall-clock time. We present applications of MSTAR on few particle systems, studying the Kozai mechanism and N-body systems like star clusters with up to N_part = 10⁴ particles. Combined with a tree or fast multipole-based integrator, the high performance of MSTAR removes a major computational bottleneck in simulations with regularized subsystems. It will enable the next-generation galactic-scale simulations with up to 10⁹ stellar particles (e.g. m_\star = 100 M_⊙ for an M_\star = 10^{11} M_⊙ galaxy), including accurate collisional dynamics in the vicinity of nuclear supermassive black holes.