MSTAR -- a fast parallelised algorithmically regularised integrator with minimum spanning tree coordinates

Abstract

We present the novel algorithmically regularised integration method MSTAR for high accuracy ($|\Delta E/E|\gtrsim 10^{-14}$) integrations of N-body systems using minimum spanning tree coordinates. The two-fold parallelisation of the $\mathcal{O}(N_{\mathrm{part}}^2)$ force loops and the substep divisions of the extrapolation method allows for a parallel scaling up to $N_{\mathrm{CPU}}=0.2\times N_{\mathrm{part}}$. The efficient parallel scaling of MSTAR makes the accurate integration of much larger particle numbers possible compared to the traditional algorithmic regularisation chain (AR-CHAIN) methods, e.g. $N_{\mathrm{part}}=5000$ 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 $N_{\mathrm{part}}=10^4$ particles. Combined with a tree or a fast multipole based integrator the high performance of MSTAR removes a major computational bottleneck in simulations with regularised subsystems. It will enable the next generation galactic-scale simulations with up to $10^9$ stellar particles (e.g. $m_{\star }=100M_{\odot }$ for a $M_{\star }=10^{11}{M}_{\odot }$ galaxy) including accurate collisional dynamics in the vicinity of nuclear supermassive black holes.

20 pages, 16 figures, accepted for publication in MNRAS

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• Forming Hot Subluminous Stars from Hierarchical Triples -- I. The Role of an Outer Tertiary on Formation Channels