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From Nbody1 to Nbody7: the Growth of Sverres Industry

Rainer Spurzem

TL;DR

The paper surveys the evolution of direct $N$-body simulations, tracing historical milestones from von Hoerner’s early work to Aarseth’s development of robust integrators and regularization schemes. It highlights the Hermite integration, time-stepping criteria, Ahmad-Cohen neighbour scheme, and regularization techniques that enabled accurate, scalable simulations, complemented by hardware acceleration via GRAPE, MPI, and GPUs. It then discusses two cutting-edge approaches, PeTar and BiFrost, as well as recent large-scale simulations (Dragon series) that demonstrate the industry’s capacity to model complex star cluster dynamics and gravitational-wave progenitors. The work emphasizes open-source collaboration, ongoing maintenance, and competition as drivers of rapid progress, with a view toward sustaining Sverre Aarseth’s open, collaborative legacy in the field.

Abstract

From NBODY1 to NBODY6 : The Growth of an Industry is the title of a 1999 invited review by Sverre Aarseth, for Publications of the Astronomical Society of the Pacific (PASP). I took this as an inspiration for the title of this paper; it describes how Sverres NBODY Industry has further grown since 90s of the previous century, and how it is further flourishing and hopefully developing, in his spirit, even after the sad news of his passing away reached us. My contact and friendship with Sverre started a few decades ago being sent to Cambridge to learn NBODY5, counting input parameters, and learning about the fact that even a sophisticated code (which had already at that time quite a history) requires permanent maintenance and bug fixes. Managed by Sverre, who relentlessly ran his code and responded to the widely spread crowd of customer colleagues. There has been a phase of massive and fast development and improvements due to vectorization, parallelization, GRAPE and GPU acceleration, and Sverre has been always on top of it if not ahead, but also fully adopting ideas of collaborators, once they tested well. NBODY6++GPU and NBODY7 entered the scene, and also recent new competitors, such as PETAR or BIFROST . We all have learnt a lot from Sverre, and strive to continue in his open-minded spirit, for open source and exchange. A striking evidence for the further growth of the industry is the number of papers here (and two of them follow in this session, but also in other sessions) using and further developing the aforementioned codes, as well as the occurrence of new and competing codes, which keep the field alive.

From Nbody1 to Nbody7: the Growth of Sverres Industry

TL;DR

The paper surveys the evolution of direct -body simulations, tracing historical milestones from von Hoerner’s early work to Aarseth’s development of robust integrators and regularization schemes. It highlights the Hermite integration, time-stepping criteria, Ahmad-Cohen neighbour scheme, and regularization techniques that enabled accurate, scalable simulations, complemented by hardware acceleration via GRAPE, MPI, and GPUs. It then discusses two cutting-edge approaches, PeTar and BiFrost, as well as recent large-scale simulations (Dragon series) that demonstrate the industry’s capacity to model complex star cluster dynamics and gravitational-wave progenitors. The work emphasizes open-source collaboration, ongoing maintenance, and competition as drivers of rapid progress, with a view toward sustaining Sverre Aarseth’s open, collaborative legacy in the field.

Abstract

From NBODY1 to NBODY6 : The Growth of an Industry is the title of a 1999 invited review by Sverre Aarseth, for Publications of the Astronomical Society of the Pacific (PASP). I took this as an inspiration for the title of this paper; it describes how Sverres NBODY Industry has further grown since 90s of the previous century, and how it is further flourishing and hopefully developing, in his spirit, even after the sad news of his passing away reached us. My contact and friendship with Sverre started a few decades ago being sent to Cambridge to learn NBODY5, counting input parameters, and learning about the fact that even a sophisticated code (which had already at that time quite a history) requires permanent maintenance and bug fixes. Managed by Sverre, who relentlessly ran his code and responded to the widely spread crowd of customer colleagues. There has been a phase of massive and fast development and improvements due to vectorization, parallelization, GRAPE and GPU acceleration, and Sverre has been always on top of it if not ahead, but also fully adopting ideas of collaborators, once they tested well. NBODY6++GPU and NBODY7 entered the scene, and also recent new competitors, such as PETAR or BIFROST . We all have learnt a lot from Sverre, and strive to continue in his open-minded spirit, for open source and exchange. A striking evidence for the further growth of the industry is the number of papers here (and two of them follow in this session, but also in other sessions) using and further developing the aforementioned codes, as well as the occurrence of new and competing codes, which keep the field alive.
Paper Structure (9 sections, 2 equations, 3 figures, 1 table)

This paper contains 9 sections, 2 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Nbody -- the beginning
  3. Nbody -- the growth
  4. Hermite Scheme
  5. Time-step choice
  6. Ahmad-Cohen neighbour scheme
  7. Regularizations
  8. Nbody with Parallel and GPU computing
  9. New approaches

Figures (3)

  • Figure 1: Sverre Aarseth (right) and Chris Tout (left), with visitor Emmanuil Vilkoviski of Fesenkov observatory in Almaty, Kazakhstan; in mid 90's.
  • Figure 2: Radii containing 10%, 50%, 90% of the mass, plotted versus time for a cluster with stars of equal masses. Open triangles and squares: Nbody integration with $N=100$ and $N=250$ (Wielen). Filled triangles and squares: Nbody Integration with $N=250$ (Aarseth). Full lines: Monte Carlo models (Hénon1971). Dotted lines: Monte Carlo model (Shull and Spitzer). Dashed lines: fluid-dynamical model (Larson). From: Aarsethetal1974; for citations and further discussion see that paper.
  • Figure 3: Sverre Aarseth and Seppo Mikkola, discussing chain regularization, in 2007.