Nemesis: A Multi-Scale, Multi-Physics Algorithm for Astrophysics

Abstract

In this work, an updated version of the multi-scale, multi-physics algorithm, Nemesis which makes use of the Astrophysical Multipurpose Software Environment (AMUSE). The algorithm is formally introduced and validated. A suite of simulations is run to assess its performance in simulating star clusters containing planetary systems, its ability to capture the von Zeipel-Lidov-Kozai effect, and its computational scalability. Nemesis is found to yield indistinguishable results in both the global and local scales when compared with the direct N-body code Ph4. The same conclusion is found when analysing its ability to capture the von Zeipel-Lidov-Kozai effect. When analysing its computational performance, the wall-clock time scales roughly as $t_{\rm sim \propto 1/ \sqrt{δt_{\rm nem}}$ where $δt_{\rm nem}$ represents the time synchronisation between the global and local scales. When changing the number of planetary systems, the wall-clock time remains unchanged as long as the number of available cores exceeds the number of systems. Beyond this, it's found that at worst, the computational time increases linearly with the number of excess systems. The method introduced here can find it's use in numerous domains of astronomy thanks to its flexibility and modularity, from simulating protoplanetary disks in star clusters to binary black holes in the galactic center.

Figures (7)

• Figure 1: Nemesis workflow. star_evol is a parameter in Nemesis toggling on or off stellar evolution. Communication between codes is internally handled by AMUSE via channels. Orange boxes represent the setup and termination of the simulation, red boxes indicate steps where work is offloaded to external codes, and blue boxes denote tasks handed back to Python for manipulation of Nemesis-structured data.
• Figure 2: Evolution of simulation's energy error in time.
• Figure 3: Bottom: Cumulative distribution function of asteroid eccentricities after $t_{\rm end}=0.1$ Myr. Top: Residuals in distributions between Nemesis and Ph4, computed as $\Delta y(e)=(y_{\rm \texttt{Nem}}(e)-y_{\rm \texttt{Ph4}}(e))$.
• Figure 4: Same as figure \ref{['Fig:CDF_Plots_ecc']} but for asteroid semi-major axis. The two vertical black lines in the upper panel represent the range in parent radius initially considered ($0.5\leq M_{\rm par}$ [M$_\odot$]$\leq2.0$) when using equation \ref{['Eqn:Rpar']} and $A=100$. The red vertical line represents the linking length parameter which flags children dissolution (section \ref{['Sec:Child_Dissolutions']}) for a $M_{\rm par}=2$ M$_\odot$ parent host.
• Figure 5: Diagram illustrating how children on wide orbits are not as well resolved in Nemesis since it manages external interactions via correction kicks applied every bridge time-step ($\delta t_{\rm nem}$). As a result, the outer planet (blue) is diverted along the black trajectory. Meanwhile, a direct $N$-body integrator computes interactions at every internal time-step ($\delta t$). With better resolution of the close encounter, the planet feels a stronger gravitational effect and is scattered outwards along the red path.