A repository of vanilla long term integrations of the Solar System (2012.05177v1)

Abstract: We share the source code and a 121 GB dataset of 96 long-term N-body simulations of the Solar System. This dataset can be analyzed by itself to study the dynamics of the Solar System. In addition, our simulations can be the starting point for future studies wishing to explore different initial conditions or additional physical effects on the Solar System. Our simulations can also be used as a comparison and benchmark for new numerical algorithms.

• The paper presents a 121 GB repository of 96 long-term N-body simulations that benchmark Solar System dynamics.
• It utilizes the REBOUND integrator with 17th order symplectic correctors to achieve a relative energy error of ~2.5×10⁻⁹ over a 5 Gyr span.
• The dataset enables reproducible open science and provides a framework for exploring chaos and testing new numerical algorithms.

Vanilla Long-Term Integrations of the Solar System

The paper "A Repository of Vanilla Long Term Integrations of the Solar System" by Brown et al. presents a significant contribution to the field of celestial mechanics by sharing both a 121 GB dataset comprised of 96 long-term N-body simulations and the associated source code. The primary objective of this research is to provide a robust foundation for further exploration of the dynamical properties and stability of the Solar System using these comprehensive simulations. This dataset serves as a benchmark against which new numerical algorithms can be compared, enhancing transparency and reproducibility in the field.

Overview of the Methodology

The simulations are executed using the open-source $N$-body integrator REBOUND, with the symplectic integrator WHFast and Jacobi coordinates. These choices facilitate high precision in capturing the complex gravitational interactions within the Solar System over a 5 Gyr timespan. Notably, the simulations maintain a high average relative energy error, approximately $\Delta E/E \sim 2.5 \times 10^{-9}$, ensuring the reliability of the results for studying scenarios with moderate eccentricity ($e \lesssim 0.4$).

The simulations are implemented using a sophisticated numerical scheme involving 17th order symplectic correctors, employing a modified kick step compatible with relativistic corrections, thereby enabling fidelity in the long-term integration of planetary orbits. Each simulation uses initial conditions procured from NASA's Horizon system, marking the state of the Solar System as of January 1, 2000, inclusive of relativistic effects modeled by an additional $1/r^3$ term in the potential.

Data and Computational Insights

The simulations incorporate minor perturbations applied to Mercury’s initial conditions across 96 datasets, exemplified by a systematically varied shift in its $x$ coordinate. These perturbations are small yet sufficient to explore the chaotic sensitivity inherent to the Solar System's dynamics. The demonstration of this chaotic behavior is vividly expressed in the correlation of Mercury's eccentricity across simulations for the first $\sim 100$ Myrs.

Despite the immense computational expense, approximately six core years of processing, the project adheres to principles of open science. Computational resources were optimized, resulting in an analysis framework where assessing time-series data from the entire dataset requires a mere few minutes on a modern desktop. This underscores the potential for both detailed analysis and rapid model reevaluation from archival snapshots.

Implications and Future Work

The implications of this work are extensive. Practically, the dataset enables researchers to conduct less computationally expensive parameterized studies by allowing them to start from these existing simulations and explore differential initial conditions or additional forces. This provision significantly reduces the threshold for entry into high-complexity studies, distributing both the burden and accessibility across the research community.

Theoretically, the dataset supports investigations into questions of long-term stability, chaos, and resonance within multi-body celestial systems, consistent with prior theoretical predictions of potential instabilities on geological timescales (e.g., Laskar & Gastineau 2009). Researchers can exploit the derived statistical properties of instability over the full 5 Gyr duration to refine current models on Solar System evolution.

Future directions might include the adaptation and scaling of such datasets to accommodate the exploration of hypothetical planetary systems or the synthesis of similar databases under varied parameter sets reflective of exoplanetary studies. As computational capabilities expand, so too might the complexity and application scope of models derived from these data-driven benchmarks, propelling forward our understanding of celestial mechanics.