Modeling Stellar Collisions in Galactic Nuclei Using Hydrodynamic Simulations and Machine Learning

TL;DR

This paper uses hydrodynamic simulations and machine learning to model stellar collisions in galactic nuclei, providing new predictive tools for understanding their outcomes and effects on stellar dynamics.

Contribution

It introduces a large dataset of SPH simulations, develops fitting formulae, and compares machine learning methods for predicting collision results in dense stellar environments.

Findings

Neural networks outperform k-Nearest Neighbors in prediction accuracy.

Collision outcomes follow theoretical limits for grazing encounters.

ML methods may be more scalable for complex initial conditions.

Abstract

Nuclear star clusters represent some of the most extreme collisional environments in the Universe. A nuclear star cluster like that of the Milky Way harbors a supermassive black hole at its center, which accelerates stars to high speeds ($\gtrsim 100$-$1000$ km/s) in a region where millions of other stars reside. Direct collisions occur in such high-density environments, where they can shape the stellar populations and influence the evolution of the cluster. We present a suite of a couple hundred high-resolution smoothed-particle hydrodynamics (SPH) simulations of collisions between $1$ M$_\odot$ stars, at impact speeds representative of galactic nuclei. We use our SPH dataset to develop physically-motivated fitting formulae for predicting collision outcomes. While collision-driven mass loss has been examined in detail in the literature, we present a new framework for understanding the effects of ``hit-and-run'' collisions on a star's trajectory. We demonstrate that the change in stellar velocity follows the tidal-dissipation limit for grazing encounters, while the deflection angle is well-approximated by point-particle dynamics for periapses $\gtrsim 0.3$ times the stellar radii. We use our SPH dataset to test two machine learning (ML) algorithms, k-Nearest Neighbors and neural networks, for predicting collision outcomes. We find that the neural network out-performs k-Nearest Neighbors and delivers results on par with and in some cases exceeding the accuracy of our fitting formulae. We conclude that both fitting formulae and ML have merits for modeling collisions in dense stellar environments, however ML may prove more effective as the parameter space of initial conditions expands.