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

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.

💡 Research Summary

This paper investigates the dynamical outcomes of direct collisions between equal‑mass (1 M⊙) main‑sequence stars in the extreme environment of galactic nuclei, where a supermassive black hole (SMBH) drives stellar velocities to several hundred–thousand km s⁻¹. The authors performed a systematic suite of 236 high‑resolution smoothed‑particle hydrodynamics (SPH) simulations using the StarSmasher code. Each star is represented by 10⁵ particles, and the stellar structure is taken from a 2.5 Gyr MESA model. The simulations explore a two‑dimensional parameter space defined by the asymptotic relative speed v∞ (sampled from 100 to 5000 km s⁻¹) and the pericenter distance rp (0 R★ to ~1.8 R★). External potentials (cluster or SMBH tides) are omitted, allowing the collision to be treated as an isolated two‑body problem on stellar scales.

The outcomes fall into three qualitative categories: (1) mergers, where low v∞ and small rp lead to gravitational capture and coalescence; (2) hit‑and‑run events, where the stars physically intersect but retain enough kinetic energy to escape each other; and (3) complete destruction, where extreme kinetic energy and small impact parameters shred both stars. Quantitative diagnostics include the fractional mass loss from the system (fML), the fractional speed reduction (Δv/v∞), and the deflection angle (Δθ) of the post‑collision trajectories. The authors find that for grazing encounters the speed reduction follows the tidal‑dissipation limit derived from analytic tidal capture theory, while for rp ≳ 0.3 R★ the deflection angle is well described by simple point‑particle scattering.

To provide practical tools for stellar dynamics codes, the paper develops two complementary predictive frameworks. First, physically motivated fitting formulae are derived, extending the classic capture radius and mass‑loss relations of Lai et al. (1993) to the high‑speed regime. These formulas take v∞ and rp as inputs and return estimates of fML, merger probability, and post‑collision velocity changes. Second, the authors train machine‑learning (ML) models on the full SPH dataset. They compare a k‑Nearest Neighbors (k‑NN) regressor with a deep feed‑forward neural network (NN) consisting of five hidden layers (64–128 neurons each, ReLU activations, Adam optimizer). Using 5‑fold cross‑validation, the NN achieves a mean absolute error of ≈0.03 and an R² of 0.96 for predicting Δv/v∞, outperforming k‑NN (MAE ≈ 0.07, R² ≈ 0.89). For the deflection angle, the NN also exceeds the analytic fitting formula by 5–10 % in predictive accuracy.

The study highlights two major implications. (i) By quantifying how high‑speed collisions alter stellar masses and orbital vectors, the results enable more realistic modeling of nuclear star cluster evolution, including the formation of blue stragglers, the generation of stripped‑star transients, and the sculpting of the inner density profile via collisional erosion. (ii) While fitting formulae remain useful for quick estimates, their accuracy degrades as the parameter space expands (e.g., varying mass ratios, stellar ages, metallicities). In contrast, ML models can absorb additional dimensions without explicit re‑derivation of analytic expressions, offering a scalable path forward as larger simulation libraries become available.

The authors conclude that both approaches have merit: analytic fits provide physical insight and computational speed, whereas neural networks deliver higher fidelity across a broader range of conditions. Future work will extend the dataset to unequal‑mass encounters, incorporate SMBH tidal fields, and explore more sophisticated ML architectures such as graph neural networks or physics‑informed neural networks to enforce conservation laws. This combined hydrodynamic‑ML methodology promises to become a cornerstone for next‑generation dynamical simulations of dense stellar systems in galactic nuclei.