Estimating Halo Merging Timescales through Emulation-Based Models

This project studies dark-matter halo merger timescales using controlled N-body simulations and probabilistic emulation. By combining orbital and structural halo parameters with simulation-based merger labels, the analysis evaluates how well machine-learning emulators recover merger times compared with classical analytic prescriptions based on dynamical friction.

LEAPS 2024 project: This work was developed during the Leiden/ESA Astrophysics Program for Summer Students (LEAPS 2024) at Leiden Observatory, in collaboration with researchers working on galaxy formation and evolution.
5,000N-body simulations (BOOMPJE)
106particles per simulation
R2 ≈ 0.98Gaussian Process emulator
MSE ≈ 0.06improved predictive performance

BOOMPJE pipeline Latin hypercube sampling NEMO initial conditions BONSAI GPU tree code Gaussian Process regression

Why it matters

Merger timescales are a fundamental ingredient in galaxy evolution, since mergers contribute to mass assembly, morphological transformation, and the growth of central supermassive black holes. Accurate estimates are therefore important both for interpreting simulation outputs and for improving semi-analytic descriptions of galaxy formation.

Physical framework: the comparison is anchored in merger-time prescriptions motivated by dynamical friction, while the emulator is trained directly on simulation outcomes to capture non-linear dependencies that fixed fitting formulae may miss.

Methodology

The BOOMPJE workflow samples merger configurations across orbital and structural parameter space, generates N-body initial conditions, evolves them numerically, and assigns merger-time labels from dynamical diagnostics measured along the simulations.

  • Orbital parameters: pericentric distance rp and eccentricity e.
  • Structural parameters: mass ratio η = Msat/Mcen, density inner slopes, and concentrations for the central and satellite halos.
  • Merger-time criteria: timescales are determined using both the relative distance r(t) and the specific angular momentum js(t), with threshold-based definitions.
  • Emulation: an exact Gaussian Process with Gaussian likelihood and additive/RBF-style kernel components is used to model tmerge from the physical input parameters.

What this project produces

  • Simulation-based merger-time catalogues: derived from a broad set of controlled halo-merger experiments.
  • Comparisons with analytic prescriptions: to test where classical fitting formulae succeed or fail.
  • Gaussian Process predictions: providing accurate merger-time estimates across a wider parameter range.
  • Parameter-importance trends: showing which orbital and structural variables most strongly drive merger times.

Key results

  • Predictive performance: the Gaussian Process model reaches an R² coefficient of about 0.98 and a mean squared error of about 0.06.
  • Improved generalization: the emulator performs better over a broader range of parameter values than the analytic prescriptions used for comparison.
  • Dominant parameter: eccentricity emerges as the most significant driver of the merger-time predictions when analyzed across the full sampled range.

Resources

This project was presented as part of the LEAPS 2024 summer research program and summarizes work on emulation-based merger-time estimation for idealized halo interactions.

Collaborators