Julian Chan
Academic and research departments
About
My research project
Machine Learning Surrogates for N-body Dynamics of Supermassive Black Hole BinariesAccurately modellng the merger timescales of supermassive binary black holes (BHBs) is crucial for interpreting the stochastic gravitational wave background (GWB) detected by Pulsar Timing Arrays. To address this challenge, neural ordinary differential equations (Neural ODEs) are employed to distill the coarse-grained dynamics of binary black holes, yielding compact and interpretable models of their evolutionary trajectories. Complementarily, graph-based learning approaches, particularly spatio-temporal graph neural networks, are used to model the full phase space of N-body systems relevant to galaxy mergers involving binary black holes, capturing detailed and time-varying interactions. By integrating these state-of-the-art machine learning techniques, this research enhances predictions of BHB merger timescales and furthers astrophysical insights into the origins and properties of the GWB as observed by Pulsar Timing Arrays.
Supervisors
Accurately modellng the merger timescales of supermassive binary black holes (BHBs) is crucial for interpreting the stochastic gravitational wave background (GWB) detected by Pulsar Timing Arrays. To address this challenge, neural ordinary differential equations (Neural ODEs) are employed to distill the coarse-grained dynamics of binary black holes, yielding compact and interpretable models of their evolutionary trajectories. Complementarily, graph-based learning approaches, particularly spatio-temporal graph neural networks, are used to model the full phase space of N-body systems relevant to galaxy mergers involving binary black holes, capturing detailed and time-varying interactions. By integrating these state-of-the-art machine learning techniques, this research enhances predictions of BHB merger timescales and furthers astrophysical insights into the origins and properties of the GWB as observed by Pulsar Timing Arrays.
ResearchResearch interests
- Neural Differential Equations
- Graph Representation Learning
- N-body simulations
- Supermassive Binary Black Holes
- Scalable Surrogate Models
Research interests
- Neural Differential Equations
- Graph Representation Learning
- N-body simulations
- Supermassive Binary Black Holes
- Scalable Surrogate Models
Publications
Binaries of supermassive black holes [massive black hole binaries (MBHBs)] represent the primary sources of the gravitational wave background (GWB) detectable by pulsar timing arrays (PTAs). The eccentricity with which binaries form in galactic mergers is the key parameter determining their evolutionary timescale from pairing to coalescence. Ho we ver, accurately determining the binary eccentricity at formation is difficult in simulations due to stochastic effects. We present a numerical study of the formation and evolution of MBHBs that are potential PTA sources. We simulate mergers of equal-mass galaxies on different initial orbits and follow the dynamics of the MBHBs through the hardening phase. We find that low-resolution simulations are affected by stochasticity due to torques from the stellar distribution acting at pericentre passages. The dispersion in binary eccentricity decreases with increasing central resolution, as expected for a Poisson process. We provide a fitting formula for the resolution requirement of an N-body simulation of MBHB formation and evolution as a function of the initial eccentricity of the merger, e 0 , and the required accuracy in the binary eccentricity, e b. We find that binaries experience a torque at first pericentre that is approximately independent of initial eccentricity, producing a general trend in which the binary eccentricity decreases abo v e sufficiently large initial orbital eccentricities. While this behaviour is generic, the precise cross-o v er eccentricity (e 0 ∼ 0. 97 in our models) and the sharpness of the drop-off depend on the galaxy initial conditions. We provide a fitting formula for e b (e 0) that can be used in semi-analytical models to determine the merger timescales of MBHBs as well as the amplitude and slope of the GWB.
Pulsar timing arrays (PTAs) can detect the low-frequency stochastic gravitational-wave background (GWB) generated by an ensemble of supermassive black hole binaries (BHBs). Accurate determination of BHB merger timescales is essential for interpreting GWBs and constraining key astrophysical quantities such as black hole (BH) occupation fractions and galaxy coalescence rates. High-accuracy í µí±-body codes such as Griffin can resolve sub-pc BHB dynamics but are too costly to explore a wide range of initial conditions, motivating the need for surrogate models that emulate their long-term evolution at much lower computational cost. We investigate neural ordinary differential equations (NODEs) as surrogates for the secular orbital evolution of BHBs. Our primary contribution is a parameterised NODE (PNODE) trained on an ensemble of í µí±-body simulations of galaxy mergers spanning a two-dimensional parameter space defined by the initial orbital eccentricity and particle resolution (í µí± í µí± , í µí±), with the learned vector field explicitly conditioned on these parameters. A single PNODE thereby learns a simulation-parameter-conditioned dynamical model for the coupled evolution of the BH pair's orbital state across the ensemble, yielding smooth trajectories from which stable hardening and eccentricity growth rates can be extracted. The PNODE accurately reproduces the secular evolution of the specific orbital energy and angular momentum, and the corresponding Keplerian orbital elements, for held-out trajectories, with modest generalisation to a partially unseen high-resolution case. Combining PNODE predictions with semi-analytical prescriptions for stellar hardening and gravitational-wave emission yields BHB merger timescales consistent with those obtained from direct í µí±-body inputs within current theoretical uncertainties.