FLORAH-Tree: Emulating Dark Matter Halo Merger Trees with Graph Generative Models

Abstract

Merger trees track the hierarchical assembly of dark matter halos across cosmic time and serve as essential inputs for semi-analytic models of galaxy formation. However, conventional methods for constructing merger trees rely on ad-hoc assumptions and are unable to incorporate environmental information. Nguyen et al. (2024) introduced FLORAH, a generative model based on recurrent neural networks and normalizing flows, for modeling main progenitor branches of merger trees. In this work, we extend this model, now referred to as FLORAH-Tree, to generate complete merger trees by representing them as graph structures that capture the full branching hierarchy. We trained FLORAH-Tree on merger trees extracted from the Very Small MultiDark Planck cosmological N-body simulation. To validate our approach, we compared the generated merger trees with both the original simulation data and with semi-analytic trees produced using the Extended Press-Schechter (EPS) formalism. We show that FLORAH-Tree accurately reproduces key merger rate statistics across a wide range of mass and redshift, outperforming the conventional EPS-based approach. We demonstrate its utility by applying the Santa Cruz semi-analytic model (SAM) to generated trees and showing that the resulting galaxy-halo scaling relations, such as the stellar-to-halo-mass relation and supermassive black hole mass-halo mass relation, closely match those from applying the SAM to trees extracted directly from the simulation. FLORAH-Tree provides a computationally efficient method for generating merger trees that maintain the statistical fidelity of N-body simulations.