GroArnold: A Framework for Constructing Action-based Models for Triaxial Galaxies and Dark Matter Halos

Abstract Action-based distribution functions f(J) provide a powerful description of stellar systems and are increasingly used to model the Milky Way and external galaxies in the era of Gaia and large spectroscopic surveys. Consequently, the construction of physically accurate and dynamically stable f(J) for galactic components has emerged as a key challenge in the field. In this study, we present GroArnold, a computational framework designed to construct analytical f(J) expressions for axisymmetric and triaxial galaxies and dark matter haloes. The framework integrates modules for N-body initial condition generation, N-body simulation, angle--action variable estimation, and distribution-function fitting into a unified workflow. It supports a wide range of density profiles and kinematic properties, and is uniquely designed to generate stable N-body models for user-specified galactic systems, in the hope that the resulting f(J) approximates a dynamically stable and physically consistent state. To this end, we extend the Triaxial Stackel Fudge (TSF) method of the TACT code of Sanders \& Binney (2015), implemented in our Nbody-TACT module, to enable action estimation directly from N-body gravitational potentials. GroArnold provides a robust and flexible tool for deriving numerically empirical, explicitly analytical distribution functions for user-specified galaxies or haloes, thereby facilitating a wide range of practical f(J)-based modeling applications. In addition, it serves as a powerful tool for investigating the dynamics of realistic triaxial galaxies and haloes beyond the scope of traditional spherical or axisymmetric models. We assessed the accuracy of the output f(J) by comparing its predicted spatial and velocity distributions with those of the input N -body snapshot, and confirmed that it provides a reasonably accurate representation of the input. The code is modular, publicly available, and designed to support future extensions and adaptations.