Unveiling Gravitational Waves from Galactic Nuclei

Project Information

GWnucleus

Grant agreement ID: 101103134

DOI

10.3030/101103134

Project closed

EC signature date 20 March 2023

Start date 1 April 2023

End date 31 March 2025

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 230 774,40

Coordinated by

KOBENHAVNS UNIVERSITET
Denmark

Periodic Reporting for period 1 - GWnucleus (Unveiling Gravitational Waves from Galactic Nuclei)

Reporting period: 2023-04-01 to 2025-03-31

Summary of the context and overall objectives of the project

Gravitational wave (GW) astronomy has revolutionized our view of the Universe by providing direct evidence of the coalescence of compact-object binaries, such as black holes and neutron stars. Since the first detection in 2015, over 90 GW events have been recorded, yet the astrophysical origin of these sources remains unclear. This fundamental uncertainty hampers our ability to interpret the observed population and forecast the discoveries expected from next-generation detectors like the Einstein Telescope and LISA.

Current models suggest two broad pathways for binary formation: isolated evolution of stellar pairs and dynamical assembly in dense stellar environments. However, both fail to fully explain the observed properties of GW sources, such as their masses, spins, and eccentricities. This has highlighted the need to explore alternative environments, particularly galactic nuclei — regions hosting supermassive black holes surrounded by dense stellar populations and, in some cases, gas disks associated with active galactic nuclei (AGNs). These extreme environments can facilitate the formation and merger of compact-object binaries through mechanisms such as gravitational perturbations, gas drag, and multi-body interactions.

The GWnucleus project addresses this gap by systematically investigating the role of galactic nuclei in shaping GW sources. The project develops a new generation of computational models that combine high-precision N-body dynamics with fast Monte Carlo simulations, tailored to account for the complex physics of dense stellar environments and AGN disks. By simulating millions of binary systems across a wide range of conditions, GWnucleus will build mock catalogs of GW sources that can be directly compared with real observations.

The project is structured around three main objectives. First, it quantifies how gravitational perturbations from the central black hole and surrounding stars influence binary evolution. Second, it models the effects of gas physics in AGN disks, such as migration and disk-induced torques. Third, it connects these theoretical models with current GW observations through population synthesis and Bayesian inference, providing a framework to assess the likelihood that a given observed GW event originated in a galactic nucleus.

The expected impact of GWnucleus is significant. It will deliver an open-source simulation framework and public data products, enabling researchers to explore a new formation channel for GW sources. This contributes directly to the goals of the European Research Area in fostering open science, interdisciplinary collaboration, and data-driven discovery. By improving our understanding of compact-object mergers, GWnucleus also supports broader astrophysical questions, including galaxy evolution, stellar dynamics, and the formation of supermassive black holes.

In a broader context, the project aligns with strategic European priorities in space science and research infrastructures, complementing the scientific missions of upcoming observatories. It also contributes to public engagement through scientific outreach, visualizations, and open-access dissemination of results. By combining innovative computational techniques with pressing scientific questions, GWnucleus stands at the frontier of gravitational-wave astrophysics and aims to transform our understanding of where and how the most extreme objects in the Universe are born.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The GWnucleus project developed and applied a novel computational framework to study the formation and evolution of gravitational-wave (GW) sources in galactic nuclei, where dense stellar populations and massive black holes create unique dynamical and gaseous environments. Over the course of the project, significant technical and scientific milestones were achieved.

A key outcome was the implementation of a hybrid simulation framework combining direct N-body integration and secular dynamics, embedded within a Monte Carlo scheme named PROMENADE. This modular structure enabled the self-consistent modeling of compact-object binaries interacting with both background stars and the central black hole. PROMENADE was integrated with two purpose-built numerical codes: TSUNAMI, a high-precision N-body integrator with post-Newtonian corrections, and OKINAMI, a fast secular code designed to model long-term dynamical evolution under Kozai-Lidov perturbations. These tools allowed the simulation of over 3 million binary evolutions across a broad range of galactic nucleus models.

The project explored both gas-free and gas-rich environments. In dry nuclei, the combined effects of three-body encounters and Kozai-Lidov oscillations were shown to efficiently drive compact-object binaries to merger, especially in the presence of intermediate-mass black holes. A major result was the quantification of how these mechanisms act together to shape the distribution of orbital parameters, including eccentricity and merger time. In AGN environments, gas drag and gravitational torques from the disk were modeled and implemented in both TSUNAMI and OKINAMI. This enabled the first simulations tracking the full orbital evolution of compact objects as they migrate into the disk, interact, and potentially merge.

The simulations led to the creation of two large mock catalogs of merging binaries: one for dry nuclei and one for AGN disks. These catalogs provide distributions of masses, eccentricities, and spin orientations at merger, and were used to predict the gravitational-wave signatures detectable by current and future observatories. Bayesian hierarchical analysis was then employed to compare these theoretical predictions with observed GW events from LIGO/Virgo/KAGRA, providing evidence that a fraction of the observed mergers may originate in galactic nuclei.

In summary, GWnucleus delivered the first self-consistent modeling framework that captures both dynamical and environmental effects in galactic nuclei, leading to several scientific insights:

- Identification of the role of chaos and lack thereof in the production of gravitational wave events from three-body encounters among black holes.
- Demonstrated that AGN disks can efficiently trap and merge compact objects under state-of-the-art disk models.
- Quantified the effect of black hole disk velocity dispersion on the merger efficiency of black holes

All codes and data products are have been prepared for public release, with technical documentation and scientific publications detailing the methods and findings. These results lay the groundwork for a new class of astrophysical models linking galactic nuclei with gravitational-wave astronomy.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

A major scientific advance achieved in this project was the first fully consistent treatment of binary formation from three initially unbound compact objects in astrophysical environments. Classical approaches assumed binary systems formed either from primordial stellar evolution or through dynamical exchange processes in dense clusters. This project demonstrated, with high-precision simulations, that direct capture and binary formation can arise from purely gravitational interactions among three unbound objects, without the need for pre-existing binaries. This finding opens new avenues for modeling GW source populations in dynamically hot environments such as nuclear star clusters and AGN disks, particularly where frequent interactions are expected. These results significantly expand the theoretical parameter space for gravitational wave progenitors beyond what was previously considered.
Previous models of active galactic nucleus (AGN) discs relied on simplified prescriptions that were either too coarse or limited in scope. This project introduced a unified, flexible simulation toolkit capable of modeling the structure, dynamics, and evolution of gas discs surrounding supermassive black holes with high fidelity. This framework captures both the long-term secular effects and the short-term hydrodynamic interactions of embedded objects, including gas drag, torques, and migration traps. The versatility of this modeling suite allows researchers to simulate realistic conditions leading to compact-object mergers within AGN discs, enabling for the first time robust predictions of merger rates, eccentricities, and spin alignment distributions for this elusive channel.
The project significantly advanced the theoretical understanding of intermediate-mass black holes (IMBHs), particularly their dynamical impact on nearby stellar or compact-object systems. It was shown that IMBHs embedded in low-metallicity environments, such as primordial clusters, can induce complex hierarchical triple configurations that lead to rapid mergers via secular or resonant mechanisms. Furthermore, in AGN environments, IMBHs may acquire and retain their own mini-discs, forming transient, self-gravitating substructures within the larger AGN disc. These findings suggest that IMBHs are not merely passive actors but active participants in the formation and evolution of GW sources. This opens a new observational window for distinguishing formation environments via GW signal properties and could guide future detection strategies.
The project also brought conceptual advances in gravitational dynamics by identifying previously unknown islands of regularity in the chaotic regime of the three-body problem. These islands correspond to specific initial conditions that yield predictable outcomes despite the global chaotic nature of the system. This challenges the long-standing assumption that statistical treatment is the only viable approach to such encounters. By isolating these non-chaotic pathways, the project offers a path forward for more accurate modeling of close interactions near supermassive black holes and in hierarchical systems. These insights are expected to have implications not only for astrophysical modeling but also for mathematical physics, where the three-body problem remains a foundational challenge.
To enable further uptake and maximize the scientific return of these advances, several needs have been identified. Continued development and optimization of simulation frameworks is essential to scale up to the sensitivity requirements of next-generation GW detectors. Interdisciplinary collaboration with hydrodynamics and machine learning experts will be crucial to handle large datasets and incorporate additional physics such as accretion and radiation feedback. Wider adoption will benefit from robust, FAIR-compliant data repositories, including public catalogs of merger predictions. No immediate commercial or regulatory frameworks are required, but community-driven standardization of simulation inputs and outputs would enhance reproducibility and interoperability. The tools and insights developed here set the stage for more predictive and discriminating models of GW formation pathways in future multimessenger astrophysics.

Mix of chaos and regularity in dynamical interactions among black holes