Demography of black hole binaries in the era of gravitational wave astronomy

Project Information

DEMOBLACK

Grant agreement ID: 770017

DOI

10.3030/770017

Project closed

EC signature date 28 May 2018

Start date 1 November 2018

End date 30 April 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 994 764,00

EU contribution

€ 1 994 764,00

Coordinated by

RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Germany

Periodic Reporting for period 4 - DEMOBLACK (Demography of black hole binaries in the era of gravitational wave astronomy)

Reporting period: 2023-08-01 to 2025-04-30

Summary of the context and overall objectives of the project

About 10 years ago, the LIGO-Virgo collaboration obtained the first direct detection of gravitational waves: GW150914, interpreted as the merger of two black holes. This result marks the dawn of gravitational-wave astronomy and poses one crucial question to astrophysicists: what are the formation channels of binary black holes?
DEMOBLACK aims to address this question by means of innovative numerical models. We will study two main scenarios: the formation of binary black holes via isolated binary evolution and their possible dynamical formation in star clusters. Reconstructing the formation pathways of binary black holes is one of the most urgent steps to take if we want to interpret gravitational-wave observations. To achieve this long-term goal, DEMOBLACK will
i) develop a novel approach to population-synthesis simulations of binary evolution;
ii) perform hydrodynamical and N-body simulations of star clusters with realistic initial conditions and advanced population-synthesis calculations;
iii) investigate the evolution of binary black holes across cosmic time;
iv) use a new Bayesian inference framework to predict the distribution of masses, spins, eccentricities and merger rates of gravitational-wave sources observed by LIGO and Virgo at design sensitivity and by future gravitational-wave detectors (Einstein Telescope and Cosmic Explorer).

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

WORK-PACKAGE 1: Hydrodynamics and stellar evolution
1a. Population-synthesis:
– We completed the development of the new version of the SEVN code with binary star evolution processes. The new code has been successfully used for an innovative study of binary black hole demography from isolated binaries (Spera et al. 2019; Mapelli et al. 2020; Iorio et al. 2023; Dall'Amico 2025).
– We included rotating stellar models in SEVN and we studied their impact on the maximum mass of black holes from single stellar evolution (Mapelli et al. 2020).
– We implemented new prescriptions for natal kicks. The new prescriptions allow us to recover the merger-rate density of binary compact objects inferred from LIGO-Virgo data and are consistent with the proper motions of Galactic binary pulsars (Giacobbo & Mapelli 2020).
– We investigated the boundaries of the pair-instability mass gap (Costa et al. 2021, 2022; Ballone et al. 2023).
1b. Hydrodynamical simulations:
– We ran a large set of hydro- simulations to produce realistic initial conditions for N-body simulations and designed a new algorithm to derive these initial conditions (Ballone et al. 2020A; Ballone et al. 2020b; Torniamenti et al. 2021, 2022a).

WORK-PACKAGE 2: Stellar dynamics
– We wrote an interface between the direct N-body code NBODY6++GPU and our population-synthesis code MOBSE, presented in Di Carlo et al. (2019).
– With the new code, we performed the largest set of direct N-body simulations with population synthesis ever performed to study binary black holes: >10000 simulations of massive young star clusters and >100’000 simulations of small young star clusters. We found that star cluster dynamics has a key impact on the mass function of binary black holes. This study led to several peer-reviewed publications (Di Carlo et al. 2019, 2020a, 2020b, 2021; Rastello et al. 2020, 2021; Bouffanais et al. 2019, 2021; Santoliquido et al. 2020).
– With the new code we discovered a new possible formation channel for binary black holes in the pair instability mass gap (Di Carlo et al. 2019, 2020a; Torniamenti et al. 2022).
- We developed a new semi-analytic dynamical code (FASTCLUSTER) to study hierarchical black hole mergers in the most massive star clusters (Mapelli et al. 2021, 2022; Torniamenti et al. 2024) and AGN disks (Vaccaro et al. 2024).

WORK-PACKAGE 3: Cosmological context
1a. Cosmological simulations
– We developed a numerical model that couples binary black hole catalogs from population synthesis with cosmological simulations.
– we investigated the properties of binary compact objects across cosmic time (Mapelli et al. 2019);
– we estimated the cosmic merger rate evolution in early- and late-type galaxies (Artale et al. 2019, 2020a, 2020b);
- we characterized the host galaxies across cosmic time (Toffano et al. 2019; Artale et al. 2020b; Santoliquido et al. 2022). This study is important for low-latency search and for ranking the possible host galaxies in the uncertainty box of gravitational-wave detectors.
1b. Data-driven model
- We developed a data-driven and very fast code to estimate cosmic merger rate evolution in a very fast way (Baibhav et al. 2019; Santoliquido et al. 2020, 2021).
- We modeled the formation of binary black holes from Population II and Population III stars (Costa et al. 2022; Santoliquido et al. 2023; Mestichelli et al. 2024).

WORK-PACKAGE 4: Learning from observations
– We developed a new hierarchical Bayesian inference tool (Bouffanais et al. 2019, 2021) to i) convert the results of our models into mock gravitational-wave events; ii) calculate the Bayesian odds ratios for different models; iii) calculate the mixing fraction assuming that part of the observed events are dynamical and part are isolated. The final goal is to infer the fraction of LIGO-Virgo events that have dynamical vs isolated origin.
- We found a tension between the merger rate density of binary black holes and the observations from LIGO-Virgo (Sgalletta et al. 2025).

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)

Our main results (as detailed below) represent a crucial key to understand the formation channels of gravitational wave sources.
a) MASS AND DYNAMICS OF BLACK HOLES:
– We predict that the mass of a black hole strongly depends on the equatorial rotation of its progenitor star (Mapelli et al. 2020).
– We highlight the dramatic impact of the collapse of a residual H-rich envelope on the final mass of a black hole (Mapelli et al. 2020; Costa et al. 2021, 2022; Ballone et al. 2023).
– In Di Carlo et al. (2019) and Bouffanais et al. (2019, 2021), we demonstrated that young star clusters’ dynamics plays a major role to shape the mass function of binary black holes. This will enable us to differentiate between dynamical and isolated formation channel.
– In Di Carlo et al. (2019, 2020a), we predicted the formation, via stellar mergers, of black holes in the pair instability mass gap. The observation of GW190521 demonstrated that black holes with mass in the gap exist and can be explained by our models.
b) REDSHIFT EVOLUTION:
– Mapelli et al. (2019) predict mild evolution of black hole mass with redshift.
c) HOST GALAXIES:
Artale et al. (2019, 2020a,2020b) and Santoliquido et al. (2022) show that the merger rate density per galaxy correlates with the mass of the host galaxy.
d) INNOVATIVE CODES FOR ASTROPHYSICS:
Our codes provide a new approach to computational astrophysics. Here below, we summarize our main codes:
- population-synthesis codes: MOBSE (Giacobbo & Mapelli 2020), SEVN (Spera et al. 2019; Mapelli et al. 2020; Iorio et al. 2023; Dall'Amico et al. 2025);
- algorithms to generate realistic initial conditions of star clusters (Ballone et al. 2020a, 2020b; Torniamenti et al. 2021a, 2021b);
- FASTCLUSTER: fast semi-analytic code for star cluster evolution and black hole dynamics (Mapelli et al. 2021, 2022);
- CosmoRate: semi-analytic code for merger rate density evolution (Santoliquido et al. 2020, 2021, 2022, 2023; Sgalletta et al. 2025);
- BAYESBLACK: performs model selection via hierarchical Bayesian inference (Bouffanais et al. 2019, 2021).

DEMOBLACK logo

Mass of binary black holes from our dynamical and isolated simulations (Di Carlo et al. 2020)

Second-generation black hole spin parameters from Mapelli et al. (2021) compared to GW190521

Conceptual map of DEMOBLACK

Second-generation black hole mass from Mapelli et al. (2021) compared to GW190521

A black hole surrounded by gas structures (hydro- simulation)