Black hole-black hole mergers with and without an electromagnetic counterpart: A model for stable tertiary mass transfer in hierarchical triple systems

Context. Triple stars are prevalent within the population of observed stars. Their evolution compared to binary systems is notably more complex and is influenced by unique dynamical, tidal, and mass transfer processes inherent in higher order multiples. Understanding these phenomena is essential for comprehensive insight into multistar evolution and the formation of energetic transients, including gravitational wave (GW) mergers. Aims. Our study aims to probe the evolution of triple star systems when the tertiary component fills its Roche lobe and transfers mass to the inner binary. Specifically, we focus on the impact of tertiary mass transfer on the evolution of the inner orbit and investigate whether it could lead to the formation of GW sources with distinct properties. Methods. To achieve this, we developed an analytical model that describes the evolution of the inner and outer orbits of hierarchical triples undergoing stable mass transfer from the tertiary component. We have publicly released this model as a python package on Zenodo. Utilising population synthesis simulations, we investigated triples with a Roche-lobe filling tertiary star and an inner binary black hole (BBH). These systems stem from inner binaries experiencing chemically homogeneous evolution (CHE). Our analysis encompasses two distinct populations with metallicities of Z = 0.005 and Z = 0.0005, focusing on primary components in the inner binary with initial masses ranging from 20-100 Mo and inner and outer orbital separations of up to 40 Ro and 105 Ro, respectively, targeting the parameter space where chemically homogeneous evolution is anticipated. Results. Our results indicate that for the systems we studied, the mass transfer phase predominantly leads to orbital shrinkage of the inner binary and evolution towards non-zero eccentricities and is accompanied by an expansion of the outer orbit. In the systems where the inner binary components evolve in a chemically homogeneous manner, 9.5% result in mass transfer from the tertiary onto an inner BBH. Within this subset, we predict a high formation efficiency of GW mergers ranging from 85.1-100% at Z = 0.005 and 100% at Z = 0.0005 with short delay times, partly attributable to the mass transfer phase. Owing to the rarity of triples with a CHE inner binary in the stellar population, we project local merger rates in the range of 0.69-1.74 Gpc-3 yr-1. Of the prospected BBH mergers that enter the LISA and aLIGO frequency band due to GW emission, a fraction is still accreting gas from the tertiary star. This could produce a strong electromagnetic (EM) counterpart to the GW source and maintain high eccentricities as the system enters the frequency range detectable by GW detectors. The occurrence of EM signals accompanying mergers varies significantly depending on model assumptions, with fractions ranging from less than 0.03% to as high as 46.8% of all mergers if the formation of a circumbinary disc is allowed. © The Authors 2025.