2023MNRAS.520.4502W

Gas accretion of embedded stellar-mass black holes (sBHs) or stars in the accretion disc of active galactic nuclei (AGNs) will modify the mass distribution of these sBHs and stars, which will also affect the migration of the sBHs/stars. With the introduction of the mass accretion effect, we simulate the evolution of the sBH/star distribution function in a consistent way by extending the Fokker-Planck equation of sBH/star distributions to the mass-varying scenario, and explore the mass distribution of sBHs in the nuclear region of the galaxy centre. We find that the sBHs can grow up to several tens solar mass and form heavier sBH binaries, which will be helpful for us to understand the black-hole mass distribution as observed by the current and future ground-based gravitational wave detectors (e.g. LIGO/Virgo, ET and Cosmic Explorer). We further estimate the event rate of extreme mass-ratio inspirals (EMRI) for sBH surrounding the massive black hole and calculate the stochastic gravitational wave (GW) background of the EMRIs. We find that the background can be detected in future space-borne GW detectors after considering the sBHs embedded in the AGN disc, while the mass accretion has a slight effect on the GW background.