Active galactic nuclei: metallicity and gravitational wave radiation

In theory, accretion disks around supermassive black holes (SMBHs) exhibit complex structures in the outer regions, where self-gravity inevitably leads to star formation; in observations, particularly from quasar metallicity and recent LIGO gravitational wave detections, there is increasing evidence indicating the presence of massive star formation and evolution in the central regions of active galactic nuclei (AGNs). Due to the dense gas environment in the accretion disks of AGNs, stars and compact objects on these disks have high accretion rates, leading to significant changes in their fate, referred to as "accretion-modified stars'' (AMSs). This serves as a focal point for studying the evolution of population evolution, metallicity evolution, and gravitational wave radiation on AGN disks. This has given rise to a novel field with abundant theoretical problems and observational phenomena. The AMSs are allowed to have any metallicity but without significant loss due to stellar winds, since the winds are choked by the dense medium of the disks and return to the core stars. AMS mass functions undergo rapid evolution through accretion, irrespective of the initial mass functions, leading to top-heavy forms characterized by a pile-up or cutoff pile-up shape. Particularly, the cutoff pile-up shape caused by strong stellar winds presents a novel mechanism for generating a narrow window of very massive stars, enabling efficient production of iron through pair-instability supernovae in AGNs. This naturally explains the non-cosmological evolution of [Fe/Mg] of AGNs. Moreover, supernova explosions of AMSs support an inflated disk as a dusty torus. On the other hand, AMSs can generate stellar-mass black holes through supernova explosions, forming a population of satellite black holes around SMBHs. Stellar-mass black holes on accretion disks typically exhibit extremely high accretion rates. The intense gravitational energy release process can result in strong outflows, interacting with the surrounding gas and leading to a Bondi explosion. The nonthermal radiation of Bondi explosions peaks in the X-ray and gamma-ray bands, with the luminosity of the thermal radiation reaching up to $ ∼ 10^{44}\, \rm erg\,s^{-1}$. If black holes on accretion disks are close enough during their migration process, they may form binary black holes. The interaction with the surrounding gas could accelerate the merger process, providing a potential explanation for mergers of massive black holes. Furthermore, the AMS model can provide a reasonable explanation for the top-heavy stellar disk and metallicity in the Galatic center, where a satellite black hole with $40\,M_{\odot}$ can account for phenomena such as infrared flickering period and flaring orbit. It may represent the closest EMRI (extreme mass ratio inspiral) object to Earth. In the future, the combination of more gravitational wave detections with spectroscopic and photometric observation programs holds the promise of better addressing the evolution and merger issues of stars and compact objects on AGN disks.