A research team from the Yunnan Observatories of the Chinese Academy of Sciences (CAS), in collaboration with other researchers, has developed a new method to estimate how stellar-mass compact objects (COs)—including black holes, neutron stars, and white dwarfs—accrete matter within active galactic nucleus (AGN) disks. This work provides new insights into the evolution of these objects in extreme cosmic environments.

The team's findings were recently published in Monthly Notices of the Royal Astronomical Society.

AGNs are bright galactic centers powered by supermassive black holes (SMBHs) surrounded by gaseous disks. Within these disks, stellar-mass COs can grow, migrate, and form merging binaries—processes critical to generating gravitational wave events and high-energy transients. Prior studies have typically relied on Bondi or Bondi–Hoyle–Lyttleton (BHL) models to calculate accretion rates. However, these models ignore the angular momentum in the relative motion between gas and COs, leading to potential overestimates of accretion rates.

To address this challenge, the researchers established a unified analytical framework that incorporates the effects of angular momentum. Their analysis shows that differential rotation within AGN disks imparts significant angular momentum to gas approaching an embedded CO. This usually results in the formation of a viscous accretion disk around the CO, rather than the classical Bondi/BHL flow patterns assumed in earlier models.

The team derived a new formula to calculate viscous accretion rates and proposed that the actual CO accretion rate is the minimum of this viscous rate and the BHL rate. The shift between these two accretion modes depends on the CO–SMBH mass ratio, AGN disk aspect ratio, and orbital configurations. Specifically, in thin AGN disks, COs primarily undergo viscosity-limited accretion. In contrast, BHL accretion dominates in thicker disks, such as slim disks or advection-dominated accretion flows (ADAFs).

A key outcome of the study is a scaling relation: the viscous accretion rate of COs is proportional to the global accretion rate of the AGN disk, with a proportionality factor of approximately 0.38 for COs in corotating Keplerian orbits. This relation is valuable for population-level studies, such as estimating the mass growth of embedded COs or predicting the merger rates of binary black holes.

The new framework offers a more physically accurate foundation for studying CO evolution in AGN disks, the researchers noted. Additionally, it can integrate established outflow correction factors, enabling more precise calculations of super-Eddington flows.

This research was supported by funding from the CAS Grand Challenges Program, the Yunnan Province Special Fund for the Construction of the South and Southeast Asia–Oriented Center for Technological Innovation, and other research initiatives.