Dr. JIAO Chengliang, an associate researcher at the Binaries and Variables Group of Yunnan Observatories, Chinese Academy of Sciences, and his collaborators have recently published a paper in The Astrophysical Journal titled “Spherically Symmetric Accretion with Self-gravity: Analytical Formulae and Numerical Validation.” The research presents a novel self-consistent model that resolves long-standing theoretical issues in self-gravitating spherical accretion.
Accretion, the process by which matter falls onto a central object, is a cornerstone of modern astrophysics. The widely adopted classical Bondi model, established in the 1950s, neglects the self-gravity of the accreted gas, which may significantly affect the flow structure and accretion rate in high-density astrophysical environments. Previous studies incorporating self-gravity also have limitations such as incorrect gravitational potential formulae in analytical treatments or the need for ad hoc parameters in numerical solutions.
To address these issues, the researchers constructed a complete three-point boundary value problem formulation for spherically symmetric accretion incorporating self-gravity, and solved it using the relaxation method. They also derived simple analytical formulae that allow rapid estimation of self-gravity effects. The model introduces a dimensionless parameter, β, which quantifies the self-gravity effects based on the external medium’s density, sound speed, outer radius, and adiabatic index.
The results revealed that when β increases, the sonic point of the accretion flow shifts inward and the accretion rate rises significantly for adiabatic indices γ between 1 and 5/3. At γ = 5/3, however, self-gravity no longer enhances the accretion rate due to the large stiffness (resistance to compression) of the gas. The study also identified an upper limit of β, beyond which steady accretion becomes unsustainable, in close agreement with classical gravitational instability theory (e.g., the Bonnor-Ebert threshold).
The researchers further demonstrated the model’s applicability to two representative astrophysical scenarios. One involves hyper-Eddington accretion onto supermassive black hole seeds in the early Universe, where self-gravity plays a significant role. The other concerns accretion onto stellar-mass objects embedded in active galactic nucleus disks, where self-gravity is non-negligible under certain conditions and should be evaluated using β.
This research was supported by the Chinese Academy of Sciences Grand Challenges Program, the Yunnan Province Special Fund for Construction of the South and Southeast Asia–Oriented Center for Technological Innovation, the Yunnan Province Key Project Fund, and the Yunnan Revitalization Talent Support Program.
Figure 1. Global solutions of the TPBVP for β = 0.65 and γ = 4/3, with different boundary conditions. Away from the outer boundary, the radial profiles of normalized physical quantities quickly converge, demonstrating the efficacy of β in characterizing self-gravity effects. Image by JIAO.
Figure 2. Normalized accretion rate as a function of β. Blue and red solid lines represent our numerical and analytical results, respectively. Yellow dashed lines indicate the theoretical predictions of previous study. Image by JIAO.
Contact:
JIAO Chengliang
Yunnan Observatories, CAS
E-mail:jiaocl@ynao.ac.cn
