A research team led by Prof. JIAO Chengliang at the Yunnan Observatories of the Chinese Academy of Sciences, along with collaborators, has introduced a self-consistent model that addresses long-unresolved theoretical gaps in the study of self-gravitating spherical accretion. This study was recently published in The Astrophysical Journal.
Accretion, the fundamental astrophysical process by which matter is drawn onto a central celestial object (such as a black hole or star), underpins our understanding of phenomena ranging from star formation to black hole growth. For decades, the classical Bondi model-developed in the 1950s and still widely used today-has served as the backbone of accretion research. However, this foundational framework overlooks a critical factor: the self-gravity of the gas being accreted. This omission, the researchers note, can drastically alter flow structures and accretion rates in high-density astrophysical environments, limiting the model's accuracy in key scenarios.
To address this challenge, the team developed a comprehensive mathematical framework: a three-point boundary value problem tailored to spherically symmetric accretion that fully incorporates the self-gravity of the accreted gas.
The researchers used a relaxation method, a numerical technique ideal for refining solutions to nonlinear systems, and derived simplified analytical formulas, enabling astronomers to quickly estimate the impact of self-gravity without intensive computational work.
At the core of the new model is a dimensionless parameter, denoted as β, which quantifies self-gravity effects based on four measurable properties of the surrounding medium: density, sound speed, outer radius, and adiabatic index (a measure of how a gas responds to temperature and pressure changes).
These findings reveal key insights into how self-gravity shapes accretion:
As β increases (indicating stronger self-gravity), the "sonic point" of the accretion flow-where the gas transitions from subsonic to supersonic speed-shifts inward toward the central object.
For adiabatic indices (γ) between 1 and 5/3 (a range encompassing most astrophysical gases), higher β values also lead to a significant increase in accretion rate.
A critical exception emerges at γ = 5/3: Here, the gas's high "stiffness" (resistance to compression) negates self-gravity's effect, and no further increase in accretion rate is observed.
The study also identifies an upper limit for β: Exceeding this threshold makes steady accretion impossible-a result that aligns closely with classical gravitational instability theory, including the well-known Bonnor-Ebert threshold (which defines when a gas cloud collapses under its own weight).
To validate the model's real-world utility, the researchers applied it to two iconic astrophysical scenarios:
Hyper-Eddington accretion onto supermassive black hole seeds in the early Universe: This extreme process, where accretion occurs far faster than the rate predicted by the Eddington limit (a traditional upper bound), depends heavily on self-gravity-making the new model critical for understanding how the first supermassive black holes formed.
Accretion onto stellar-mass objects in active galactic nucleus (AGN) disks: AGNs-luminous cores of galaxies powered by supermassive black holes-host disks of gas and dust where stars and compact objects (e.g., neutron stars) form. The study shows self-gravity becomes non-negligible in these disks under certain conditions, and β provides a reliable tool to assess its influence.
This study offers a novel framework to study accretion across cosmic scales-from stellar formation to the evolution of the earliest black holes.
This work was supported by the CAS Grand Challenges Program, and the Yunnan Province Special Fund for Construction of the South and Southeast Asia, among other sources.
