
Accretion disks interact gravitationally with surrounding objects like stars and dark matter.Gravitational interaction in accretion disks refers to the mutual gravitational influence between the disk of matter spiraling into a central object (like a black hole or neutron star) and other bodies, such as companion stars, planets, or dark matter particles. These interactions can shape the disk's structure, cause warping or precession, and even drive the migration of embedded objects. In binary systems, the gravitational pull of a companion star can truncate the disk or induce periodic variations in its brightness.
The study of accretion disk dynamics dates back to the 1970s with the development of the standard thin disk model by Shakura and Sunyaev. The role of external gravitational perturbations was recognized early on in the context of binary X-ray sources.
The gravitational force from an external object perturbs the orbits of particles in the disk, leading to density waves, resonances, and torques that transfer angular momentum. For example, a companion star can create a gap in the disk if its gravitational influence is strong enough, or it can cause the disk to precess like a spinning top. Dark matter interactions, though weaker, could leave subtle signatures in the disk's dynamics or in the timing of signals from the central object.
These interactions are crucial for interpreting observations of X-ray binaries and active galactic nuclei, where periodic variations in light curves can reveal the presence of companion objects or the disk's response to gravitational perturbations.
In some systems, the gravitational interaction between a black hole's accretion disk and a misaligned companion star can cause the disk to warp and precess, leading to quasi-periodic oscillations in X-ray emission.
| \dot{M} | variable | mass accretion rate — mass accretion rate kilogram per second |
| M | variable | mass of the gravitating body — mass kilogram |
| \rho_\infty | variable | ambient gas density at infinity — mass density kilogram per cubic metre |
| c_s | variable | sound speed in the gas — speed metre per second |
| v_{\text{rel}} | variable | relative velocity of the body through the gas — velocity metre per second |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \lambda | constant | dimensionless accretion efficiency factor of order unity — accretion efficiency = 1 |
| r_H | variable | Accretion horizon radius — radius metre |
| \dot{M} | variable | Mass accretion rate — mass flow rate kilogram per second |
| \rho | variable | Mass density of accreting material — mass density kilogram per cubic metre |
| c_s | variable | Sound speed in accreting material — speed metre per second |
| P | variable | accretion power — power watt |
| η | variable | efficiency of mass-to-energy conversion |
| Ṁ | variable | mass accretion rate — mass flow rate kilogram per second |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |










