Accretion rates of stellar-mass compact objects embedded in AGN discs

Abstract

Stellar-mass compact objects (COs) embedded in active galactic nucleus (AGN) discs are commonly assumed to accrete via Bondi or Bondi-Hoyle-Lyttleton (BHL) prescriptions, neglecting gas angular momentum. We show that differential rotation in AGN discs can impart non-negligible angular momentum, in which case accretion proceeds through a viscous disc rather than Bondi/BHL flow. Our model provides a new framework estimating the CO accretion rate as ${\dot{M}}_{\mathrm{CO}}=\min \{{\dot{M}}_{\mathrm{vis}},{\dot{M}}_{\mathrm{BHL}}\}$, where the viscous rate ${\dot{M}}_{\mathrm{vis}}$ accounts for gas--CO relative motion decomposed into a local gradient term (due to differential rotation) and bulk motion (from differing orbital parameters). This rate can be expressed as ${\dot{M}}_{\mathrm{vis}}=\alpha \xi (r_{\mathrm{H}}/r_{\mathrm{BHL}}{)}^3{\dot{M}}_{\mathrm{BHL}}$, where $\xi$ is a coefficient of order unity. It can also be approximately scaled to the global AGN accretion rate as ${\dot{M}}_{\mathrm{vis}}\propto {\dot{M}}_1$, with the scaling coefficients in both forms determined by the specific dynamical configuration. The accretion is viscosity-limited when $q>[\alpha \xi (1+{\mathcal{M}}^2{)}^3/3{]}^{1/2}{h}^3$, where $q$ is the mass ratio between the CO and the supermassive black hole, $\alpha$ the viscosity parameter, $\mathcal{M}$ the Mach number of the bulk relative motion, and $h$ the aspect ratio of the AGN disc. In thin AGN discs this condition is satisfied for most stellar-mass or more massive COs. Our framework also naturally allows for the inclusion of established outflow corrections, thereby enabling a more realistic treatment of super-Eddington flows. Our formulation thus improves upon Bondi/BHL prescriptions and offers a more physically motivated basis for studying CO evolution in AGN environments.

14 pages, 5 figures, accepted for publication in MNRAS

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