Accretion-modified Stars in Accretion Disks of Active Galactic Nuclei: Contribution to AGN disk viscosity

Abstract

It is widely believed that stellar-mass black holes (sMBHs) exist within the accretion disks of active galactic nuclei (AGN), forming a distinct population termed ``accretion-modified star" (AMS). Gas from the dense disk accretes onto these AMSs, dissipating substantial gravitational energy through a mini-disk around the sMBHs, which drives powerful outflows that interact with the surrounding disk gas. In this study, we investigate two scenarios for AMS accretion: episodic Bondi explosions with hyper-Eddington accretion (Scenario A) and steady Eddington accretion (Scenario B). These outflows generate turbulence, facilitating outward angular momentum transport in the AGN disk via shock interactions and angular momentum exchange. We explore a broad parameter space-spanning the central supermassive black hole (SMBH) mass ($M_{\rm p}$), dimensionless accretion rate ($\dot{\mathscr{M}}_{\rm p}$), sMBH mass function, and spatial distribution-to calculate the effective viscosity parameter $\alpha_{\rm AMS}$. Our analysis reveals the scaling relations $\alpha_{\rm AMS}\propto\zeta M_{\rm p}^2\dot{\mathscr{M}}_{\rm p}$ for Scenario A and $\alpha_{\rm AMS}\propto\zeta M_{\rm p}^{1.5}\dot{\mathscr{M}}_{\rm p}^{0.1}$ for Scenario B, where $\zeta$ denotes the ratio of total sMBH mass to the SMBH disk mass. For $\zeta={0.01}$ and $M_{\rm p}=10^8 M_\odot$, $\alpha_{\rm AMS}$ ranges from $\sim{3\times10^{-4}}$ to ${0.01}$ (Scenario A) and $\sim{3\times10^{-3}}$ to ${0.04}$ (Scenario B) from the inner to outer disk regions. These results demonstrate that AMS feedback provides an efficient mechanism for angular momentum transport in AGN disks.