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 $α_{\rm AMS}$. Our analysis reveals the scaling relations $α_{\rm AMS}\proptoζM_{\rm p}^2\dot{\mathscr{M}}_{\rm p}$ for Scenario A and $α_{\rm AMS}\proptoζM_{\rm p}^{1.5}\dot{\mathscr{M}}_{\rm p}^{0.1}$ for Scenario B, where $ζ$ denotes the ratio of total sMBH mass to the SMBH disk mass. For $ζ={0.01}$ and $M_{\rm p}=10^8 M_\odot$, $α_{\rm AMS}$ 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.

Figures (11)

• Figure 1: Radial distribution of the gas density $\rho$, half-thickness $H$, sound speed $c_{\rm s}$, midplane temperature $T_{\rm c}$, and total pressure $p$ for a standard disk model, shown for different SMBH masses ($M_{\rm p}$) and accretion rates ($\dot{\mathscr{M}}_{\rm p}$).
• Figure 2: Schematic illustration of AMSs in an AGN accretion disk. The upper left panel depicts a Type I AMS during the Bondi explosion phase, in which a strong outflow interacts with the surrounding disk gas. The upper right panel shows a Type II AMS in the subsequent rejuvenation phase, characterized by a low-density cavity. The bottom panel illustrates the general scenario of sMBHs embedded in the dense AGN disk, accreting gas and forming AMSs. Gas density is color-coded: yellow (high), red (medium), and brown (low).
• Figure 3: Top: The disk height $H$, the Hill radius $R_{\rm Hill}$, the Bondi radius $R_{\rm Bon}$, and the size of the sMBH disk $X_{\rm out}$ as functions of the disk radius $R$. Bottom: The sound speed $c_{\rm s}$ and the differential velocity $\Delta v$ between the sMBH and the disk gas. The left, middle, and right panels correspond to sMBH masses of 10$M_\odot$, 100$M_\odot$, and 1000 $M_\odot$, respectively. The SMBH mass and accretion rate are fixed at $M_{\rm p}=10^8M_\odot$ and $\dot{\mathscr{M}}_{\rm p}=1$.
• Figure 4: Radial profiles of key quantities in the Bondi explosion scenario (Scenario A), showing their variation with disk radius and sMBH mass ($M_{\rm s}$). Quantities include $\dot{\mathscr{M}}_{\rm s}$ (dimensionless sMBH accretion rate), $f_{\rm acc}$ (accretion rate fraction), $L_{\rm out}$ (outflow power), $t_{\rm out}$ (outflow expansion time), $E_{\rm out}$ (total outflow energy), $v_{\rm out}$ (outflow velocity), $t_{\rm rej}$ (rejuvenation time), $\delta$ (duty cycle), and $\dot{\mathscr{M}}_{\rm grow}$ (net sMBH growth rate). The SMBH mass and accretion rate are fixed at $M_{\rm p}=10^8M_\odot$ and $\dot{\mathscr{M}}_{\rm p}=1$.
• Figure 5: Radial profiles of the effective viscosity parameter $\alpha_{\rm eff}$ for Scenario A (top) and B (bottom), comparing different sMBH number density distributions parameterized by $\beta$ and $\gamma$. The SMBH mass and accretion rate are fixed at $M_{\rm p}=10^8M_\odot$ and $\dot{\mathscr{M}}_{\rm p}=1$.