Thick Disks, Thin Hopes: Suppressed Capture and Merger Rates in AGN

TL;DR

The paper demonstrates that AGN disk thickness, governed by the dominant pressure source, sets the rates of gravitationally mediated processes through a steep $(H/R)^{-8}$ scaling, meaning thicker, magnetically or turbulently supported disks can drastically suppress capture and merger rates compared to thin, radiation-dominated models. By deriving general rate expressions and evaluating several analytic disk models (radiation, gas, gravito-turbulent, magnetic) they show that $H/R$ and $\Sigma(R)$ profiles vary by large factors across models, leading to rate differences spanning tens of orders of magnitude. This challenges previous predictions for GW/EM merger rates, accretion onto embedded objects, and gap-opening in AGN disks, suggesting that many events may be far rarer than previously thought in realistic, thicker disks. The results highlight the need to incorporate accurate disk pressure physics and geometry when forecasting observable rates for LIGO/Virgo/KAGRA and related transients, as well as the growth and dynamics of embedded objects within AGN environments.

Abstract

Multiple models have been suggested over the years to explain the structure and support of accretion disks around supermassive black holes, from the standard thin thermal-pressure-dominated $α$-disk model to more recent models that describe geometrically thicker radiation or magnetic or turbulence-dominated disks. In any case, objects embedded in the disk (e.g. compact objects, stars, gas, dust) can undergo gravitational and hydrodynamic interactions with each other leading to interesting processes such as binary interaction/capture, gravitational wave merger events, dynamical friction, accretion, gap opening, etc. It has long been argued that disks of active galactic nuclei (AGN) can enhance the rates for many of these events; however, almost all of that analysis has assumed specific thin-disk models (with aspect ratios $H/R \lesssim 0.01$). We show here that the rates for processes such as these that are mediated by gravitational cross-sections has a very strong inverse dependence on the thickness $H/R$ (scaling as steeply as $(H/R)^{-8}$), and $H/R$ can vary in the outer disk (where these processes are often invoked) by factors $\gtrsim 1000$ depending on the assumed source of pressure support in the disk. This predicts rates that can be lower by tens of orders-of-magnitude in some models, demonstrating that it is critical to account for disk parameters such as aspect ratio and different sources of disk pressure when computing any meaningful predictions for these rates. For instance, if magnetic pressure is important in the outer disk, as suggested in recent work, capture rates would be suppressed by factors $\sim 10^{10}-10^{20}$ compared to previous studies where magnetic pressure was ignored.

Figures (2)

• Figure 1: Disk aspect ratio or thickness $H/R$ versus radius $R$ (distance from the SMBH, in units of the Schwarzschild radius $R_{\rm S}$), for different assumptions corresponding to different assumed sources of dominant pressure within the disk (§\ref{['sec:models']}). For all models we assume a central SMBH mass of $10^{8}\,{\rm M}_{\odot}$ and accretion rate $\dot{M}$ equal to half the Eddington rate $\dot{M}_{\rm Edd} \equiv L_{\rm Edd}/(0.1\,c^{2})$. For the radiation and thermal-pressure dominated disks, we assume the common literature value of $0.1$ for the $\alpha$ parameter. Depending on the assumed pressure in the disk, $H/R$ at a given radius can vary by factors $\gtrsim 1000$. The right vertical axis shows $(H/R)^{-8}$, the approximate scaling for rates of multi-body gravitational interactions (e.g. binary pairing, mergers, gravitational wave events, inspiral/sinking, accretion rates onto stars or stellar-mass BHs in the disk, etc.). This can differ enormously.
• Figure 2: The total two-body capture/interaction/accretion/merger/friction/migration rate, as a function of radius for different disk models (as Fig. \ref{['fig:hor']}, same model parameters assumed). The vertical axis has arbitrary units because the absolute number/mass of interacting objects depends on the specific model assumed, but note the extremely large range in orders of magnitude. Disks with multiple comparable forms of pressure will essentially trace the lowest curve here of the different pressure terms assumed, so "adding pressure" strongly decreases the rates. Regardless of details, rates are extremely sensitive to the pressure source at each $R$. Historical models for these processes have generally assumed something between the thermal and turbulent lines here, and largely neglect magnetic pressure, but this shows that magnetic fields can lower the predicted rates by $\sim 20-30$ orders of magnitude.