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

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 $\alpha$-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.