Viscous torque in turbulent magnetized active galactic nucleus accretion disks and its effects on the gravitational waves of extreme mass ratio inspirals

The merger of supermassive black holes produces millihertz gravitational waves (GWs), which are potentially detectable by the future Laser Interferometer Space Antenna (LISA). Such binary systems are usually embedded in an accretion disk environment at the center of an active galactic nucleus (AGN). Recent studies suggest the plasma environment imposes measurable imprints on the GW signal if the mass ratio of the binary is around q ∼ 10⁻⁴ − 10⁻³. The effect of the gaseous environment on the GW signal is strongly dependent on the disk's parameters; therefore, it is believed that future low-frequency GW detections will provide us with precious information about the physics of AGN accretion disks. We investigated this effect by measuring the viscous torque via modeling of the evolution of magnetized tori around the primary massive black hole. Using the general relativistic magnetohydrodynamic HARM-COOL code, we performed 2D and 3D simulations of weakly magnetized, thin accretion disks, with a possible truncation and transition to advection-dominated accretion flow. We studied the angular momentum transport and turbulence generated by the magnetorotational instability. We quantified the disk's effective alpha viscosity and its evolution over time. We applied our numerical results to quantify the relativistic viscous torque on a hypothetical low-mass secondary black hole via a 1D analytical approach, and we estimated the GW phase shift due to the gas environment.