Viscous torque in turbulent magnetized AGN accretion disks and its effects on EMRI's gravitational waves

The merger of supermassive black holes (SMBHs) produces mHz gravitational waves (GW), which are potentially detectable by future Laser Interferometer Space Antenna (LISA). Such binary systems are usually embedded in an accretion disk environment at the centre of the 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 $ \sim10^{-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 investigate this effect by measuring the viscous torque via modelling the evolution of magnetized tori around the primary massive black hole. Using GRMHD HARM-COOL code, we perform 2D and 3D simulations of weakly-magnetized thin accretion disks, with a possible truncation and transition to advection-dominated accretion flow (ADAF). We study the angular momentum transport and turbulence generated by magnetorotational instability (MRI). We quantify the disk's effective alpha viscosity and its evolution over time. We apply our numerical results to quantify the relativistic viscous torque on a hypothetical low-mass secondary black hole via a 1D analytical approach, and we estimate the GW phase shift due to the gas environment.