Gravitational wave emission from a binary black hole system in the presence of an accretion disk

We study the time evolution and gravitational wave emission properties of a black hole orbiting inside an accretion disk surrounding a massive black hole. We simultaneously solve the structure equations of the accretion disk in the presence of heating, cooling, and viscosity as well as the equations governing the companion orbit. The deviation from the Keplerian distribution of the angular momentum of the disk due to pressure and advection effects causes a significant exchange of angular momentum between the disk and the companion. This significantly affects the gravitational wave emission properties from the binary system. We show that when the companion is light, the effect is extremely important and must be taken into account while interpreting gravitational wave signals from such systems.