Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. II. Importance of the second-order dissipative effect

Abstract

We consider the importance of the second-order dissipative self-force for gravitational wave dephasing for an extreme or intermediate mass ratio system moving along a quasicircular Schwarzschild orbit. For the first-order self-force we use the fully relativistic force in the Lorenz gauge for eternally circular geodesics. The second-order self-force is modeled by its 3.5 post-Newtonian counterpart. We evolve the system using the osculating orbits method, and obtain the gravitational waveforms, whose phase includes all the terms---within our approximation (and using the self-force along circular geodesics)---that are independent of the system's mass ratio. The partial dephasing due to the second-order dissipative self-force is substantially smaller than that of the first-order conservative self-force, although they are both at the same order in the mass ratio.