Fast Evolution and Waveform Generator for Extreme-Mass-Ratio Inspirals in Equatorial-Circular Orbits

In this paper we discuss the development of a fast and accurate waveform model for the quasi-circular orbital evolution of extreme-mass-ratio-inspirals (EMRIs). This model simply employs the data of a few numerical Teukoulsky-based energy fluxes and waveforms to fit out a set of polynomials for the entire fluxes and waveforms. These obtained polynomials are accurate enough in the entire evolution domain, and much more accurate than the resummation post-Newtonian (PN) energy fluxes and waveforms, especially when the spin of a black hole becomes large. The dynamical equation we adopted for orbital revolution is the effective-one-body (EOB) formalism. Because of the simplified expressions, the efficiency of calculating the orbital evolution with our polynomials is also better than the traditional method which uses the resummed PN analytical fluxes. Our model should be useful in calculation of waveform templates of EMRIs for the gravitational wave detectors such as the evolved Laser Interferometer Space Antenna (eLISA).