Inspiral of the SBH into the IMBH from top to bottom and from left to right in the eccentricity-semi-major axis plane. The red solid curve starting at a very eccentric orbit shows the results of the Nbody simulation. The dashed green region corresponds to the band of a LISA-like mission. Dashed blue curves correspond to the trajectories due only to the emission of GWs in the Peters & Mathews (1963) approximation. We also plot the corresponding merger timescales in the same approximation in dashed blue lines starting at 10¹⁰ years, and in solid black lines the corresponding trajectories for evolution by GW emission Peters (1964) approximation. The black-shaded region on the right corresponds to the last stable circular orbit. Since the binary starts at a very high eccentricity, it basically follows one of the solid black lines, because it merges quickly and does not interact with other stars in the system.