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.
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