The role of the supermassive black hole spin in the estimation of the EMRI event rate

One of the main channels of interactions in galactic nuclei between stars and the central massive black hole (MBH) is the gradual inspiral of compact remnants into the MBH due to the emission of gravitational radiation. This process is known as an 'extreme mass ratio inspiral' (EMRI). Previous works about the estimation of how many events space observatories such as LISA will be able to observe during its operational time differ in orders of magnitude, due to the complexity of the problem. Nevertheless, a common result to all investigations is that the possibility that a compact object merges with the MBH after only one intense burst of gravitational waves is much more likely than a slow adiabatic inspiral, an EMRI. The latter is referred to as a 'plunge' because the compact object dives into the MBH, crosses the horizon and is lost as a probe of strong gravity for evolved Laser Interferometer Space Antenna (eLISA). The event rates for plunges are orders of magnitude larger than slow inspirals. On the other hand, nature MBH's are most likely Kerr and the magnitude of the spin has been sized up to be high. We calculate the number of periapsis passages that a compact object set on to an extremely radial orbit goes through before being actually swallowed by the Kerr MBH and we then translate it into an event rate for a LISA-like observatory, such as the proposed European Space Agency mission eLISA/New Gravitational wave Observatory. We prove that a 'plunging' compact object is conceptually indistinguishable from an adiabatic, slow inspiral; plunges spend on average up to hundred of thousands of cycles in the bandwidth of the detector for a 2 yr mission. This has an important impact on the event rate, enhancing in some cases significantly, depending on the spin of the MBH and the inclination. If the orbit of the EMRI is prograde, the effective size of the MBH becomes smaller for larger spin, whilst if retrograde, it becomes bigger. However, this situation is not symmetric, resulting in an effective enhancement of the rates. The effect of vectorial resonant relaxation on the sense of the orbit does not affect the enhancement. Moreover, it has been recently proved that the production of low-eccentricity EMRIs is severely blocked by the presence of a blockade in the rate at which orbital angular momentum change takes place. This is the result of relativistic precession on to the stellar potential torques and hence affects EMRIs originating via resonant relaxation at distances of about similar to 10(-2) pc from the MBH. Since high-eccentricity EMRIs are a result of two-body relaxation, they are not affected by this phenomenon. Therefore, we predict that eLISA EMRI event rates will be dominated by high-eccentricity binaries, as we present here.