Extreme mass ratio inspiral

Scientific potential or eLISA, but outside the band for ground-based detectors like advanced LIGO (aLIGO) or pulsar timing arrays such as the European Pulsar Timing Array (EPTA). If successfully detected, the gravitational wave signal from an EMRI will carry a wealth of astrophysical data. EMRIs evolve slowly and complete many (~10,000) cycles before eventually plunging. Therefore, the gravitational wave signal encodes a precise map of the spacetime geometry of the supermassive black hole. Consequently, the signal can be used as an accurate test of the predictions of general relativity in the regime of strong gravity; a regime in which general relativity is completely untested. In particular, it is possible to test the hypothesis that the central object is indeed a supermassive black hole to high accuracy by measuring the quadrupole moment of the gravitational field to an accuracy of a fraction of a percent. • The mass of the orbiting object to an accuracy of 1 in 10,000. The population of these masses could yield interesting insights in the population of compact objects in the nuclei of galaxies. ==Formation==

It is currently thought that the centers of most (large) galaxies consist of a supermassive black hole of 106 to 109 solar masses () surrounded by a cluster of 107 to 108 stars maybe 10 light-years across, called the nucleus. However, if the object passes too close to the central supermassive black hole, it will make a direct plunge across the event horizon. This will produce a brief violent burst of gravitational radiation which would be hard to detect with currently planned observatories. Consequently, the creation of EMRI requires a fine balance between objects passing too close and too far from the central supermassive black hole. Currently, the best estimates are that a typical supermassive black hole of , will capture an EMRI once every 106 to 108 years. This makes witnessing such an event in our Milky Way unlikely. However, a space based gravitational wave observatory like LISA will be able to detect EMRI events up to cosmological distances, leading to an expected detection rate somewhere between a few and a few thousand per year. As the orbit shrinks due to the emission of gravitational waves, it becomes more circular. When it has shrunk enough for the gravitational waves to become strong and frequent enough to be continuously detectable by LISA, the eccentricity will typically be around 0.7. Since the distribution of objects in the nucleus is expected to be approximately spherically symmetric, there is expected to be no correlation between the initial plane of the inspiral and the spin of the central supermassive black holes. The "Schwarzschild Barrier" was thought to be an upper limit to the eccentricity of orbits near a supermassive black hole. Gravitational scattering would drive by torques from the slightly asymmetric distribution of mass in the nucleus ("resonant relaxation"), resulting in a random walk in each star's eccentricity. When its eccentricity would become sufficiently large, the orbit would begin to undergo relativistic precession, and the effectiveness of the torques would be quenched. It was believed that there would be a critical eccentricity, at each value of the semi-major axis, at which stars would be "reflected" back to lower eccentricities. However, it is now clear that this barrier is nothing but an illusion, probably originating from an animation based on numerical simulations, as described in detail in two works. The role of the spin It was realised that the role of the spin of the central supermassive black hole in the formation and evolution of EMRIs is crucial. proved that these capture orbits accumulate thousands of cycles in the detector band. Since they are driven by two-body relaxation, which is chaotic in nature, they are ignorant of anything related to a potential Schwarzchild barrier. Moreover, since they originate in the bulk of the stellar distribution, the rates are larger. Additionally, due to their larger eccentricity, they are louder, which enhances the detection volume. It is therefore expected that EMRIs originate at these distances, and that they dominate the rates. There are many uncertainties in the expected frequency for such events, but some calculations suggest there may be up to several tens of these events detectable by LISA per year. If these events do occur, they will result in an extremely strong gravitational wave signal, that can easily be detected. ==Modelling==

Although the strongest gravitational wave from EMRIs may easily be distinguished from the instrumental noise of the gravitational wave detector, most signals will be deeply buried in the instrumental noise. However, since an EMRI will go through many cycles of gravitational waves (~105) before making the plunge into the central supermassive black hole, it should still be possible to extract the signal using matched filtering. In this process, the observed signal is compared with a template of the expected signal, amplifying components that are similar to the theoretical template. To be effective this requires accurate theoretical predictions for the wave forms of the gravitational waves produced by an extreme mass ratio inspiral. This, in turn, requires accurate modelling of the trajectory of the EMRI. Issues with traditional binary modelling approaches Post-Newtonian expansion One common approach is to expand the equations of motion for an object in terms of its velocity divided by the speed of light, v/c. This approximation is very effective if the velocity is very small, but becomes rather inaccurate if v/c becomes larger than about 0.3. For binary systems of comparable mass, this limit is not reached until the last few cycles of the orbit. EMRIs, however, spend their last thousand to a million cycles in this regime, making the post-Newtonian expansion an inappropriate tool. And significant progress has been made for calculating the gravitational self force around a rotating black hole.{{cite journal |first1=Niels |last1=Warburton |first1=Niels |last1=Warburton ==Notes==