Analytical effective one-body formalism for extreme-mass-ratio inspirals with eccentric orbits

Extreme-mass-ratio inspirals(EMRIs) are among the most important sources for future spaceborne gravitational wave detectors. In this kind of system, compact objects usually orbit around central supermassive black holes on complicated trajectories. Usually, these trajectories are approximated as the geodesics of Kerr space-times, and orbital evolution is simulated with the help of the adiabatic approximation. However, this approach omits the influence of the compact object on its background. In this paper, using the effective one-body formalism, we analytically calculate the trajectory of a nonspinning compact object around a massive Kerr black hole in an equatorial eccentric orbit(omitting the orbital inclination) and express the fundamental orbital frequencies in explicit forms. Our formalism includes the first-order corrections for the mass ratio in the conservative orbital motion. Furthermore, we insert the mass-ratio-related terms into the first post-Newtonian energy fluxes. By calculating the gravitational waves using the Teukolsky equations, we quantitatively reveal the influence of the mass of the compact object on the data analysis. We find that the shrinking of geodesic motion by taking small objects as test particles may not be appropriate for the detection of EMRIs.     

Binary compact object inspiral: Detection expectations

We review the current estimates of binary compact object inspiral rates in particular in view of the recently discovered highly relativistic binary pulsar J0737-3039. One of the robust results is that, because of this discovery, the rate estimates for binary neutron stars have increased by a factor of 6–7 independent of any uncertainties related to the pulsar population properties. This rate increase has dramatic implications for gravitational wave detectors. For initial LIGO, the most probable detection rates for double neutron star (DNS) inspirals is 1 event/(5-250) yr; at 95% confidence we obtain rates up to 1/1.5 yr. For advanced LIGO, the most probable rates are 20–1000 events/yr. These predictions, for the first time, bring the expectations for DNS detections by initial LIGO to the astrophysically relevant regime. We also use our models to predict that the largescale Parkes multibeam pulsar survey with acceleration searches could detect an average of three to four binary pulsars similar to those known at present. In comparison, rate estimates for binaries with black holes are derived based on binary evolution calculation, and based on the optimistic ends of the ranges, remain an important candidate for inspiral detection in the next few years. We also consider another aspect of the detectability of binary inspiral: the effect of precession on the detection efficiency of astrophysically relevant binaries. Based on our current astrophysical expectations, large tilt angles are not favored. As a result the decrease in detection rate varies rather slowly with black hole spin magnitude and is within 20–30% of the maximum possible values.