Gravitational Waves from a Compact Star in a Circular, Inspiral Orbit, in the Equatorial Plane of a Massive, Spinning Black Hole, as Observed by LISA

Abstract

Results are presented from high-precision computations of the orbital evolution and emitted gravitational waves for a stellar-mass object spiraling into a massive black hole in a slowly shrinking, circular, equatorial orbit. The focus of these computations is inspiral near the innermost stable circular orbit (isco)---more particularly, on orbits for which the angular velocity Omega is 0.03 < Omega/Omega_{isco} < 1. The computations are based on the Teukolsky-Sasaki-Nakamura formalism, and the results are tabulated in a set of functions that are of order unity and represent relativistic corrections to low-orbital-velocity formulas. These tables can form a foundation for future design studies for the LISA space-based gravitational-wave mission. A first survey of applications to LISA is presented: Signal to noise ratios S/N are computed and graphed as functions of the time-evolving gravitational-wave frequency for representative values of the hole's mass M and spin a and the inspiraling object's mass \mu, with the distance to Earth chosen to be r_o = 1 Gpc. These S/N's show a very strong dependence on the black-hole spin, as well as on M and \mu. A comparison with predicted event rates shows strong promise for detecting these waves, but not beyond about 1Gpc if the inspiraling object is a white dwarf or neutron star. This argues for a modest lowering of LISA's noise floor. A brief discussion is given of the prospects for extracting information from the observed waves