Spin-dominated waveforms for unequal mass compact binaries

Abstract

We derive spin-dominated waveforms (SDW) for binary systems composed of spinning black holes with unequal masses (less than $1\ensuremath{\mathbin:}30$). Such systems could be formed by an astrophysical black hole with a smaller black hole or a neutron star companion; and typically arise for supermassive black hole encounters. SDW characterize the last stages of the inspiral, when the larger spin dominates over the orbital angular momentum (while the spin of the smaller companion can be neglected). They emerge as a double expansion in the post-Newtonian parameter $\ensuremath{\epsilon}$ and the ratio $\ensuremath{\xi}$ of the orbital angular momentum and dominant spin. The SDW amplitudes are presented to $({\ensuremath{\epsilon}}^{3/2},\ensuremath{\xi})$ orders, while the phase of the gravitational waves to $({\ensuremath{\epsilon}}^{2},\ensuremath{\xi})$ orders (omitting the highest order mixed terms). To this accuracy the amplitude includes the (leading order) spin-orbit contributions, while the phase the (leading order) spin-orbit, self-spin and mass quadrupole-monopole contributions. While the SDW hold for any mass ratio smaller than $1\ensuremath{\mathbin:}30$, lower bounds for the mass ratios are derived from the best sensitivity frequency range expected for Advanced LIGO (giving $1\ensuremath{\mathbin:}140$), the Einstein Telescope ($7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$), the LAGRANGE ($7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$) and LISA missions ($7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$), respectively.