Accurate effective-one-body waveforms of inspiralling and coalescing black-hole binaries

Abstract

The effective-one-body (EOB) formalism contains several flexibility parameters, notably ${a}_{5}$, ${v}_{\mathrm{pole}}$, and ${\overline{a}}_{\mathrm{RR}}$. We show here how to jointly constrain the values of these parameters by simultaneously best-fitting the EOB waveform to two, independent, numerical relativity (NR) simulations of inspiralling and/or coalescing binary black-hole systems: published Caltech-Cornell inspiral data (considered for gravitational wave frequencies $M\ensuremath{\omega}\ensuremath{\le}0.1$) on one side, and newly computed coalescence data on the other side. The resulting, approximately unique, ``best-fit'' EOB waveform is then shown to exhibit excellent agreement with NR coalescence data for several mass ratios. The dephasing between this best-fit EOB waveform and published Caltech-Cornell inspiral data is found to vary between $\ensuremath{-}0.0014$ and $+0.0008$ radians over a time span of $\ensuremath{\sim}2464M$ up to gravitational wave frequency $M\ensuremath{\omega}=0.1$, and between $+0.0013$ and $\ensuremath{-}0.0185$ over a time span of $96M$ after $M\ensuremath{\omega}=0.1$ up to $M\ensuremath{\omega}=0.1565$. The dephasings between EOB and the new coalescence data are found to be smaller than: (i) $\ifmmode\pm\else\textpm\fi{}0.025$ radians over a time span of $730M$ (11 cycles) up to merger, in the equal-mass case, and (ii) $\ifmmode\pm\else\textpm\fi{}0.05$ radians over a time span of about $950M$ (17 cycles) up to merger in the $2\ensuremath{\mathbin:}1$ mass-ratio case. These new results corroborate the aptitude of the EOB formalism to provide accurate representations of general relativistic waveforms, which are needed by currently operating gravitational wave detectors.