Circular orbits of corotating binary black holes: comparison between analytical and numerical results

TL;DR

The paper tests spinning effective-one-body (EOB) predictions against helically symmetric (HKV) numerical results for corotating binary black holes on circular orbits, exploring robustness across PN orders and resummation schemes. It finds good agreement between EOB and HKV for multiple invariant orbital functions, with spin effects in corotating sequences being small due to near-cancellation between kinetic-spin and spin-orbit contributions. The work argues for a practical analytic-numerical hybrid approach, where EOB describes inspiral up to the onset of plunge and HKV/numerical methods handle plunge and merger, and shows that the EOB Hamiltonian can be tuned via a few parameters to better fit numerical data. It also explains discrepancies with older IVP results and highlights the flexibility and robustness of the EOB framework for spinning binaries.

Abstract

We compare recent numerical results, obtained within a ``helical Killing vector'' (HKV) approach, on circular orbits of corotating binary black holes to the analytical predictions made by the effective one body (EOB) method (which has been recently extended to the case of spinning bodies). On the scale of the differences between the results obtained by different numerical methods, we find good agreement between numerical data and analytical predictions for several invariant functions describing the dynamical properties of circular orbits. This agreement is robust against the post-Newtonian accuracy used for the analytical estimates, as well as under choices of resummation method for the EOB ``effective potential'', and gets better as one uses a higher post-Newtonian accuracy. These findings open the way to a significant ``merging'' of analytical and numerical methods, i.e. to matching an EOB-based analytical description of the (early and late) inspiral, up to the beginning of the plunge, to a numerical description of the plunge and merger. We illustrate also the ``flexibility'' of the EOB approach, i.e. the possibility of determining some ``best fit'' values for the analytical parameters by comparison with numerical data.

Figures (6)

• Figure 1: Various representations of the function $\overline{A} (u , \widehat{a}^2)$. The right figure is a enlargement of the LSO region.
• Figure 2: Various Padé approximants of the function $\overline{A} (u , \widehat{a}^2)$. The right figure is a enlargement of the LSO region.
• Figure 3: Maximum binding energy configurations (LSO) obtained with various analytical and numerical methods. Empty (resp. filled) symbols denote irrotational (resp. corotating) systems. 'EOB 3PN' denotes the computation performed with the Padé approximant $\overline{A}(u,{\hat{a}}^2)$ given by Eq. (\ref{['eq2.14']}), whereas 'EOB 3PN (1-2u)' corresponds to the $\overline{A}'(u,{\hat{a}}^2)$ form given by Eq. (\ref{['eq2.15']}). References are as follows: Blanchet 2002 B02; Buonanno & Damour 1999 BD00; Damour et al. 2000 DJS00; Baumgarte 2000 baumgarte; Cook 1994 cook; Pfeiffer et al. 2000 PfeifTC00; Grandclément et al. GGB2.
• Figure 4: Binding energy as a function of the orbital velocity, for the various alternatives to the $\overline{A}(u,{\hat{a}}^2)$ function.
• Figure 5: Binding energy as a function of the orbital angular velocity, according to various analytical and numerical methods.