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

TL;DR

This paper demonstrates strong agreement between analytical EOB predictions and numerical simulations for circular orbits of corotating binary black holes, supporting the integration of these methods for modeling inspiral, plunge, and merger phases.

Contribution

It shows that the EOB analytical model accurately predicts numerical results for corotating binary black holes, validating its use across different post-Newtonian orders and resummation choices.

Findings

Good agreement between numerical and analytical results for invariant functions.

Agreement improves with higher post-Newtonian accuracy.

EOB approach can be calibrated with numerical data for better modeling.

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.