Eccentricity content of binary black hole initial data

Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.

Figure 1

Binding energy (left) and angular momentum (right) for the corotating and nonspinning BH-BH initial data from 11. Circles (squares) are nonspinning (corotating) data from 11, the solid lines are circular PN diagnostics with $e=0$, the dashed lines are eccentric PN diagnostics with $e=0.025$.

Figure 2

Eccentricity required to match data points for nonspinning (left) and corotating data (right). Black lines are solutions for the energy, red lines are solutions for the angular momentum. In the nonspinning case, continuous lines refer to the Caudill et al. data [11], dashed lines to the earlier Cook-Pfeiffer data [10].

Figure 3

Eccentricity solutions for puncture initial data. Solid and dashed lines are solutions for the Tichy-Brügmann puncture data using 3PN and 2PN diagnostics, respectively. Dotted lines are from 3PN solutions for the Lazarus puncture data.