Unequal Mass Binary Black Hole Plunges and Gravitational Recoil

TL;DR

This work investigates gravitational recoil from unequal-mass binary black hole mergers by simulating plunges from the innermost stable circular orbit and tracking gravitational-wave emission and the remnant kick. They perform fully nonlinear evolutions with the moving-puncture/BSSN framework using QC-0 initial data and mass ratios q in {1,0.85,0.78,0.55,0.32} (corresponding reduced mass parameters in {0.25,0.248,0.246,0.229,0.183}). Waveforms are extracted mainly from the l=2,m=2 and l=3,m=3 modes, yielding radiated energy Erad, radiated angular momentum Jrad, and recoil velocities V in the range 25 to 82 km/s, with uncertainties due to near-ISCO initial conditions. The results align with prior numerical and PN estimates in similar regimes and underscore plunge-dominated kicks, while noting limitations from close initial separations and possible eccentricities requiring future work with widely separated, quasi-circular configurations.

Abstract

We present results from fully nonlinear simulations of unequal mass binary black holes plunging from close separations well inside the innermost stable circular orbit with mass ratios q = M_1/M_2 = {1,0.85,0.78,0.55,0.32}, or equivalently, with reduced mass parameters $η=M_1M_2/(M_1+M_2)^2 = {0.25, 0.248, 0.246, 0.229, 0.183}$. For each case, the initial binary orbital parameters are chosen from the Cook-Baumgarte equal-mass ISCO configuration. We show waveforms of the dominant l=2,3 modes and compute estimates of energy and angular momentum radiated. For the plunges from the close separations considered, we measure kick velocities from gravitational radiation recoil in the range 25-82 km/s. Due to the initial close separations our kick velocity estimates should be understood as a lower bound. The close configurations considered are also likely to contain significant eccentricities influencing the recoil velocity.

Figures (5)

• Figure 1: The irreducible mass of the apparent horizon as a function of time for different mass ratios $q$.
• Figure 2: Snapshots of the AH location in the $xy$-plane for the case $q=0.78$. The larger BH is on the left moving toward the bottom. The snapshots are taken every $4.6\,M_\text{ADM}$ prior to merger and at $t=\lbrace 40,80,105 \rbrace\,M_\text{ADM}$ after merger. The first common AH is found at $t=9.9\,M_\text{ADM}$. The trajectories of the AH centroids are also shown. The common AH moves to the right and slightly upward after merger.
• Figure 3: The dominant modes ($\ell=2, m=2$ and $\ell=3, m=3$) of the real part of the Zerilli function $\psi_{\ell m}$ against time for the different $q$ ratios. The waveforms were extracted at $r=15$. The $\ell=2, m=2$ mode decreases in amplitude with decreasing $q$ while the $\ell=3,m=3$ mode increases and then decreases again.
• Figure 4: Recoil velocity accumulated against time for the different models. Note that in comparison to far separated inspiral models (Baker:2006vnGonzalez:2006md) the inspiral contribution is missing. Also the $q=0.32$ case shows an initial offset from zero which comes from the too close extraction radius.
• Figure 5: A comparison of recoil velocity estimates as a function of $\eta$. The 2PN estimates of Blanchet et al. Blanchet:2005rj are denoted by the solid line and those from Gopakumar-Damour Damour:2006tr by a dashed line. Campanelli 2005CQGra..22S.387C and Baker et al. Baker:2006vn kicks are labeled by a circle and a box, respectively, and our recoil velocities are labeled with diamonds. Note that the smaller $\eta$ cases present lower bounds due to the initial data configurations studied.