Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions

TL;DR

This work studies the collision of two highly boosted equal-mass, nonrotating black holes with generic impact parameter and finds such systems to exhibit zoom-whirl behavior when fine-tuning the impact parameter.

Abstract

We study the collision of two highly boosted equal mass, nonrotating black holes with generic impact parameter. We find such systems to exhibit zoom-whirl behavior when fine tuning the impact parameter. Near the threshold of immediate merger the remnant black hole Kerr parameter can be near maximal (a/M about 0.95) and the radiated energy can be as large as 35% of the center-of-mass energy.

Figures (3)

• Figure 1: An illustration of how we estimate $n_{\rm GW}$, here for $b=3.36M$. The horizontal lines correspond to maximum, half-maximum and zero luminosity in the flux; the vertical line is when the flux drops below half maximum. For reference, in the inset are puncture trajectories of one BH for this case (thick solid blue line), $b=3.34M$ (thin solid black line) and $b=3.39M$ (dash-dotted red line). All trajectories overlap early on during the whirl; the $b=3.39M$ trajectory peels off first before merging later, while the $b=3.34M$ case immediately spirals in after the whirl. The $b=3.36M$ case marginally peels off before merging, but it is clear from the luminosity that the merger/ringdown phase beginning after $t/M\sim 280$ is quite distinct from the preceeding whirl phase.
• Figure 2: Estimated number of orbits using puncture trajectories (left) and GWs (right) as a function of distance from $b^{*}$ for immediate and nonprompt merger cases in sequence 1. The uncertainties in the fitted slopes to Eq. (\ref{['n_gamma']}) are purely from the linear regression analysis.
• Figure 3: Total energy radiated (left) and final BH spin (right) vs. impact parameter from sequence 2, the latter calculated using several methods. The vertical dashed green (dotted red) line is the estimated immediate merger threshold $b^*$ (the scattering threshold $b_{\rm scat}$).