Zoom-Whirl Orbits in Black Hole Binaries

Zoom-whirl behavior has the reputation of being a rare phenomenon. The concern has been that gravitational radiation would drain angular momentum so rapidly that generic orbits would circularize before zoom-whirl behavior could play out, and only rare highly tuned orbits would retain their imprint. Using full numerical relativity, we catch zoom-whirl behavior despite dissipation. The larger the mass ratio, the longer the pair can spend in orbit before merging and therefore the more zooms and whirls seen. Larger spins also enhance zoom whirliness. An important implication is that these eccentric orbits can merge during a whirl phase, before enough angular momentum has been lost to truly circularize the orbit. Waveforms will be modulated by the harmonics of zoom-whirls, showing quiet phases during zooms and louder glitches during whirls.

Figure 1

The 3PN effective potential. Top: $L_{\mathrm{IBCO}}\sim 4.4$. The straight line corresponds to the orbit $r_a=30M$. Bottom: $L\sim 4.1$, for which the orbit with $r_a=30M$ is the separatrix.

Figure 2

The initial apastron is $r_a=30M$. Left-hand column, from the top, frame 1: $L=4.10$ and the orbit rapidly moves through zoom-whirl cycles precessing by $>\pi$ ($q\sim 1/2$) between apastra. The orbit rapidly loses eccentricity but still merges with nonzero eccentricity. Frame 2: $L=3.95$ and the orbit precesses by nearly $>2\pi$ ($q\sim 1$) in the first radial cycle before merging. Frame 3: $L=3.915$ and the orbit is very nearly homoclinic, precessing by $\sim 4\pi$ ($q\sim 2$) around the unstable circular orbit before radiative losses cause merger. Right-hand column: The gravitational waveforms versus simulation time were extracted at a finite radius of $60M$.

Figure 3

The relative orbital separation in units of $M$ plotted versus the orbital phase for the series of $L$ in Fig. 2.