Why do spinning black hole binaries "bob" and "kick"?

Abstract

Numerical simulations of binary black holes with spin have revealed some surprising behavior: for antialigned spins in the orbital plane, 1) one sees an up-and-down "bobbing" of the entire orbital plane at the orbital frequency and 2) the merged black hole receives an enormous kick that depends on the phase at merger. Natural questions are: What causes the bobbing? Can the kick be viewed as a post-merger continuation of the bobbing? We show that this type of bobbing is in fact ubiquitous in relativistic mechanics, occurring independently of the type of force holding two spinning bodies in orbit. The cause can be identified as a spin correction to the naive center of mass of a body; the effect is analogous to Thomas precession and is ``purely kinematical'' in the same way. Since a kick requires the release of field momentum, it is instead very dependent on the type of force holding bodies in orbit. In a mechanical analog (spinning balls connected by a string), there is bobbing but can be no kick. In an electromagnetic analog, one should be able to tune the kick independently of the bobbing. In the gravitational case the spin parameter happens to control both bobbing and kick, making separate tuning impossible and giving the appearance of causation to two essentially unrelated phenomena. Our answers are therefore: the bobbing is caused by a purely kinematical effect of spin, and the kick cannot be viewed its post-merger continuation.