Spin-flip - Physics of Spin-Flips

Physics of Spin-Flips

A spin-flip is a late stage in the evolution of a binary black hole. The binary consists of two black holes, with masses and, that revolve around their common center of mass. The total angular momentum of the binary system is the sum of the angular momentum of the orbit, plus the spin angular momenta of the two holes:

If the orbital separation is sufficiently small, emission of energy and angular momentum in the form of gravitational radiation will cause the orbital separation to drop. Eventually, the smaller hole reaches the innermost stable circular orbit, or ISCO, around the larger hole. Once the ISCO is reached, there no longer exists a stable orbit, and the smaller hole plunges into the larger hole, coalescing with it. The final angular momentum after coalescence is just

the spin angular momentum of the single, coalesced hole. Neglecting the angular momentum that is carried away by gravitational waves during the final plunge—which is small -- conservation of angular momentum implies

is of order times and can be ignored if is much smaller than . Making this approximation,

This equation states that the final spin of the hole is the sum of the larger hole's initial spin plus the orbital angular momentum of the smaller hole at the last stable orbit. Since the vectors and are generically oriented in different directions, will point in a different direction than -- a spin-flip.

The angle by which the black hole's spin re-orients itself depends on the relative size of and, and on the angle between them. At one extreme, if is very small, the final spin will be dominated by and the flip angle can be large. At the other extreme, the larger black hole might be a maximally-rotating Kerr black hole initially. Its spin angular momentum is then of order

The orbital angular momentum of the smaller hole at the ISCO depends on the direction of its orbit, but is of order

Comparing these two expressions, it follows that even a fairly small hole, with mass about one-fifth that of the larger hole, can reorient the larger hole by 90 degrees or more.