Ablack hole spin-flip occurs when thespin axis of arotating black hole undergoes a sudden change in orientation due to absorption of a second (smaller) black hole. Spin-flips are believed to be a consequence ofgalaxy mergers, when twosupermassive black holes form a bound pair at the center of the mergedgalaxy and coalesce after emittinggravitational waves. Spin-flips are significant astrophysically since a number of physical processes are associated with black hole spins; for instance,jets inactive galaxies are believed to be launched parallel to the spin axes of supermassive black holes.A change in the rotation axis of a black hole due to a spin-flip would therefore result in a change in the direction of the jet.

A spin-flip is a late stage in the evolution of abinary black hole. The binary consists of two black holes, with masses${\displaystyle M_1}$ and${\displaystyle M_2}$, that revolve around their commoncenter of mass. The totalangular momentum${\displaystyle J}$ of the binary system is the sum of the angular momentum of theorbit,${\displaystyle L}$, plus thespin angular momenta${\displaystyle S_{1,2}=S_1+S_2}$ of the two holes. If we write${\displaystyle {\mathbf{M}}_{\mathbf{1}},{\mathbf{M}}_{\mathbf{2}}}$ as the masses of each hole and${\displaystyle {\mathbf{a}}_{\mathbf{1}},{\mathbf{a}}_{\mathbf{2}}}$ as theirKerr parameters,^[1] then use the angle from north of their spin axes as given by${\displaystyle \theta }$, we can write,

$${\displaystyle {\mathbf{S}}_1=\{{\mathbf{a}}_1{\mathbf{M}}_1\cos (\pi /2-\theta ),{\mathbf{a}}_1{\mathbf{M}}_1\sin (\frac{\pi }{2}-\theta )\}}$$$${\displaystyle {\mathbf{S}}_2=\{{\mathbf{a}}_2{\mathbf{M}}_2\cos (\frac{\pi }{2}-\theta ),{\mathbf{a}}_2{\mathbf{M}}_2\sin (\frac{\pi }{2}-\theta )\}}$$$${\displaystyle {\mathbf{J}}_{\text{init}}={\mathbf{L}}_{\text{orb}}+{\mathbf{S}}_1+{\mathbf{S}}_2.}$$

If the orbital separation is sufficiently small, emission of energy and angular momentum in the form ofgravitational radiation will cause the orbital separation to drop. Eventually, the smaller hole${\displaystyle M_2}$ 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

$${\displaystyle {\mathbf{J}}_{\text{final}}=\mathbf{S},}$$

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^[2]—conservation of angular momentum implies

$${\displaystyle \mathbf{S}\approx {\mathbf{L}}_{\text{ISCO}}+{\mathbf{S}}_1+{\mathbf{S}}_2.}$$

${\displaystyle S_2}$ is of order${\displaystyle (M_2/M_1{)}^2}$ times${\displaystyle S_1}$ and can be ignored if${\displaystyle M_2}$ is much smaller than${\displaystyle M_1}$. Making this approximation,

$${\displaystyle \mathbf{S}\approx {\mathbf{L}}_{\text{ISCO}}+{\mathbf{S}}_1.}$$

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${\displaystyle S_1}$ and${\displaystyle L}$ are generically oriented in different directions,${\displaystyle S}$ will point in a different direction than${\displaystyle S_1}$—a spin-flip.^[3]

The angle by which the black hole's spin re-orients itself depends on the relative size of${\displaystyle L_{\mathrm{I}\mathrm{S}\mathrm{C}\mathrm{O}}}$ and${\displaystyle S_1}$, and on the angle between them. At one extreme, if${\displaystyle S_1}$ is very small, the final spin will be dominated by${\displaystyle L_{\mathrm{I}\mathrm{S}\mathrm{C}\mathrm{O}}}$ and the flip angle can be large. At the other extreme, the larger black hole might be a maximally-rotatingKerr black hole initially. Its spin angular momentum is then of order

$${\displaystyle S_1\approx G{M}_1^2/c.}$$

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

$${\displaystyle L_{\text{ISCO}}\approx G{M}_1{M}_2/c.}$$

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.^[3]

Black hole spin-flips were first discussed in the context of a particular class ofradio galaxy, theX-shaped radio sources.^[3] The X-shaped galaxies exhibit two, misaligned pairs of radio lobes: the "active" lobes and the "wings". It is believed that the wings are oriented in the direction of the jet prior to the spin-flip, and that the active lobes point in the current jet direction. The spin-flip could have been caused by absorption of a second black hole during agalaxy merger.

• Supermassive black hole – Largest type of black hole
• Gravitational wave – Aspect of relativity in physics
• Radio galaxy – Type of active galaxy that is very luminous at radio wavelengths

• Massive black hole binary evolution An article on binary black holes.
• Scientists Detect "Smoking Gun" of Colliding Black Holes

• Radio galaxies
• Supermassive black holes
• Black holes

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