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As it is said here (https://physicsworld.com/a/couple-emerges-from-trio-of-supermassive-black-holes/) a system of two orbiting black holes could disrupt the gas and stars at the center of the galaxy and could even cause one of the black holes to be ejected from the galaxy.

As a pair of supermassive black holes orbit one another, for example, the binary system’s gravity would disrupt the gas and stars at the centre of the host galaxy. This, in turn, could lead to a burst of star formation or even the ejection of one of the black holes from the galaxy.

How can this happen? Can one of the black holes in a binary be ejected at high speeds somehow before they are merged?

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An inspiralling binary black hole radiates energy and angular momentum through gravitational waves, that much is understood by most people interested in the problem. However, a more subtle effect is the fact that the gravitational waves also radiate plain old linear momentum to some degree. Since the total momentum of the system has to be conserved with respect to faraway observers, this results in a "kick" of opposite momentum to the remnant, which can be sufficient to escape the galaxy in some cases.

In a quasi-circular inspiral the binary very slowly descends through nearly circular orbits. At each point the radiation is anisotropic because the system has a characteristic direction, the direction of the displacement between the two black holes. As a result, the binary can be seen as constantly radiating a small amount of linear momentum. However, this anisotropy is mostly averaged out, since the displacement is rotating on a time-scale which is generally faster than the orbital decay. Nevertheless, sooner or later the orbit looses stability and the two black holes merge within very few cycles. Once the orbit looses stability, the averaging argument does not apply and one ends up with an overall radiation of momentum in some direction.

This is a small effect when expressed in relativistic units and compared to the other quantities showing up in the merger, but it can be quite important for astrophysics. For comparison, the black holes radiate about $30\%$ of their mass-energy for an equal-mass quasi-circular inspiral (this corresponds to more than 40% of the mass of the final remnant). If all of this energy was radiated coherently as linear momentum in a single direction, the remnant would have to move at almost 40% of the speed of light in the opposite direction as a result. On the other hand, escape velocities from galaxies are of the order of hundreds of km/s, or few times $10^{-3} c$. This means that if the anisotropy of the total momentum radiation is even at the level of a few percent of the total flux, it is enough to kick the remnant out of the galaxy. A "vanilla" quasi-circular inspiral of black holes of comparable masses does not actually reach those numbers, but once the masses are asymmetric, the orbits eccentric, or when the black holes have spins that are misaligned, the breaking of the symmetry becomes sufficient, enough momentum is radiated, and black holes can often reach escape velocities.

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    $\begingroup$ This is not answering the question asked! $\endgroup$
    – TimRias
    Commented Jul 28, 2023 at 10:30
  • $\begingroup$ @Void could one of the black holes in the binary be ejected before merging? $\endgroup$
    – vengaq
    Commented Jul 28, 2023 at 17:31

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