At the centre of a spherical and kinematically isotropic galaxy, theorientation of a massive binary black hole (BBH) orbit (i.e., the direction ofthe BBH orbital angular momentum) undergoes a random walk. If the stars in aspherical system have a non-zero total angular momentum, the BBH orbitalorientation evolves towards aligning with the total stellar angular momentumdirection. In this paper, we show that a triaxial galaxy has analignment-erasing effect, that is, the alignment of the BBH orientationstowards the galaxy rotation axis can be decreased significantly or erased. Wealso show that in a non-rotating axisymmetric galaxy, the BBH orbitalorientation evolves towards the axisymmetric axis and precesses about it in aretrograde direction. Our results provide a step towards understanding the spinorientations of the final merged BH (and hence probable orientation of any jetproduced) within its host galaxy, and may help to constrain the recoilingvelocity of the merged BH arose from gravitational wave radiation as well.
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