Distribution of spin–orbit tilt angle (Δi) caused by the tilting of the binary plane during the encounter. An isotropic distribution would appear as flat in cos θ. Solid thin lines indicate the sets with the SMBH (σn), while thick dashed lines indicate the sets in isolation (σn-i). The disc velocity dispersion for each distribution decreases from left to right and from top to bottom. For σ ≥ 10⁻⁴, the bimodality of the tilt angle distribution is strongly damped by the tidal field of the SMBH, leaving a majority of spin–orbit aligned binaries.