Combined evolution of the black holes’ parameters for the pre-merging and merging stages (including the PN phases) of the NGC 7727 SMBHB. Left upper panel: Separation ΔR between SMBHB for the numerical model C_rnd1 . Horizontal black dashed lines represent 10, 100, and 1000 times the Schwarzschild radii for the SMBHBs’ mass. The solid black line shows the size of the semi-major axis at the time when the binary starts to harden. Right upper panel: Evolution of the inverse semi-major axis for the same model. Left and right bottom panels: Evolution of eccentricity, e, and pericentre for the SMBHB system. Different colours represent the different phases of the SMBHB evolution, with dark blue: unbound phase, blue: pre-merging, and light blue: merging, including the PN terms.