Evolution of the orbital eccentricity of the first (top panel), second (middle panel), and third (bottom panel) BHBs formed in Tree 197109-HR. We highlight with vertical coloured lines the key times in the binary’s evolution: the initial time of the galactic merger (t₀, cyan), time of binary formation (t_b, red), time at which we start the SAM (t_SAM, orange), time when the binary enters the PTA band (t_PTA, blue), and time of coalescence (t_coal, green). For each time, we also report the corresponding eccentricity value, plotted as a point, following the same colour scheme. The horizontal orange line denotes the MCMC best-fit value of the initial eccentricity used for the semi-analytical evolution.