Radii of Roche lobes of BBHs and rotating velocity of the secondary BH at the orbital pericenter as a function of orbital eccentricity of the two BHs. The left and middle panels show the radii of Roche lobes ($R_{\mathrm{crit}}^{\mathrm{pri}}$ and $R_{\mathrm{crit}}^{\sec }$) in units of the Schwarzschild radii for the primary ($R_{\mathrm{Sch}}^{\mathrm{pri}}$) and secondary ($R_{\mathrm{Sch}}^{\sec }$) BHs, respectively. The typical radius of the UV emission (r_UV) in the accretion disk for a M_• = 10^8.6 M_⊙ is shown as a horizontal dashed line for comparison. The right panel presents the rotating velocity of the secondary BH at the pericenter ($V_{\mathrm{peri}}^{\sec }$), which is the maximum velocity in each period. In each panel are shown the results of M_•• = 10⁸ (blue), 10^8.5 (green), and 10⁹ M_⊙ (red) with T_orb = 2 yr and q_M = 0.5. Considering that the UV emission might disappear when R_crit ≲ r_UV, the current model configuration only focuses on those systems with R_crit ≳ r_UV, i.e., e ≲ 0.6 for M_•• = 10⁹ M_⊙ as a case study.