Schematic plot of binary disruption and the subsequent evolution of the captured star. A binary is disrupted by the central SMBH when the binary approaches r_t,b, with one of the two stars being ejected and the other being captured. In r_p−a phase space, the captured star is deposited at the green dashed line, where the two ⋆ symbols denote the upper and the lower limits [Equation (36)], respectively. Depending on the initial separation of the binary, the captured star faces two possible fates: rpTDE or stellar EMRI. In the upper panel (for M_• = 10⁶ M_⊙), the captured stars are in the two-body-scattering-dominated regime [Equation (34)], where those with a_GW < a < a_10yr finally end as observable rpTDEs. In the lower panel (M_• = 10⁷ M_⊙), the captured stars with T_obt < 10 yr are in the GW-emission-dominated regime (a_10yr < a_GW), where those with r_p ≈ 2r_t start the rpTDE phase immediately after the binary disruption, while others gradually circularize and end as stellar EMRIs.