Ratio of T_sync/T_He as a function of the He-rich star initial mass and orbital period. Left panel: 10 M_⊙ BH as the companion, middle panel: 30 M_⊙ BH as the companion, right panel: 1.4 M_⊙ NS as the companion. Outer circle: T_sync/T_He for dynamical tides, inner dot: T_sync/T_He for equilibrium tides. The selected stellar structure profile for the calculation of T_sync refers to the stage when the central mass fractional He abundance is 0.5. The black line denotes the lower limit in orbital period, below which a He-rich star of a given mass would overfill its Roche lobe at ZAHeMS (Zero Age He Main Sequence: the time when a He star starts to burn He in the core, which is analogous to ZAMS for core H burning). The metallicity of the He-rich star models shown in this figure is 0.01 Z_⊙, but the dependence of T_sync/T_He on metallicity is very weak. Therefore, two similar figures corresponding to the He-rich stars at 0.1 Z_⊙ and Z_⊙ are not shown here.