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tokens: CO core mass M CO , and the surface mass fractions of He ( X S (He)), C ( X S (C)), and O ( X S (O)) of the stellar models. We calculate the evolution during PPI stage using the stellar evolution code and a ppm hydrodynamic code (e.g. Colella Woodward 1984 ; Umeda Nomoto 2005 ) as follows. This is because it is difficult to solve unbound surface structure during the PPI mass ejection using the stellar evolution code. We describe the calculation method using the second pulsation of the 140 M ⊙ star model as an example. Fig. 1 shows the evolutionary track of the 140 M ⊙ star model on the plane of log ρ C (the central density) and log T C (the central temperature). Two points (A) and (B) in the second pulsation are assigned. First, we calculate the stellar evolution passing through points (A) and (B) without mass-loss by the PPI using the stellar evolution code. Figure 1. The evolution of the 140 M ⊙ model on the plane of log ρ C − log T C after He core burning. The shaded region shows unstable region against electron–positron pair instability. Details for points (A) and (B) are explained in text. Next, using the ppm code, we calculate the mass ejection of the star for about 10 4 s, corresponding to the period until the mass ejection is almost completed. The initial structure is set to be the structure at the time when the star has the maximum total energy during the pulsation (point (A) in the second pulsation). During the expansion, outermost region of the star accelerates and exceeds escape velocity. Thus, the mass exceeding the escape velocity is considered as the ejected mass. Then, we restart the stellar evolution calculation from the time when the central temperature is almost minimal (point (B) in the second pulsation). We artificially reduce stellar mass with a constant mass-loss rate evaluated in the previous hydrodynamic calculation. The mass-loss continues until the lost mass is equal to the ejected mass obtained from the hydrodynamic calculation. After several pulsations, the star forms an Fe core and collapses. We stop the calculation of the stellar evolution when the central temperature reaches 10 10 K. 2.2 Stellar evolution during PPI stage First, we show the evolution of the 140 M ⊙ model after the C-burning. Fig. 2 shows the mass fraction distribution after the C-burning. The central temperature is log T C = 9.14. The main component at the centre is O, Ne, and Mg. The mass fraction of Si also increases. The central C-burning occurs radiatively. The O/C/Ne layer is in the range of ∼6–48 M ⊙ in the mass coordinate. The surface component is mainly O and C, and 19 per cent 4 He by mass fraction remains as shown in Table 1 . Figure 2. Mass fraction distribution of the 140 M ⊙ model after the C-burning at log T C = 9.14. Black, sky-blue, blue, purple, dark-green, green, and orange lines indicate the mass fractions of 4 He, 12 C, 16 O, 20 Ne, 24 Mg, intermediate-mass elements (Si-Sc), and Fe-peak elements (Ti-), respectively. The time