2023MNRAS.518.3274B

We discuss a GC formation scenario in which the first generation (1G) of single asymptotic giant branch (AGB) stars and intermediate-mass close binaries (IMCBs) eject gas, from which the second generation (2G) of stars can be formed. The two key parameters in the scenario are the fractions of binary stars (f_b) and the slopes (α) of the stellar initial mass functions (IMFs) for 1G stars. Principle results derived by analytic and one-zone models of GC formation are as follows. The mass fraction of 2G stars (f_2g) can be higher than ≈0.4 for α < 1.8 and is not so dependent on f_b. The ratio of the initial mass of a GC to the present-day mass (M_gc) ranges from 2 to 7 depending on α for 0.5 ≤ f_b ≤ 0.9. The differences in [Na/Fe] between 1G and 2G stars can be as large as 0.7 for a wide range of model parameters. The Li abundances of 2G stars can be as high as those of 1G even if the pristine gas from IMCBs is assumed to be Li-free. Formation histories of 2G stars show at least two peaks owing to two peaks in the total ejection rate of gas from IMCB populations. The observed correlation between f_2g and M_gc can be due to α depending on M_gc. The hypothetical long duration of 2G formation (≈10⁸ yr) is possible, because massive star formation can be suppressed through frequent dynamical interaction between 1G stars and gas clouds.