Star formation within globular clusters:discrete multiple bursts and top-light mass functions

The observed discrete multiple stellar populations and internal abundance spreads in r- and s-process elements within globular clusters (GCs) have been suggested to be explained self-consistently by discrete star formation events over a longer timescale (10^8 yr). We here investigate whether such star formation is really possible within GCs using numerical simulations that include effects of dynamical interaction between individual stars and the accumulated gas ("star-gas interaction") on star formation. The principal results are as follows. Small gas clouds with densities larger than $10^{10}$ atoms cm^{-3} corresponding to first stellar cores can be developed from gas without turbulence. Consequently, new stars can be formed from the gas with high star formation efficiencies (>0.5) in a bursty manner. However, star formation can be suppressed when the gas mass fractions within GCs (f_g) are less than a threshold value (f_g, th). This f_g, th is larger for GCs with lower masses and larger gas disks. Star-gas interaction and gravitational potentials of GCs can combine to suppress the formation of massive stars (i.e., "top-light" stellar initial mass function). Formation of He-rich stars directly from gas of massive AGB stars is possible in massive GCs due to low f_g, th (<0.01). Short bursty star formation only for f_g>f_g, th can be partly responsible for discrete multiple star formation events within GCs.