On the formation of globular clusters: comparison with observations

Abstract: The paper deals with the conditions required to form at least two stellar generations in globular clusters under the constraints generated by feedback from massive stars as well as radiative cooling and the metallicity of the primordial clouds. Our calculations are based on two main constraints to the star formation efficiency of the first stellar generation (1G) $\epsilon_{1G}$. First, $\epsilon_{1G}$ is restricted to warrant that stellar winds and supernovae do not disrupt the leftover gas out of which a second generation (2G) would form. Second, $\epsilon_{1G}$ is also limited such that the metallicity enhancement caused by trapped supernovae is, in agreement with the observations, not larger than $\sim$ 0.1 dex. Several central parameters define the globular clusters end result: the mass and radius of the primordial clouds, their metallicity and $\epsilon_{1G}$. The parameter space composed by models which fulfilled all constraints, is here shown to coincide remarkably well with the scattered observed anti-correlation between the fraction of first generation stars ($f_{\textrm{1G}}$) and total cluster mass. Our models also discern, in agreement with the data, between single and multiple population clusters in a metallicity versus mass (or radius) plane. Hence, our results suggest that the presence of multiple stellar populations is closely linked to the ability of proto-globular clusters to retain a fraction of leftover gas.