Suppression of globular cluster formation in metal-poor gas clouds by Lyman-alpha radiation feedback

We study the impact of Ly$\alpha$ radiation feedback on globular cluster (GC) formation. In this Letter, we analytically derive the relation between star formation efficiency (SFE) and metallicity in spherical clouds with the Ly$\alpha$ radiation feedback. Our models show that the SFE becomes small as the metallicity decreases. In metal-poor gas clouds, Ly$\alpha$ photons are trapped for a long time and exert strong radiation force to the gas, resulting in the suppression of star formation. We find that bound star-clusters (SFE $\gtrsim$ 0.5) form only for the metallicity higher than $\sim 10^{-2.5}~Z_{\odot}$ in the case with the initial cloud mass $10^5~{\rm M}_\odot$ and the radius 5 pc. Our models successfully reproduce the lower bound of observed metallicity of GCs. Thus, we suggest that the Ly$\alpha$ radiation feedback can be essential in understanding the formation of GCs.