Conditions for HD cooling in the first galaxies revisited: Interplay between far-ultraviolet and cosmic ray feedback in Population III star formation

HD dominates the cooing of primordial clouds with enhanced ionization, e.g. shock-heated clouds in structure formation or supernova remnants, relic H II regions of Pop III stars and clouds with cosmic ray (CR) irradiation. There, the temperature decreases to several 10 K and the characteristic stellar mass decreases to ~10M_⊙, in contrast with first stars formed from undisturbed pristine clouds (~100M_⊙). However, without CR irradiation, even weak farultraviolet (FUV) irradiation suppresses HD formation/cooling. Here, we examine conditions for HD cooling in primordial clouds including both FUV and CR feedback. At the beginning of collapse, the shock-compressed gas cools with its density increasing, while the relic H II region gas cools at a constant density. Moreover, shocks tend to occur in denser environments than H II regions. Owing to the higher column density and the more effective shielding, the critical FUV intensity for HD cooling in a shock-compressed gas becomes ~10 times higher than that in relic H II regions. Consequently, in the shock-compressed gas, the critical FUV intensity exceeds the background level for most of the redshift we consider (6 ≲ z ≲ 15), while in relic H II regions, HD cooling becomes effective after the CR intensity increases enough at z ≲ 10. Our result suggests that less massive (~10M_⊙) Pop III stars may be more common than previously considered and could be the dominant population of Pop III stars.