HD dominates the cooling of primordial clouds with enhanced ionization, e.g. shock-heated clouds in structure formation or supernova remnants, relic HII regions of Pop III stars, and clouds with cosmic-ray (CR) irradiation. There, the temperature dec
reases to several 10 K and the characteristic stellar mass decreases to $sim 10 {rm M}_{odot}$, in contrast with first stars formed from undisturbed pristine clouds ($sim 100 {rm M}_{odot}$). However, without CR irradiation, even weak far ultra-violet (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 HII region gas cools at a constant density. Moreover, shocks tend to occur in denser environments than HII 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 $sim 10$ times higher than in relic HII regions. Consequently, in the shock-compressed gas, the critical FUV intensity exceeds the background level for most of the redshift we consider ($6 lesssim z lesssim 15$), while in relic HII regions, HD cooling becomes effective after the CR intensity increases enough at $z lesssim 10$. Our result suggests that less massive ($sim 10 {rm M}_{odot}$) Pop III stars may be more common than previously considered and could be the dominant population of Pop III stars.
We perform population synthesis simulations for Population III (Pop III) coalescing binary neutron stars (NS-NSs), neutron star - black hole binaries (NS-BHs), and binary black holes (BH-BHs) which merge within the age of the universe. We found that
the typical mass of Pop III BH-BHs is $sim 30 rm{M}_{odot}$ so that the inspiral chirp signal of gravitational waves can be detected up to z=0.28 by KAGRA, Adv. LIGO, Adv. Virgo and GEO network. Our simulations suggest that the detection rate of the coalescing Pop III BH-BHs is $140 (68) cdot ({rm SFR}_{rm p}/10^{-2.5} rm{M}_{odot} {rm yr}^{-1} {rm Mpc}^{-3}) cdot {rm Err}_{rm sys} ~{rm events} ~{rm yr}^{-1}$ for the flat (Salpeter) initial mass function (IMF), respectively, where $rm SFR_p$ and $rm Err_{sys}$ are the peak value of the Pop III star formation rate and the possible systematic errors due to the assumptions in Pop III population synthesis, respectively. $rm Err_{sys}=1$ correspond to conventional parameters for Pop I stars. From the observation of the chirp signal of the coalescing Pop III BH-BHs, we can determine both the mass and the redshift of the binary for the cosmological parameters determined by Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH-BHs depends almost only on the cosmological parameters. We might be able to confirm the existence of Pop III massive stars of mass $sim 30~rm M_{odot}$ by the detections of gravitational waves if the merger rate of the Pop III massive BH-BHs dominates that of Pop I BH-BHs.
