On the Possibility of Observing the Double Emission Line Feature of H₂ and HD from Primordial Molecular Cloud Cores

We study the prospects for observing H$_2$ and HD emission during the assembly of primordial molecular cloud cores. The primordial molecular cloud cores, which resemble those at the present epoch, can emerge around $1+z \sim 20$ according to recent numerical simulations. A core typically contracts to form the first generation of stars and the contracting core emits H$_2$ and HD line radiation. These lines show a double peak feature. The higher peak is the H$_2$ line of the $J=2-0$ (v=0) rotational transition, and the lower peak is the HD line of the $J=4-3$ (v=0) rotational transition. The ratio of the peaks is about 20, this value characterising the emission from primordial galaxies. The expected emission flux at the redshift of $1+z \sim 20$ (e.g. $\Omega_m = 0.3$ and $\Omega_\Lambda =0.7$), in the $J=2-0$ (v=0) line of H$_2$ occurs at a rate $\sim 2 \times 10^{-7}$ Jy, and in the $J=4-3$ (v=0) line of HD at a rate $\sim 4 \times 10^{-9}$ Jy. The former has a frequency of 5.33179$\times 10^{11}$ Hz and the latter is at 5.33388 $\times 10^{11}$Hz, respectively. Since the frequency resolution of ALMA is about 40 kHz, the double peak is resolvable. While an individual object is not observable even by ALMA, the expected assembly of primordial star clusters on subgalactic scales can result in fluxes at the 2000-50 $\mu$Jy level. These are marginally observable. The first peak of H$_2$ is produced when the core gas cools due to HD cooling, while the second peak of HD occurs because the medium maintains thermal balance by H$_2$ cooling which must be enhanced by three-body reactions to form H$_2$ itself.