Formation of metal-free binaries: Impact of H2 line cooling and CIE cooling

During primordial star formation, the main cooling channel is provided by H₂ and super-molecules, such as H₂ or H₂, at sufficiently high densities. When the latter form at $n_{\rm H}\, \ge \, 10^{14}$ cm^-3, collision-induced emission (CIE) provides efficient gas cooling. We investigate how CIE cooling affects the formation of metal-free binaries comparing simulations with and without this process. Irrespective of the cooling mechanism, we find a typical protostellar mass range between 0.01 and 100 M_⊙. However, models with only H₂ line cooling produce a greater number of low-mass protostars that exhibit stronger variations in their radial velocities than the high-mass protostars. Similarly, in models with both H₂ cooling and CIE cooling, significant variations in the radial velocities are found for protostars in the intermediate-mass range. The initial number of fragments N_max decreases with increasing strength of turbulence. Cooling via super-molecules lets the most massive protobinaries (MMPBs) efficiently accrete mass. The maximum mass accretion rate $\dot{M}_{\rm max}$ for the MMPBs is more than an order of magnitude higher in the presence of CIE cooling than for pure H₂ line cooling. As a result, compact binaries with a semimajor axis as small as 3.57 au may form through the H₂- H₂ cooling channel. Our results indicate that, in addition to the MMPBs, most population III (Pop. III) binaries should be in eccentric i.e. non-circular orbits. This provides an important connection to the eccentric binaries reported in previous studies, which were found to exhibit rich temporal accretion signals during their evolution.