Effect of molecular hydrogen self-shielding modeling on early Reionization Era galaxies in radiative hydrodynamic cosmological simulations

Accurately modeling molecular hydrogen (${\text{H}}_2$) is an important task in cosmological simulations because it regulates star formation. One fundamental property of ${\text{H}}_2$ is the ability to self-shield, a phenomenon in which the ${\text{H}}_2$ in the outer layer of a molecular cloud absorbs the photodissociating Lyman-Werner UV radiation and shields the inner ${\text{H}}_2$. Historically, numerical approximations have been utilized to avoid intensive ray-tracing calculations. This paper evaluates the use of the Sobolev-like density-gradient approximation in ${\text{H}}_2$ self-shielding modeling and tests its agreement with a more rigorous adaptive ray-tracing method in cosmological simulations. We ran four high-resolution zoom-in cosmological simulations to investigate the models’ effects in the early Reionization Era ($z\ge 12$). We find that the approximation model returns a higher ${\text{H}}_2$ photodissociation rate in low gas density environments but a lower rate when gas density is high, resulting in low-mass halos having less ${\text{H}}_2$ while high-mass halos having more ${\text{H}}_2$. The approximation also hinders star formation in small halos, but it less affects the stellar mass of larger halos. Inside a halo, the discrepancies between the two models regarding ${\text{H}}_2$ fraction, temperature, and stellar mass are radially dependent. On a large scale, the simulations using the approximation have less ${\text{H}}_2$ in the intergalactic medium and may experience a slower reionization process. These results show that the Sobolev-like approximation alters properties of galaxies and the large-scale universe when compared to the ray-tracing treatment, emphasizing a need for caution when interpreting results from these two techniques in cosmological simulations.