Molecular Hydrogen in High-redshift Damped Lyman-{\alpha} Absorbers

Simulations predict that circumgalactic hydrogen gas surrounding massive ($M_{\rm{halo}}^{z=1}=10^{12}-10^{13}\ M_{\odot}$) galaxies at $z\sim4$ may be predominantly neutral, and could produce damped Ly$\alpha$ absorbers (DLAs) along sight-lines to background quasars \citep{Stern2021}. A circumgalactic medium (CGM) origin for DLAs naturally explains high redshift HI absorption-selected galaxy detections at physical separations much greater than the likely extents of the galaxy disks \citep{Neeleman2017, Neeleman2019}. The observed $z\sim 4$ DLA HI column densities are large and comparable to interstellar (ISM) gas columns at which substantial molecular hydrogen (H$_2$) abundances occur. We therefore investigate the possible molecular content of high-redshift CGM gas, and its potential detectability via (rest-frame) far-ultraviolet (UV) absorption line studies. For this purpose we develop an analytic sub-grid model for HI-to-H$_2$ transitions and incorporate the model with zoom-in FIRE-2 simulations of evolving high-$z$ galaxies. We include dust absorption and scattering computations for the transfer of photodissociating Lyman-Werner (LW) band radiation. We find that the typical extents of detectable H$_2$ sightlines are $\approx 0.1\, R_{\rm vir}$, independent of redshift from $z=2.5$ to 5. We argue that a CGM origin for DLAs naturally explains the low detection rates of H$_2$ in DLA observations, as the low CGM densities and relatively strong far-UV fields lead to molecular fractions much lower than observed in the ISM at comparable HI columns.