Gas-Grain Modeling of Interstellar O $ _\textbf{2} $

Molecular oxygen (O $ _2 $ ) is essential to human beings on the earth. Although elemental oxygen is rather abundant, O $ _2 $ is rare in the interstellar medium. It was only detected in two galactic and one extra-galactic region. The inconsistency between observations and theoretical studies is a big challenge for astrochemical models. Here we report a two-phase modeling research of molecular oxygen, using the Nautilus gas-grain code. We apply the isothermal cold dense models in the interstellar medium with two typical sets of initial elemental abundances, as well as the warm-up models with various physical conditions. Under cold dense conditions, we find that the timescales for gas-phase CO, O $ _2 $ and H $ _2 $ O to reach peak values are dependent on the hydrogen density and are shortened when hydrogen density increases. In warm-up models, O $ _2 $ abundances are in good agreement with observations at temperatures rising after 10 $ ^5 $ yr. In both isothermal and warm-up models, the steady-state O $ _2 $ fractional abundance is independent of the hydrogen density, as long as the temperature is high enough ( $ > $ 30 K), at which O $ _2 $ is prevented from significant depleting onto grain surface. In addition, low density is preferable for the formation of O $ _2 $ , whether molecular oxygen is under cold conditions or in warm regions.