Simulating the formation of molecular clouds. I. Slow formation by gravitational collapse from static initial conditions

We study the formation of H-2 in the ISM, using a modified version of the astrophysical magnetohydrodynamical code ZEUS-MP that includes a nonequilibrium treatment of the formation and destruction of H-2. We examine two different approximations to treat the shielding of H-2 against photodissociation: a local approximation, which gives us a solid lower bound on the amount of shielding, and a method based on ray-tracing that is considerably more accurate in some circumstances but that produces results that are harder to clearly interpret. In both cases, the computational cost of determining H-2 photodissociation rates is reduced by enough to make three-dimensional high-resolution simulations of cloud formation feasible with modest computational resources. Our modification to ZEUS-MP also includes a detailed treatment of the thermal behavior of the gas. In this paper, we focus on the problem of molecular cloud formation in gravitationally unstable, initially static gas. ( In a subsequent paper, we consider turbulent flow.) We show that in these conditions, and for initial densities consistent with those observed in the cold, neutral atomic phase of the interstellar medium, H-2 formation occurs on a timescale t >= 10 Myr, comparable to or longer than the gravitational free-fall timescale of the cloud. We also show that the collapsing gas very quickly reaches thermal equilibrium and that the equation of state of the thermal equilibrium gas is generally softer than isothermal. Finally, we demonstrate that although these results show little sensitivity to variations in most of our simulation parameters, they are highly sensitive to the assumed initial density n(i). Reducing n(i) significantly increases the cloud formation timescale and decreases the amount of hydrogen ultimately converted to H-2.