On the role of the H2 ortho:para ratio in gravitational collapse during star formation

Hydrogen molecules (H2) come in two forms in the interstellar medium, ortho- and para-hydrogen, corresponding to the two different spin configurations of the two hydrogen atoms. The relative abundances of the two flavours in the interstellar medium are still very uncertain, and this abundance ratio has a significant impact on the thermal properties of the gas. In the context of star formation, theoretical studies have recently adopted two different strategies when considering the ortho:para ratio (OPR) of H2 molecules; the first considers the OPR to be frozen at 3:1 while the second assumes that the species are in thermal equilibrium. As the OPR potentially affects the protostellar cores which form as a result of the gravitational collapse of a dense molecular cloud, the aim of this paper is to quantify precisely what role the choice of OPR plays in the properties and evolution of the cores. We used two different ideal gas equations of state for a hydrogen and helium mix in a radiation hydrodynamics code to simulate the collapse of a dense cloud and the formation of the first and second Larson cores; the first equation of state uses a fixed OPR of 3:1 while the second assumes thermal equilibrium. Simulations using an equilibrium ratio collapse faster at early times and show noticeable oscillations around hydrostatic equilibrium, to the point where the core expands for a short time right after its formation before resuming its contraction. In the case of a fixed 3:1 OPR, the core's evolution is a lot smoother. The OPR was however found to have little impact on the size, mass and radius of the two Larson cores. We conclude that if one is solely interested in the final properties of the cores when they are formed, it does not matter which OPR is used. On the other hand, if one's focus lies primarily in the evolution of the first core, the choice of OPR becomes important.Comment: 9 pages, 5 figures. Accepted for publication in Astronomy & Astrophysic

The Athena++ Adaptive Mesh Refinement Framework: Multigrid Solvers for Self-Gravity

We describe the implementation of multigrid solvers in the Athena++ adaptive mesh refinement (AMR) framework and their application to the solution of the Poisson equation for self-gravity. The new solvers are built on top of the AMR hierarchy and TaskList framework of Athena++ for efficient parallelization. We adopt a conservative formulation for the Laplacian operator that avoids artificial accelerations at level boundaries. Periodic, fixed, and zero-gradient boundary conditions are implemented, as well as open boundary conditions based on a multipole expansion. Hybrid parallelization using both MPI and OpenMP is adopted, and we present results of tests demonstrating the accuracy and scaling of the methods. On a uniform grid we show multigrid significantly outperforms methods based on FFTs, and requires only a small fraction of the compute time required by the (highly optimized) magnetohydrodynamic solver in Athena++. As a demonstration of the capabilities of the methods, we present the results of a test calculation of magnetized protostellar collapse on an adaptive mesh.Comment: 28 pages, 13 figures, submitted to AAS Journal