The Internal Energy for Molecular Hydrogen in Gravitationally Unstable Protoplanetary Disks

The gas equation of state may be one of the critical factors for the disk instability theory of gas giant planet formation. This letter addresses the treatment of H2 in hydrodynamical simulations of gravitationally unstable disks. In our discussion, we point out possible consequences of erroneous specific internal energy relations, approximate specific internal energy relations with discontinuities, and assumptions of constant Γ1. In addition, we consider whether the ortho/para ratio for H2 in protoplanetary disks should be treated dynamically as if the species are in equilibrium. Preliminary simulations indicate that the correct treatment is particularly critical for the study of gravitational instability when T = 30-50 K. Subject headings: equation of state – hydrodynamics – instabilities – molecular processes – planetary systems: protoplanetary disks