Formation of H2-He Substellar Bodies in Cold Conditions: Gravitational Stability of Binary Mixtures in a Phase Transition
Füglistaler et al
Molecular clouds consist typically of 3/4 H2, 1/4 He and traces of heavier elements. In an earlier work we showed that at very low temperatures and high densities, H2 can be in a phase transition leading to the formation of ice clumps as large as comets, or even planets. However, He has very different chemical properties and no phase transition is expected before H2 in dense ISM conditions. The gravitational stability of fluid mixtures has been studied before, but not including a phase transition.
We study the gravitational stability of binary fluid mixtures with special emphasis if one component is in a phase transition. The results are aimed at applications in molecular cloud conditions.
We study the gravitational stability of van der Waals fluid mixtures using linearised analysis and examine virial equilibrium conditions using the Lennard-Jones inter-molecular potential. Then, combining the Lennard-Jones and gravitational potentials, the non-linear dynamics of fluid mixtures are studied using the molecular dynamics code LAMMPS.
Besides the classical ideal-gas Jeans instability criterion, a fluid mixture is always gravitationally unstable if it is in a phase transition. In unstable situations the species can separate: in some conditions He precipitates faster than H2, while in other conditions the converse occurs. Also, for an initial gas phase collapse the geometry is essential: contrary to spherical or filamentary collapses, sheet-like collapses starting below 15 K allow to easily reach H2 condensation conditions because then it is the fastest, and both the increase of heating and opacity are limited.
Depending on density, temperature and mass, either rocky H2 planetoids, or gaseous He planetoids form. H2 planetoids are favoured by high density, low temperature and low mass, while He planetoids need more mass and can form at temperature well above the critical one.