Formation of H2-He substellar bodies in cold conditions: Gravitational
  stability of binary mixtures in a phase transition
  Molecular clouds typically consist 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
interstellar medium (ISM) conditions. The gravitational stability of fluid
mixtures has been studied before, but these studies did not include a phase
transition.
  First, we study the gravitational stability of van der Waals fluid mixtures
using linearized analysis and examine virial equilibrium conditions using the
Lennard-Jones intermolecular potential. Then, combining the Lennard-Jones and
gravitational potentials, the non-linear dynamics of fluid mixtures are studied
via computer simulations using the molecular dynamics code LAMMPS.
  Along with the classical, ideal-gas Jeans instability criterion, a fluid
mixture is always gravitationally unstable if it is in a phase transition
because compression does not increase pressure. However, the condensed phase
fraction increases. 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 15K easily reach H2 condensation conditions because then they
are 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 value.
