Formation of H₂-He substellar bodies in cold conditions

Gravitational stability of binary mixtures in a phase transition

Geneva Observatory, University of Geneva, 1290 Sauverny, Switzerland
e-mail: andreas.fueglistaler@unige.ch

Received: 16 July 2015
Accepted: 25 March 2016

Abstract

Context. 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 conditions. The gravitational stability of fluid mixtures has been studied before, but these studies did not include a phase transition.

Aims. We study the gravitational stability of binary fluid mixtures with special emphasis on when one component is in a phase transition. The numerical results are aimed at applications in molecular cloud conditions, but the theoretical results are more general.

Methods. 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.

Results. 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 15 K easily reach H₂ condensation conditions because then they are fastest and both the increase of heating and opacity are limited.

Conclusions. 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.