Miscibility of Hydrogen and Helium under Astrophysical Conditions

Abstract

We investigate the stability and structural properties of dense hydrogen-helium mixtures under planetary interior conditions (Jupiter and Saturn). The excess free energy of mixing $\ensuremath{\Delta}G(x)$ is determined as a function of the helium atomic fraction $x$ by ab initio molecular dynamics simulations in the pressure range $4\ensuremath{\le}P\ensuremath{\le}24\mathrm{Mbar}$ at temperatures $T\ensuremath{\le}3000\mathrm{K}$. Energy, volume, and entropic contributions are evaluated. Demixing temperatures at $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1$ (the solar abundance) are 4000--9000 K (dependent on $P$), close to what planetary interior models predict for Saturn but well below the corresponding interior temperatures in Jupiter.