Thermodynamically Governed Interior Models of Uranus and Neptune

Interior models of Uranus and Neptune often assume discrete layers, but sharp interfaces are expected only if major constituents are immiscible. Diffuse interfaces could arise if accretion favored a central concentration of the least volatile constituents (also incidentally the most dense); compositional gradients arising in such a structure would likely inhibit convection. Currently, two lines of evidence suggest possible hydrogen-water immiscibility in ice giant interiors. The first arises from crude extrapolation of the experimental hydrogen-water critical curve to $\sim 3$ GPa (Bali et al. 2013). The data are obtained for an impure system containing silicates, though Uranus and Neptune could also be "dirty." Current ab initio models disagree (Soubiran & Militzer 2015), though hydrogen and water are difficult to model from first-principles quantum mechanics with the necessary precision. The second argument for hydrogen-water immiscibility in ice giants, outlined herein, invokes reasoning about the gravitational and magnetic fields. While consensus remains lacking, here we examine the immiscible case. Applying the resulting thermodynamic constraints, we find that Neptune models with envelopes containing a substantial water mole fraction, as much as $\chi \gtrsim 0.1$ relative to hydrogen, can satisfy observations. In contrast, Uranus models appear to require $\chi \lesssim 0.01$, potentially suggestive of fully demixed hydrogen and water. Enough gravitational potential energy would be available from gradual hydrogen-water demixing, to supply Neptune's present-day heatflow for roughly ten solar system lifetimes. Hydrogen-water demixing could slow Neptune's cooling rate by an order of magnitude; different hydrogen-water demixing states could account for the different heatflows of Uranus and Neptune.