Reply to “Comment on ‘Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants’ ”

We have recently proposed the dynamic transition of molecular hydrogen in gas giants around 10 GPa based on the recent understanding of a supercritical state related to the Frenkel line. In the preceding Comment, Bryk makes several remarks with regard to the Frenkel line and its relationship to the speed of sound. We disagree with this discussion and respond to it in this Reply.

Figure 1

The Frenkel line and adiabats in gas giants. Black dashed lines show pressure and temperature adiabats inside Jupiter, Saturn, exoplanet HD 209458b, and brown dwarf Gl 229B [20]. Empty black bullets show the melting line of ${\mathrm{H}}_2$ [12], with the straight line in the double-logarithmic plot showing the linear range. The dotted line shows the melting line in a wider pressure and temperature range [20]. Open blue diamonds correspond to pressure and temperature at the minima of the speed of sound [8] shown in Fig. 1 in Ref. [1], and the solid red diamond shows the critical point of ${\mathrm{H}}_2$. The thick red line shows the Frenkel line starting just below the critical point and running parallel to the melting line in the range 0.5–50 GPa and through the minima of the speed of sound. The dashed red line shows a tentative extrapolation of the Frenkel line in the high-pressure range based on existing melting data. The dash-dotted line at low pressure separates molecular hydrogen ${\mathrm{H}}_2$ and dissociated hydrogen H [20]. Two vertical dash-dotted lines approximately separate nonmetallic solid (NMS) and metallic solid (MS) at low temperature, and nonmetallic liquid (NML) and metallic liquid (ML) at high temperature [20]. Filled squares are new points for the Frenkel line calculated by rescaling the previous data derived using the velocity autocorrelation function criterion [5].

Figure 2

The speed of sound in the soft-sphere system where the gas-liquid coexistence line and the critical point are absent. The speed of sound is calculated along the isobar. The speed of sound, temperature, and pressure are in relative soft-sphere units.