Astrophysical Relevance

Giant planets and brown dwarfs consist of more than 90% hydrogen. The same hydrogen content is found in main sequence stars in the initial phase when they formed by the collapse of hydrogen clouds. Then nuclear reactions reduce the fraction of hydrogen in the process of stellar evolution. The high content of hydrogen is the reason why the high temperature equation of state is relevant for the static properties of these objects and why they enter into models that determine their evolution (Burrows et al., 1997). In these model, one assumes a well mixed state that corresponds to an isentropic change of state from core to surface.

Figure 1.2: Hydrogen phase diagram as displayed in Fig. 1.1 showing the equation of state for different stars and giant planets (Saumon et al., 1995). The dashed line indicates where the radiation pressure equals the gas pressure. The solid lines correspond to Jupiter and stars having 0.3, 1, and 15 times the mass of the sun.

   

In Fig. 1.2, curves from models for the interior of Jupiter and different stars are shown. The gaseous envelope of Jupiter is dominated by molecules. Further inside, pressure and density are sufficiently high that one can expect to find metallic hydrogen. If there existed a PPT, there would be a critical radius, at which the density is discontinuous. The two phases would have different properties such as the solubility of helium. As a consequence, helium would primarily be concentrated in one of the two phases.

The other curves in Fig. 1.2 represent stars with 0.3, 1, and 15 solar masses ($M_\odot$). The low mass star of $0.3 M_\odot$ exhibits a complex change of properties. Near its core, one finds a moderately degenerate plasma ($\theta=1$). With increasing radius, the temperature decreases, which increases the coupling and promotes recombination processes. Eventually, all free electrons will be bound in atoms, which leads to a non-degenerate atomic fluid. Near the surface, the temperature will be low enough so that molecules can form, which at some point will become the predominant species.

The sun is hotter and less dense. Near the core, it is weakly coupled and moderately degenerate. The coupling parameter stays approximately constant ( $\Gamma \approx 0.1$). Near the surface, the temperature is reduced to about $10^4\rm\,K$, recombination takes place and atoms are formed.

For a more massive star of $15\,M_\odot$, the modeling is simpler because it remains in a weakly coupled and hardly degenerate regime. However, the radiation leads to a significant contribution to the pressure. Brown dwarfs occupy the region between the curves of Jupiter and the $0.3 M_\odot$ star.