Liquid metallic hydrogen can form at extreme temperatures and pressures like that in the center of Jupiter and Saturn. I was just curious since some of the conditions can occur on stars is it possible for their to be a layer of liquid metallic hydrogen present in a star?
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2 Answers
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Liquid metallic hydrogen appear possible at least at 20,000 K under enough pressure. However, as one increases temperature it is possible that there is a critical point making the liquid metal fade over into a plasma. This seems to happen even in 0.07 solar mass brown dwarfs, which presumably means that in real stars (that are hotter) there will not be any liquid metal.
It is not obvious that there should be a difference between a plasma and a liquid metal. In a sense the electron gas makes the liquid metal already a plasma. However, it is also degenerate in the sense that it is held up by the electron degeneracy pressure rather than thermal effects; when the thermal effects dominate the degeneracy one can view it as a plasma.
answered Jan 24, 2018 at 0:36
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To get liquid metallic hydrogen you need to compress a gas hard enough to make it become electron-degenerate.
A convenient parameterisation is that $E_{F,e}/k_B T$ needs to be much greater than unity, where $E_{F,e}$ is the Fermi (kinetic) energy of the electrons in the gas.
In turn, the Fermi energy depends on the number density of the electrons and hence on the mass density of the gas, and it goes roughly as $n_e^{2/3}$.
When a big ball of gas collapses under gravity, both the central density and the temperature rise. If the gas can cool, then eventually, the degeneracy parameter I defined above will rise and the gas will become electron degenerate. This is what happens in brown dwarfs (with $M<0.075 M_{\odot}$) - their interior temperatures do not rise high enough to begin nuclear fusion and they cool and become supported by electron degeneracy pressure. In that respect, their interiors might be very similar to those of gas giant planets, but they are not stars.
By definition a star is undergoing nuclear fusion and this requires interior temperatures of $\geq 10^{7}$ K (for hydrogen fusion). It turns out that in a more massive ball of gas these temperatures are reached when the interior density is not large enough for what could be considered any more than partial degeneracy, and since their interiors do not cool once fusion is initiated, this remains the case. So although electron degeneracy is becoming an issue in the lowest mass stars I do not think it is high enough to put it into the "metallic hydrogen" regime.
