Is There an Upper Limit to Planetary Core Density?

[Loren Booda]

Is there an upper limit to the density of a planet's core?

 

[Astronuc]

Obviously there has to be given that the size of a planet is finite/definite.

The density will depend on the elements in the core, and temperature and pressure, which are determined by the mass/size of the planet.

 

[Loren Booda]

For instance, might the upper limit for the density of planet cores in general be the limiting density of solid hydrogen, or even that of neutronium?

 

[mgb_phys]

Probably depends on what you are classifying as a planet rather than a binary star but the upper limit is probably the density of small white dwarf approx 10^6 g/cc

 

[Astronuc]

For instance, might the upper limit for the density of planet cores in general be the limiting density of solid hydrogen, or even that of neutronium?

Well, I believe Jupiter has a core of hydrogen, but apparently its state is not known.
http://www2.jpl.nasa.gov/galileo/jupiter/core.html
http://www2.jpl.nasa.gov/galileo/jupiter/interior.html

Space scientist proposes new model for Jupiter's core
http://news-info.wustl.edu/news/page/normal/4376.html

Neutron stars have cores of neutronium, but they are considered stars, not planets. Actually, it appears that scientists and academics do not like to use the term neutronium, or is just not commonly referenced by scientists and academics in conjunction with neutron stars. It is mentioned on Wikipedia though.

See - http://en.wikipedia.org/wiki/Degenerate_matter

This might be of interest -
Physics of neutron star interiors By David Blaschke, Norman K. Glendenning, Armen Sedrakian
http://books.google.com/books?id=EeB9ILxkGyQC&pg=PA127&lpg=PA127

 

[Loren Booda]

Astronuc,

The links regarding the composition of Jupiter and evolution of the solar nebula were informative and understandable. As with the last link on neutron stars, I think even Chandrasekhar would have a hard read.

mgb,

I believe that is the figure I was looking for.

__________


Could the Pleiades be seven white dwarfs, and could they all fit in a Subaru?

 

[Astronuc]

Perhaps the cores of exoplanets that are not quite brown dwarfs represent the upper limit.

Hydrogen provides the first source of thermonuclear power to stars. The most massive stars, those over 100 times the Sun's mass, blast through this fuel in 1 million years or less. The Sun, with its dramatically lower rate of power generation, takes about 9 billion years to burn through its smaller reservoir of hydrogen. This trend of slower power generation by smaller stars continues down to the common 1/4 solar mass stars, which are expected to burn their fuel in about 100 billion years. Below 0.072 solar masses, the thermonuclear fusion of hydrogen becomes impossible. The objects immediately below this critical mass are called brown dwarfs.

More precisely, a brown dwarf is a massive ball of hydrogen, helium, and trace amounts of metals that is not massive enough to burn hydrogen, but is massive enough to burn deuterium. Brown dwarfs are expected to have masses ranging from just below 0.072 solar masses (78 times Jupiter's mass), the mass below which hydrogen fusion becomes impossible, down to 0.012 solar masses (13 time Jupiter's mass), the mass below which deuterium fusion becomes impossible. Anything smaller than 0.012 solar masses is a giant gaseous planet. From its spectrum, the brown dwarf appears to be simply an exceedingly cool star, but a brown-dwarf's inability to burn hydrogen betrays a fundamental physical difference between it and a star: unlike a star, a brown dwarf does not need thermonuclear fusion to hold itself up.

http://www.astrophysicsspectator.com/topics/degeneracy/BrownDwarf.html
http://www.astrophysicsspectator.com/topics/degeneracy/BrownDwarfStructure.html



The following wikipedia article gives a range of densities 10 to 10³ g/cc.
http://en.wikipedia.org/wiki/Brown_dwarf

Those density numbers are supported by
http://webusers.astro.umn.edu/~gehrz/Astro_4001_Talks/Brown_Dwarf_Stars_Katie_Leonard.ppt

I was unable to readily locate a density in this source - but it may be of interest
The Brown Dwarf - Exoplanet Connection, Exoplanets By John W. Mason
https://www.amazon.com/gp/product/3540740074/?tag=pfamazon01-20

 

[Loren Booda]

Could one calculate a standard density at the brown dwarf/giant gaseous planet interface from the corresponding degeneracy pressure?

__________I am reminded that a professor of mine at George Mason University, Menas Kafatos, authored an article on brown dwarfs in Scientific American in 1986.

 

[qraal]

Is there an upper limit to the density of a planet's core?

No. But the material has to be under sufficient pressure to be confined against electrostatic forces trying to return it to normal density.

A related question is: is there a maximum radius for a planet?

And the answer is: Yes, there is. For a particular composition there is a maximum radius at which electrostatic and gravitational forces are in balance. Beyond that radius, and corresponding mass, the planet only gets smaller because the core is increasingly degenerate, thus compressing the core even more. For objects supported by electron degeneracy pressure the limiting mass is the Chandrasekhar Limit - as you evidently know - and it's different depending on the ratio of charges to nucleons. Thus the Limit for iron (Z = 26, A = 56) is smaller than the limit for carbon (Z = 6, A = 12.)

I'm still trying to get my head around the relevant Lane-Embden equations, but it's not really that hard to get the relevant maths. The real puzzle is what happens inside stars past the Chandrasekhar Limit - are they "neutron stars", "quark stars" or something else. We don't have a lot of data at such extremes. Heavier compact stars, some observed to be 2 solar masses, seem to imply a stiffer equation of state than the usual 'neutron star' models.