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Consider a large spherical planet made of pure iron. Think of something similar to Mercury or Earth without its mantle, only much bigger, though those planets have elements other than iron mixed in their core.

What is the highest possible mass such a planet could have while still being stable? Can you tell the approximate radius it would have (if this is meaningful), and the pressure at the center?

If you tried to make a planet with mass larger than that, what would stop you?

I can think of two possible obstacles that would stop a heavier iron planet to form.

  • The gravity of the planet cannot keep all its mass, so some of the iron will leak away to open space.
  • The planet (or at least its center) will collapse under its own pressure, and undergo some sort of phase change so it is no longer made of liquid iron, but of something else: plasma or some other exotic phase of matter made of mostly iron nucleuses, matter made of fused or split atoms other than iron, neutron degenerate matter, other degenerate matter not containing nucleuses, black hole.

I am specifically not asking how heavy a planet could form in nature, but rather, how heavy a planet would be stable if it somehow got formed.

I did not specify a temperature for the planet. Imagine the planet to orbit around a star or as a free planet, whichever is convenient for you, and choose a realistic equilibrium temperature it could attain from radiation in that case. The iron ball shall not be a core inside a star or gas planet.

The planet shall rotate slowly enough that the rotation cannot significantly reduce the gravitational acceleration on its surface.

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  • $\begingroup$ How could such a planet form? $\endgroup$ – HDE 226868 Jul 28 '15 at 22:01
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    $\begingroup$ I don't understand the process you imagine by which iron would "leak away". The larger the planet, the stronger the gravitational field at the surface. $\endgroup$ – Floris Jul 28 '15 at 22:25
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    $\begingroup$ en.wikipedia.org/wiki/Chandrasekhar_limit $\endgroup$ – Count Iblis Jul 28 '15 at 22:30
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    $\begingroup$ Gravity increases with mass, so I do not think that such an event would occur. $\endgroup$ – Jimmy360 Jul 28 '15 at 22:36
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    $\begingroup$ @WetSavanna: no, I'm not asking for the most stable form, but instead about the phase that's only one step more stable than an iron planet. There are likely multiple steps between an iron planet and a black hole. $\endgroup$ – b_jonas Jul 28 '15 at 22:37
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You can create a massive sphere of cold iron up to about 1.1 solar masses that could be supported by electron degeneracy pressure.

The exact point of instability is likely to be caused by inverse beta decay reducing the electron number density (it could also be modified upwards slightly by extremely rapid rotation). [NB: This is lower than the "Chandrasekhar mass" commonly quoted for white dwarfs because (i) there are more mass units per electron in iron than for the usual carbon/oxygen assumed to be in most white dwarfs, and this reduces the degeneracy pressure for a given density; and (ii) more importantly, inverse beta decay sets in at much lower densities for iron than in carbon.]

The structure of such objects is studied in detail by Rotondo et al. (2011). The instability occurs at a finite density and hence radius, which is about 2200 km (the exact value is uncertain). The central density would be about $1.1\times 10^{12}$ kg m$^{-3}$ (this is where the electron Fermi energy equals the threshold energy for inverse beta decay in iron). The central pressure is essentially ideal relativistic electron degeneracy pressure - which I calculate to be about $5\times 10^{25}$ Pa. The temperature of the object would not really matter - the electrons would be completely degenerate unless it substantially exceeds $10^{8}$ K (e.g. see this link, setting the log density to 12 and the mass units per electron $\mu_e$ to $\sim 2.2$.)

Thus what you ask about is not in the planetary regime at all.

If you did try to add more iron to this maximal mass iron white dwarf, it would collapse. The outcome of that would likely be a low-mass neutron star.

Such spheres of iron (or iron peak elements) are created in the cores of massive stars, but are always thought to grow past the instability point and collapse, initiating a supernova explosion.

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  • $\begingroup$ I learnt a new expression today - "reverse beta decay". How is this different than "electron capture"? Either way - I understand the result to be "fewer electrons, more neutrons" and thus a collapse (into a neutron star, but with too much energy to be stable and hence the supernova?) $\endgroup$ – Floris Jul 30 '15 at 12:40
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    $\begingroup$ @Floris Inverse beta decay. e + p -> n + nu The semantic difference between that and electron capture is that I think electron capture would normally be due to an electron that was bound to the nucleus in the first place. But they are essentially the same thing. Also called neutronisation. $\endgroup$ – Rob Jeffries Jul 30 '15 at 14:23
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    $\begingroup$ Thanks for the clarification (and the correction - reminder to self: must not PSE on phone before coffee, without reading glasses...) $\endgroup$ – Floris Jul 30 '15 at 14:30

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