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- TL;DR Summary
- More specifically, what are the possible cold, equilibrium, spherically symmetric states of iron.
This thread is meant to discuss a topic that arose in https://www.physicsforums.com/threads/is-there-a-theoretical-size-limit-of-a-planet.1045983/ in a more precisely specified, idealized way.
Further details:
1) Standard model + GR assumed, no other theories intended for this discussion.
2) Proton decay assumed not to exist (a consequence of (1), just for emphasis).
3) The question of formation or existence of such a body in our universe is irrelevant to this discussion.
4) We assume no cosmological constant, dark matter or CMB. More specifically, we assume that the GR solution is vacuum Shwarzschild outside of some 2-shere of symmetry. This formalizes the notion of an isolated ball in an otherwise empty universe that has the same laws of physics as ours.
5) I assume a cold, equilibrium state. Again, how this arose is irrelevant to the discussion.
6) By iron, assume iron 56.
This still leaves quite a number of questions, many of which probably cannot be answered in detail with our current state of knowledge.
My initial thoughts are as follows, and I really welcome discussion, disagreement, etc. within this idealized framework.
For small mass, you have an "ordinary iron ball", with iron in its standard cold low pressure molecular configuration, and the round feature being purely a matter of initial condition as opposed to being forced by self gravity.
At some larger mass, you have that self gravity is significant in that a major perturbation from round would settle back to round. I believe in this state, the center of the ball would likely be in high pressure phase of iron different than above, even with a requirement of being cold throughout. I would call this range of balls "planets" using an older (and IMO better definition of planet - round by self gravity, but not exhibiting any stellar features). Already here, there are interesting questions - to go beyond theory, one would be looking at experiments using diamond anvils to achieve the relevant pressures.
At some larger mass you would have an electron degenerate state of iron in the core - no atomic or molecular structure at all, but the iron nucleii would be intact, so it still make sense to call it iron. I would call such a state a cold, iron, black dwarf. I do not know what the minimum mass for this state is. It seems it would have to be a purely theoretical calculation, because no similar objects are known in our universe. Just for comparison, I see that white dwarfs below .2 solar mass exist, but these have quite a few differences from this cold iron black dwarf. I would think it would take less mass for this state, maybe even less that .1 solar mass. I don't know any name for the mass when some ball of matter must enter electron degeneracy. Thus, one might say the largest possible iron planet is .1 to .17 solar mass.
Finally, you would run into the Chandresekhar limit, when electron degeneracy would be insufficient to maintain equlibrium. Here, calculations have been done with heavier elements, and perhaps 1.2 solar masses (or even a bit less) would be the maximum cold iron black dwarf. Note, the common 1.4 solar mass figure assumes nuclear compositions typical of reality. Thus one answer to the largest possible iron ball is around 1.2 solar masses. Above the relevant Chandresekhar limit, you would no longer have iron possible except at the surface. I guess we can allow a cold, iron coated, neutron star as a possible state. This type of object could exist up to the Oppenheimer-Volkoff limit for neutron stars. That is, if you had a maximal size iron coated neutron star, surrounded by a shell of very cold iron dust allowed to infall, the infall would trigger a collapse to a BH. This limit is not well known, but recent figure would be around 2.3 solar masses.
Further details:
1) Standard model + GR assumed, no other theories intended for this discussion.
2) Proton decay assumed not to exist (a consequence of (1), just for emphasis).
3) The question of formation or existence of such a body in our universe is irrelevant to this discussion.
4) We assume no cosmological constant, dark matter or CMB. More specifically, we assume that the GR solution is vacuum Shwarzschild outside of some 2-shere of symmetry. This formalizes the notion of an isolated ball in an otherwise empty universe that has the same laws of physics as ours.
5) I assume a cold, equilibrium state. Again, how this arose is irrelevant to the discussion.
6) By iron, assume iron 56.
This still leaves quite a number of questions, many of which probably cannot be answered in detail with our current state of knowledge.
My initial thoughts are as follows, and I really welcome discussion, disagreement, etc. within this idealized framework.
For small mass, you have an "ordinary iron ball", with iron in its standard cold low pressure molecular configuration, and the round feature being purely a matter of initial condition as opposed to being forced by self gravity.
At some larger mass, you have that self gravity is significant in that a major perturbation from round would settle back to round. I believe in this state, the center of the ball would likely be in high pressure phase of iron different than above, even with a requirement of being cold throughout. I would call this range of balls "planets" using an older (and IMO better definition of planet - round by self gravity, but not exhibiting any stellar features). Already here, there are interesting questions - to go beyond theory, one would be looking at experiments using diamond anvils to achieve the relevant pressures.
At some larger mass you would have an electron degenerate state of iron in the core - no atomic or molecular structure at all, but the iron nucleii would be intact, so it still make sense to call it iron. I would call such a state a cold, iron, black dwarf. I do not know what the minimum mass for this state is. It seems it would have to be a purely theoretical calculation, because no similar objects are known in our universe. Just for comparison, I see that white dwarfs below .2 solar mass exist, but these have quite a few differences from this cold iron black dwarf. I would think it would take less mass for this state, maybe even less that .1 solar mass. I don't know any name for the mass when some ball of matter must enter electron degeneracy. Thus, one might say the largest possible iron planet is .1 to .17 solar mass.
Finally, you would run into the Chandresekhar limit, when electron degeneracy would be insufficient to maintain equlibrium. Here, calculations have been done with heavier elements, and perhaps 1.2 solar masses (or even a bit less) would be the maximum cold iron black dwarf. Note, the common 1.4 solar mass figure assumes nuclear compositions typical of reality. Thus one answer to the largest possible iron ball is around 1.2 solar masses. Above the relevant Chandresekhar limit, you would no longer have iron possible except at the surface. I guess we can allow a cold, iron coated, neutron star as a possible state. This type of object could exist up to the Oppenheimer-Volkoff limit for neutron stars. That is, if you had a maximal size iron coated neutron star, surrounded by a shell of very cold iron dust allowed to infall, the infall would trigger a collapse to a BH. This limit is not well known, but recent figure would be around 2.3 solar masses.
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