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Since we know that stars burn out, collapse, or blow up when too many of their atoms fuse inti iron, then how come, with all the ancient galaxies we've been observing, there isn't one galaxy whose stars have become giant balls of iron, which would eventually collide into one galaxy-sized iron globule in space?

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meta: I also recommend tags like star-death and star-lifecycle –  Supuhstar Aug 19 at 2:04
    
Your hypothesis is not correct: not all stars produce iron. Conversely, the most of them have not enough mass to do it. –  Py-ser Aug 19 at 6:10

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In short, you can't make a galaxy-mass ball of iron because there's no way to support the ball against the inward crush of its own gravity. First, it would collapse into a neutron star, but even neutron stars can't hold themselves up beyond about 2-3 solar masses. Your galaxy-sized object would collapse into a black hole. But we do see these! All massive galaxies are believed to have supermassive black holes at their centres. These are up to 10 billion solar masses in size, which is comparable to smaller galaxies.

In any star, be it a main-sequence star like the Sun, a giant, or even a white dwarf or neutron star, the inward force of gravity must be balanced by some outward force or pressure. (In fact, we basically assume this when we construct stellar models, although it's a very good assumption.) In main-sequence stars, this pressure is provided by the nuclear reactions happening inside them but as a star evolves, it gets a bit more complicated. In some situations, the nuclei get so close together that they their electrons begin to share quantum states. And because no two electrons can be in the same state, they have to occupy higher energy states. This in effect exerts a kind of pressure (called degeneracy pressure), because the electrons are forced to move around faster than they otherwise would. This is what supports white dwarfs and the cores of some evolved stars. e.g. low-mass red giants.

Degeneracy pressure is fine up to a limit known as the Chandrasekhar limit, which is about 1.44 solar masses (depending on the composition of the object in question). Anything above this would collapse. First, this collapse would yield a neutron star, where things are a bit different. But a similar principle holds, and there's a degeneracy pressure because the neutrons themselves also occupy one quantum state each. The details are much more difficult here, but the overall consensus is that neutron degeneracy pressure can support objects up to about 2-3 solar masses. After that, there's nothing left to balance gravity, and the star collapses into a black hole.

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Apart from the good reasons given in the other answers as to why a ball of iron in excess of about $1.4$M$_\odot$ cannot be stable, there is another reason. Namely, there is no way to form that much pure iron. Iron is produced in supernovae, but only a fraction of the matter expelled by a supernova is actually iron and there is no natural way to select is. The remaining matter is locked in the stellar remnant, either a white dwarf, neutron star, or (stellar-mass) black hole. The latter two are already to massive for the material to be in the form of iron, while the a white dwarf may only contain some iron, but never is a ball of iron.

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Our sun will eventually become a white dwarf. A star 10 times it mass will become a neutron star. A star 100 times the mass of the sun will become a black hole. So if 100 stars came together into one mass, it would collapse into a black hole. It is currently believed that a super massive black hole (at least 1000 times the mass of our sun) is at the center of our galaxy and also in the Andromeda galaxy. This is where all the iron might be found from this region of space.

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You wouldn't need 100 stars to come together to make a black hole. Also, the masses of the two black holes mentioned are way more than 1,000 solar masses. And would an atom of iron really survive deep inside a black hole? –  HDE 226868 Aug 19 at 16:50
    
@HDE226868 I knew that. I just didn't want to take the time to look up the correct amounts. –  LDC3 Aug 20 at 0:30

If you had a galaxy sized ball of iron the gravitational force emitted would be immense, and without any force pushing out from it the ball would collapse into itself to form a black hole. In stars such as the sun (main-sequence stars) the outward force of nuclear reactions taking place in its core keep it from collapsing into itself. However, with a ball of iron the only force acting on it would be the pull of gravity, eventually crushing the ball into itself.

The ball of iron wouldn't even be able to reach the size of a galaxy. There is a limit known as the Chandrasekhar limit, which says anything that is about 1.44 solar masses would collapse. This would most likely form a neutron star, but this also has a limit to the amount of mass it can hold. Eventually, even this will collapse upon itself to form a black hole.

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Isn't this essentially what @Warrick said about an hour ago? –  Jan Dvorak Aug 19 at 8:29
    
It is similar to his answer. We both had the same ideas –  Nirvik Baruah Aug 19 at 8:34

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