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If a black hole comes from a dying star, do we have a record or proof that our galactic center was once a huge ball of burning plasma? I'm not an astronomy student.

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We don't know. It's a supermassive black hole and there are several theories about their formation:

The origin of supermassive black holes remains an open field of research. Astrophysicists agree that black holes can grow by accretion of matter and by merging with other black holes. There are several hypotheses for the formation mechanisms and initial masses of the progenitors, or "seeds", of supermassive black holes. Independently of the specific formation channel for the black hole seed, given sufficient mass nearby, it could accrete to become an intermediate-mass black hole and possibly a SMBH if the accretion rate persists.

The early progenitor seeds may be black holes of tens or perhaps hundreds of solar masses that are left behind by the explosions of massive stars and grow by accretion of matter. Another model involves a dense stellar cluster undergoing core collapse as the negative heat capacity of the system drives the velocity dispersion in the core to relativistic speeds.

As far as I know, nothing extra is known about the black hole in the center of our own galaxy.

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    $\begingroup$ The pedantic answer is "no, maybe a lot of stars, but not just the one". $\endgroup$
    – Spencer
    May 25 at 21:55
  • $\begingroup$ Also note that galaxy centric BH's haven't been evidenced to be post-date the big bang - the start. $\endgroup$ May 25 at 23:11
  • $\begingroup$ @LifeInTheTrees Wait, are you saying that the reason we haven't found any primordial black holes is because they all became anchors for subsequent galaxy formation? $\endgroup$
    – Michael
    May 26 at 17:24
  • $\begingroup$ That's reading an awful lot into one comment @Michael. $\endgroup$
    – Lee Mosher
    May 27 at 1:20
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    $\begingroup$ @LeeMosher I've got my Jumping to Conclusions mat right here... $\endgroup$
    – Michael
    May 27 at 2:32
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No. There is a maximum possible mass of a star - any larger and the star would blow itself apart because its radiation is stronger than its gravity. This is known as the Eddington limit. The theoretical maximum possible mass is not well constrained, but it's certainly not more than a few hundred solar masses at most.

The black hole at the center of our galaxy is supermassive, and is over a million solar masses. Therefore it cannot have come from a star (stars lose mass when they become a black hole, as well). It could potentially have come from several hundred thousand stars, however.

By the way there is also a lower mass limit for so-called stellar black holes (i.e. black holes that form from stars), and it is possible that there are black holes of smaller masses than these. These are known as primordial black holes, and if they exist, would have formed shortly after the Big Bang.

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    $\begingroup$ Why couldn't a SMBH like SgrA* have started out as a stellar black hole and grown to supermassiveness by swallowing millions of solar masses' worth of matter? $\endgroup$
    – Vikki
    May 26 at 12:19
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    $\begingroup$ @Vikki it could, but at that point, can you say it is a former star? Like, if you bake a cake, can you say the cake was formerly sugar? I suppose you could, but then one could equally say the cake was formerly flour, formerly cheese, etc. $\endgroup$
    – Allure
    May 26 at 12:33
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    $\begingroup$ Vikki asks a good question. This is a current field of research, but supermassive black holes are surprisingly large surprisingly early in the Universe, which means they must have either started out very massive or grew very fast (super-Eddington). We don't know, but even starting from a stellar black hole might be physically difficult to produce those SMBH (not necessarily Sgr A* though), and may require a direct collapse model. $\endgroup$
    – Alwin
    May 26 at 16:42
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    $\begingroup$ @Allure: Most of an adult human's mass is made up of matter that wasn't part of them when they were a baby; does that mean that the adult wasn't previously the baby? $\endgroup$
    – Vikki
    May 26 at 21:38
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    $\begingroup$ @Vikki I just want to point out that you risk running into an argument about definitions. Allure's interpretation of OP's question is valid. Your interpretation of OP's question is also valid. Both are interesting, but subtly different questions. Suppose Sgr A* merged with many other black holes while growing... which "star" would you say it used to be? If you want, you can say it used to be the largest of the stars that formed it, but that's just a choice of how you say things. Due to mergers and accretion, your baby analogy does not exactly translate to black holes. $\endgroup$
    – Alwin
    May 26 at 22:21

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