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A quasi-star is a hypothetical supermassive star that is so heavy its core collapses into a black hole as it is still forming. The matter accreting into the black hole then generates radiation pressure that keeps the star from imploding.

These are supposed to be extremely massive stars of 1000 or more M☉, but the most massive regular star is about 250 M☉.

There is a gap there, as well as a precedent in the form of Thorne–Żytkow objects, which are stars with a neutron star at their core due to a collision. The neutron star will feed on its host until the entire host star is consumed or it collapses into a black hole and the host star falls in, whichever comes first.

Based on this, a supermassive star with a neutron star at its core, formed the same way as a quasi-star but with less mass involved, looks plausible, but I don't know enough about the physics involved to tell for sure.

Is this realistic, and if not, what does happen to a 500 or 750 M☉ star as it is forming?

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You couldn't have a quasi-star with a neutron star at its core; the formation of the neutron star, unlike the collapse to a black hole, would be accompanied by a shockwave and a burst of energetic neutrinos that would tear the rest of the star apart. In any case, stars in the mass-range of 250 to 1000 solar masses reach core temperatures where they would instead suffer a pair-instability collapse followed by photodisintegration resulting in a black-hole.

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  • $\begingroup$ Thorne–Żytkow objects are not formed by collapse of a part of the host star, but a merger with an existing neutron star, e.g. in a binary. $\endgroup$
    – Anders Sandberg
    Commented Aug 3, 2022 at 14:56
  • $\begingroup$ @AndersSandberg I was almost going to say "...are not thought to be formed by..." but then discovered that that's by definition :-) fyi I've just asked "Holy grail" future observation to confirm presence of neutron stars in the centers of massive, otherwise conventional stars? (Thorne–Żytkow objects) $\endgroup$
    – uhoh
    Commented Aug 3, 2022 at 22:09
  • $\begingroup$ I would have thought that the collision of a neutron star and regular star would almost by definition push the NS over the mass limit to become a black hole. Either that or somehow eject material from the regular star, in any case I would have been very surprised by any neutron star sitting comfortably in the center of anything like a regular star. $\endgroup$
    – SoronelHaetir
    Commented Aug 3, 2022 at 22:48
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    $\begingroup$ The collapse to a black hole is accompanied by a shockwave as well isn't it? The idea of a quasi-star is that it is massive enough to be able to "absorb" that shockwave $\endgroup$
    – SirHawrk
    Commented Aug 4, 2022 at 11:38
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If a 500 M☉ cloud of gas is collapsing under gravity it will tend to fragment *due to inevitable non-uniformity in the initial density distribution, and the result will not be a star, but a multiple star or a cluster.

This limits the formation of very large stars, except by exceptional events like stellar collisions (very rare)

This limit is very dependent on the opacity of the collapsing gas, and therefore on the presence (or not) of "metals" i.e. elements other than hydrogen and helium. In the very early universe, population III stars with much larger masses could have formed. Population II and I stars with such large masses are not able to form.

The keywords to read more about how a cloud of gas can collapse to form a star or multiple stars is Jeans instability; fragmentation.

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