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This informative answer to What was the absolute limit to the possible sizes of the first stars formed from “primordial material with no metals”? led me to Wikipedia's Quasi-star; Formation and properties which says:

A quasi-star would result from the core of a large protostar collapsing into a black hole, where the outer layers of the protostar are massive enough to absorb the resulting burst of energy without being blown away or falling into the black hole, as occurs with modern supernovae. [...] Formation of quasi-stars could only happen early in the development of the Universe, before hydrogen and helium were contaminated by heavier elements; thus, they may have been very massive Population III stars.

But neither the answer nor Wikipedia plainly state just what it is about the presence of metals that would make Quasi-stars impossible, such that if they ever did exist it would only have been in the early universe.

Question: Why could Quasi-stars ("black hole stars") have only existed when everything was hydrogen and helium? (no metal "contamination")

uhoh
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    As ProfRob says at https://astronomy.stackexchange.com/a/37127/16685 "Primordial gas is quite transparent to radiation, but this also means it is poor at radiating away the heat from gravitational contraction." Pela gives more details here: https://astronomy.stackexchange.com/a/27555/16685 – PM 2Ring Jan 02 '21 at 07:14

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The presence of heavier elements makes the medium absorb more radiation. This means a nascent star that would have been able to collapse in the absence of metals, will lose its outer layers to radiation pressure as the core starts to heat up.