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Wouldn't such supermassive stars blow themselves apart first via radiation pressure (per the Eddington limit)?

But they apparently exist, or at least are plausible:

Assistant Research Fellow, Ke-Jung Chen from ASIAA Taiwan proposed a relativistic instability supernova from a primordial supermassive star ($10^4–10^5$ solar masses) in his 2014 research paper. "There may be a small number of the first stars in the early universe with tens of thousands of solar masses. They are likely to be the progenitors of supermassive black holes in galaxies. Because the more massive of the black hole seed, the more efficient it is to swallow the surrounding matter. The black holes don't need to maintain a high accretion rate to grow quickly," said Chen.

These stars apparently led to supermassive black holes when they died in the very early universe (per Wikipedia on Direct Collapse Black Hole).

I'm looking for an explanation of why a star of this size doesn't explode from radiation pressure.

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    $\begingroup$ from this general article scientificamerican.com/article/the-first-stars-in-the-un it seems that the conditions of the early universe would be different and radiation pressure calculations etc would have to be reconsidered . $\endgroup$
    – anna v
    Commented Aug 30, 2023 at 4:50
  • $\begingroup$ From the SciAm article linked by Anna, "But because the temperatures of the first collapsing gas clumps were almost 30 times higher than those of molecular clouds, their Jeans mass would have been almost 1,000 times larger." OTOH, $10^4–10^5\, M_\odot$ is surprisingly large. $\endgroup$
    – PM 2Ring
    Commented Aug 30, 2023 at 6:38
  • $\begingroup$ The argument at one point was that radiation pressure was basically 0 for Pop III stars, so one could rhetorically ask, "What radiation pressure?" Whether the science has advanced since then is beyond my ken, since I've been out of the game for a long time. $\endgroup$
    – Kyle Kanos
    Commented Aug 30, 2023 at 10:47
  • $\begingroup$ Stars in the current universe above ~100 solar masses do blow off the outer part of their atmospheres, but it's not fast on human time scales. It's fast compared to more stable stars like our Sun, but for how long need they live before you would argue they were "alive" versus they "blew themselves apart"? It takes time for fusion to initiate and even once it starts, it is extremely slow on human time scales and only works to power stars because there are so many opportunities (i.e., particles crammed together). $\endgroup$ Commented Sep 15, 2023 at 18:56

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