What threshold did dark matter annihilation prevent the protostar core from reaching?

Answer

The necessary threshold for hydrogen fusion to begin

The formation scenario for Dark Stars places them in the very early universe, potentially before conventional stars ignited. In this context, gas clouds initially collapsed under gravity. However, if the concentration of dark matter within the collapsing core was sufficiently high, the resulting energy from dark matter annihilation provided an intense, prolonged heating effect. This thermal support generated enough outward pressure to keep the protostar inflated and hot, but crucially, it prevented the core temperature and pressure from ever reaching the specific, necessary threshold required to ignite sustained thermonuclear hydrogen fusion, thus defining the object as a Dark Star rather than a Population III star.

What threshold did dark matter annihilation prevent the protostar core from reaching?
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