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Protostellar Accretion
The core accretes as long as the protostar radiates below the Eddington luminosity:
The accretion rate is given by:
If the clump is asymmetric then a disk forms so that radiation escapes from along the rotational axis and matter accretes from the disk.
The primordial star mass range is estimated according to these factors as:
Notes:
The Eddington luminosity is derived by balancing Thompson scattering off photons with the gravitational force. The upper limit is derived simply by assuming that the star cannot accrete for longer than its lifetime (between several hundred thousand to a million years).
Currently the most massive star known is the Pistol Star weighing in at around 150 Ms. However, for this and other massive luminous stars, resolution limits create uncertainty whether these stars are single isolated stars or unresolved multiple stars