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Rotation plays a key role in the star-formation process, from pre-stellarcores to pre-main-sequence (PMS) objects. Understanding the formation ofmassive stars requires taking into account the accretion of angular momentumduring their PMS phase. We study the PMS evolution of objects destined tobecome massive stars by accretion, focusing on the links between the physicalconditions of the environment and the rotational properties of young stars. Inparticular, we look at the physical conditions that allow the production ofmassive stars by accretion. We present PMS models computed with a new versionof the Geneva Stellar Evolution code self-consistently including accretion androtation according to various accretion scenarios for mass and angularmomentum. We describe the internal distribution of angular momentum in PMSstars accreting at high rates and we show how the various physical conditionsimpact their internal structures, evolutionary tracks, and rotation velocitiesduring the PMS and the early main sequence. We find that the smooth angularmomentum accretion considered in previous studies leads to an angular momentumbarrier and does not allow the formation of massive stars by accretion. Abraking mechanism is needed in order to circumvent this angular momentumbarrier. This mechanism has to be efficient enough to remove more than 2/3 ofthe angular momentum from the inner accretion disc. Due to the weak efficiencyof angular momentum transport by shear instability and meridional circulationduring the accretion phase, the internal rotation profiles of accreting starsreflect essentially the angular momentum accretion history. As a consequence,careful choice of the angular momentum accretion history allows circumventionof any limitation in mass and velocity, and production of stars of any mass andvelocity compatible with structure equations.

Massive star formation by accretion II. Rotation: how to circumvent the angular momentum barrier?