The collapsar model is the most promising scenario to explain the hugerelease of energy associated with long duration gamma-ray-bursts (GRBs). Withinthis scenario GRBs are believed to be powered by accretion through arotationally support torus or by fast rotation of a compact object. In bothcases then, rotation of the progenitor star is one of the key propertiesbecause it must be high enough for the torus to form, the compact object torotate very fast, or both. Here, we check what rotational properties aprogenitor star must have in order to sustain torus accretion over relativelylong activity periods as observed in most GRBs. We show that simple, oftencited, estimates of the total mass available for torus formation andconsequently the duration of a GRB are only upper limits. We revise theseestimates by taking into account the long term effect that as the compactobject accretes the minimum specific angular momentum needed for torusformation increases. This in turn leads to a smaller fraction of the stellarenvelope that can form a torus. We demostrate that this effect can lead to asignificant, an order of magnidute, reduction of the total energy and overallduration of a GRB event. This of course can be mitigated by assuming that theprogenitor star rotates faster then we assumed. However, our assumed rotationis already high compared to observational and theoretical constraints. We alsodiscuss implications of our result.
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