2007/08/31 by Agnieszka Janiuk, Daniel Proga
Mathematics · Physics and Astronomy · #Accretion (finance) #Angular momentum #Astro and Planetary Science #Astronomy #Astrophysics #Classical mechanics #Compact star #Gamma-ray burst #Gamma-ray bursts and supernovae #Geometry #Kinetic energy #Mathematics #Physics #Pulsars and Gravitational Waves Research #Rotation (mathematics) #Rotational energy #Specific relative angular momentum #Stars #Torus #Total angular momentum quantum number #astro-ph
paper · pdf · doi:10.1086/526511
29 pages, 10 figures, including 1 color fig., revised version accepted by ApJ
arxiv created 2007/11/30 · openalex publication_date 2008/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The collapsar model is the most promising scenario to explain the huge release of energy associated with long-duration gamma-ray bursts (GRBs). Within this scenario GRBs are believed to be powered by accretion through a rotationally supported torus or by fast rotation of a compact object. In both cases rotation of the progenitor star is a key property, because it must be high enough for the torus to form, the compact object to rotate very fast, or both. Here, we check what rotational properties a progenitor star must have in order to sustain torus accretion over relatively long activity periods such as observed in most GRBs. We show that simple, often cited, estimates of the total mass available for torus formation and consequently the duration of a GRB are only upper limits. We revise these estimates by taking into account the long-term effect that as the compact object accretes, the minimum specific angular momentum needed for torus formation increases. This in turn leads to a smaller fraction of the stellar envelope that can form a torus. We demonstrate that this effect can lead to a significant (an order of magnitude) reduction of the total energy and overall duration of a GRB event. This of course can be mitigated by assuming that the progenitor star rotates faster then we assumed. However, our assumed rotation is already high compared to observational and theoretical constraints. We estimate the GRB duration times, first by assuming a constant accretion rate, an also by explicitly calculating the free-fall time of the gas during the collapse. We discuss the implications of our results.