The connection between long Gamma Ray Bursts (GRBs) and Supernovae (SNe) have been established through the well observed cases. These events can be explained as the prompt collapse to a black hole (BH) of the core of a massive star (M≳40M⊙). The energies of these GRB-SNe were much larger than those of typical SNe, thus these SNe are called Hypernovae (HNe). The case of SN 2006aj/GRB060218 appears different: the GRB was weak and soft, being called an X-Ray Flash (XRF); the SN is dimmer and has very weak oxygen lines. The explosion energy of SN 2006aj was smaller, as was the ejected mass. In our model, the progenitor star had a smaller mass than other GRB-SNe (M~20M⊙), suggesting that a neutron star (NS) rather than a BH was formed. If the nascent NS was strongly magnetized as a magnetar and rapidly spinning, it may launch a weak GRB or an XRF. The peculiar light curve of Type Ib SN 2005bf may also be powered by a magnetar. The blue-shifted nebular emission lines of 2005bf indicate the unipolar explosion possibly related to standing accretion shock instability (SASI) associated with a newly born NS.
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