The Connection between Gamma-Ray Bursts and Extremely Metal-poor Stars: Black Hole-forming Supernovae with Relativistic Jets

Long-duration gamma-ray bursts (GRBs) are thought to be connected to luminous and energetic supernovae (SNe) called hypernovae (HNe), resulting from the black hole (BH)-forming collapse of massive stars. For recent nearby GRBs 060505 and 060614, however, the expected SNe have not been detected. The upper limits to the SN brightness are about 100 times fainter than GRB-associated HNe (GRB-HNe), corresponding to the upper limits to the ejected ⁵⁶Ni masses of M(⁵⁶Ni) ~ 10^-3 M_☉. SNe with a small amount of ⁵⁶Ni ejection are observed as faint Type II SNe. HNe and faint SNe are thought to be responsible for the formation of extremely metal-poor (EMP) stars. In this Letter, a relativistic jet-induced BH-forming explosion of the 40 M_☉ star is investigated and hydrodynamic and nucleosynthetic models are presented. These models can explain both GRB-HNe and GRBs without bright SNe in a unified manner. Their connection to EMP stars is also discussed. We suggest that GRBs without bright SNe are likely to synthesize M(⁵⁶Ni) ~ 10^-4 to 10^-3 M_☉ or ~10^-6 M_☉.