New evidence of multiple channels for the origin of gamma-ray bursts with extended emission

Gamma-ray bursts (GRBs) are the most intense explosions in the Universe. GRBs with extended emission (GRBs EE) constitute a small subclass of GRBs. GRBs EE are divided into EE-I GRBs and EE-II GRBs, according to the Amati empirical relationship rather than duration. We test here if these two types of GRB have different origins based on their luminosity function (and formation rate). Therefore, we use Lynden-Bell's c(-) method to investigate the luminosity function and formation rate of GRBs with EE without any assumption. We calculate the formation rate of two types of GRBs. For EE-I GRBs, the fitting function can be written as rho(z) proportional to (1 + z)(-0.34 +/- 0.04) for z < 2.39 and rho(z) proportional to (1 + z)(-2.34 +/- 0.24) for z > 2.39. The formation rate of EE-II can describe as rho(z) proportional to (1 + z)(-1.05 +/- 1.10) for z < 0.43 and rho(z) proportional to (1 + z)(-8.44 +/- 1.10) for z > 0.43. The local formation rate is rho(0) =0.03 Gpc(-3 )yr(-1)for some EE-IGRB sand rho(0) =0.32 Gpc(-3)yr(-1)for EE-I I GRBs . Based on these results, we provide new evidence that the origins of EE-I GRBs are different from EE-II GRBs from the perspective of event rate. The EE-I GRB could be produced from the death of the massive star, but EE-II GRB may come from other processes that are unrelated to the star formation rate. Our findings indicate that the GRBs with EE could have multiple production channels.