Long gamma-ray burst rate at very high redshift

Future missions for long gammma-ray burst (GRB) observations at high redshift such as HiZ-GUNDAM and THESEUS will provide clue to the star formation history in our universe. In this paper focusing on high redshift (z>8) GRBs, we calculate the detection rate of long GRBs by future observations, considering both Population (Pop) I&II stars and Pop III stars as GRB progenitors. For the Pop I&II star formation rate (SFR), we adopt an up-to-date model of high-redshift SFR based on the halo mass function and dark matter accretion rate obtained from cosmological simulations. We show that the Pop I&II GRB rate steeply decreases with redshift. This would rather enable us to detect the different type of GRBs, Pop III GRBs, at very high redshift. If 10% or more Pop III stars die as an ultra-long GRB, the future missions would detect such GRBs in one year in spite of their low fluence. More luminous GRBs are expected from massive compact Pop III stars produced via the binary merger. In our conventional case, the detection rate of such luminous GRBs is 3-20 /yr (z>8). Those future observations contribute to revealing of the Pop III star formation history.