Long Gamma-Ray Burst Rate at Very High Redshift

Future missions for long gamma-ray burst (GRB) observations at high redshift, such as the High-z Gamma-ray bursts for Unraveling the Dark Ages Mission and the Transient High-Energy Sky and Early Universe Surveyor, will provide clues 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 I and II stars and Population III stars as GRB progenitors. For the Population I and II star formation rate (SFR), we adopt an up-to-date model of a high-redshift SFR based on the halo mass function and the dark matter accretion rate obtained from cosmological simulations. We show that the Population I and II GRB rate steeply decreases with redshift. This would rather enable us to detect the different type of GRBs, Population III GRBs, at very high redshift. If 10% or more Population 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 Population III stars produced via the binary merger. In our conventional case, the detection rate of such luminous GRBs is 3-20 yr(-1) (z > 8). Those future observations contribute to revealing the Population III star formation history.