Simulations on High-z Long Gamma-Ray Burst Rate
  Since the launch of Swift satellite, the detections of high-z (z>4) long
gamma-ray bursts (LGRBs) have been rapidly growing, even approaching the very
early Universe (the record holder currently is z=8.3). The observed high-z LGRB
rate shows significant excess over that estimated from the star formation
history. We investigate what may be responsible for this high productivity of
GRBs at high-z through Monte Carlo simulations, with effective Swif/BAT trigger
and redshift detection probabilities based on current Swift/BAT sample and
CGRO/BATSE LGRB sample. We compare our simulations to the Swift observations
via log N-log P, peak luminosity (L) and redshift distributions. In the case
that LGRB rate is purely proportional to the star formation rate (SFR), our
simulations poorly reproduce the LGRB rate at z>4, although the simulated log
N-log P distribution is in good agreement with the observed one. Assuming that
the excess of high-z GRB rate is due to the cosmic metallicity evolution or
unknown LGRB rate increase parameterized as (1+z)^delta, we find that although
the two scenarios alone can improve the consistency between our simulations and
observations, incorporation of them gives much better consistency. We get
0.2<epsilon<0.6 and delta<0.6, where epsilon is the metallicity threshold for
the production of LGRBs. The best consistency is obtained with a parameter set
(epsilon, delta)=(~0.4, ~0.4), and BAT might trigger a few LGRBs at z~14. With
increasing detections of GRBs at z>4 (~15% of GRBs in current Swift LGRB sample
based on our simulations), a window for very early Universe is opening by Swift
and up-coming SVOM missions.
