Probing the Cosmic Gamma-Ray Burst Rate with Trigger Simulations of the
  Swift Burst Alert Telescope
  The gamma-ray burst (GRB) rate is essential for revealing the connection
between GRBs, supernovae and stellar evolution. Additionally, the GRB rate at
high redshift provides a strong probe of star formation history in the early
universe. While hundreds of GRBs are observed by Swift, it remains difficult to
determine the intrinsic GRB rate due to the complex trigger algorithm of Swift.
Current studies of the GRB rate usually approximate the Swift trigger algorithm
by a single detection threshold. However, unlike the previously flown GRB
instruments, Swift has over 500 trigger criteria based on photon count rate and
additional image threshold for localization. To investigate possible systematic
biases and explore the intrinsic GRB properties, we develop a program that is
capable of simulating all the rate trigger criteria and mimicking the image
threshold. Our simulations show that adopting the complex trigger algorithm of
Swift increases the detection rate of dim bursts. As a result, our simulations
suggest bursts need to be dimmer than previously expected to avoid
over-producing the number of detections and to match with Swift observations.
Moreover, our results indicate that these dim bursts are more likely to be high
redshift events than low-luminosity GRBs. This would imply an even higher
cosmic GRB rate at large redshifts than previous expectations based on
star-formation rate measurements, unless other factors, such as the luminosity
evolution, are taken into account. The GRB rate from our best result gives a
total number of 4571^{+829}_{-1584} GRBs per year that are beamed toward us in
the whole universe.
  SPECIAL NOTE (2015.05.16): This new version incorporates an erratum. All the
GRB rate normalizations ($R_{\rm GRB}(z=0)$) should be a factor of 2 smaller
than previously reported. Please refer to the Appendix for more details. We
sincerely apologize for the mistake.
