Correlations between Event Rates of Short Gamma-Ray Bursts and Star Formation Rates with/without Time Delay

Abstract

In this Letter, we systematically investigate the redshift and luminosity distributions as well as the event rates of short gamma-ray bursts (SGRBs) detected by Swift, Fermi, and Konus–Wind satellites. It is found that the distributions of redshift and luminosity of Fermi and Konus–Wind SGRBs are identical, and they obviously differ from those of Swift/Burst Alert Telescope (BAT) SGRBs. The luminosity distributions of SGRBs detected by diverse detectors can be uniformly fitted by a smoothly broken power-law function. The median luminosity of Swift SGRBs is about 1 order of magnitude smaller than that of Fermi/Gamma-ray Burst Monitor (GBM) or Konus–Wind SGRBs. We also compare the local event rates of Swift/BAT, Fermi/GBM, and Konus–Wind SGRBs and find that the local rate of Swift SGRBs is around 2 orders of magnitude larger than that of either Fermi or Konus–Wind SGRBs, while the latter two rates are comparable. The observed SGRB rates can be successfully fitted by a power law plus Gauss function. The SGRB rates of three kinds of detectors match the delayed/undelayed star formation rates (SFRs) well, except the delayed lognormal and/or Gaussian SFRs at higher redshift, and exceed all types of SFRs at lower redshifts of z < 1. After deducting the diverse SFR components from the SGRB rates, to our surprise, we notice that the remaining SGRB rates steeply decline with redshift in a power-law-like form, indicating that these SGRBs could emerge from the old star populations or compact binary star mergers.