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I have used a sample of long gamma-ray bursts (GRBs) common to both Swift and Fermi to re-derive the parameters of the Yonetoku correlation. This allowed me to self-consistently estimate pseudo-redshifts of all the bursts with unknown redshifts. This is the first time such a large sample of GRBs from these two instruments is used, both individually and in conjunction, to model the long GRB luminosity function. The GRB formation rate is modelled as the product of the cosmic star formation rate and a GRB formation efficiency for a given stellar mass. An exponential cut-off power-law luminosity function fits the data reasonably well, with ν = 0.6 and Lb = 5.4 × 1052 ergs-1, and does not require a cosmological evolution. In the case of a broken power law, it is required to incorporate a sharp evolution of the break given by Lb ∼ 0.3 × 10^52(1 + z)2.90 erg s-1, and the GRB formation efficiency (degenerate up to a beaming factor of GRBs) decreases with redshift as ∝ (1 + z)-0.80. However, it is not possible to distinguish between the two models. The derived models are then used as templates to predict the distribution of GRBs detectable by CZT Imager onboard AstroSat as a function of redshift and luminosity. This demonstrates that via a quick localization and redshift measurement of even a few CZT Imager GRBs, AstroSat will help in improving the statistics of GRBs both typical and peculiar.
The luminosity function of short Gamma Ray Bursts (GRBs) is modelled by using the available catalogue data of all short GRBs (sGRBs) detected till October, 2017. The luminosities are estimated via the `pseudo-redshifts' obtained from the `Yonetoku correlation', assuming a standard delay distribution between the cosmic star formation rate and the production rate of their progenitors. While the simple powerlaw is ruled out to high confidence, the data is fit well both by exponential cutoff powerlaw and broken powerlaw models. Using the derived parameters of these models along with conservative values in the jet opening angles seen from afterglow observations, the true rate of short GRBs is derived. Assuming a short GRB is produced from each binary neutron star merger (BNSM), the rate of gravitational wave (GW) detections from these mergers are derived for the past, present and future configurations of the GW detector networks. Stringent lower limits of 1.87 per year for the aLIGO-VIRGO, and 3.11 per year for the upcoming aLIGO-VIRGO-KAGRA-LIGO/India configurations are thus derived for the BNSM rate at 68% confidence. The BNSM rates calculated from this work and that independently inferred from the observation of the only confirmed BNSM observed till date, are shown to have a mild tension; however the scenario that all BNSMs produce sGRBs cannot be ruled out.