Resolving the Excess of Long GRBs at low redshift in the Swift Era

Utilizing more than 100 long gamma-ray bursts (LGRBs) in the Swift-Ryan-2012 sample that include the observed redshifts and jet angles, Le & Mehta performed a timely study of the rate-density of LGRBs with an assumed broken power law GRB spectrum and obtained a GRB-burst-rate functional form that gives acceptable fits to the preSwift and Swift redshift and jet angle distributions. The results indicated an excess of LGRBs at redshift below $z \sim 2$ in the Swift sample. In this work, we are investigating if the excess is caused by the cosmological Hubble constant $H_0$, the $\gamma$-ray energy released $E_\gamma$, the low- and high-energy indices ($\alpha, \beta$) of the Band function, the minimum and maximum jet angles $\theta_{\rm j,min}$ and $\theta_{\rm j, max}$, or that the excess is due to a biased in the Swift-Ryan-2012 sample. Our analyses indicate that none of the above physical parameters resolved the excess problem, but suggesting that the Swift-Ryan-2012~sample is biased with possible afterglow selection effect. The following model physical parameter values provide the best fit to the Swift-Ryan-2012 and preSwift~samples: the Hubble constant $H_0 = 72 \, {\rm km s^{-1} Mpc^{-1}}$, the energy released $E_\gamma \sim 4.47 \times 10^{51}$ erg, the energy indices $\alpha \sim 0.9$ and $\beta \sim -2.13$, the jet angles of $\theta_{\rm j,max} \sim 0.8$ rad, and $\theta_{\rm j, min} \sim 0.065$ and $\sim 0.04$ rad for preSwift and Swift, respectively, $s \sim -1.55$ the jet angle power-law index, and a GRB formation rate that is similar to the Hopkins & Beacom observed star formation history and as extended by Li. Using the Swift Gamma-Ray Burst Host Galaxy Legacy Survey (SHOALS) Swift-Perley LGRB sample and applying the same physical parameter values as above, however, our model provides consistent results with this data set and indicating no excess of LGRBs at any redshift.