The short gamma-ray burst population in a quasi-universal jet scenario

Abstract

We describe a model of the short gamma-ray burst (SGRB) population under a `quasi-universal jet' scenario in which jets can differ in their on-axis peak prompt emission luminosity $L_c$, but share a universal angular luminosity profile $\ell(\theta_v)=L(\theta_v)/L_c$ as a function of the viewing angle $\theta_v$. The model is fitted, through a Bayesian hierarchical approach inspired by gravitational wave (GW) population analyses, to 3 observed SGRB samples simultaneously: the Fermi/GBM sample of SGRBs with spectral information in the catalogue (367 events); a flux-complete sample of 16 Swift/BAT SGRBs also detected by GBM, with a measured redshift; and a sample of SGRBs with a binary neutron star (BNS) merger counterpart, which only includes GRB~170817A at present. The results favour a narrow jet core with half-opening angle $\theta_c=2.1_{-1.4}^{+2.4}$ deg (90\% credible intervals from our fiducial `full sample' analysis) whose on-axis peak luminosity is distributed as $p(L_c) \propto L_c^{-A}$ with $A=3.2_{-0.4}^{+0.7}$ above a minimum luminosity $L_c^\star = 5_{-2}^{+11}\times 10^{51}$ erg s$^{-1}$. For $\theta_v>\theta_c$, the luminosity scales as a power law $\ell\propto \theta_v^{-\alpha_L}$ with $\alpha_L=4.7_{-1.4}^{+1.2}$, with no evidence for a break. While the model implies an intrinsic `Yonetoku' correlation between $L$ and the peak photon energy $E_p$, its slope is somewhat shallower $E_p\propto L^{0.4\pm 0.2}$ than the apparent one, and the normalization is offset towards larger $E_p$, due to selection effects. The implied local rate density of SGRBs is between about 100 up to several thousands of events per Gpc$^{3}$ yr, in line with the BNS merger rate density inferred from GW observations. Based on the model, we predict 0.2 to 1.3 joint GW+SGRB detections per year by the Advanced GW detector network and Fermi/GBM during the O4 observing run.