Intrinsic Distribution of Gamma-Ray Bursts. I. Insights from Fermi-GBM Observations

Abstract Investigating the intrinsic distributions of gamma-ray bursts (GRBs) is essential for understanding their physical origins, as these properties are closely tied to the central engine, radiation mechanisms, and cosmological evolution. In this study, we examine the intrinsic parameters of GRBs using synthetic populations calibrated to Fermi Gamma-ray Burst Monitor (Fermi-GBM) observations. We generated a large GRB population through Monte Carlo–based population modeling, simulated the Fermi-GBM detector response, and performed spectral fitting for simulated detected bursts. By comparing the simulation output with actual Fermi-GBM data, we find that the observed properties of the simulated bursts show good agreement with real observations, demonstrating the reliability of our simulation pipeline and spectral-fitting procedures. We also identify a noticeable deviation in the β parameter between the intrinsic distribution (before detector response) and the observed distribution (after detector response), which is likely driven by statistical uncertainties under low signal-to-noise conditions. Based on the validated simulations, we derive the intrinsic distributions of key long-GRB properties—including luminosity, isotropic energy, and redshift—and estimate a local GRB rate of 1.41 ± 0.22 Gpc −3 yr −1 .