Time Delay of Fast Radio Burst Population with Respect to the Star Formation History

In spite of significant progress in the research of fast radio bursts (FRBs) in recent decades, their origin is still under extensive debate. Investigation of the population of FRBs can provide new insight into this interesting problem. In this paper, based on the first Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB catalog, we construct a Bayesian framework to analyze the FRB population, with the selection effect of the CHIME telescope being properly taken into account. The energy function is modeled as the power law with an exponential cutoff. Four redshift distribution models are considered, i.e., the star formation history (SFH) model, and three time-delayed models (Gaussian delay, log-normal delay, and power-law delay). The free parameters are simultaneously constrained using the Bayesian inference method, and the Bayesian information criterion (BIC) is used in model comparison. According to the BIC, the log-normal delay model fits the data best. The power-law delay model and Gaussian delay model can also give reasonable fits, although they are not as good as the log-normal delay model. However, the SFH model is strongly disfavored compared with the three time-delayed models. The energy function is tightly constrained and is almost independent of the redshift models, with the best-fitting power-law index α ≈ 1.8 and cut-off energy $\mathrm{log}({E}_{c}/\mathrm{erg})\approx 42$ . The FRB population shows on average a 3 ∼ 5 billion yr time delay with respect to the SFH. Therefore, the hypothesis that the FRB population traces the SFH is conclusively ruled out.