Frequency Dependent Event Rates of Repeating Fast Radio Bursts

How the event rate of fast radio bursts (FRBs) evolves with redshift is a hot topic to explore their cosmological origin and the circum-burst environment. Particularly, it is important to know what the difference of event rates between repeating and non-repeating FRBs is. Here, we calculate the event rates of repeating FRBs detected by diverse telescopes at frequencies higher/lower than 1 GHz. Luminosity and redshift are found to be positively correlated with a power law form for both high- and low-frequency FRBs, showing an obvious evolution of luminosity with redshift. Furthermore, we compare the differentical luminosity and local event rate distributions of high- and low-luminosity FRBs at different frequencies. It is found that the event rates of these sub-samples of repeating FRBs similarly exceed the star formation rate at lower redshift (z < 1). Interestingly, we confirm with bootstrap method that the event rates of low-frequency FRBs exhibit different evolution patterns and they are systematically higher than those of high-frequency FRBs. Our results support the idea that repeating FRBs are most probably produced by magnetars.