2024ApJ...973L..54C

Fast radio bursts (FRBs) are millisecond-duration flashes with unknown origins. Their formation rate is crucial for unveiling physical origins. However, the luminosity and formation rate are degenerate when directly fitting the redshift distribution of FRBs. In contrast to previous forward-fitting methods, we use Lynden-Bell's c^– method to derive the luminosity function and formation rate of FRBs without any assumptions. Using the nonrepeating FRBs from the first Canadian Hydrogen Intensity Mapping Experiment FRB catalog, we find a relatively strong luminosity evolution, and luminosity function can be fitted by a broken power-law model with a break at 1.33 × 10⁴¹ erg s^–1. The formation rate declines rapidly as (1 + z)^–4.9±0.3 with a local rate of 1.13 × 10⁴ Gpc^–3 yr^–1. This monotonic decrease is similar to the rate of short gamma-ray bursts. After comparing this function with the star formation rate and stellar mass density, we conclude that the old populations, including neutron stars and black holes, are closely related to the origins of FRBs.