Bias-corrected Fast Radio Bursts Population and Spectra Using CHIME Injection Data

Fast Radio Bursts (FRBs), a class of millisecond-scale, highly energetic phenomena with unknown progenitors and radiation mechanisms, require proper statistical analysis as a key method for uncovering their mysteries. In this research, we build upon the bias correction method using pulse injections for the first CHIME/FRB catalog, to include correlations between properties, and to analyze the FRB population spectrum. This model includes six FRB properties: dispersion measure (DM), pulse width, scattering timescale, spectral index, spectral running, and fluence. By applying the multidimensional weight function calculated by the model, we update the corrected distributions, suggesting that more low-DM, short and long-width, and short-scattering timescale events may exist. Using one-off events and the first bursts from repeaters, the derived intrinsic population spectrum has a best-fit power-law of $F(\nu)\propto\nu^{\alpha}$, where $\alpha=-2.29\pm0.29$. This confirms previous indications that FRBs are brighter or more numerous at low frequencies. Analysing non-repeaters only, we find $\alpha=-2.50\pm0.43$, while including all bursts from repeaters produces $\alpha=-1.91\pm0.20$. This hints that active repeaters, low-rate repeaters, and non-repeaters may have different progenitors, mechanisms, or evolutionary stage.