Inferring the Energy and Distance Distributions of Fast Radio Bursts using the First CHIME/FRB Catalog

Fast radio bursts (FRBs) are brief, energetic, extragalactic flashes of radio emission whose progenitors are largely unknown. Although studying the FRB population is essential for understanding how these astrophysical phenomena occur, such studies have been difficult to conduct without large numbers of FRBs and characterizable observational biases. Using the recently released catalog of 536 FRBs published by the Canadian Hydrogen Intensity Mapping Experiment/Fast Radio Burst (CHIME/FRB) collaboration, we present a study of the FRB population that also calibrates for selection effects. Assuming a Schechter luminosity function, we infer a characteristic energy cut-off of $E_\mathrm{char} =$ $2.38^{+5.35}_{-1.64} \times 10^{41}$ erg and a differential power-law index of $\gamma =$ $-1.3^{+0.7}_{-0.4}$. Simultaneously, we infer a volumetric rate of [$7.3^{+8.8}_{-3.8}$(stat.)$^{+2.0}_{-1.8}$(sys.)]$\times 10^4$ Gpc$^{-3}$ year$^{-1}$ above a pivot energy of 10$^{39}$ erg and below a scattering timescale of 10 ms at 600 MHz, and find we cannot significantly constrain the cosmic evolution of the FRB population with star formation rate. Modeling the host dispersion measure (DM) contribution as a log-normal distribution and assuming a total Galactic contribution of 80 pc cm$^{-3}$, we find a median value of $\mathrm{DM}_\mathrm{host} =$ $84^{+69}_{-49}$ pc cm$^{-3}$, comparable with values typically used in the literature. Proposed models for FRB progenitors should be consistent with the energetics and abundances of the full FRB population predicted by our results. Finally, we infer the redshift distribution of FRBs detected with CHIME, which will be tested with the localizations and redshifts enabled by the upcoming CHIME/FRB Outriggers project.