A maximum-likelihood estimate of the parameters of the fast radio burst population. Issue 1 (22nd September 2021) - Bhattacharyya, Siddhartha; Tiwari, Himanshu; Bharadwaj, Somnath; Majumdar, Suman
ABSTRACT: We consider a sample of 82 non-repeating fast radio bursts (FRBs) detected at Parkes, ASKAP, CHIME, and UTMOST, each of which operates over a different frequency range and has a different detection criterion. Using simulations, we perform a maximum-likelihood analysis to determine the FRB population model that best fits these data. Our analysis shows that models where the pulse scatter broadening increases moderately with redshift ( z ) are preferred to those where this increases very sharply or where scattering is absent. Further, models where the comoving event rate density is constant over z are preferred to those where it follows the cosmological star formation rate. Two models for the host dispersion measure (DMHost ) distribution (a fixed and a random DMHost ) are found to predict comparable results. We obtain the best-fitting parameter values $α =-1.53^{+0.29}_{-0.19}$, $\overline{E}_{33}=1.55^{+0.26}_{-0.22}$, and γ = 0.77 ± 0.24. Here α is the spectral index, γ is the exponent of the Schechter luminosity function, and $\overline{E}_{33}$ is the mean FRB energy in units of $10^{33} \, {\rm J}$ across 2128–2848 MHz in the FRB rest frame.