A maximum likelihood estimate of the parameters of the FRB population

Abstract

\n We consider a sample of 82 non-repeating FRBs detected at Parkes, ASKAP, CHIME and UTMOST each of which operates over a different frequency range and has a different detection criteria. Using simulations, we perform a maximum likelihood analysis to determine the FRB population model which best fits this data. Our analysis shows that models where the pulse scatter broadening increases moderately with redshift (z) are preferred over 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 over 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 fit parameter values $\\alpha =-1.53^{+0.29}_{-0.19}$, $\\overline{E}_{33}=1.55^{+0.26}_{-0.22}$ 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 1033\u2009J across 2128 − 2848\u2009MHz in the FRB rest frame.