A maximum likelihood estimate of the parameters of the FRB population

Abstract

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 ($D{M}_{\mathrm{host}}$) distribution (a fixed and a random $D{M}_{\mathrm{host}}$) are found to predict comparable results. We obtain the best fit parameter values $\alpha =-1.53_{-0.19}^{+0.29}$, ${\overline{E}}_{33}=1.55_{-0.22}^{+0.26}$ and $\gamma =0.77\pm 0.24$. Here $\alpha$ is the spectral index, $\gamma$ is the exponent of the Schechter luminosity function and ${\overline{E}}_{33}$ is the mean FRB energy in units of $10^{33}\mathrm{J}$ across $2128-2848\mathrm{MHz}$ in the FRB rest frame.

5 pages, 3 figures, Accepted for Publication in the MNRAS Letter

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• Modelling the energy distribution in CHIME/FRB Catalog-1
• A targeted search for repeating fast radio bursts with the MWA
• Distribution of gamma-ray bursts on the t90-hardness ratio plane and their classification revisited