A maximum likelihood estimate of the parameters of the FRB population

TL;DR

This paper uses maximum likelihood analysis on a diverse sample of 82 non-repeating FRBs to determine the most plausible population model, favoring moderate scatter broadening with redshift and a constant comoving event rate density.

Contribution

It introduces a comprehensive maximum likelihood framework to analyze FRB population properties across multiple detection surveys, accounting for different frequency ranges and detection criteria.

Findings

Moderate pulse scatter broadening with redshift is preferred.

Constant comoving event rate density over redshift is favored.

Best-fit parameters include spectral index -1.53, mean energy 1.55×10^{33} J, and luminosity function exponent 0.77.

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 ($DM_{\rm host}$) distribution (a fixed and a random $DM_{\rm host}$) 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 $\gamma=0.77\pm 0.24$. 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 $10^{33} \, {\rm J}$ across $2128 - 2848\; {\rm MHz}$ in the FRB rest frame.