The z-DM distribution of fast radio bursts

We develop a sophisticated model of fast radio burst (FRB) observations, accounting for the intrinsic cosmological gas distribution and host galaxy contributions, and give the most detailed account yet of observational biases due to burst width, dispersion measure, and the exact telescope beamshape. Our results offer a significant increase in both accuracy and precision beyond those previously obtained. Using results from ASKAP and Parkes, we present our best-fitting FRB population parameters in a companion paper. Here, we consider in detail the expected and fitted distributions in redshift, dispersion measure, and signal to noise. We estimate that the unlocalized ASKAP FRBs arise from z < 0.5, with between a third and a half within z < 0.1. Our predicted source-counts ('logN-logS') distribution confirms previous indications of a steepening index near the Parkes detection threshold of 1 Jy ms. We find no evidence for a minimum FRB energy, and rule out E-min > 10(39.0) erg at 90 per cent C.L. Importantly, we find that above a certain DM, observational biases cause the Macquart (DM-z) relation to become inverted, implying that the highest-DM events detected in the unlocalized Parkes and ASKAP samples are unlikely to be the most distant. More localized FRBs will be required to quantitatively estimate this effect, though its cause is a well-understood observational bias. Works assuming a 1-1 DM-z relation may therefore derive erroneous results. Our analysis of errors suggests that limiting factors in our analysis are understanding of FRB spectral behaviour, sensitivity response of search experiments, and the treatment of the repeating population and luminosity function.

Automated summary

We have developed a sophisticated model to investigate fast radio bursts (FRBs), considering various factors such as cosmological gas distribution, host galaxy contributions, and observational biases. Our analysis provides the most detailed account of observational biases and significantly improves the accuracy and precision of FRB observations. Based on the data from ASKAP and Parkes, we present the best-fitting FRB population parameters and discuss the expected and fitted distributions in redshift, dispersion measure, and signal to noise. Our results suggest that the highest-dispersion measure events detected in the unlocalized Parkes and ASKAP samples are unlikely to be the most distant. This study highlights the importance of localized FRBs for understanding the DM-z relation and points out the limitations in our analysis, such as uncertainties in FRB spectral behavior and sensitivity response of search experiments, as well as the treatment of the repeating population and luminosity function.