Constraining the redshifts of unlocalised fast radio bursts

Context. The relationship between the dispersion measures (DMs) and redshifts of fast radio bursts (FRBs) is of scientific interest. Upcoming commensal surveys may detect and localise many FRBs to the sub-arcsecond angular resolutions required for accurate redshift determination. Meanwhile, it is important to exploit sources accumulated with more limited localisation to their maximum scientific potential. Aims. We present techniques for the DM-redshift analysis of large numbers of unlocalised FRBs, accounting for uncertainties due to their extragalactic DM components, redshift dependences, and progenitor scenarios. Methods. We reviewed the components comprising observed FRB DMs. We built redshift-scalable probability distribution functions for these components, which we combined in cases of multiple progenitor scenarios. Accounting for prior FRB redshift distributions we inverted these models, enabling FRB redshifts to be constrained. Results. We illustrate the influence of FRB progenitors on their observed DMs, which may remain significant to redshift z ~ 3. We identify the FRB sample sizes required to distinguish between multiple progenitor scenarios. We place new, physically motivated redshift constraints on all catalogued FRBs to date and use these to reject potential host galaxies in the localisation area of an FRB according to various models. We identify further uses for DM-redshift analysis using many FRBs. We provide our code so that these techniques may be employed using increasingly realistic models as our understanding of FRBs evolves