Modeling the dispersion measure-redshift relation for fast radio bursts

This theoretical work investigates different models to predict the redshift of fast radio bursts (FRBs) from their observed dispersion measure (DM) and other reported properties. We performed an extended revision of the FRBs with confirmed galaxy hosts in the literature and built the most updated catalog to date. With this sample of FRBs, we propose four models that relate the DM and z: a linear trend (inspired by the Macquart relation), a log-parabolic function, a power law, and an interpolation for DM that includes z and the position of the host galaxy of the transient. The latter model has the highest success rate according to the metrics implemented: likelihood, median of the z difference, and the Akaike and Bayesian information criteria. Although the performance of model D is closely followed by the power law and linear models, the former has the advantage of accounting for anisotropies in the dispersion measure due to the angular coordinates. Conversely, the log-parabolic formula performs poorly in this task but provides a good prediction for FRBs with low DM at a low redshift. Additionally, we use the reported galaxy properties of the hosts to establish a connection between the observed DM with the star formation rate (SFR) and stellar mass (M s ) of the galaxies where the FRBs reside. In both cases, we find a weak correlation. Although the studied correlations are well-motivated, the sample of FRBs is not statistically significant enough to draw solid conclusions in this second part of our work. With the advent of new facilities devoted to studying the localization and nature of these transients, we will get access to new data that will enrich the proposed models and give us hints on the astrophysical origin and evolution of FRBs.