Redshift estimates for fast radio bursts and implications on intergalactic magnetic fields

Context: Fast Radio Bursts are transient radio pulses from presumably compact stellar sources of extragalactic origin. With new telescopes detecting multiple events per day, statistical methods are required in order to interpret observations and make inferences regarding astrophysical and cosmological questions. Purpose: We present a method that uses probability estimates of fast radio burst observables to obtain likelihood estimates for the underlying models. Method: Considering models for all regions along the line-of-sight, including intervening galaxies, we perform Monte-Carlo simulations to estimate the distribution of the dispersion measure, rotation measure and temporal broadening. Using Bayesian statistics, we compare these predictions to observations of Fast Radio Bursts. Results: By applying Bayes theorem, we obtain lower limits on the redshift of Fast Radio Bursts with extragalactic DM $\gtrsim 400$ pc cm$^{-3}$. We find that intervening galaxies cannot account for all highly scattered Fast Radio Bursts in FRBcat, thus requiring a denser and more turbulent environment than a SGR 1935+2154-like magnetar. We show that a sample of $\gtrsim 10^3$ unlocalized Fast Radio Bursts with associated extragalactic RM $\geq 1$ rad m$^{-2}$ can improve current upper limits on the strength of intergalactic magnetic fields.