Joint inference on the redshift distribution of fast radio burst and on the intergalactic baryon content

Context: Fast radio bursts are transient radio pulses of extragalactic origin. Their dispersion measure is indicative of the baryon content in the ionized intergalactic medium between the source and the observer. However, inference using unlocalized fast radio bursts is degenerate to the distribution of redshifts of host galaxies. Method: We perform a joint inference of the intergalactic baryon content and the fast radio burst redshift distribution with the use of Bayesian statistics by comparing the likelihood of different models to reproduce the observed statistics in order to infer the most likely models. In addition to two models of the intergalactic medium, we consider contributions from the local environment of the source, assumed to be a magnetar, as well as a representative ensemble of host and intervening galaxies. Results: Assuming that the missing baryons reside in the ionized intergalactic medium, our results suggest that the redshift distribution of observed fast radio bursts peaks at $z \lesssim 0.6$. However, conclusions from different instruments regarding the intergalactic baryon content diverge and thus require additional changes to the observed distribution of host redshifts, beyond those caused by telescope selection effects.