In recent years, millisecond-duration radio signals originating in distant galaxies appear to have been discovered in the so-called fast radio bursts. These signals are dispersed according to a precise physical law and this dispersion is a key observable quantity, which, in tandem with a redshift measurement, can be used for fundamental physical investigations. Every fast radio burst has a dispersion measurement, but none before now have had a redshift measurement, because of the difficulty in pinpointing their celestial coordinates. Here we report the discovery of a fast radio burst and the identification of a fading radio transient lasting ~6 days after the event, which we use to identify the host galaxy; we measure the galaxy's redshift to be z = 0.492 ± 0.008. The dispersion measure and redshift, in combination, provide a direct measurement of the cosmic density of ionized baryons in the intergalactic medium of ΩIGM = 4.9 ± 1.3 per cent, in agreement with the expectation from the Wilkinson Microwave Anisotropy Probe, and including all of the so-called 'missing baryons'. The ~6-day radio transient is largely consistent with the radio afterglow of a short γ-ray burst, and its existence and timescale do not support progenitor models such as giant pulses from pulsars, and supernovae. This contrasts with the interpretation of another recently discovered fast radio burst, suggesting that there are at least two classes of bursts.

Fast radio bursts (FRBs) are millisecond-duration events thought to originate beyond the Milky Way galaxy. Uncertainty surrounding the burst sources, and their propagation through intervening plasma, has limited their use as cosmological probes. We report on a mildly dispersed (dispersion measure 266.5 ± 0.1 parsecs per cubic centimeter), exceptionally intense (120 ± 30 janskys), linearly polarized, scintillating burst (FRB 150807) that we directly localize to 9 square arc minutes. On the basis of a low Faraday rotation (12.0 ± 0.7 radians per square meter), we infer negligible magnetization in the circum-burst plasma and constrain the net magnetization of the cosmic web along this sightline to <21 nanogauss, parallel to the line-of-sight. The burst scintillation suggests weak turbulence in the ionized intergalactic medium.

The discovery that at least some Fast Radio Bursts (FRBs) repeat has ruled out cataclysmic events as the progenitors of these particular bursts. FRB 121102 is the most well-studied repeating FRB but despite extensive monitoring of the source, no underlying pattern in the repetition has previously been identified. Here, we present the results from a radio monitoring campaign of FRB 121102 using the 76 m Lovell telescope. Using the pulses detected in the Lovell data along with pulses from the literature, we report a detection of periodic behaviour of the source over the span of 5 yr of data. We predict that the source is currently ‘off’ and that it should turn ‘on’ for the approximate MJD range 59002−59089 (2020 June 2 to 2020 August 28). This result, along with the recent detection of periodicity from another repeating FRB, highlights the need for long-term monitoring of repeating FRBs at a high cadence. Using simulations, we show that one needs at least 100 h of telescope time to follow-up repeating FRBs at a cadence of 0.5–3 d to detect periodicities in the range of 10–150 d. If the period is real, it shows that repeating FRBs can have a large range in their activity periods that might be difficult to reconcile with neutron star precession models.