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Fast radio bursts (FRBs) are flashes of unknown physical origin1. The majority of FRBs have been seen only once, although some are known to generate multiple flashes2,3. Many models invoke magnetically powered neutron stars (magnetars) as the source of the emission4,5. Recently, the discovery6of another repeater (FRB 20200120E) was announced, in the direction of the nearby galaxy M81, with four potential counterparts at other wavelengths6. Here we report observations that localized the FRB to a globular cluster associated with M81, where it is 2 parsecs away from the optical centre of the cluster. Globular clusters host old stellar populations, challenging FRB models that invoke young magnetars formed in a core-collapse supernova. We propose instead that FRB 20200120E originates from a highly magnetized neutron star formed either through the accretion-induced collapse of a white dwarf, or the merger of compact stars in a binary system7. Compact binaries are efficiently formed inside globular clusters, so a model invoking them could also be responsible for the observed bursts.

The discovery of a radioactively powered kilonova associated with the binary neutron-star merger GW170817 remains the only confirmed electromagnetic counterpart to a gravitational-wave event1,2. Observations of the late-time electromagnetic emission, however, do not agree with the expectations from standard neutron-star merger models. Although the large measured ejecta mass3,4could be explained by a progenitor system that is asymmetric in terms of the stellar component masses (that is, with a mass ratio qof 0.7 to 0.8)5, the known Galactic population of merging double neutron-star systems (that is, those that will coalesce within billions of years or less) has until now consisted only of nearly equal-mass (q> 0.9) binaries6. The pulsar PSR J1913+1102 is a double system in a five-hour, low-eccentricity (0.09) orbit, with an orbital separation of 1.8 solar radii7, and the two neutron stars are predicted to coalesce in 470−11+12million years owing to gravitational-wave emission. Here we report that the masses of the pulsar and the companion neutron star, as measured by a dedicated pulsar timing campaign, are 1.62 ± 0.03 and 1.27 ± 0.03 solar masses, respectively. With a measured mass ratio of q= 0.78 ± 0.03, this is the most asymmetric merging system reported so far. On the basis of this detection, our population synthesis analysis implies that such asymmetric binaries represent between 2 and 30 per cent (90 per cent confidence) of the total population of merging binaries. The coalescence of a member of this population offers a possible explanation for the anomalous properties of GW170817, including the observed kilonova emission from that event.

Fast radio bursts (FRBs) are brief, bright, extragalactic radio flashes1,2. Their physical origin remains unknown, but dozens of possible models have been postulated3. Some FRB sources exhibit repeat bursts4–7. Although over a hundred FRB sources have been discovered8, only four have been localized and associated with a host galaxy9–12, and just one of these four is known to emit repeating FRBs9. The properties of the host galaxies, and the local environments of FRBs, could provide important clues about their physical origins. The first known repeating FRB, however, was localized to a low-metallicity, irregular dwarf galaxy, and the apparently non-repeating sources were localized to higher-metallicity, massive elliptical or star-forming galaxies, suggesting that perhaps the repeating and apparently non-repeating sources could have distinct physical origins. Here we report the precise localization of a second repeating FRB source6, FRB 180916.J0158+65, to a star-forming region in a nearby (redshift 0.0337 ± 0.0002) massive spiral galaxy, whose properties and proximity distinguish it from all known hosts. The lack of both a comparably luminous persistent radio counterpart and a high Faraday rotation measure6further distinguish the local environment of FRB 180916.J0158+65 from that of the single previously localized repeating FRB source, FRB 121102. This suggests that repeating FRBs may have a wide range of luminosities, and originate from diverse host galaxies and local environments.

Lightning is a dangerous yet poorly understood natural phenomenon. Lightning forms a network of plasma channels propagating away from the initiation point with both positively and negatively charged ends—called positive and negative leaders1. Negative leaders propagate in discrete steps, emitting copious radio pulses in the 30–300-megahertz frequency band2–8that can be remotely sensed and imaged with high spatial and temporal resolution9–11. Positive leaders propagate more continuously and thus emit very little high-frequency radiation12. Radio emission from positive leaders has nevertheless been mapped13–15, and exhibits a pattern that is different from that of negative leaders11–13,16,17. Furthermore, it has been inferred that positive leaders can become transiently disconnected from negative leaders9,12,16,18–20, which may lead to current pulses that both reconnect positive leaders to negative leaders11,16,17,20–22and cause multiple cloud-to-ground lightning events1. The disconnection process is thought to be due to negative differential resistance18, but this does not explain why the disconnections form primarily on positive leaders22, or why the current in cloud-to-ground lightning never goes to zero23. Indeed, it is still not understood how positive leaders emit radio-frequency radiation or why they behave differently from negative leaders. Here we report three-dimensional radio interferometric observations of lightning over the Netherlands with unprecedented spatiotemporal resolution. We find small plasma structures—which we call ‘needles’—that are the dominant source of radio emission from the positive leaders. These structures appear to drain charge from the leader, and are probably the reason why positive leaders disconnect from negative ones, and why cloud-to-ground lightning connects to the ground multiple times.

Fast radio bursts are millisecond-duration, extragalactic radio flashes of unknown physical origin. The only known repeating fast radio burst source—FRB 121102—has been localized to a star-forming region in a dwarf galaxy at redshift 0.193 and is spatially coincident with a compact, persistent radio source. The origin of the bursts, the nature of the persistent source and the properties of the local environment are still unclear. Here we report observations of FRB 121102 that show almost 100 per cent linearly polarized emission at a very high and variable Faraday rotation measure in the source frame (varying from +1.46 × 105radians per square metre to +1.33 × 105radians per square metre at epochs separated by seven months) and narrow (below 30 microseconds) temporal structure. The large and variable rotation measure demonstrates that FRB 121102 is in an extreme and dynamic magneto-ionic environment, and the short durations of the bursts suggest a neutron star origin. Such large rotation measures have hitherto been observed only in the vicinities of massive black holes (larger than about 10,000 solar masses). Indeed, the properties of the persistent radio source are compatible with those of a low-luminosity, accreting massive black hole. The bursts may therefore come from a neutron star in such an environment or could be explained by other models, such as a highly magnetized wind nebula or supernova remnant surrounding a young neutron star.

Fast radio bursts are astronomical radio flashes of unknown physical nature with durations of milliseconds. Their dispersive arrival times suggest an extragalactic origin and imply radio luminosities that are orders of magnitude larger than those of all known short-duration radio transients. So far all fast radio bursts have been detected with large single-dish telescopes with arcminute localizations, and attempts to identify their counterparts (source or host galaxy) have relied on the contemporaneous variability of field sources or the presence of peculiar field stars or galaxies. These attempts have not resulted in an unambiguous association with a host or multi-wavelength counterpart. Here we report the subarcsecond localization of the fast radio burst FRB 121102, the only known repeating burst source, using high-time-resolution radio interferometric observations that directly image the bursts. Our precise localization reveals that FRB 121102 originates within 100 milliarcseconds of a faint 180-microJansky persistent radio source with a continuum spectrum that is consistent with non-thermal emission, and a faint (twenty-fifth magnitude) optical counterpart. The flux density of the persistent radio source varies by around ten per cent on day timescales, and very long baseline radio interferometry yields an angular size of less than 1.7 milliarcseconds. Our observations are inconsistent with the fast radio burst having a Galactic origin or its source being located within a prominent star-forming galaxy. Instead, the source appears to be co-located with a low-luminosity active galactic nucleus or a previously unknown type of extragalactic source. Localization and identification of a host or counterpart has been essential to understanding the origins and physics of other kinds of transient events, including gamma-ray bursts and tidal disruption events. However, if other fast radio bursts have similarly faint radio and optical counterparts, our findings imply that direct subarcsecond localizations may be the only way to provide reliable associations.

High-resolution radio measurements of air showers—cascades of secondary particles in the atmosphere initiated by cosmic rays—reveal that cosmic rays with energies of 1017–1017.5electronvolts have a mixed composition, with light elements (protons and helium nuclei) making up 80 per cent of their mass.

Fast radio bursts are millisecond-duration astronomical radio pulses of unknown physical origin that appear to come from extragalactic distances. Previous follow-up observations have failed to find additional bursts at the same dispersion measure (that is, the integrated column density of free electrons between source and telescope) and sky position as the original detections. The apparent non-repeating nature of these bursts has led to the suggestion that they originate in cataclysmic events. Here we report observations of ten additional bursts from the direction of the fast radio burst FRB 121102. These bursts have dispersion measures and sky positions consistent with the original burst. This unambiguously identifies FRB 121102 as repeating and demonstrates that its source survives the energetic events that cause the bursts. Additionally, the bursts from FRB 121102 show a wide range of spectral shapes that appear to be predominantly intrinsic to the source and which vary on timescales of minutes or less. Although there may be multiple physical origins for the population of fast radio bursts, these repeat bursts with high dispersion measure and variable spectra specifically seen from the direction of FRB 121102 support an origin in a young, highly magnetized, extragalactic neutron star.

Context.The ROSATX-ray source 1RXS J141256.0+792204 has recently been identified as a likely compact object whose properties suggest it could be a very nearby radio millisecond pulsar at $d = 80{-}260$pc.

Nature 531, 70–73 (2016); doi:10.1038/nature16976 In this Letter, we omitted to cite preliminary results from the low-energy extension of the Pierre Auger Observatory, as presented at the International Cosmic Ray Conference 2015 (ref. 1). Figure 1 of this Corrigendum shows measurements of the average value of Xmax for the Low Frequency Array (LOFAR), and earlier experiments using different techniques, now including the data from the Pierre Auger Observatory1, specifically the contribution of A.

Low frequency radio waves, while challenging to observe, are a rich source of information about pulsars. The LOw Frequency ARray (LOFAR) is a new radio interferometer operating in the lowest 4 octaves of the ionospheric “radio window”: 10–240 MHz, that will greatly facilitate observing pulsars at low radio frequencies. Through the huge collecting area, long baselines, and flexible digital hardware, it is expected that LOFAR will revolutionize radio astronomy at the lowest frequencies visible from Earth. LOFAR is a next-generation radio telescope and a pathfinder to the Square Kilometre Array (SKA), in that it incorporates advanced multi-beaming techniques between thousands of individual elements. We discuss the motivation for low-frequency pulsar observations in general and the potential of LOFAR in addressing these science goals. We present LOFAR as it is designed to perform high-time-resolution observations of pulsars and other fast transients, and outline the various relevant observing modes and data reduction pipelines that are already or will soon be implemented to facilitate these observations. A number of results obtained from commissioning observations are presented to demonstrate the exciting potential of the telescope. This paper outlines the case for low frequency pulsar observations and is also intended to serve as a reference for upcoming pulsar/fast transient science papers with LOFAR.