4Cosmic rays are the highest energy particles found in nature. Measurements of the mass composition of cosmic rays between 10 17 eV and 10 18 eV are essential to understand whether this energy range is dominated by Galactic or extragalactic sources. It has also been proposed that the astrophysical neutrino signal 1 comes from accelerators capable of producing cosmic rays of these energies 2 . Cosmic rays initiate cascades of secondary particles (air showers) in the atmosphere and their masses are inferred from measurements of the atmospheric depth of the shower maximum, X max 3 , or the composition of shower particles reaching the ground 4 .Current measurements 5 suffer from either low precision, and/or a low duty cycle. Radio detection of cosmic rays 6-8 is a rapidly developing technique 9 , suitable for determination of X max 10, 11 with a duty cycle of in principle nearly 100%. The radiation is generated by the separation of relativistic charged particles in the geomagnetic field and a negative charge excess in the shower front 6, 12 . Here we report radio measurements of X max with a mean precision of 16 g/cm 2 between 10 17 − 10 17.5 eV. Because of the high resolution in X max we can determine the mass spectrum and find a mixed composition, containing a light mass fraction of ∼ 80%. Unless the extragalactic component becomes significant already below 10 17.5 eV, our measurements indicate an additional Galactic component dominating at this energy range.Observations were made with the Low Frequency Array (LOFAR 13 ), a radio telescope consisting of thousands of crossed dipoles, with built-in air shower detection capability 14 . LOFAR records the radio signals from air showers continuously while running astronomical observations simultaneously. It comprises a scintillator array (LORA), that triggers the readout of buffers, stor-5 ing the full waveforms received by all antennas.We have selected air showers from the period June 2011 -January 2015 with radio pulses in at least 192 antennas. The total uptime was ∼150 days, limited by construction and commissioning of the telescope. Showers that occurred within an hour from lightning activity, or have a polarisation pattern that is indicative of influences from atmospheric electric fields are excluded from the sample 15 .Radio intensity patterns from air showers are asymmetric due to the interference between geomagnetic and charge excess radiation. They can be reproduced from first principles by summing the radio contributions of all electrons and positrons in the shower. We use the radio simulation code CoREAS 16 , a plug-in of CORSIKA 17 , which follows this approach.It has been shown that X max can be accurately reconstructed from densely sampled radio measurements 18 . We use a hybrid approach, simultaneously fitting the radio and particle data. The radio component is very sensitive to X max , while the particle component is used for the energy measurement.The fit contains four free parameters: the shower core position (x, y), and scaling factors for the partic...

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Context. Repeating fast radio bursts (FRBs) present excellent opportunities to identify FRB progenitors and host environments, as well as decipher the underlying emission mechanism. Detailed studies of repeating FRBs might also hold clues to the origin of FRBs as a population. Aims. We aim to detect bursts from the first two repeating FRBs: FRB 121102 (R1) and FRB 180814.J0422+73 (R2), and characterise their repeat statistics. We also want to significantly improve the sky localisation of R2 and identify its host galaxy. Methods. We use the Westerbork Synthesis Radio Telescope to conduct extensive follow-up of these two repeating FRBs. The new phased-array feed system, Apertif, allows covering the entire sky position uncertainty of R2 with fine spatial resolution in a single pointing. The data were searched for bursts around the known dispersion measures of the two sources. We characterise the energy distribution and the clustering of detected R1 bursts. Results. We detected 30 bursts from R1. The non-Poissonian nature is clearly evident from the burst arrival times, consistent with earlier claims. Our measurements indicate a dispersion measure of 563.5(2) pc cm −3 , suggesting a significant increase in DM over the past few years. Assuming a constant position angle across the burst, we place an upper limit of 8% on the linear polarisation fraction for the brightest burst in our sample. We did not detect any bursts from R2. Conclusions. A single power-law might not fit the R1 burst energy distribution across the full energy range or widely separated detections. Our observations provide improved constraints on the clustering of R1 bursts. Our stringent upper limits on the linear polarisation fraction imply a significant depolarisation, either intrinsic to the emission mechanism or caused by the intervening medium, at 1400 MHz that is not observed at higher frequencies. The non-detection of any bursts from R2, despite nearly 300 hrs of observations, implies either a highly clustered nature of the bursts, a steep spectral index, or a combination of both assuming the source is still active. Another possibility is that R2 has turned off completely, either permanently or for an extended period of time.

Dispersion in the interstellar medium is a well known phenomenon that follows a simple relationship, which has been used to predict the time delay of dispersed radio pulses since the late 1960s. We performed wide-band simultaneous observations of four pulsars with LOFAR (at 40-190 MHz), the 76-m Lovell Telescope (at 1400 MHz) and the Effelsberg 100-m Telescope (at 8000 MHz) to test the accuracy of the dispersion law over a broad frequency range. In this paper we present the results of these observations which show that the dispersion law is accurate to better than 1 part in 10 5 across our observing band. We use this fact to constrain some of the properties of the interstellar medium along the line-of-sight and use the lack of any aberration or retardation effects to determine upper limits on emission heights in the pulsar magnetosphere. We also discuss the effect of pulse profile evolution on our observations, and the implications that it could have for precision pulsar timing projects such as the detection of gravitational waves with pulsar timing arrays.

Super massive black holes at the centres of galaxies can cycle through periods of activity and quiescence. Characterising the duty cycle of active galactic nuclei (AGN) is crucial for understanding the impact of the energy they release on the host galaxy. For radio AGN, this can be done by identifying dying (remnant) and restarted radio galaxies from their radio spectral properties. Using the combination of the images at 1400 MHz produced by Apertif, the new phased-array feed receiver installed on the Westerbork Synthesis Radio Telescope, and images at 150 MHz provided by LOFAR, we have derived resolved spectral index images (at a resolution of ~15 arcsec) for all the sources within an approximately 6 deg2 area of the Lockman Hole region. In this way, we were able to select 15 extended radio sources with emission (partly or entirely) characterised by extremely steep spectral indices (steeper than 1.2). These objects represent cases of radio sources in the remnant or the restarted phases of their life cycle. Our findings confirm that these objects are not as rare as previously thought, suggesting a relatively fast cycle. They also show a variety of properties that can be relevant for modelling the evolution of radio galaxies. For example, the restarted activity can occur while the remnant structure from a previous phase of activity is still visible. This provides constraints on the duration of the “off” (dying) phase. In extended remnants with ultra-steep spectra at low frequencies, the activity likely stopped a few hundred megayears ago, and they correspond to the older tail of the age distribution of radio galaxies, in agreement with the results of simulations of radio source evolution. We find remnant radio sources with a variety of structures (from double-lobed to amorphous), possibly suggesting different types of progenitors. The present work sets the stage for exploiting the powerful tool of low-frequency spectral index studies of extended sources by taking advantage of the large areas common to the LOFAR and the Apertif surveys.