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The LOw Frequency ARray (LOFAR) is a next-generation radio telescope which uses thousands of stationary dipoles to observe celestial phenomena. These dipoles are grouped in various ‘stations’ which are centred on the Netherlands with additional ‘stations’ across Europe. The telescope is designed to operate at frequencies from 10 to 240 MHz with very large fractional bandwidths (25 – 100 %). Several ‘beam-formed’ observing modes are now operational and the system is designed to output data with high time and frequency resolution, which are highly configurable. This makes LOFAR eminently suited for dynamic spectrum measurements with applications in solar and planetary physics. In this paper we describe progress in developing automated data analysis routines to compute dynamic spectra from LOFAR time–frequency data, including correction for the antenna response across the radio frequency pass-band and mitigation of terrestrial radio-frequency interference (RFI). We apply these data routines to observations of interplanetary scintillation (IPS), commonly used to infer solar wind velocity and density information, and present initial science results.

Until recently the dynamical evolution of the interstellar medium (ISM) was simulated using collisional ionization equilibrium (CIE) conditions. However, the ISM is a dynamical system, in which the plasma is naturally driven out of equilibrium due to atomic and dynamic processes operating on different timescales. A step forward in the field comprises a multi-fluid approach taking into account the joint thermal and dynamical evolutions of the ISM gas.

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.

Observations were made with the Low Frequency Array (LOFAR13), a radio telescope consisting of thousands of crossed dipoles with built-in air-shower-detection capability14. LOFAR continuously records the radio signals from air showers, while simultaneously running astronomical observations. It comprises a scintillator array (LORA) that triggers the read-out of buffers, storing the full waveforms received by all antennas.

Cosmic rays are the highest-energy particles found in nature. Measurements of the mass composition of cosmic rays with energies of 10 17 –10 18 electronvolts are essential to understanding whether they have 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 air showers—cascades of secondary particles in the atmosphere—and their masses can be inferred from measurements of the atmospheric depth of the shower maximum 3 ( X max ; the depth of the air shower when it contains the most particles) or of the composition of shower particles reaching the ground 4 . Current measurements 5 have either high uncertainty, or a low duty cycle and a high energy threshold. Radio detection of cosmic rays 6, 7, 8 is a rapidly developing technique 9 for determining X max (refs 10, 11) with a duty cycle of, in principle, nearly 100 per cent. The radiation is generated by the separation of relativistic electrons and positrons 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 uncertainty of 16 grams per square centimetre for air showers initiated by cosmic rays with energies of 10 17 –10 17.5 electronvolts. This high resolution in X max enables us to determine the mass spectrum of the cosmic rays: we find a mixed composition, with a light-mass fraction (protons and helium nuclei) of about 80 per cent. Unless, contrary to current expectations, the extragalactic component of cosmic rays contributes substantially to the total flux below 10 17.5 electronvolts, our measurements indicate the existence of an additional galactic component, to account for the light composition that we measured in the 10 17 –10 17.5 electronvolt range.

The Low-Frequency Array (LOFAR) Long-Baseline Calibrator Survey (LBCS) was conducted between 2014 and 2019 in order to obtain a set of suitable calibrators for the LOFAR array. In this paper we present the complete survey, building on the preliminary analysis published in 2016 which covered approximately half the survey area. The final catalogue consists of 30006 observations of 24713 sources in the northern sky, selected for a combination of high low-frequency radio flux density and flat spectral index using existing surveys (WENSS, NVSS, VLSS, and MSSS). Approximately one calibrator per square degree, suitable for calibration of \\(\\geq\\) 200 km baselines is identified by the detection of compact flux density, for declinations north of 30 degrees and away from the Galactic plane, with a considerably lower density south of this point due to relative difficulty in selecting flat-spectrum candidate sources in this area of the sky. Use of the VLBA calibrator list, together with statistical arguments by comparison with flux densities from lower-resolution catalogues, allow us to establish a rough flux density scale for the LBCS observations, so that LBCS statistics can be used to estimate compact flux densities on scales between 300 mas and 2 arcsec, for sources observed in the survey. The LBCS can be used to assess the structures of point sources in lower-resolution surveys, with significant reductions in the degree of coherence in these sources on scales between 2 arcsec and 300 mas. The LBCS survey sources show a greater incidence of compact flux density in quasars than in radio galaxies, consistent with unified schemes of radio sources. Comparison with samples of sources from interplanetary scintillation (IPS) studies with the Murchison Widefield Array (MWA) shows consistent patterns of detection of compact structure in sources observed both interferometrically with LOFAR and using IPS.

[abridged] The International LOFAR Telescope is an interferometer with stations spread across Europe. With baselines of up to ~2,000 km, LOFAR has the unique capability of achieving sub-arcsecond resolution at frequencies below 200 MHz, although this is technically and logistically challenging. Here we present a calibration strategy that builds on previous high-resolution work with LOFAR. We give an overview of the calibration strategy and discuss the special challenges inherent to enacting high-resolution imaging with LOFAR, and describe the pipeline, which is publicly available, in detail. We demonstrate the calibration strategy by using the pipeline on P205+55, a typical LOFAR Two-metre Sky Survey (LoTSS) pointing. We perform in-field delay calibration, solution referencing to other calibrators, self-calibration, and imaging of example directions of interest in the field. For this specific field and these ionospheric conditions, dispersive delay solutions can be transferred between calibrators up to ~1.5 degrees away, while phase solution transferral works well over 1 degree. We demonstrate a check of the astrometry and flux density scale. Imaging in 17 directions, the restoring beam is typically 0.3\" x 0.2\" although this varies slightly over the entire 5 square degree field of view. We achieve ~80 to 300 \\(\\mu\\)Jy/bm image rms noise, which is dependent on the distance from the phase centre; typical values are ~90 \\(\\mu\\)Jy/bm for the 8 hour observation with 48 MHz of bandwidth. Seventy percent of processed sources are detected, and from this we estimate that we should be able to image ~900 sources per LoTSS pointing. This equates to ~3 million sources in the northern sky, which LoTSS will entirely cover in the next several years. Future optimisation of the calibration strategy for efficient post-processing of LoTSS at high resolution (LoTSS-HR) makes this estimate a lower limit.

The four persistent radio sources in the northern sky with the highest flux density at metre wavelengths are Cassiopeia A, Cygnus A, Taurus A, and Virgo A; collectively they are called the A-team. Their flux densities at ultra-low frequencies (<100 MHz) can reach several thousands of janskys, and they often contaminate observations of the low-frequency sky by interfering with image processing. Furthermore, these sources are foreground objects for all-sky observations hampering the study of faint signals, such as the cosmological 21 cm line from the epoch of reionisation. We aim to produce robust models for the surface brightness emission as a function of frequency for the A-team sources at ultra-low frequencies. These models are needed for the calibration and imaging of wide-area surveys of the sky with low-frequency interferometers. This requires obtaining images at an angular resolution better than 15 arcsec with a high dynamic range and good image fidelity. We observed the A-team with the Low Frequency Array (LOFAR) at frequencies between 30 MHz and 77 MHz using the Low Band Antenna (LBA) system. We reduced the datasets and obtained an image for each A-team source. The paper presents the best models to date for the sources Cassiopeia A, Cygnus A, Taurus A, and Virgo A between 30 MHz and 77 MHz. We were able to obtain the aimed resolution and dynamic range in all cases. Owing to its compactness and complexity, observations with the long baselines of the International LOFAR Telescope will be required to improve the source model for Cygnus A further.