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The Small and Large Magellanic Clouds are the only galaxies outside our own in which radio pulsars have been discovered to date. The sensitivity of the MeerKAT radio interferometer offers an opportunity to search for a population of more distant extragalactic pulsars. The TRAPUM (TRansients And PUlsars with MeerKAT) collaboration has performed a radio-domain search for pulsars and transients in the dwarf star-forming galaxies Sextans A and B, situated at the edge of the local group 1.4 Mpc away. We conducted three 2-hour multi-beam observations at L-band (856-1712 MHz) with the full array of MeerKAT. No pulsars were found down to a radio pseudo-luminosity upper limit of 7.9$\pm$0.4 Jy kpc$^{2}$ at 1400 MHz, which is 28 times more sensitive than the previous limit from the Murriyang telescope. This luminosity is 30 per cent greater than that of the brightest known radio pulsar and sets a cut-off on the luminosity distributions of the entire Sextans A and B galaxies for unobscured radio pulsars beamed in our direction. A Fast Radio Burst was detected in one of the Sextans A observations at a Dispersion Measure (DM) of 737 pc cm$^{-3}$. We believe this is a background event not associated with the dwarf galaxy due to its large DM and its S/N being strongest in the wide-field incoherent beam of MeerKAT., Comment: 11 pages, 9 figures, 5 tables. Accepted for publication in Monthly Notices of the Royal Astronomical Society

The S-band Polarisation All Sky Survey (SPASS/ATCA) rotation measure (RM) catalogue is the largest broadband RM catalogue to date, increasing the RM density in the sparse southern sky. Through analysis of this catalogue, we report a latitude dependency of the Faraday complexity of polarised sources in this catalogue within 10$^\circ$ of the Galactic plane towards the inner Galaxy. In this study, we aim to investigate this trend with follow-up observations using the Australia Telescope Compact Array (ATCA). We observe 95 polarised sources from the SPASS/ATCA RM catalogue at 1.1 - 3.1 GHz with ATCA's 6 km configuration. We present Stokes QU fitting results and a comparative analysis with the SPASS/ATCA catalogue. We find an overall decrease in complexity in these sources with the higher angular resolution observations, with a complexity fraction of 42\%, establishing that the majority of the complexity in the SPASS/ATCA sample is due to the mixing-in of diffuse Galactic emission at scales $\theta > 2.8'$. Furthermore, we find a correlation between our observed small-scale complexity $\theta < 2.8'$ and the Galactic spiral arms, which we interpret to be due to Galactic turbulence or small-scale polarised emission. These results emphasise the importance of considering the maximum angular scale to which the observations are sensitive in the classification of Faraday complexity; the effect of which can be more carefully investigated with SKA-precursor and pathfinder arrays (e.g. MeerKAT and ASKAP)., Comment: 16 pages, 16 figures

Galactic plane radio surveys play a key role in improving our understanding of a wide range of astrophysical phenomena. Performing such a survey using the latest interferometric telescopes produces large data rates necessitating a shift towards fully or quasi-real-time data analysis with data being stored for only the time required to process them. We present here the overview and setup for the 3000 hour Max-Planck-Institut fuer Radioastronomie (MPIfR) MeerKAT Galactic Plane survey (MMGPS). The survey is unique by operating in a commensal mode, addressing key science objectives of the survey including the discovery of new pulsars and transients as well as studies of Galactic magnetism, the interstellar medium and star formation rates. We explain the strategy coupled with the necessary hardware and software infrastructure needed for data reduction in the imaging, spectral and time domains. We have so far discovered 78 new pulsars including 17 confirmed binary systems of which two are potential double neutron star systems. We have also developed an imaging pipeline sensitive to the order of a few tens of micro-Jansky with a spatial resolution of a few arcseconds. Further science operations with an in-house built S-Band receiver operating between 1.7-3.5 GHz are about to commence. Early spectral line commissioning observations conducted at S-Band, targeting transitions of the key molecular gas tracer CH at 3.3 GHz already illustrate the spectroscopic capabilities of this instrument. These results lay a strong foundation for future surveys with telescopes like the Square Kilometre Array (SKA)., Comment: 25 pages, 10 figures, Accepted in MNRAS

We present new radio continuum images of the edge-on starburst galaxy NGC 5775, from LOFAR (140 MHz) and the Karl G. Jansky Very Large Array CHANG-ES survey (1500 MHz). We trace the non-thermal radio halo up to 13 kpc from the disc, measuring the non-thermal spectral index and estimating the total equipartition magnetic field strength ($\approx13\mu$G in the disc and $\approx7\mu$G above the plane). The radio halo has a similar extent at both frequencies, displays evidence for localized cosmic ray streaming coinciding with prominent H$\alpha$ filaments and vertical extensions of the regular magnetic field, and exhibits a boxy morphology especially at 140 MHz. In order to understand the nature of the disc-halo flow, we extend our previous model of cosmic ray propagation by implementing an iso-thermal wind with a tunable `flux tube' (approximately hyperboloidal) geometry. This updated model is successful in matching the vertical distribution of non-thermal radio emission, and the vertical steepening of the associated spectral index, in a consistent conceptual framework with few free parameters. Our new model provides the opportunity to estimate the mass outflow driven by the star formation process, and we find an implied rate of $\dot{M}\approx3-6\,\mathrm{M_{\odot}\,yr^{-1}}$ ($\approx40-80$ per cent of the star formation rate) if the escape velocity is reached, with substantial uncertainty arising from the poorly-understood distribution of ISM material entrained in the vertical flow. The wind may play a role in influencing the vertical gradient in rotational velocity., Comment: Accepted for publication in MNRAS. 28 pages, 19 figures

In this paper we present recent Low Frequency Array (LOFAR) observations of the pulsar J1740+1000. We confirm that its spectrum has a turnover at 260 MHz, which is unusual for a typical pulsar. We argue that in this case interferometric imaging provides more accurate pulsar flux estimates than other, more traditional, means such as beamformed observations. We conclude that existing calibration and imaging techniques can be used for a more comprehensive study of the influence of the interstellar medium on the point-like sources at very low frequencies in the near future., Comment: 6 pages, 3 figures

We present LOFAR observations at 150 MHz of the borderline FRI/FRII giant radio galaxy NGC 6251. This paper presents the most sensitive and highest-resolution images of NGC 6251 at these frequencies to date, revealing for the first time a low-surface-brightness extension to the northern lobe, and a possible backflow associated with the southern lobe. The integrated spectra of components of NGC 6251 are consistent with previous measurements at higher frequencies, similar to results from other LOFAR studies of nearby radio galaxies. We find the outer structures of NGC 6251 to be either at equipartition or slightly electron dominated, similar to those of FRII sources rather than FRIs; but this conclusion remains tentative because of uncertainties associated with the geometry and the extrapolation of X-ray measurements to determine the external pressure distribution on the scale of the outer lobes. We place lower limits on the ages of the extension of the northern lobe and the backflow of the southern lobe of $t \gtrsim 250$ Myr and $t \gtrsim 210$ Myr respectively. We present the first detection of polarisation at 150 MHz in NGC 6251. Taking advantage of the high Faraday resolution of LOFAR, we place an upper limit on the magnetic field in the group of $B < 0.2 (\Lambda_B / 10 {\rm kpc})^{-0.5} \mu$G for a coherence scale of $\Lambda_B < 60 {\rm kpc}$ and $B < 13 \mu$G for $\Lambda_B = 240$ kpc., Comment: 19 pages, 17 figures; accepted by MNRAS

Cosmic rays play a pivotal role in launching galactic winds, particularly in quiescently star-forming galaxies where the hot gas alone is not sufficient to drive a wind. Except for the Milky Way, not much is known about the transport of cosmic rays in galaxies. In this Letter, we present low-frequency observations of the nearby edge-on spiral galaxy NGC 4565 using the LOw-Frequency ARray (LOFAR). With our deep 144-MHz observations, we obtain a clean estimate of the emission originating from old cosmic-ray electrons (CRe), which is almost free from contamination by thermal emission. We measured vertical profiles of the non-thermal radio continuum emission that we fitted with Gaussian and exponential functions. The different profile shapes correspond to 1D cosmic-ray transport models of pure diffusion and advection, respectively. We detect a warp in the radio continuum that is reminiscent of the previously known HI warp. Because the warp is not seen at GHz-frequencies in the radio continuum, its minimum age must be about 100 Myr. The warp also explains the slight flaring of the thick radio disc that can otherwise be well described by a Gaussian profile with an FWHM of 65 arcsec (3.7 kpc). The diffusive radio halo together with the extra-planar X-ray emission may be remnants of enhanced star-forming activity in the past where the galaxy had a galactic wind, as GHz-observations indicate only a weak outflow in the last 40 Myr. NGC 4565 could be in transition from an outflow- to an inflow-dominated phase., Comment: 5 pages, 4 figures, 2 tables; A\&A Letters accepted; appendix with cosmic-ray transport models

The LOFAR Two-metre Sky Survey (LoTSS) is an ongoing sensitive, high-resolution 120-168MHz survey of the entire northern sky for which observations are now 20% complete. We present our first full-quality public data release. For this data release 424 square degrees, or 2% of the eventual coverage, in the region of the HETDEX Spring Field (right ascension 10h45m00s to 15h30m00s and declination 45$^\circ$00$'$00$''$ to 57$^\circ$00$'$00$''$) were mapped using a fully automated direction-dependent calibration and imaging pipeline that we developed. A total of 325,694 sources are detected with a signal of at least five times the noise, and the source density is a factor of $\sim 10$ higher than the most sensitive existing very wide-area radio-continuum surveys. The median sensitivity is S$_{\rm 144 MHz} = 71\,\mu$Jy beam$^{-1}$ and the point-source completeness is 90% at an integrated flux density of 0.45mJy. The resolution of the images is 6$''$ and the positional accuracy is within 0.2$''$. This data release consists of a catalogue containing location, flux, and shape estimates together with 58 mosaic images that cover the catalogued area. In this paper we provide an overview of the data release with a focus on the processing of the LOFAR data and the characteristics of the resulting images. In two accompanying papers we provide the radio source associations and deblending and, where possible, the optical identifications of the radio sources together with the photometric redshifts and properties of the host galaxies. These data release papers are published together with a further $\sim$20 articles that highlight the scientific potential of LoTSS., Comment: 16 figures, 1 table and 22 pages. This paper is part of the LOFAR surveys data release 1 and has been accepted for publication in a special edition of A&A that will appear in Feb 2019, volume 622. The catalogues and images from the data release will be publicly available on lofar-surveys.org upon publication of the journal

Rotation measure (RM) synthesis is a widely used polarization processing algorithm for reconstructing polarized structures along the line of sight. Performing RM synthesis on large datasets produced by telescopes like LOFAR can be computationally intensive as the computational cost is proportional to the product of the number of input frequency channels, the number of output Faraday depth values to be evaluated and the number of lines of sight present in the data cube. The required computational cost is likely to get worse due to the planned large area sky surveys with telescopes like the Low Frequency Array (LOFAR), the Murchison Widefield Array (MWA), and eventually the Square Kilometre Array (SKA). The massively parallel General Purpose Graphical Processing Units (GPGPUs) can be used to execute some of the computationally intensive astronomical image processing algorithms including RM synthesis. In this paper, we present a GPU-accelerated code, called cuFFS or CUDA-accelerated Fast Faraday Synthesis, to perform Faraday rotation measure synthesis. Compared to a fast single-threaded and vectorized CPU implementation, depending on the structure and format of the data cubes, our code achieves an increase in speed of up to two orders of magnitude. During testing, we noticed that the disk I/O when using the Flexible Image Transport System (FITS) data format is a major bottleneck and to reduce the time spent on disk I/O, our code supports the faster HDFITS format in addition to the standard FITS format. The code is written in C with GPU-acceleration achieved using Nvidia's CUDA parallel computing platform. The code is available at https://github.com/sarrvesh/cuFFS., Comment: Accepted for publication in Astronomy & Computing

The low-frequency polarisation properties of radio sources are poorly studied, particularly in statistical samples. However, the new generation of low-frequency telescopes, such as the Murchison Widefield Array (MWA; the precursor for the low-frequency component of the Square Kilometre Array) offers an opportunity to probe the physics of radio sources at very low radio frequencies. In this paper, we present a catalogue of linearly-polarised sources detected at 216 MHz, using data from the Galactic and Extragalactic All-sky MWA (GLEAM) survey. Our catalogue covers the Declination range $-17^{\circ}$ to $-37^{\circ}$ and 24 hours in Right Ascension, at a resolution of around 3 arcminutes. We detect 81 sources (including both a known pulsar and new pulsar candidate) with linearly-polarised flux densities in excess of 18 mJy across a survey area of approximately 6400 square degrees, corresponding to a surface density of 1 source per 79 square degrees. The level of Faraday rotation measured for our sources is broadly consistent with those recovered at higher frequencies, with typically more than an order of magnitude improvement in the uncertainty compared to higher-frequency measurements. However, our catalogue is likely incomplete at low Faraday rotation measures, due to our practice of excluding sources in the region where instrumental leakage appears. The majority of sources exhibit significant depolarisation compared to higher frequencies; however, a small sub-sample repolarise at 216 MHz. We also discuss the polarisation properties of four nearby, large-angular-scale radio galaxies, with a particular focus on the giant radio galaxy ESO 422$-$G028, in order to explain the striking differences in polarised morphology between 216 MHz and 1.4 GHz., Comment: 32 pages, 13 figures, 3 tables. Accepted for publication in PASA

The shape of low-frequency radio continuum spectra of normal galaxies is not well understood, the key question being the role of physical processes such as thermal absorption in shaping them. In this work we take advantage of the LOFAR Multifrequency Snapshot Sky Survey (MSSS) to investigate such spectra for a large sample of nearby star-forming galaxies. Using the measured 150MHz flux densities from the LOFAR MSSS survey and literature flux densities at various frequencies we have obtained integrated radio spectra for 106 galaxies. The spectra are explained through the use of a three-dimensional model of galaxy radio emission, and radiation transfer dependent on the galaxy viewing angle and absorption processes. Spectra of our galaxies are generally flatter at lower compared to higher frequencies but as there is no tendency for the highly inclined galaxies to have more flattened low-frequency spectra, we argue that the observed flattening is not due to thermal absorption, contradicting the suggestion of Israel & Mahoney (1990). According to our modelled radio maps for M51-like galaxies, the free-free absorption effects can be seen only below 30MHz and in the global spectra just below 20MHz, while in the spectra of starburst galaxies, like M82, the flattening due to absorption is instead visible up to higher frequencies of about 150MHz. Locally, within galactic disks, the absorption effects are distinctly visible in M51-like galaxies as spectral flattening around 100-200MHz in the face-on objects, and as turnovers in the edge-on ones, while in M82-like galaxies there are strong turnovers at frequencies above 700MHz, regardless of viewing angle. Our modelling suggests that the weak spectral flattening observed in the nearby galaxies studied here results principally from synchrotron spectral curvature due to cosmic ray energy losses and propagation effects., Comment: Accepted for publication in Astronomy and Astrophysics (corrected typo in the title)

The new generation of broad-band radio continuum surveys will provide large data sets with polarization information. New algorithms need to be developed to extract reliable catalogs of linearly polarized sources that can be used to characterize those sources and produce a dense rotation measure (RM) grid to probe magneto-ionized structures along the line of sight via Faraday rotation. The aim of the paper is to develop a computationally efficient and rigorously defined source-finding algorithm for linearly polarized sources. We used a calibrated data set from the LOw Frequency ARray (LOFAR) at 150 MHz centered on the nearby galaxy M51 to search for polarized background sources. With a new imaging software, we re-imaged the field at a resolution of 18''x15'' and cataloged a total of about 3000 continuum sources within 2.5 degrees of the center of M51. We made small Stokes Q and U images centered on each source brighter than 100 mJy in total intensity (201 sources) and used RM synthesis to create corresponding Faraday cubes that were analyzed individually. For each source, the noise distribution function was determined from a subset of measurements at high Faraday depths where no polarization is expected; the peaks in polarized intensity in the Faraday spectrum were identified and the p-value of each source was calculated. Finally, the false discovery rate method was applied to the list of p-values to produce a list of polarized sources and quantify the reliability of the detections. We also analyzed sources fainter than 100 mJy but that were reported as polarized in the literature at at least another radio frequency. Of the 201 sources that were searched for polarization, 6 polarized sources were detected confidently (with a false discovery rate of 5 percent). This corresponds to a number density of 1 polarized source per 3.3 square degrees, or 0.3 source/square degree. [Abridged], Comment: 17 pages, 11 figures, accepted for publication in A&A

We present a new analysis of the widely used relation between cavity power and radio luminosity in clusters of galaxies with evidence for strong AGN feedback. We study the correlation at low radio frequencies using two new surveys - the First Alternative Data Release of the TIFR GMRT Sky Survey (TGSS ADR1) at 148 MHz and LOFAR's first all-sky survey, the Multifrequency Snapshot Sky Survey (MSSS) at 140 MHz. We find a scaling relation $P_{\rm cav} \propto L_{148}^{\beta}$, with a logarithmic slope of $\beta = 0.51 \pm 0.14$, which is in good agreement with previous results based on data at 327 MHz. The large scatter present in this correlation confirms the conclusion reached at higher frequencies that the total radio luminosity at a single frequency is a poor predictor of the total jet power. We show that including measurements at 148 MHz alone is insufficient to reliably compute the bolometric radio luminosity and reduce the scatter in the correlation. For a subset of four well-resolved sources, we examine the detected extended structures at low frequencies and compare with the morphology known from higher frequency images and Chandra X-ray maps. In Perseus we discuss details in the structures of the radio mini-halo, while in the 2A 0335+096 cluster we observe new diffuse emission associated with multiple X-ray cavities and likely originating from past activity. For A2199 and MS 0735.6+7421, we confirm that the observed low-frequency radio lobes are confined to the extents known from higher frequencies. This new low-frequency analysis highlights the fact that existing cavity power to radio luminosity relations are based on a relatively narrow range of AGN outburst ages. We discuss how the correlation could be extended using low frequency data from the LOFAR Two-metre Sky Survey (LoTSS) in combination with future, complementary deeper X-ray observations.

We report on the discovery in the LOFAR Multifrequency Snapshot Sky Survey (MSSS) of a giant radio galaxy (GRG) with a projected size of $2.56 \pm 0.07$ Mpc projected on the sky. It is associated with the galaxy triplet UGC 9555, within which one is identified as a broad-line galaxy in the Sloan Digital Sky Survey (SDSS) at a redshift of $0.05453 \pm 1 \times 10^{-5} $, and with a velocity dispersion of $215.86 \pm 6.34$ km/s. From archival radio observations we see that this galaxy hosts a compact flat-spectrum radio source, and we conclude that it is the active galactic nucleus (AGN) responsible for generating the radio lobes. The radio luminosity distribution of the jets, and the broad-line classification of the host AGN, indicate this GRG is orientated well out of the plane of the sky, making its physical size one of the largest known for any GRG. Analysis of the infrared data suggests that the host is a lenticular type galaxy with a large stellar mass ($\log~\mathrm{M}/\mathrm{M}_\odot = 11.56 \pm 0.12$), and a moderate star formation rate ($1.2 \pm 0.3~\mathrm{M}_\odot/\mathrm{year}$). Spatially smoothing the SDSS images shows the system around UGC 9555 to be significantly disturbed, with a prominent extension to the south-east. Overall, the evidence suggests this host galaxy has undergone one or more recent moderate merger events and is also experiencing tidal interactions with surrounding galaxies, which have caused the star formation and provided the supply of gas to trigger and fuel the Mpc-scale radio lobes., Comment: Compressed for arXiv, see journal for full resolution images

The new generation of low-frequency radio telescopes, such as the Low Frequency Array (LOFAR: a Square Kilometre Array-low pathfinder), provides advancements in our capability of probing Galactic magnetism through low-frequency polarimetry. Maps of diffuse polarized radio emission and Faraday rotation can be used to infer properties of, and trace structure in, the magnetic fields in the ISM. However, to date very little of the sky has been probed at high angular and Faraday depth resolution. We observed a 5x5 degree region centred on the nearby galaxy IC342 using LOFAR in the frequency range 115-178 MHz at 4 arcmin resolution and performed Faraday tomography to detect foreground Galactic polarized synchrotron emission separated by Faraday depth (different amounts of Faraday rotation). Our Faraday depth cube shows rich polarized structure, with up to 30 K of polarized emission at 150 MHz. We detect two overlapping diffuse polarized features that are clearly separated in Faraday depth. Faraday-thick structures at such low frequencies would be too strongly depolarized to explain the observations and are therefore rejected. Only Faraday thin structures will not be strongly depolarized; producing such structures requires localized variations in the ratio of synchrotron emissivity to Faraday depth per unit distance, which can arise from several physical phenomena, such as a transition between regions of ionized and neutral gas. We conclude that the observed polarized emission is Faraday thin, and propose that the emission originates from two neutral clouds in the local ISM. We have modeled the Faraday rotation for this line of sight and estimated that the line of sight component of magnetic field of the local ISM for this direction varies between -0.86 and +0.12 uG. We propose that this may be a useful method for mapping magnetic fields within the local ISM., Comment: 17 pages, 12 figures, accepted for publication in A&A

The LOFAR Two-metre Sky Survey (LoTSS) is a deep 120-168 MHz imaging survey that will eventually cover the entire Northern sky. Each of the 3170 pointings will be observed for 8 hrs, which, at most declinations, is sufficient to produce ~5arcsec resolution images with a sensitivity of ~0.1mJy/beam and accomplish the main scientific aims of the survey which are to explore the formation and evolution of massive black holes, galaxies, clusters of galaxies and large-scale structure. Due to the compact core and long baselines of LOFAR, the images provide excellent sensitivity to both highly extended and compact emission. For legacy value, the data are archived at high spectral and time resolution to facilitate subarcsecond imaging and spectral line studies. In this paper we provide an overview of the LoTSS. We outline the survey strategy, the observational status, the current calibration techniques, a preliminary data release, and the anticipated scientific impact. The preliminary images that we have released were created using a fully-automated but direction-independent calibration strategy and are significantly more sensitive than those produced by any existing large-area low-frequency survey. In excess of 44,000 sources are detected in the images that have a resolution of 25arcsec, typical noise levels of less than 0.5 mJy/beam, and cover an area of over 350 square degrees in the region of the HETDEX Spring Field (right ascension 10h45m00s to 15h30m00s and declination 45d00m00s to 57d00m00s)., Comment: 23 pages, 15 figures, 3 tables, accepted for publication in A&A

We present the first wide area (19 deg$^2$), deep ($\approx120-150$ {\mu}Jy beam$^{-1}$), high resolution ($5.6 \times 7.4$ arcsec) LOFAR High Band Antenna image of the Bo\"otes field made at 130-169 MHz. This image is at least an order of magnitude deeper and 3-5 times higher in angular resolution than previously achieved for this field at low frequencies. The observations and data reduction, which includes full direction-dependent calibration, are described here. We present a radio source catalogue containing 6276 sources detected over an area of $19$\,deg$^2$, with a peak flux density threshold of $5\sigma$. As the first thorough test of the facet calibration strategy, introduced by van Weeren et al., we investigate the flux and positional accuracy of the catalogue. We present differential source counts that reach an order of magnitude deeper in flux density than previously achieved at these low frequencies, and show flattening at 150 MHz flux densities below 10 mJy associated with the rise of the low flux density star-forming galaxies and radio-quiet AGN., Comment: 29 pages, 27 figures, accepted for publication in MNRAS

With Low-Frequency Array (LOFAR) observations, we have discovered a diverse assembly of steep spectrum emission that is apparently associated with the intra cluster medium (ICM) of the merging galaxy cluster Abell 2034. Such a rich variety of complex emission associated with the ICM has been observed in few other clusters. This not only indicates that Abell 2034 is a more interesting and complex system than previously thought but it also demonstrates the importance of sensitive and high-resolution, low-frequency observations. These observations can reveal emission from relativistic particles which have been accelerated to sufficient energy to produce observable emission or have had their high energy maintained by mechanisms in the ICM. The most prominent feature in our maps is a bright bulb of emission connected to two steep spectrum filamentary structures, the longest of which extends perpendicular to the merger axis for 0.5Mpc across the south of the cluster. The origin of these objects is unclear, with no shock detected in the X-ray images and no obvious connection with cluster galaxies or AGNs. We also find that the X-ray bright region of the cluster coincides with a giant radio halo with an irregular morphology and a very steep spectrum. In addition, the cluster hosts up to three possible radio relics, which are misaligned with the cluster X-ray emission. Finally, we have identified multiple regions of emission with a very steep spectral index that seem to be associated with either tailed radio galaxies or a shock., Comment: 15 pages, 9 figures, 1 table, accepted for publication in MNRAS

LOFAR, the Low-Frequency Array, is a powerful new radio telescope operating between 10 and 240 MHz. LOFAR allows detailed sensitive high-resolution studies of the low-frequency radio sky. At the same time LOFAR also provides excellent short baseline coverage to map diffuse extended emission. However, producing high-quality deep images is challenging due to the presence of direction dependent calibration errors, caused by imperfect knowledge of the station beam shapes and the ionosphere. Furthermore, the large data volume and presence of station clock errors present additional difficulties. In this paper we present a new calibration scheme, which we name facet calibration, to obtain deep high-resolution LOFAR High Band Antenna images using the Dutch part of the array. This scheme solves and corrects the direction dependent errors in a number of facets that cover the observed field of view. Facet calibration provides close to thermal noise limited images for a typical 8 hr observing run at $\sim$ 5arcsec resolution, meeting the specifications of the LOFAR Tier-1 northern survey., Comment: 17 pages, 12 figures, accepted for publication in ApJS

We present deep LOFAR observations between 120-181 MHz of the "Toothbrush" (RX J0603.3+4214), a cluster that contains one of the brightest radio relic sources known. Our LOFAR observations exploit a new and novel calibration scheme to probe 10 times deeper than any previous study in this relatively unexplored part of the spectrum. The LOFAR observations, when combined with VLA, GMRT, and Chandra X-ray data, provide new information about the nature of cluster merger shocks and their role in re-accelerating relativistic particles. We derive a spectral index of $\alpha = -0.8 \pm 0.1$ at the northern edge of the main radio relic, steepening towards the south to $\alpha \approx - 2$. The spectral index of the radio halo is remarkably uniform ($\alpha = -1.16$, with an intrinsic scatter of $\leq 0.04$). The observed radio relic spectral index gives a Mach number of $\mathcal{M} = 2.8^{+0.5}_{-0.3}$, assuming diffusive shock acceleration (DSA). However, the gas density jump at the northern edge of the large radio relic implies a much weaker shock ($\mathcal{M} \approx 1.2$, with an upper limit of $\mathcal{M} \approx 1.5$). The discrepancy between the Mach numbers calculated from the radio and X-rays can be explained if either (i) the relic traces a complex shock surface along the line of sight, or (ii) if the radio relic emission is produced by a re-accelerated population of fossil particles from a radio galaxy. Our results highlight the need for additional theoretical work and numerical simulations of particle acceleration and re-acceleration at cluster merger shocks., Comment: 20 pages, 18 figures, accepted for publication in ApJ