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M. E. Bell

Publications and source records attributed to M. E. Bell.

At least 19 recordsLinked to original sources

The radio flare and multi-wavelength afterglow of the short GRB 231117A: energy injection from a violent shell collision

We present the early radio detection and multi-wavelength modeling of the short gamma-ray burst (GRB) 231117A at redshift $z=0.257$. The Australia Telescope Compact Array automatically triggered a 9-hour observation of GRB 231117A at 5.5 and 9 GHz following its detection by the Neil Gehrels Swift Observatory just 1.3 hours post-burst. Splitting this observation into 1-hour time bins, the early radio afterglow exhibited flaring, scintillating and plateau phases. The scintillation allowed us to place the earliest upper limit ($<10$ hours) on the size of a GRB blast wave to date, constraining it to $<1\times10^{16}$ cm. Multi-wavelength modeling of the full afterglow required a period of significant energy injection between $\sim 0.02$ and $1$ day. The energy injection was modeled as a violent collision of two shells: a reverse shock passing through the injection shell explains the early radio plateau, while an X-ray flare is consistent with a shock passing through the leading impulsive shell. Beyond 1 day, the blast wave evolves as a classic decelerating forward shock with an electron distribution index of $p=1.66\pm0.01$. Our model also indicates a jet-break at $\sim2$ days, and a half-opening angle of $θ_j=16\mathring{.}6 \pm 1\mathring{.}1$. Following the period of injection, the total energy is $ζ\sim18$ times the initial impulsive energy, with a final collimation-corrected energy of $E_{\mathrm{Kf}}\sim5.7\times10^{49}$ erg. The minimum Lorentz factors this model requires are consistent with constraints from the early radio measurements of $Γ>35$ to $Γ>5$ between $\sim0.1$ and $1$ day. These results demonstrate the importance of rapid and sensitive radio follow-up of GRBs for exploring their central engines and outflow behaviour.

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Constraints on Short Gamma-Ray Burst Physics and Their Host Galaxies from Systematic Radio Follow-up Campaigns

Short gamma-ray bursts (GRBs) are explosive transients caused by binary mergers of compact objects containing at least one neutron star. Multi-wavelength afterglow observations provide constraints on the physical parameters of the jet, its surrounding medium, and the microphysics of the enhanced magnetic fields and accelerated electrons in the blast wave at the front of the jet. The synchrotron radio emission can be tracked for much longer than in other spectral regimes, and it can pin down the evolution of the spectral peak. We present the results of a systematic observing campaign of eight short GRBs with the MeerKAT radio telescope. Additionally, we present observations of four of these short GRBs using the ATCA radio telescope and two of these short GRBs with the e-MERLIN radio telescope. Using these results we report one possible detection of a short GRB afterglow from GRB 230217A and deep upper limits for the rest of our short GRB observations. We use these observations to place constraints on some of the physical parameters, in particular those related to electron acceleration, the circumburst density, and gamma-ray energy efficiency. We discuss how deeper observations with new and upgraded telescopes should be able to determine if the gamma-ray efficiency differs between long and short GRBs. We also report detections of the likely host galaxies for four of the eight GRBs and upper limits for another GRB, increasing the number of detected host galaxies in the radio with implications for the star formation rate in these galaxies.

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Rapid radio brightening of GRB 210702A

We observed the rapid radio brightening of GRB 210702A with the Australian Telescope Compact Array (ATCA) just 11hr post-burst, tracking early-time radio variability over a 5hr period on ~15min timescales at 9.0, 16.7, and 21.2GHz. A broken power-law fit to the 9.0GHz light curve showed that the 5hr flare peaked at a flux density of 0.4+/-0.1mJy at ~13hr post-burst with a steep rise and decline. The observed temporal and spectral evolution are not expected in the standard internal-external shock model, where forward and reverse shock radio emission evolves on much longer timescales. The early-time (<1day) optical and X-ray light curves from the Neil Gehrels Swift Observatory demonstrated typical afterglow forward shock behaviour, allowing us to use blast wave physics to determine a likely homogeneous circumburst medium and an emitting electron population power-law index of p=2.9+/-0.1. We suggest the early-time radio flare is likely due to weak interstellar scintillation (ISS), which boosted the radio afterglow emission above the ATCA sensitivity limit on minute timescales. Using weak ISS relations, we were able to place an upper limit on the size of the blast wave of $\leq6 \times 10^{16}$cm in the plane of the sky, which is consistent with the theoretical forward shock size prediction of $8\times10^{16}$cm for GRB 210702A at ~13h post-burst. This represents the earliest ISS size constraint on a GRB blast wave to date, demonstrating the importance of rapid (<1day) radio follow-up of GRBs using several-hour integrations to capture the early afterglow evolution, and to track scintillation over a broad frequency range.

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High time resolution search for prompt radio emission from the long GRB 210419A with the Murchison Widefield Array

We present a low-frequency (170\textendash200\,MHz) search for prompt radio emission associated with the long GRB 210419A using the rapid-response mode of the Murchison Widefield Array (MWA), triggering observations with the Voltage Capture System (VCS) for the first time. The MWA began observing GRB 210419A within 89\,s of its detection by \textit{Swift}, enabling us to capture any dispersion delayed signal emitted by this GRB for a typical range of redshifts. We conducted a standard single pulse search with a temporal and spectral resolution of $100\,\upmu$s and 10\,kHz over a broad range of dispersion measures from 1 to $5000\,\text{pc}\,\text{cm}^{-3}$, but none were detected. However, fluence upper limits of $77\text{--}224$\,Jy\,ms derived over a pulse width of $0.5\text{--}10$\,ms and a redshift of $0.6<z<4$ are some of the most stringent at low radio frequencies. We compared these fluence limits to the GRB jet-interstellar medium (ISM) interaction model, placing constraints on the fraction of magnetic energy ($ε_{\text{B}}\lesssim[0.05 \text{--} 0.1]$). We also searched for signals during the X-ray flaring activity of GRB 210419A on minute timescales in the image domain and found no emission, resulting in an intensity upper limit of $0.57\,\text{Jy}\,\text{beam}^{-1}$, corresponding to a constraint of $ε_{\text{B}}\lesssim10^{-3}$. Our non-detection could imply that GRB 210419A was at a high redshift, there was not enough magnetic energy for low-frequency emission, or that the radio waves did not escape from the GRB environment.

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Early-time Searches for Coherent Radio Emission from Short GRBs with the Murchison Widefield Array

Here we present a low frequency (170-200MHz) search for coherent radio emission associated with nine short GRBs detected by the Swift and/or Fermi satellites using the Murchison Widefield Array (MWA) rapid-response observing mode. The MWA began observing these events within 30 to 60s of their high-energy detection, enabling us to capture any dispersion delayed signals emitted by short GRBs for a typical range of redshifts. We conducted transient searches at the GRB positions on timescales of 5s, 30s and 2min, resulting in the most constraining flux density limits on any associated transient of 0.42, 0.29, and 0.084Jy, respectively. We also searched for dispersed signals at a temporal and spectral resolution of 0.5s and 1.28MHz but none were detected. However, the fluence limit of 80-100Jy ms derived for GRB 190627A is the most stringent to date for a short GRB. We compared the fluence and persistent emission limits to short GRB coherent emission models, placing constraints on key parameters including the radio emission efficiency of the nearly merged neutron stars ($\lesssim10^{-4}$), the fraction of magnetic energy in the GRB jet ($\lesssim2\times10^{-4}$), and the radio emission efficiency of the magnetar remnant ($\lesssim10^{-3}$). Comparing the limits derived for our full GRB sample to the same emission models, we demonstrate that our 30-min flux density limits were sensitive enough to theoretically detect the persistent radio emission from magnetar remnants up to a redshift of $z\sim0.6$. Our non-detection of this emission could imply that some GRBs in the sample were not genuinely short or did not result from a binary neutron star merger, the GRBs were at high redshifts, these mergers formed atypical magnetars, the radiation beams of the magnetar remnants were pointing away from Earth, or the majority did not form magnetars but rather collapse directly into black holes.

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The GLEAM 200 MHz Local Radio Luminosity Function for AGN and Star-forming Galaxies

The GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) is a radio continuum survey at 76-227 MHz of the entire southern sky (Declination $<+30°$) with an angular resolution of $\approx 2$ arcmin. In this paper, we combine GLEAM data with optical spectroscopy from the 6dF Galaxy Survey to construct a sample of 1,590 local (median $z \approx 0.064$) radio sources with $S_{200\,\mathrm{MHz}} > 55$ mJy across an area of $\approx 16,700~\mathrm{deg}^{2}$. From the optical spectra, we identify the dominant physical process responsible for the radio emission from each galaxy: 73 per cent are fuelled by an active galactic nucleus (AGN) and 27 per cent by star formation. We present the local radio luminosity function for AGN and star-forming galaxies at 200 MHz and characterise the typical radio spectra of these two populations between 76 MHz and $\sim 1$ GHz. For the AGN, the median spectral index between 200 MHz and $\sim 1$ GHz, $α_{\mathrm{high}}$, is $-0.600 \pm 0.010$ (where $S \propto ν^α$) and the median spectral index within the GLEAM band, $α_{\mathrm{low}}$, is $-0.704 \pm 0.011$. For the star-forming galaxies, the median value of $α_{\mathrm{high}}$ is $-0.650 \pm 0.010$ and the median value of $α_{\mathrm{low}}$ is $-0.596 \pm 0.015$. Among the AGN population, flat-spectrum sources are more common at lower radio luminosity, suggesting the existence of a significant population of weak radio AGN that remain core-dominated even at low frequencies. However, around 4 per cent of local radio AGN have ultra-steep radio spectra at low frequencies ($α_{\mathrm{low}} < -1.2$). These ultra-steep-spectrum sources span a wide range in radio luminosity, and further work is needed to clarify their nature.

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Murchison Widefield Array rapid-response observations of the short GRB 180805A

Here we present stringent low-frequency 185MHz limits on coherent radio emission associated with a short gamma-ray burst (SGRB). Our observations of the short GRB 180805A were taken with the upgraded Murchison Widefield Array (MWA) rapid-response system, which triggered within 20s of receiving the transient alert from Swift, corresponding to 83.7s post-burst. The SGRB was observed for 30m, resulting in a 3sigma persistent flux density upper-limit of 40.2mJy/beam. Transient searches were conducted at the Swift position of this GRB on 0.5s, 5s, 30s, and 2m timescales, resulting in 3sigma limits of 570-1830, 270-630, 200-420, and 100-200mJy/beam, respectively. We also performed a dedispersion search for prompt signals at the position of the SGRB with a temporal and spectral resolution of 0.5s and 1.28MHz, resulting in a 6sigma fluence upper-limit range from 570Jyms at DM=3000pc/cm^3 (z~2.5) to 1750Jyms at DM=200pc/cm^3 (z~0.1). We compare the fluence prompt emission limit and the persistent upper-limit to SGRB coherent emission models assuming the merger resulted in a stable magnetar. Our observations were not sensitive enough to detect prompt emission associated with the alignment of magnetic fields of a binary neutron star just prior to the merger, from the interaction between the relativistic jet and the interstellar medium or persistent pulsar-like emission from the spin-down of the magnetar. However, in the case of a more powerful SGRB (a gamma-ray fluence an order of magnitude higher than GRB 180805A and/or a brighter X-ray counterpart), our MWA observations may be sensitive enough to detect coherent radio emission from the jet-ISM interaction and/or the magnetar remnant. Finally, we demonstrate that of all current low-frequency radio telescopes, only the MWA has the sensitivity and response times capable of probing prompt emission models associated with the initial SGRB merger event.

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LOFAR imaging of Cygnus A -- Direct detection of a turnover in the hotspot radio spectra

The low-frequency radio spectra of the hotspots within powerful radio galaxies can provide valuable information about the physical processes operating at the site of the jet termination. These processes are responsible for the dissipation of jet kinetic energy, particle acceleration, and magnetic-field generation. Here we report new observations of the powerful radio galaxy Cygnus A using the Low Frequency Array (LOFAR) between 109 and 183 MHz, at an angular resolution of ~3.5 arcsec. The radio emission of the lobes is found to have a complex spectral index distribution, with a spectral steepening found towards the centre of the source. For the first time, a turnover in the radio spectrum of the two main hotspots of Cygnus A has been directly observed. By combining our LOFAR imaging with data from the Very Large Array at higher frequencies, we show that the very rapid turnover in the hotspot spectra cannot be explained by a low-energy cut-off in the electron energy distribution, as has been previously suggested. Thermal (free-free) absorption or synchrotron self absorption models are able to describe the low-frequency spectral shape of the hotspots, however, as with previous studies, we find that the implied model parameters are unlikely, and interpreting the spectra of the hotspots remains problematic.

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Rapid-response radio observations of short GRB 181123B with the Australia Telescope Compact Array

We introduce the Australia Telescope Compact Array (ATCA) rapid-response mode by presenting the first successful trigger on the short-duration gamma-ray burst (GRB) 181123B. Early-time radio observations of short GRBs may provide vital insights into the radio afterglow properties of Advanced LIGO- and Virgo-detected gravitational wave events, which will in turn inform follow-up strategies to search for counterparts within their large positional uncertainties. The ATCA was on target within 12.6 hr post-burst, when the source had risen above the horizon. While no radio afterglow was detected during the 8.3 hr observation, we obtained force-fitted flux densities of $7 \pm 12$ and $15 \pm 11~μ$Jy at 5.5 and 9 GHz, respectively. Afterglow modelling of GRB 181123B showed that the addition of the ATCA force-fitted radio flux densities to the Swift X-ray Telescope detections provided more stringent constraints on the fraction of thermal energy in the electrons (log$ε_e = -0.75^{+0.39}_{-0.40}$ rather than log$ε_e = -1.13^{+0.82}_{-1.2}$ derived without the inclusion of the ATCA values), which is consistent with the range of typical $ε_e$ derived from GRB afterglow modelling. This allowed us to predict that the forward shock may have peaked in the radio band $\sim10$ days post-burst, producing detectable radio emission $\gtrsim3-4$ days post-burst. Overall, we demonstrate the potential for extremely rapid radio follow-up of transients and the importance of triggered radio observations for constraining GRB blast wave properties, regardless of whether there is a detection, via the inclusion of force-fitted radio flux densities in afterglow modelling efforts.

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Spectral Variability of Radio Sources at Low Frequencies

Spectral variability of radio sources encodes information about the conditions of intervening media, source structure, and emission processes. With new low-frequency radio interferometers observing over wide fractional bandwidths, studies of spectral variability for a large population of extragalactic radio sources are now possible. Using two epochs of observations from the GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) survey that were taken one year apart, we search for spectral variability across 100--230 MHz for 21,558 sources. We present methodologies for detecting variability in the spectrum between epochs and for classifying the type of variability: either as a change in spectral shape or as a uniform change in flux density across the bandwidth. We identify 323 sources with significant spectral variability over a year-long timescale. Of the 323 variable sources, we classify 51 of these as showing a significant change in spectral shape. Variability is more prevalent in peaked-spectrum sources, analogous to gigahertz-peaked spectrum and compact steep-spectrum sources, compared to typical radio galaxies. We discuss the viability of several potential explanations of the observed spectral variability, such as interstellar scintillation and jet evolution. Our results suggest that the radio sky in the megahertz regime is more dynamic than previously suggested.

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LOFAR 144-MHz follow-up observations of GW170817

We present low-radio-frequency follow-up observations of AT 2017gfo, the electromagnetic counterpart of GW170817, which was the first binary neutron star merger to be detected by Advanced LIGO-Virgo. These data, with a central frequency of 144 MHz, were obtained with LOFAR, the Low-Frequency Array. The maximum elevation of the target is just 13.7 degrees when observed with LOFAR, making our observations particularly challenging to calibrate and significantly limiting the achievable sensitivity. On time-scales of 130-138 and 371-374 days after the merger event, we obtain 3$σ$ upper limits for the afterglow component of 6.6 and 19.5 mJy beam$^{-1}$, respectively. Using our best upper limit and previously published, contemporaneous higher-frequency radio data, we place a limit on any potential steepening of the radio spectrum between 610 and 144 MHz: the two-point spectral index $α^{610}_{144} \gtrsim -2.5$. We also show that LOFAR can detect the afterglows of future binary neutron star merger events occurring at more favourable elevations.

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Field sources near the southern-sky calibrator PKS B1934-638: effect on spectral line observations with SKA-MID and its precursors

Accurate instrumental bandpass corrections are essential for the reliable interpretation of spectral lines from targeted and survey-mode observations with radio interferometers. Bandpass correction is typically performed by comparing measurements of a strong calibrator source to an assumed model, typically an isolated point source. The wide field-of-view and high sensitivity of modern interferometers means that additional sources are often detected in observations of calibrators. This can introduce errors into bandpass corrections and subsequently the target data if not properly accounted for. Focusing on the standard calibrator PKS B1934-638, we perform simulations to asses this effect by constructing a wide-field sky model. The cases of ASKAP (0.7-1.9 GHz), MeerKAT (UHF: 0.58-1.05 GHz; L-band: 0.87-1.67 GHz) and Band 2 (0.95-1.76 GHz) of SKA-MID are examined. The use of a central point source model during bandpass calibration is found to impart amplitude errors into spectra measured by the precursor instruments at the ~0.2-0.5% level dropping to ~0.01% in the case of SKA-MID. This manifests itself as ripples in the source spectrum, the behaviour of which is coupled to the distribution of the array baselines, the solution interval, the primary beam size, the hour-angle of the calibration scan, as well as the weights used when imaging the target. Calibration pipelines should routinely employ complete field models for standard calibrators to remove this potentially destructive contaminant from the data, a recommendation we validate by comparing our simulation results to a MeerKAT scan of PKS B1934-638, calibrated with and without our expanded sky model.

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Murchison Widefield Array and XMM-Newton observations of the Galactic supernova remnant G5.9+3.1

In this paper we discuss the radio continuum and X-ray properties of the so-far poorly studied Galactic supernova remnant (SNR) G5.9+3.1. We present the radio spectral energy distribution (SED) of the Galactic SNR G5.9+3.1 obtained with the Murchison Widefield Array (MWA). Combining these new observations with the surveys at other radio continuum frequencies, we discuss the integrated radio continuum spectrum of this particular remnant. We have also analyzed an archival XMM-Newton observation, which represents the first detection of X-ray emission from this remnant. The SNR SED is very well explained by a simple power-law relation. The synchrotron radio spectral index of G5.9+3.1, is estimated to be 0.42$\pm$0.03 and the integrated flux density at 1GHz to be around 2.7Jy. Furthermore, we propose that the identified point radio source, located centrally inside the SNR shell, is most probably a compact remnant of the supernova explosion. The shell-like X-ray morphology of G5.9+3.1 as revealed by XMM-Newton broadly matches the spatial distribution of the radio emission, where the radio-bright eastern and western rims are also readily detected in the X-ray while the radio-weak northern and southern rims are weak or absent in the X-ray. Extracted MOS1+MOS2+PN spectra from the whole SNR as well as the north, east, and west rims of the SNR are fit successfully with an optically thin thermal plasma model in collisional ionization equilibrium with a column density N_H~0.80x$10^{22}$ cm$^{-2}$ and fitted temperatures spanning the range kT~0.14-0.23keV for all of the regions. The derived electron number densities n_e for the whole SNR and the rims are also roughly comparable (ranging from ~$0.20f^{-1/2}$ cm$^{-3}$ to ~$0.40f^{-1/2}$ cm$^{-3}$, where f is the volume filling factor). We also estimate the swept-up mass of the X-ray emitting plasma associated with G5.9+3.1 to be ~$46f^{-1/2}M_{\odot}$.

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The Murchison Widefield Array Transients Survey (MWATS). A search for low frequency variability in a bright Southern hemisphere sample

We report on a search for low-frequency radio variability in 944 bright (> 4Jy at 154 MHz) unresolved, extragalactic radio sources monitored monthly for several years with the Murchison Widefield Array. In the majority of sources we find very low levels of variability with typical modulation indices < 5%. We detect 15 candidate low frequency variables that show significant long term variability (>2.8 years) with time-averaged modulation indices M = 3.1 - 7.1%. With 7/15 of these variable sources having peaked spectral energy distributions, and only 5.7% of the overall sample having peaked spectra, we find an increase in the prevalence of variability in this spectral class. We conclude that the variability seen in this survey is most probably a consequence of refractive interstellar scintillation and that these objects must have the majority of their flux density contained within angular diameters less than 50 milli-arcsec (which we support with multi-wavelength data). At 154 MHz we demonstrate that interstellar scintillation time-scales become long (~decades) and have low modulation indices, whilst synchrotron driven variability can only produce dynamic changes on time-scales of hundreds of years, with flux density changes less than one milli-jansky (without relativistic boosting). From this work we infer that the low frequency extra-galactic southern sky, as seen by SKA-Low, will be non-variable on time-scales shorter than one year.

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Galactic synchrotron distribution derived from 152 HII region absorption features in the full GLEAM survey

We derive the synchrotron distribution in the Milky Way disk from HII region absorption observations over -40° < l < 40° at six frequencies of 76.2, 83.8, 91.5, 99.2, 106.9, and 114.6 MHz with the GaLactic and Extragalactic All-sky Murchison widefield array survey (GLEAM). We develop a new method of emissivity calculation by taking advantage of the Haslam et al., (1981) map and known spectral indices, which enable us to simultaneously derive the emissivity and the optical depth of HII regions at each frequency. We show our derived synchrotron emissivities based on 152 absorption features of HII regions using both the method previously adopted in the literature and our improved method. We derive the synchrotron emissivity from HII regions to the Galactic edge along the line of sight and, for the first time, derive the emissivity from HII regions to the Sun. These results provide direct information on the distribution of the Galactic magnetic field and cosmic-ray electrons for future modelling.

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RFI Flagging Implications for Short-Duration Transients

With their wide fields of view and often relatively long coverage of any position in the sky in imaging survey mode, modern radio telescopes provide a data stream that is naturally suited to searching for rare transients. However, Radio Frequency Interference (RFI) can show up in the data stream in similar ways to such transients, and thus the normal pre-treatment of filtering RFI (flagging) may also remove astrophysical transients from the data stream before imaging. In this paper we investigate how standard flagging affects the detectability of such transients by examining the case of transient detection in an observing mode used for Low Frequency Array (LOFAR; \citep{LOFAR}) surveys. We quantify the fluence range of transients that would be detected, and the reduction of their SNR due to partial flagging. We find that transients with a duration close to the integration sampling time, as well as bright transients with durations on the order of tens of seconds, are completely flagged. For longer transients on the order of several tens of seconds to minutes, the flagging effects are not as severe, although part of the signal is lost. For these transients, we present a modified flagging strategy which mitigates the effect of flagging on transient signals. We also present a script which uses the differences between the two strategies, and known differences between transient RFI and astrophysical transients, to notify the observer when a potential transient is in the data stream.

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Shock location and CME 3D reconstruction of a solar type II radio burst with LOFAR

Type II radio bursts are evidence of shocks in the solar atmosphere and inner heliosphere that emit radio waves ranging from sub-meter to kilometer lengths. These shocks may be associated with CMEs and reach speeds higher than the local magnetosonic speed. Radio imaging of decameter wavelengths (20-90 MHz) is now possible with LOFAR, opening a new radio window in which to study coronal shocks that leave the inner solar corona and enter the interplanetary medium and to understand their association with CMEs. To this end, we study a coronal shock associated with a CME and type II radio burst to determine the locations at which the radio emission is generated, and we investigate the origin of the band-splitting phenomenon.

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LOFAR 150-MHz observations of SS 433 and W 50

We present LOFAR high-band data over the frequency range 115-189 MHz for the X-ray binary SS 433, obtained in an observing campaign from 2013 February - 2014 May. Our results include a deep, wide-field map, allowing a detailed view of the surrounding supernova remnant W 50 at low radio frequencies, as well as a light curve for SS 433 determined from shorter monitoring runs. The complex morphology of W 50 is in excellent agreement with previously published higher-frequency maps; we find additional evidence for a spectral turnover in the eastern wing, potentially due to foreground free-free absorption. Furthermore, SS 433 is tentatively variable at 150 MHz, with both a debiased modulation index of 11 per cent and a $χ^2$ probability of a flat light curve of $8.2 \times 10^{-3}$. By comparing the LOFAR flux densities with contemporaneous observations carried out at 4800 MHz with the RATAN-600 telescope, we suggest that an observed $\sim$0.5-1 Jy rise in the 150-MHz flux density may correspond to sustained flaring activity over a period of approximately six months at 4800 MHz. However, the increase is too large to be explained with a standard synchrotron bubble model. We also detect a wealth of structure along the nearby Galactic plane, including the most complete detection to date of the radio shell of the candidate supernova remnant G 38.7-1.4. This further demonstrates the potential of supernova remnant studies with the current generation of low-frequency radio telescopes.

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