I present an empirical study of the properties of fast radio bursts (FRBs): Gigahertz-frequency, dispersed pulses of extragalactic origin. I focus my investigation on the sample of seventeen FRBs detected at the Parkes radio telescope with largely self-consistent instrumentation. Of this sample, six are temporally unresolved, eight exhibit evidence for scattering in inhomogeneous plasma, and five display potentially intrinsic temporal structure. The characteristic scattering timescales at a frequency of 1 GHz range between 0.005 ms and 32 ms; moderate evidence exists for a relation between FRB scattering timescales and dispersion measures. Additionally, I present constraints on the fluences of Parkes FRBs, accounting for their uncertain sky-positions, and use the multiple-beam detection of FRB 010724 (the Lorimer burst) to measure its fluence to be $800\pm400$ Jy ms. FRBs, including the repeating FRB 121102, appear to manifest with a plethora of characteristics, and it is uncertain at present whether they share a common class of progenitor object, or arise from a selection of independent progenitors.
Context: Fast Radio Bursts are transient radio pulses from presumably compact stellar sources of extragalactic origin. With new telescopes detecting multiple events per day, statistical methods are required in order to interpret observations and make inferences regarding astrophysical and cosmological questions. Purpose: We present a method that uses probability estimates of fast radio burst observables to obtain likelihood estimates for the underlying models. Method: Considering models for all regions along the line-of-sight, including intervening galaxies, we perform Monte-Carlo simulations …
Fast radio bursts (FRBs) are millisecond-duration transient signals discovered over the past decade. Here we describe the scientific usefulness of FRBs, consider ongoing work at the Parkes telescope, and examine some relevant search sensitivity and completeness considerations. We also look ahead to the results from ongoing and future planned studies in the field.
It is pointed out that the positional distribution of Fast Radio Bursts (FRBs) shows proximity and clustering around the ecliptic. Their dispersion measure (DM) has a weak (80 percent significance level) correlation with the magnitude of the ecliptic latitude. The so called Perytons, however, show no significant proximity to any one of the three astronomical planes, viz celestial, ecliptic or galactic, although they are closer to the galactic plane.
In less than a decade, fast radio bursts have gone from a single debated curiosity to a diverse extragalactic population with established host galaxies and energy scales. While a wide range of models remain viable, the central engines of FRBs are likely to involve energetic young magnetars, as confirmed by the recent discovery of a Galactic analog to these extragalactic bursts. Here we provide a brief introductory review of fast radio bursts, focusing on the rapid recent progress in observations of these enigmatic events, our understanding of their central engines, and their use as probes of t…
Fast radio bursts appear to be cosmological signals whose frequency-time structure provides a dispersion measure. The dispersion measure is a convolution of the cosmic distance element and the electron density, and contains the possibility of using these events as new cosmological distance measures. We explore the challenges of extracting the distance in a robust manner, and give quantitative estimates for the systematics control needed for fast radio bursts to become a competitive distance probe. The methodology can also be applied to assessing their use for mapping electron density fluctuati…
Fast Radio Bursts are millisecond bursts of radio radiation at frequencies of about 1 GHz, recently discovered in pulsar surveys. They have not yet been definitively identified with any other astronomical object or phenomenon. The bursts are strongly dispersed, indicating passage through a high column density of low density plasma. The most economical interpretation is that this is the interglactic medium, indicating that FRB are at "cosmological" distances with redshifts in the range 0.3--1.3. Their inferred brightness temperatures are as high as $10^{37\,\circ}$K, implying coherent emission …
Context: Fast radio bursts are transient radio pulses of extragalactic origin. Their dispersion measure is indicative of the baryon content in the ionized intergalactic medium between the source and the observer. However, inference using unlocalized fast radio bursts is degenerate to the distribution of redshifts of host galaxies. Method: We perform a joint inference of the intergalactic baryon content and the fast radio burst redshift distribution with the use of Bayesian statistics by comparing the likelihood of different models to reproduce the observed statistics in order to infer the most…
Fast Radio Bursts (FRBs) are isolated, $\ms$ radio pulses with dispersion measure (DM) of order $10^3\DMunit$. Galactic candidates for the DM of high latitude bursts detected at $\GHz$ frequencies are easily dismissed. DM from bursts emitted in stellar coronas are limited by free-free absorption and those from HII regions are bounded by the nondetection of associated free-free emission at radio wavelengths. Thus, if astronomical, FRBs are probably extra-galactic. FRB 110220 has a scattering tail of $\sim 5.6\pm 0.1 \ms$. If the electron density fluctuations arise from a turbulent cascade, the …
The detection of six Fast Radio Bursts (FRBs) has recently been reported. FRBs are short duration ($\sim$ 1 ms), highly dispersed radio pulses from astronomical sources. The physical interpretation for the FRBs remains unclear but is thought to involve highly compact objects at cosmological distance. It has been suggested that a fraction of FRBs could be physically associated with gamma-ray bursts (GRBs). Recent radio observations of GRBs have reported the detection of two highly dispersed short duration radio pulses using a 12 m radio telescope at 1.4 GHz. Motivated by this result, we have pe…
We review the potential information that can be gleaned from multi-wavelength and multi-messenger detections of Fast Radio Bursts (FRBs). The primary function of such detections, following FRB localization, will be to reveal the progenitors of FRB events. However, these observations serve a more basic function in host galaxy identification, subsequent redshift measurement, and in disentangling the contributions of various line-of-sight contributions to properties of FRBs measured at radio wavelengths.
The field of gamma-ray burst astronomy arguably went through three decades of growing pains before reaching maturity. What development lessons can be learned for the adolescent field of fast radio burst astronomy?
We report on simultaneous radio and X-ray observations of the radio-emitting magnetar 1E1547.0-5408 on 2009 January 25 and February 3, with the 64-m Parkes radio telescope and the Chandra and XMM-Newton X-ray observatories. The magnetar was observed in a period of intense X-ray bursting activity and enhanced X-ray emission. We report here on the detection of two radio bursts from 1E1547.0-5408, reminiscent of Fast Radio Bursts (FRBs). One of the radio bursts was anticipated by ~1s (about half a rotation period of the pulsar) by a bright SGR-like X-ray burst, resulting in a F_radio/F_X ~ 10^-9.…
Lyutikov (2002) predicted "radio emission from soft gamma-ray repeaters (SGRs) during their bursting activity". Detection of a Mega-Jansky radio burst in temporal coincidence with high energy bursts from a Galactic magnetar SGR 1935+2154 confirms that prediction. Similarity of this radio event with Fast Radio Bursts (FRBs) suggests that FRBs are produced within magnetar magnetospheres. We demonstrate that SGR 1935+2154 satisfies the previously derived constraints on the physical parameters at the FRBs' loci. Coherent radio emission is generated in the inner parts of the magnetosphere at $r< 10…
Observations of millisecond-long radio bursts from beyond the Milky Way have revealed a repeat pattern with a roughly 16-day period -- a finding that adds to the enigma of the origin of these bursts.
Fast radio bursts are extragalactic, sub-millisecond radio impulses of unknown origin [1,2]. Their dispersion measures, which quantify the observed frequency-dependent dispersive delays in terms of free-electron column densities, significantly exceed predictions from models [3] of the Milky Way interstellar medium. The excess dispersions are likely accrued as fast radio bursts propagate through their host galaxies, gaseous galactic halos and the intergalactic medium [4,5]. Despite extensive follow-up observations of the published sample of 72 burst sources [6], only two are observed to repeat …
The nature of fast radio bursts (FRBs) is currently unknown. Repeating FRBs offer better opportunity than non-repeating FRBs since their simultaneous multi-wavelength counterparts might be identified. The magnetar flare model of FRBs is one of the most promising models which predicts high energy emission in addition to radio burst emission. To investigate such a possibility, we have searched for simultaneous and quasi-simultaneous short-term hard X-ray bursts in all the Swift/BAT event mode data which covered the periods when fast radio bursts were reported detections in the repeating FRB 1211…
Fast radio bursts are mysterious millisecond-duration transients prevalent in the radio sky. Rapid accumulation of data in recent years has facilitated an understanding of the underlying physical mechanisms of these events. Knowledge gained from the neighboring fields of gamma-ray bursts and radio pulsars also offered insight. Here I review developments in this fast-moving field.Two generic categories of radiation model invoking either magnetospheres of compact objects (neutron stars or black holes) or relativistic shocks launched from such objects have been much debated. The recent detection …
Fast Radio Bursts (FRBs) are recently discovered extra-galactic radio transients which are now used as novel cosmological probes. We show how the Bursts' Dispersion Measure can model-independently probe the history of Hydrogen reionization. Using a FlexKnot free-form parameterization to reconstruct the reionization history we predict an 11% accuracy constraint on the CMB optical depth, and 4% accuracy on the midpoint of reionization, to be achieved with 100 FRBs originating from redshifts z>5.
As a new kind of radio transient sources detected at $\sim 1.4$ GHz, fast radio bursts are specially characterized by their short durations and high intensities. Although only ten events are detected so far, fast radio bursts may actually frequently happen at a rate of $\sim 10^{3}$ --- $10^4~\rm{sky}^{-1}~\rm{day}^{-1}$. We suggest that fast radio bursts can be produced by the collisions between neutron stars and asteroids. This model can naturally explain the millisecond duration of fast radio bursts. The energetics and event rate can also be safely accounted for. Fast radio bursts thus may …
We estimate the size of a primordial black hole exploding today via a white hole transition, and the power in the resulting explosion, using a simple model. We point out that Fast Radio Bursts, strong signals with millisecond duration, probably extragalactic and having unknown source, have wavelength not far from the expected size of the exploding hole. We also discuss the possible higher energy components of the signal.
Physical constraints on the sources of fast radio bursts are few, and therefore viable theoretical models are many. However, no one model can match all the available observational characteristics, meaning that these radio bursts remain one of the most mysterious phenomena in astrophysics.
Fast radio bursts (FRBs) are bright milliseconds radio transients with large dispersion measures. Recently, FRB 200428 was detected in temporal coincidence with a hard X-ray flare from the Galactic magnetar SGR 1935+2154, which supports that at least some FRBs are from magnetar activity. Interestingly, a portion of X-ray flares from magnetar XTE J1810-197 and the Sun are also accompanied by radio bursts. Many features of Galactic FRB 200428 and cosmological FRBs resemble solar radio bursts. However, a common physical origin among FRBs, magnetar radio pulses and solar radio bursts has not yet b…
Properties of the population of millisecond extragalactic radio bursts discovered by Thornton et al. (2013) are in good correspondence with the hypothesis that such events are related to hyperflares of magnetars, as was proposed by us after the first observation of an extragalactic millisecond radio burst by Lorimer et al. (2007). We also point that some of multiple millisecond radio bursts from M31 discovered by Rubio-Herrera et al. (2013) also can be related to weaker magnetar bursts.
Highly beamed, short-duration electromagnetic bursts could be produced by superconducting cosmic string (SCS) loops oscillating in cosmic magnetic fields. We demonstrated that the basic characteristics of SCS bursts such as the electromagnetic frequency and the energy release could be consistently exhibited in the recently discovered fast radio bursts (FRBs). Moreover, it is first showed that the redshift distribution of the FRBs can also be well accounted for by the SCS burst model. Such agreements between the FRBs and SCS bursts suggest that the FRBs could originate from SCS bursts and thus …
Recently, one fast radio burst, FRB 200428, was detected from the Galactic magnetar SGR J1935+2154 during one X-ray burst. This suggests that magnetars can make FRBs. On the other hand, the majority of X-ray bursts from SGR J1935+2154 are not associated with FRBs. One possible reason for such rarity of FRB-SGR-burst associations is that the FRB emission is much more narrowly beamed than the SGR burst emission. If such an interpretation is correct, one would expect to detect radio bursts with viewing angles somewhat outside the narrow emission beam. These "slow" radio bursts (SRBs) would have b…
Fast radio bursts were discovered just over a decade ago, and their origin remains a mystery. Despite this, astronomers have been using them to investigate the matter through which their bright, impulsive radiation travels.
To date, one repeating and many apparently non-repeating fast radio bursts have been detected. This dichotomy has driven discussions about whether fast radio bursts stem from a single population of sources or two or more different populations. Here we present the arguments for and against.
Fast radio bursts are bright, millisecond-scale radio flashes of yet unknown physical origin. Recently, their extragalactic nature has been demonstrated and an increasing number of the sources have been found to repeat. Young, highly magnetized, isolated neutron stars - magnetars - have been suggested as the most promising candidates for fast radio burst progenitors owing to their energetics and high X-ray flaring activity. Here we report the detection with the Konus-Wind of a hard X-ray event of April 28, 2020, temporarily coincident with a bright, two-peak radio burst from the Galactic magne…
Recent observations of short gamma-ray bursts (SGRBs) suggest that binary neutron star (NS) mergers can create highly magnetised, millisecond NSs. Sharp cut-offs in X-ray afterglow plateaus of some SGRBs hint at the gravitational collapse of these remnant NSs to black holes. The collapse of such `supramassive' NSs also describes the blitzar model, a leading candidate for the progenitors of fast radio bursts (FRBs). The observation of an FRB associated with an SGRB would provide compelling evidence for the blitzar model and the binary NS merger scenario of SGRBs, and lead to interesting constra…
We argue that the localization of the Repeating FRB at $\sim 1$ Gpc excludes rotationally-powered type of radio emission (e.g., analogues of Crab's giant pulses coming from very young energetic pulsars) as the origin of FRBs.
We report the discovery of a new fast radio burst (FRB), FRB~010312, in archival data from a 1.4\,GHz survey of the Magellanic Clouds using the multibeam receiver on the Parkes 64\,m-diameter radio telescope. These data sets include the Lorimer burst (FRB~010724), which it pre-dates and which we also re-detect. The new burst has a much higher dispersion measure of 1187\,cm$^{-3}$pc. The burst is one of the broadest found to date, the second earliest FRB known, and the ninth FRB discovered with a dispersion measure larger than 1000\,cm$^{-3}\,$pc. Our discovery indicates that there are likely t…
Rotation-powered pulsars and magnetars are two different observational manifestations of neutron stars: rotation powered pulsars are rapidly spinning objects that are mostly observed as pulsating radio sources, while magnetars, neutron stars with the highest known magnetic fields, often emit short-duration X-ray bursts. Here we report simultaneous observations of the high-magnetic-field radio pulsar PSR J1119-6127 at X-ray, with XMM-Newton & NuSTAR, and at radio energies with Parkes radio telescope, during a period of magnetar-like bursts. The rotationally powered radio emission shuts off coin…
The mechanism that produces fast radio burst (FRB) emission is poorly understood. Targeted monitoring of repeating FRB sources provides the opportunity to fully characterize the emission properties in a manner impossible with one-off bursts. Here, we report observations of the source of FRB 20201124A, with the Australian Square Kilometre Array Pathfinder (ASKAP) and the ultra-wideband low (UWL) receiver at the Parkes 64-m radio telescope (Murriyang). The source entered a period of emitting bright bursts during early 2021 April. We have detected 16 bursts from this source. One of the bursts det…
We undertook coordinated campaigns with the Green Bank, Effelsberg, and Arecibo radio telescopes during Chandra X-ray Observatory and XMM-Newton observations of the repeating fast radio burst FRB 121102 to search for simultaneous radio and X-ray bursts. We find 12 radio bursts from FRB 121102 during 70 ks total of X-ray observations. We detect no X-ray photons at the times of radio bursts from FRB 121102 and further detect no X-ray bursts above the measured background at any time. We place a 5$σ$ upper limit of $3\times10^{-11}$ erg cm$^{-2}$ on the 0.5--10 keV fluence for X-ray bursts at the …
The first repeating fast radio burst (FRB), FRB 121102, was found to be associated with a spatially coincident, persistent nonthermal radio source, but the origin of the persistent emission remains unknown. In this paper, we propose that the persistent emission is produced via synchrotron-heating process by multiple bursts of FRB 121102 in a self-absorbed synchrotron nebula. As a population of bursts of the repeating FRB absorbed by the synchrotron nebula, the energy distribution of electrons in the nebula will change significantly. As a result, the spectrum of the nebula will show a hump stea…
We investigate the intrinsic properties of a sample of bright (E_iso > 10^52 erg) gamma-ray bursts, comparing those with and without radio afterglows. We find that the sample of bursts with no radio afterglows has a significantly shorter mean intrinsic duration of the prompt gamma-ray radiation, and the distribution of this duration is significantly different from those bursts with a radio afterglow. Although the sample with no radio afterglow has on average lower isotropic energy, the lack of radio afterglow does not appear to be a result of simply energetics of the burst, but a reflection of…
It is suggested that fast radio bursts can probe gravitational lensing by clumpy dark matter objects that range in mass from $10^{-3}M_{\odot}$ to $10^2 M_{\odot}$. They may provide a more sensitive probe than observations of lensing of objects in the Magellanic Clouds, and could find or rule out clumpy dark matter with an extended mass spectrum.
Fast radio burst (FRBs) are an exciting class of bright, extragalactic, millisecond radio transients. The recent development of large field-of-view (FOV) radio telescopes has caused a rapid rise in the number of identified single burst and repeating FRBs. This has allowed for the extensive multi-wavelength follow-up to search for the potential counterparts predicted by theoretical models. New observations of similar radio transients in Galactic magnetars like SGR 1935+2154 have continued to motivate the search for rapid optical and very-high-energy (VHE, >100 GeV) counterparts. Since 2016 VERI…
A bright wideband radio burst from the isolated neutron star 2XMM J104608.7$-$594306
The University of Manchester（曼彻斯特大学）；The University of Oxford（牛津大学）；ASTRON, the Netherlands Institute for Radio Astronomy（荷兰射电天文研究所）；Anton Pannekoek Institute, University of Amsterdam（阿姆斯特丹大学安东·潘内科克研究所）；Sydney Institute for Astronomy, School of Physics, The University of Sydney（悉尼大学物理学院天体物理学研究所）；ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav)（引力波发现卓越研究中心）
More than a decade after their discovery, astronomical Fast Radio Bursts remain enigmatic. They are known to occur at "cosmological" distances, implying large energy and radiated power, extraordinarily high brightness and coherent emission. Yet their source objects, the means by which energy is released and their radiation processes remain unknown. This review is organized around these unanswered questions.
We explore the possibility that radio loud gamma-ray bursts (GRBs) result from the collapse of massive stars in interacting binary systems, while radio quiet GRBs are produced by the collapse of single massive stars. A binary collapsar system can have the necessary angular momentum and energy budget to explain the longer prompt gamma-ray durations and higher isotropic energies seen in the the radio loud sub-sample of long GRBs. Additionally binary systems can lead to rich and extended circumstellar environments that allow for the presence of the long-lived radio afterglows seen in the radio lo…
Fast radio bursts are mysterious transient sources likely located at cosmological distances. The derived brightness temperatures exceed by many orders of magnitude the self-absorption limit of incoherent synchrotron radiation, implying the operation of a coherent emission process. We propose a radiation mechanism for fast radio bursts where the emission arises from collisionless Bremsstrahlung in strong plasma turbulence excited by relativistic electron beams. We discuss possible astrophysical scenarios in which this process might operate. The emitting region is a turbulent plasma hit by a rel…
The CHIME/FRB collaboration recently reported the detection of a 16 day periodicity in the arrival times of radio bursts from FRB 180916.J0158+65. We study the possibility that the observed periodicity arises from free precession of a magnetized neutron star, and put constraints on different components of the star's magnetic fields. Using a simple geometric model, where radio bursts are emitted from a rotating neutron star magnetosphere, we show that the emission pattern as a function of time can match that observed from FRB 180916.J0158+65.
A number of different classes of potentially extra-terrestrial bursts of radio emission have been observed in surveys with the Parkes 64m radio telescope, including "Rotating Radio Transients", the "Lorimer burst" and "perytons". Rotating Radio Transients are radio pulsars which are best detectable in single-pulse searches. The Lorimer burst is a highly dispersed isolated radio burst with properties suggestive of extragalactic origin. Perytons share the frequency-swept nature of the Rotating Radio Transients and Lorimer burst, but unlike these events appear in all thirteen beams of the Parkes …
Popular models of repeating Fast Radio Bursts (and perhaps of all Fast Radio Bursts) involve neutron stars because of their high rotational or magnetostatic energy densities. These models take one of two forms: giant but rare pulsar-like pulses like those of Rotating RAdio Transients and outbursts like those of Soft Gamma Repeaters. Here I collate the evidence, recently strengthened, against these models, including the absence of Galactic micro-FRB, and attribute the 16 day periodicity of FRB 180916.J0158+65 to the precession of a jet produced by a massive black hole's accretion disc.
The recent discovery of a Mega-Jansky radio burst occurring simultaneously with short X-ray bursts from the Galactic magnetar (strongly magnetized neutron star (NS)) SGR 1935+2154 is a smoking gun for the hypothesis that some cosmological fast radio bursts (FRBs) arise from magnetar bursts. We argue that the X-ray bursts with high temperature $T \gtrsim 30$ keV entail an electron--positron ($e^{\pm}$) outflow from a trapped--expanding fireball, polluting the NS magnetosphere before the FRB emission. The $e^{\pm}$ outflow is opaque to FRB photons, and is strongly Compton-dragged by the X-ray bu…
Fast radio bursts (FRBs) are millisecond-duration, bright radio signals (fluence $\mathrm{0.1 - 100\,Jy\,ms}$) emitted from extragalactic sources of unknown physical origin. The recent CHIME/FRB and STARE2 detection of an extremely bright (fluence $\sim$MJy$\,$ms) radio burst from the Galactic magnetar SGR~1935$+$2154 supports the hypothesis that (at least some) FRBs are emitted by magnetars at cosmological distances. In follow-up observations totalling 522.7$\,$hrs on source, we detect two bright radio bursts with fluences of $112\pm22\mathrm{\,Jy\,ms}$ and $24\pm5\mathrm{\,Jy\,ms}$, respecti…
We study the statistical properties of the soft gamma repeater SGR 1935+2154. We find that the cumulative distributions of duration, waiting time, fluence and flux can be well fitted by bent power law. In addition, the probability density functions of fluctuations of duration, waiting time, fluence and flux well follow the Tsallis $q$-Gaussian distribution. The $q$ values keep steady for different temporal scale intervals, indicating a scale-invariant structure of the bursts. Those features are very similar to the property of the repeating fast radio burst FRB 121102, indicating the underlying…
We report the results of the rapid follow-up observations of gamma-ray bursts (GRBs) detected by the Fermi satellite to search for associated fast radio bursts. The observations were conducted with the Australian Square Kilometre Array Pathfinder at frequencies from 1.2-1.4 GHz. A set of 20 bursts, of which four were short GRBs, were followed up with a typical latency of about one minute, for a duration of up to 11 hours after the burst. The data was searched using 4096 dispersion measure trials up to a maximum dispersion measure of 3763 pc cm$^{-3}$, and for pulse widths $w$ over a range of d…
We report on the lowest-frequency detection to date of three bursts from the fast radio burst FRB 180916, observed at 328 MHz with the Sardinia Radio Telescope (SRT). The SRT observed the periodic repeater FRB 180916 for five days from 2020 February 20 to 24 during a time interval of active radio bursting, and detected the three bursts during the first hour of observations; no more bursts were detected during the remaining ~ 30 hours. Simultaneous SRT observations at 1548 MHz did not detect any bursts. Burst fluences are in the range 37 to 13 Jy ms. No relevant scattering is observed for these…
A fireball of radiation plasma created near the surface of a neutron star (NS) expands under its own pressure along magnetic field lines, and produces photon emission and relativistic matter outflow. We comprehensively classify the expanding fireball evolution into five cases and obtain the photospheric luminosity and the kinetic energy of the outflow, taking into account key processes; lateral diffusion of photons escaping from a magnetic flux tube, effects of strong magnetic field, baryon loading from the NS surface, and radiative acceleration via cyclotron resonant scattering, some of which…
Fast radio bursts (FRBs) are recently discovered mysterious single pulses of radio emission, mostly coming from cosmological distances ($\sim 1$ Gpc). Their short duration, $\sim 1$ ms, and large luminosity evidence coherent emission. I review the basic physics of coherent emission mechanisms proposed for FRBs. In particular, I discuss the curvature emission of bunches, the synchrotron maser, and the emission of radio waves by variable currents in the course of magnetic reconnection. Special attention is paid to magnetar flares as the most promising sources of FRBs. Non-linear effects are outl…
Assuming: fast radio bursts (FRBs) are produced by neutron stars at cosmological distances; FRB rate tracks core-collapse supernova rate; and all FRBs repeat with a universal energy distribution function (EDF) dN/dE ~ E^(-beta) with a high-end cutoff at burst energy E_max. We find that observations so far are consistent with a universal EDF with a power-law index 1.5 < beta < 2.2, high-end cutoff E_max/E_0 > 30 and normalization N_0 < 2 per day; where N_0 is the integrated rate above the reference burst energy E_0 = 1.2e39 f_r^(-1) erg (f_r is the radio emission efficiency). Implications of su…
