Fast Radio Bursts: An Extragalactic Enigma
James M. Cordes, Shami Chatterjee
TL;DR
Fast Radio Bursts are extragalactic millisecond radio signals occurring at a high rate, with diverse source models and potential for new discoveries through upcoming telescopes, offering insights into cosmic environments and matter.
Contribution
This paper provides a comprehensive review of FRB phenomenology, models, host galaxies, and propagation effects, highlighting recent advances and future prospects in the field.
Findings
FRBs are confirmed as an extragalactic phenomenon.
Few sources are known to repeat, but all may be repeaters.
FRBs can trace cosmic environments and matter distribution.
Abstract
We summarize our understanding of millisecond radio bursts from an extragalactic population of sources. FRBs occur at an extraordinary rate, thousands per day over the entire sky with radiation energy densities at the source about ten billion times larger than those from Galactic pulsars. We survey FRB phenomenology, source models and host galaxies, coherent radiation models, and the role of plasma propagation effects in burst detection. The FRB field is guaranteed to be exciting: new telescopes will expand the sample from the current ~80 unique burst sources (and a few secure localizations and redshifts) to thousands, with burst localizations that enable host-galaxy redshifts emerging directly from interferometric surveys. * FRBs are now established as an extragalactic phenomenon. * Only a few sources are known to repeat. Despite the failure to redetect other FRBs, they are not…
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Figure 18| Telescope/Survey | (note a) | References | |||
| (deg2 h) | (sky-1 day-1) | ||||
| Parkes / allb | 19 | Bhandari et al. (2018) | |||
| Parkes / HTRU(h) | 1549 | 9 | Thornton et al. (2013), | ||
| Champion et al. (2016) | |||||
| Parkes / HTRU(m) | 694 | 0 | Petroff et al. (2014) | ||
| Parkes / SUPERB | 1621 | 5 | Bhandari et al. (2018) | ||
| Keane et al. (2018) | |||||
| Arecibo/PALFAc | |||||
| Outer Galaxy | Spitler et al. (2014) | ||||
| Main beam | 6.2 | 1 | (FRB 121102) | ||
| Sidelobes | 29.7 | 1 | (FRB 121102) | ||
| Outer+inner Galaxy | Scholz et al. (2016) | ||||
| Main beam | 19.5 | 1 | (FRB 121102) | ||
| Sidelobes | 93 | 1 | (FRB 121102) | ||
| Outer+inner Galaxy | Patel et al. (2018) | ||||
| Main beam | 12.7 | 1 | (FRB 141113) | ||
| Sidelobes | 60 | 1 | (FRB 141113) | ||
| ASKAP/Fly’s Eye | 29.2 | 20 | Shannon et al. (2018) |
| Telescope/Survey | References | ||||
| (deg2 h) | (sky-1 day-1) | ||||
| LOFAR/ARTEMISa | 0 | Karastergiou et al. (2015) | |||
| 0.145 GHz | |||||
| GBT/GBNCCb | 580 | 0 | Chawla et al. (2017) | ||
| 0.35 GHz | |||||
| UTMOST | 11 | 3 | Caleb et al. (2016) | ||
| 0.84 GHz | |||||
| CHIME | TBD | TBD | 13 | NA | CHIME/FRB Collab |
| 0.4 - 0.8 GHz | (2019a,b) |
| FRB | % Linear | % Circular | RM | DM | Reference | |
|---|---|---|---|---|---|---|
| (deg) | ||||||
| 110523 | 623 | Masui et al. 2015 | ||||
| 121102 | 560 | MJD 57747 Michilli et al. 2018 | ||||
| MJD 57991 | ||||||
| 140514 | 563 | Petroff et al. (2015a) | ||||
| 150215 | 1106 | Petroff et al. (2017a) | ||||
| 150418 | 776 | Keane et al. (2016a) | ||||
| 151230 | 960 | Caleb et al. (2018) | ||||
| 150807 | 267 | Ravi et al. (2016) | ||||
| 160102 | 2596 | Caleb et al. (2018) | ||||
| 180301 | 520 | Price et al. 2018 |
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\jvol
AA \jyear2019
Fast Radio Bursts:
An Extragalactic Enigma
James M. Cordes1 and Shami Chatterjee1
1Department of Astronomy and Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, NY 14853, USA
email: [email protected], [email protected]
Abstract
We summarize our understanding of millisecond radio bursts from an extragalactic population of sources. FRBs occur at an extraordinary rate, thousands per day over the entire sky with radiation energy densities at the source about ten billion times larger than those from Galactic pulsars. We survey FRB phenomenology, source models and host galaxies, coherent radiation models, and the role of plasma propagation effects in burst detection. The FRB field is guaranteed to be exciting: new telescopes will expand the sample from the current unique burst sources (and a few secure localizations and redshifts) to thousands, with burst localizations that enable host-galaxy redshifts emerging directly from interferometric surveys.
FRBs are now established as an extragalactic phenomenon.
Only a few sources are known to repeat. Despite the failure to redetect other FRBs, they are not inconsistent with all being repeaters.
FRB sources may be new, exotic kinds of objects or known types in extreme circumstances. Many inventive models exist, ranging from alien spacecraft to cosmic strings but those concerning compact objects and supermassive black holes have gained the most attention. A rapidly rotating magnetar is a promising explanation for FRB 121102 along with the persistent source associated with it, but alternative source models are not ruled out for it or other FRBs.
FRBs are powerful tracers of circumsource environments, ‘missing baryons’ in the IGM, and dark matter.
The relative contributions of host galaxies and the IGM to propagation effects have yet to be disentangled, so dispersion measure distances have large uncertainties.
doi:
10.1146/(TBD) … … Preprint prepared by the authors.
keywords:
transients, radio surveys, magnetars, neutron stars, extragalactic sources
††journal: Xxxx. Xxx. Xxx. Xxx.
Contents
-
3.8 Fast Transients, Brightness Temperatures, and Coherent Radiation
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4.3 Scattering in Host Galaxies, Intervening Galaxies, and the Intergalactic Medium
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5.0.1 Reduction in survey sensitivity from free-free absorption and pulse broadening
-
5.0.2 Aggregate frequency-dependent factors relevant to FRB detection
-
6.1 The Persistent Radio Counterpart Associated with FRB 121102
1 INTRODUCTION
Fast radio bursts (FRBs) are millisecond-duration pulses that originate from as-yet unidentified extragalactic sources. They are similar in some respects to pulses from Galactic radio pulsars, but the flux density is of order ten billion times larger and their spectra are radically different from most pulsar spectra and most other radio sources. To date111Up to 2019 February 1. Literature review covered up to December 1, 2018 except for early results from CHIME. bursts from over 80 distinct sources have been reported in the literature since the discovery of the first FRB Lorimer et al. (2007). Of these, multiple bursts have been detected from only a few FRB sources and only a few have secure localizations. FRB 121102, the first to be localized, is in a star-forming region in a dwarf galaxy with a luminosity distance of about one Gpc.
The nature of FRBs and their sources are thus first and foremost a bona fide mystery about which we have several important clues that will likely lead soon to an understanding of the phenomenon. In addition, FRBs are also superb tools for probing the diverse media with dramatically different conditions along their lines of sight, including the immediate source environment, their host galaxies, and the cosmic web.
Short duration pulses have been known in radio astronomy since the discovery of pulsars in 1967. Recognition that their radio-frequency () dependent arrival times followed the characteristic scaling law expected for a tenuous, cold plasma was central to establishing an early distance scale for the first pulsars and the same approach has been taken for FRBs. Here is the dispersion measure, the integral of the electron density to a source at distance . Values for Galactic pulsars range from to , where the units follow from distances expressed in parsecs and electron densities in cm*-3*. Figure 1 shows FRB dynamic spectra where the dispersion delays have been retained, whereas Figures 2 and 3 show them with the delay removed.
The first FRB (Lorimer et al., 2007) showed dispersive arrival times combined with broadening by multipath scattering from small-scale fluctuations in electron density. The too-large-to-be-Galactic value of DM led to the conjecture that the source was extragalactic. FRBs viewed at high Galactic latitudes receive Galactic contributions of about compared to for the Lorimer burst (FRB 010724). However, establishing FRBs as an astrophysical phenomenon took another six years with the identification of further examples (Thornton et al., 2013), albeit from the same Parkes telescope in Australia. The discovery of a burst using the Arecibo radio telescope (Spitler et al., 2014) gave further credence to the phenomenon.
The slow acceptance of FRBs as an extragalactic phenomenon is a consequence of a rather long history of false positives, the fact that some Galactic objects, including pulsars, show a high degree of intermittency, and the idea that unmodeled HII regions (Kulkarni et al., 2014) or stars (Maoz et al., 2015) in the Milky Way might be responsible for the large measured values of DM. And, of course, radio-frequency interference (RFI) from artificial terrestrial sources can mimic dispersed pulses (Petroff et al., 2015c).
Some Galactic pulsars are sufficiently intermittent that they were discovered as single-pulse emitters and only subsequently determined to be periodic with properties otherwise identical to pulsars. They were consequently described as rotating radio transients (RRATs, McLaughlin et al., 2006). A handful of RRATs, like most FRBs, have defied redetection. However, their DM values are consistent with residence in the Milky Way, so — as the jargon currently stands — they are not FRBs. Eventually, a Galactic FRB may be identified as a very bright event that saturates radio receivers in telescopes and in telephones.
In the early days of pulsar astronomy, attempts were made to detect dispersed radio pulses from high-energy objects, such as the X-ray sources Sco X-1 and Cyg X-1 (Taylor et al., 1972). None were found and it is now understood that strong coherent radio emission does not occur in accreting X-ray sources. Later, Linscott & Erkes (1980) used a fast (sub-ms) spectrometer at Arecibo to search for bursts from the blazar M87. In this case, dispersed pulses were claimed but not confirmed by others and therefore were dismissed as RFI or artifacts of the hardware. In retrospect, given the apparent non-repeatibility of most FRBs, one wonders whether the M87 pulses were in fact real and await confirmation!
Other attempts were made at low frequencies, including work using the Molonglo telescope by Amy et al. (1989) at 0.84 GHz that detected many pulsars in hr along with considerable RFI and unclassified events in the ms range that were not obviously due to RFI. On average per 12 hr observation about one such unclassified event occurred that was “not ruled out as being of celestrial origin” (Amy et al., 1989, page 173). The threshold for this survey was -50 Jy ms for widths from 1 to 10 ms. A two-station survey at 0.27 GHz (Huguenin & Moore, 1974) was motivated by predictions that supernovae would emit narrow \mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}1 s pulses. The system had sr field of view and relied on pulse dispersion to discriminate RFI from events of celestial origin. Unfortunately none were found at levels above Jy for widths from 20 ms to 1 s. The notion that evaporating blackholes would emit narrow radio bursts (Rees, 1977) motivated several detection attempts (e.g. O’Sullivan et al., 1978) and has been referred to as a possible source class for FRBs. However, the original idea involved physics that is no longer thought applicable (M. Rees, private communication).
An early example of multimessenger astronomy involved searches for radio pulses that coincided with gravitational wave (GW) bursts from the Galactic center (Hughes & Retallack, 1973; Edwards et al., 1974, and references therein) claimed by Weber (1970). Dispersion delays between GW and radio bursts were considered in the analyses but the time resolutions were long (1 and 10 s, respectively). No GW-radio coincidences were found but astrophysical radio events were claimed to contribute to the overall results obtained by Hughes & Retallack (1973).
The role of dispersion delays between any prompt radio emission from gamma-ray bursts (Palmer, 1993) was built into response time goals and detection criteria for low-frequency observations triggered by GRB detections (e.g. Baird et al., 1975; Dessenne et al., 1996). Similar considerations about dispersion effects enter into multiwavelength/messenger studies of FRBs.
This incomplete but representative historical summary illustrates that the techniques used today for FRB studies have their precedents in long-ago experiments, albeit now with much greater sensitivity and insights into the properties of transient radio emission.
The timing of this review is at an inflection point when FRBs have been well established as an extragalactic phenomenon but there is not yet a deep understanding of the underlying astrophysics nor their population statistics. This will change with the rise of high duty cycle, wide-field surveys that are just beginning to dramatically increase the discovery rate. The review necessarily excludes insights that will emerge from these surveys and their multiwavelength followup. However, topics in fundamental astrophysics, methods, and interpretation that we discuss will hopefully have sustained relevance.
In this review we summarize what is currently known about the FRB phenomenon, the source physics that may underly them, and their potential as tools for extragalactic astrophysics and extreme physics. The following questions motivate the content and organization of this review: Do all FRB sources repeat? What is the FRB distance scale? Do all FRBs originate from the same type of object? What can FRBs be used for? And finally, where will the FRB field be in the long term (10 yr)?
2 SUMMARY OF THE FRB PHENOMENON
FRBs are found using data that are essentially the same as those used in pulsar surveys, namely high time resolution spectra () with frequency channels across a total bandwidth of hundreds of MHz. The key difference is that pulsar surveys seek periodic signals using Fourier methods, which become insensitive to periods not small compared to data spans and of course are completely insensitive to single pulses. Although individual ‘giant’ pulses from pulsars have long been a known phenomenon, from the mid-1970s on, researchers were largely focused on finding relativistic binary pulsars for tests of General Relativity and millisecond pulsars for use in pulsar timing arrays to detect nanohertz gravitational waves (with exceptions of course). Giant pulses from the Crab pulsar and a few other objects were well studied during this period (and to the present) but were considered a niche subject with ties to high-energy emission.
Attitudes changed during the 1990s because of interests in finding radio counterparts to gamma-ray bursts (GRBs) and recognition that the discovery phase space for fast transients was essentially unexplored territory. Discoveries of RRATs and FRBs followed directly from the decision to search for single pulses in pulsar survey data. In other words, FRBs were discovered because of attitude adjustment, not from technological innovation. However, followup observations of FRBs (especially localizations) have required innovations.
2.1 Numbers and Rates
To date FRBs have been detected from over 80 distinct sources in a variety of surveys (Table 1) since the original event from 2001 was reported in 2007222As of 2019 Feb 1; The FRBCAT catalog is at \http://www.frbcat.org (Petroff et al., 2016). Until recently, most FRBs were discovered predominantly at GHz, initially with the Parkes telescope followed by the first non-Parkes FRB using the Arecibo telescope, and a few detections at MHz with the Green Bank Telescope and UTMOST telescopes (Table 2). In the last year, the discovery rate has accelerated with the advent of widefield surveys using the ASKAP telescope in a “fly’s eye” mode at GHz (Shannon et al., 2018) and the CHIME cylinder array (CHIME/FRB Collaboration et al., 2018) in the 0.4 – 0.8 GHz band. The CHIME detections (CHIME/FRB Collaboration et al., 2019b, a) are the first to be found below 0.8 GHz and contrast with the non-detections of FRBs with the GBT at 0.35 GHz (Chawla et al., 2017) and LOFAR at 0.15 GHz Karastergiou et al. (2015). Burst detections are made on the basis of matched filtering (see sidebar).
{textbox}
[h]
3 Matched Filtering
Burst detection is based on the principle of matched filtering. A general model I({\bf X},{{\mbox{\boldmath\theta}}})=aA({\bf X},{\mbox{\boldmath\theta}})+N({\bf X}) comprises a signal , a design matrix of variables with dependence on a vector of parameters , a scale factor , and noise . If the noise is white, the matched filter is the signal shape, A({\bf X},{\mbox{\boldmath\theta}}). In practice, some aspects of the signal are known (e.g. dispersion delays) while burst shapes are not, requiring searches over a template bank of burst shapes. FRBs show stochastic structure that includes spectral confinement less than observing bandwidths and temporal substructure, knowledge of which can provide the basis for detection algorithms with better sensitivity.
The detection test statistic is the cross correlation function (CCF) of the template and events are found by requiring it to exceed a threshold. A Bayesian approach calculates the posterior PDF using priors and the likelihood function for the parameters a,{\mbox{\boldmath\theta}}.
Dispersed bursts have the form , where is the dispersion delay and is the shape in time and frequency. The parameters for this model are and width . The signal-to-noise ratio of the CCF maximum is or, equivalently, where is the fluence (area of ) and is the RMS noise. In some cases, the true DM differs slightly from those found by maximizing the CCF.
When sky coverage and selection effects are taken into account, the small number of bursts detected from distinct sources translates into an astoundingly large all-sky rate sky*-1* day*-1* above a 1 Jy ms fluence threshold333 1 Jy = erg cm*-2* s*-1* Hz*-1* = watts m*-2* Hz*-1*. (Thornton et al., 2013; Spitler et al., 2014; Scholz et al., 2016; Champion et al., 2016; Keane & Petroff, 2015; Oppermann et al., 2016; Lawrence et al., 2017). Although different surveys yield rates that vary by about an order of magnitude, allowance for survey thresholds, sky coverage, and small number statistics yields general consistency. The salient point is that the FRB rate is large, about times greater than the GRB rate for FRB fluences larger than 1 Jy ms.
The Galactic latitude dependence of burst detection rates is of high interest because it would implicate propagation effects, especially interstellar scintillation, from the Milky Way’s ISM in the detectability of FRBs and estimated population sizes. However, the empirical evidence for latitude dependence is murky (Connor et al., 2016a). Early analyses suggested a deficit of mid-latitude FRBs that might be associated with the latitude dependence of interstellar scintillation (Petroff et al., 2014; Macquart & Johnston, 2015), which can more favorably enhance high-latitude detections. More recent analyses corroborate or assume a latitude dependence (Lawrence et al., 2017; Macquart & Ekers, 2018b) while Bhandari et al. (2018) argue against it. This debate is based largely on studies of less than 20 objects from heterogeneous surveys. FRBs detected in directions through the Galactic plane do not seem to imply a low-latitude deficit. The repeating FRB 121102 (Spitler et al., 2014) and a new candidate FRB 141113 (Patel et al., 2018) were both found in the deep Arecibo pulsar survey (PALFA) covering a small field at low latitudes in the Galactic anticenter direction. Detection of the latter FRB implies a large rate if it was found in the main lobe of the telescope beam, or a factor of smaller rate if instead the burst was found in a sidelobe. Interstellar scintillation and other selection effects are discussed in Section 4.
Recently, a shallow “fly’s eye” survey with very wide angular coverage using the ASKAP telescope yielded 20 large-amplitude bursts at 1.3 GHz, implying a rate sky*-1* day*-1* (Shannon et al., 2018). The survey’s narrow range of Galactic latitudes, , minimized any latitude dependence as a factor in survey results. Comparison with deeper surveys and application of a test both indicate a steep fluence dependence of the rate, . This contrasts with other studies that indicate shallower dependences, (Vedantham et al., 2016a) based on a heterogeneous set of bursts, but is consistent with the analysis of Luo et al. (2018). As with the latitude dependence, knowledge of the rate’s dependence on fluence is currently limited by small samples of bursts whose positions within the telescope beam at the time of discovery are not known, leading to significant uncertainties on fluences. Surveys with interferometric arrays that also localize bursts (Law et al., 2015) will resolve this issue. We note that a previous fly’s eye survey with the Allen Telescope Array using smaller antennas (5-m vs. 12-m diameter) and smaller aggregate on-sky time yielded no FRB detections (Siemion et al., 2012).
3.1 Follow-Up Observations: Trials and Tribulations
The directions of all FRBs have been searched for repeat bursts and several have been investigated in comprehensive multiwavelength observations. Followup observations from radio to -ray energies include those made as soon as possible after a radio burst detection using Astronomical Telegrams and an alert system based on VOEvents now under development (Petroff et al., 2017b). Panchromatic observations have yielded no burst detections and, apart from FRB 121102, no persistent counterparts (Palaniswamy et al., 2014; Petroff et al., 2015a; Scholz et al., 2016; Bower et al., 2018; Bhandari et al., 2018).
Several FRBs have shown repeat bursts at radio frequencies from 0.4 to 8 GHz. FRB 121102, discussed in detail in Section 6, was found to repeat (Spitler et al., 2016) about 2.5 y after its initial detection (Spitler et al., 2014), but after only 10.3 h of total on-source time.
Some FRB lines of sight have been reobserved for more than h without any redetections (e.g. Petroff et al., 2015b; Shannon et al., 2018), leading some authors to argue that most FRBs differ in physical nature from FRB 121102. If so, this would sustain the prospect that most FRBs are from one-off catastrophic events rather than from objects with persistent activity. However, if most or all FRBs ultimately repeat, the time to repeat may vary significantly between sources, particularly when amplitude distributions, scintillations and lensing, and detection thresholds are taken into account. To assess repeatability, the number of statistical trials in a large survey that yields multiple FRBs needs to be considered, and this depends on the (unknown) size of the source population in the sampled volume. The number of reobservations needed for repeat detections may be very large, especially in shallow surveys.
Consider a survey that yields bursts from distinct sources. Each of the active sources in the surveyed volume repeats with an average rate . However, no repeats are detected even though each sky position is visited times for a time per visit. The total number of detected events is . Because at most one event per source is seen in visits, we have . The number of reobservations needed on average to redetect a single source is given by . Using the survey yield, . But to have detected a single repeat from any one of the sources requires , which gives the number of repeats needed (per source) .
For the ASKAP survey (Shannon et al., 2018), , h and 17 to 1308, corresponding to 16 to 1200 h of reobservations. Using the median , the required number of reobservations to see a single repeat is . A plausible fiducial population size sampled in the ASKAP survey is . Nicholl et al. (2017), for example, estimate a population number density Gpc*-3* and the ASKAP survey may have sampled a volume of Gpc3. This implies that a much larger number of reobservations instead of the median 570 or the maximum reported by Shannon et al. (2018) is needed to expect any one of the ASKAP FRBs to have repeated in ASKAP observations.
Of course higher sensitivity telescopes can significantly reduce the time-to-redetection. From the survey, the implied burst rate per source is h*-1*, or about bursts per year, a very small rate. For a differential burst amplitude distribution for sources distributed uniformly in Euclidean space (), scaling from the ASKAP survey to the Parkes surveys and assuming detection thresholds are bracketed by the distribution’s cutoffs (), we obtain a predicted rate for Parkes observations - h*-1* (for the nominal threshold or the ‘fluence complete’ threshold, respectively), compared to a rate using the Arecibo telescope h*-1*. These rates imply roughly 30 y, 600 - 4800 h, and 15 h of reobservation between detections for the ASKAP, Parkes, and Arecibo surveys respectively. Parkes (let alone ASKAP) reobservations have not reached the required time-to-redetection values, whereas the first repeat burst from FRB 121102 was found after 10.3 h of on-source time spread over y of elapsed time in Arecibo followup observations. *The rates and repeat times estimated here are therefore consistent with sources distributed uniformly in Euclidean space that all produce multiple bursts. * The possibility that all FRBs repeat removes a major argument for the conjecture that there are multiple populations of FRBs (Palaniswamy et al., 2018).
Some caveats on these estimates are needed. First, calculated yields assume all observations are statistically independent. This is not the case if burst rates or amplitudes are variable with correlation times longer than a typical observation time . Episodic detections are expected if the correlation time is between and the total span of observations on any FRB source. This is the case for FRB 121102 but it is not yet known if rate variations are intrinsic or due to propagation effects; this is discussed further in later sections. If is the intrinsic, Poisson burst rate per source and a large modulation lasting occurring at intervals is required to produce detectable bursts, the propensity for FRBs to occur singly (except for FRB 121102) implies and the apparent burst rate is . For the repeater, during episodes lasting days is much larger than the apparent rate, signifying that some kind of modulation is active that yields a variable mean burst rate (which may or may not correspond to Poisson statistics).
3.2 Dispersion and Scattering of FRBs
The arrival times of FRBs are inversely proportional to the line-of-sight integral of the group velocity. For a magnetized plasma the leading terms in the frequency-dependent part of the arrival time are (e.g. Tanenbaum et al., 1968; Tuntsov, 2014; Suresh & Cordes, 2019)
[TABLE]
where terms are included up to second order in and linear in (where and are the electron plasma and cyclotron frequencies, respectively). Each term has an associated line-of-sight integral measure. First is the dispersion measure DM (defined previously) with standard units of . The second term includes the Faraday rotation measure with standard units of when the electron density is in cm*-3* and the parallel (to the line of sight) magnetic field is in microgauss units. The third involves the emission measure, , with standard units of . The two signs of the second term correspond to the two hands of circular polarization.
Early analyses of pulsars (Tanenbaum et al., 1968) and FRBs tested arrival times against the dispersion law and found to within one percent or better (Thornton et al., 2013; Spitler et al., 2014; Scholz et al., 2016; Champion et al., 2016; Keane & Petroff, 2015; Lawrence et al., 2017). The resulting upper limits on the and terms and the absence of free-free absorption (associated with EM) ruled out the association of FRBs with very dense plasmas (Luan & Goldreich, 2014; Tuntsov, 2014; Dennison, 2014; Katz, 2014b), such as stellar envelopes (Loeb et al., 2014). However, future observations of FRBs with large RMs may show distorted burst shapes at low frequencies GHz due to the birefringent delays for the two hands of circular polarization.
Figure 4 (left panel) shows DMs plotted against Galactic latitude for FRBs and for pulsars in the Milky Way and in the Magellanic Clouds (LMC, SMC). Two conclusions can be made from the figure. First, the DMs of all FRBs with are much larger than the outer envelope for Galactic pulsars that approximately follows a dependence. An extragalactic population of FRBs would appear just this way if the total DM includes a large extragalactic contribution. Second, the DMs of FRBs cover a total range to that is comparable to the range for pulsars (3 to 1700 ), which is clearly due to the ISM of the Galaxy and in a few cases the ISM in the Magellanic clouds. The extragalactic contributions for the smallest DMs are equal to those expected from a dwarf galaxy, as indicated by the excesses seen in Figure 4 for pulsars in the Magellanic clouds. The largest DMs are comparable to those expected from either a long path through the IGM or a galaxy disk, from a galactic center like that of the Milky Way, or from a young supernova remnant (Piro, 2016). Ionized gas in galaxies is therefore a plausible source for some or most of the extragalactic part of DM. We discuss the relative contributions to DM from host galaxies and the intergalactic medium (IGM) in Section 9.
The right-hand panel of Figure 4 addresses FRB scattering. Temporal broadening of FRBs results from small-angle scattering by electron density variations on scales much larger than a wavelength. The scattered burst shape is the convolution of the emitted burst with an asymmetric pulse broadening function , . A one-sided exponential is often used for modeling of measured pulses but is a special case for thin scattering screens that only approximates realistic broadening functions. The scattering time is a strong function of frequency, .
The figure shows scattering times scaled to 1 GHz vs. Galactic latitude for both pulsars and FRBs. Pulsar scattering times span more than ten orders of magnitude. The measured scattering times of FRBs, like their DMs, are also within the range spanned by pulsars but they are much larger than those of pulsars at similar Galactic latitudes in most cases. This too is consistent with FRB scattering occurring primarily from extragalactic gas, at least for FRBs detected so far. However, only about 30% of the detected bursts show scattering. Section 9 discusses properties of the extragalactic plasma that underly FRB scattering.
3.3 Time-Frequency Burst Structure
The earliest reported FRBs showed relatively simple temporal morphologies: Gaussian-like pulses modified in some cases by scattering broadening (Lorimer et al., 2007; Thornton et al., 2013; Spitler et al., 2014) with temporal substructure in one case (Champion et al., 2016). The present understanding is that featureless bursts are in part the outcome of the limited time resolution of post-detection dedispersion used in early surveys. Recent work enabled by coherent dedispersion of repeat pulses from FRB 121102 has revealed rich - structure that differentiates some FRB bursts from their pulsar analogs. Examples are shown in Figures 2 and 3. The - structure of FRBs is therefore substantially different from that of single pulses from pulsars, which tend to show only Galactic DISS but are otherwise continuous across a wide spectrum.
Frequency structure is best studied for the repeater FRB 121102 and is described in detail in Hessels et al. (2018). With adequate signal-to-noise ratio, bursts from several FRBs show bandlimited structures of a few hundred MHz sometimes combined with narrower frequency structure, which appears to be consistent with Galactic scintillation (DISS). The broader structure is not stable between bursts from the repeater, even changing over time separations of seconds and minutes. The broad structure appears anywhere in the 1.2 to 8 GHz frequency range used for studies of FRB 121102 though rarely in two broad receiver bands observed simultaneously (Law et al., 2017). Whether the broad structure is intrinsic to the radiation process or a post-emission propagation effect near the source (e.g. Cordes et al., 2017) is yet to be determined.
3.4 Polarization
Stokes parameters are available for a relatively small subset of FRBs (Table 3). FRBCAT (currently) gives polarization information on five FRBs, with four showing significant linear polarization ranging from 8.5% to 80% and three showing circular polarization from 3% to 23%. The repeating FRB 121102 shows 100% polarization after removing Faraday rotation and FRB 180301 has % linear polarization and % circular polarization. These mixtures of linear and circular polarization are not dissimilar from those seen from pulsars. Polarization angles rotate across some FRBs by tens of degrees (FRBs 110523 and 150418) while remaining constant in time for others to less than 20 degrees for FRBs 121102, 150215, and 150807. Pulsars generally show rotation across their pulses, often showing consistency with relativistically beamed emission from a spinning dipolar field (Backer et al., 1976). It is unclear if the position angles of FRBs indicate that the durations of FRBs are unrelated to a similar spinning radiation beam, that emission comes from non-spinning objects, or that polarization is induced as a propagation effect.
Four objects in the catalog have quoted RM values of which three are significant but only one, FRB 110523 (Masui et al., 2015), has an RM value that is consistent with arising from propagation through a host galaxy disk. The total ; only about 18 and 6 are from the Milky Way and IGM, respectively. The repeating FRB 121102 stands out by showing an extraordinarily large RM , which requires narrow frequency channels to resolve rotation of with frequency. Initial studies at GHz showed no linear polarization because of Faraday depolarization across the coarse frequency channels. Only higher frequency observations allowed the Faraday rotation to be resolved. A final case is for FRB 180301 (Price et al., 2018).
The wide range of RMs for FRBs is similar, perhaps coincidentally, to the range seen for Galactic pulsars, with the largest value (in magnitude) seen from the Galactic-center (GC) magnetar J17452900, . And perhaps not so coincidentally, the RM of both the GC magnetar and FRB 121102 have decreased in magnitude by significant amounts over periods of a few years: 5% for the magnetar (Desvignes et al., 2018) and 30% for FRB 121102 (Michilli et al., 2018, and ongoing work). For both objects the accompanying change in DM is very small ().
3.5 Localizations
As pointed out by various authors (e.g. Eftekhari et al., 2018; Vedantham et al., 2016a), sub-arcsecond localizations are required to identify host galaxies associated with FRBs at Gpc distances. Rapid multiwavelength follow-up to detect the analog of GRB afterglows has not been fruitful (e.g. Petroff et al., 2017a), and the claimed rapidly fading radio transient associated with FRB 150418 (Keane et al., 2016b) was shown instead to be common AGN variability (e.g. Williams & Berger, 2016). In fact, multiwavelength observations that were simultaneous with burst detections from FRB 121102 have led to upper limits on high energy and optical emission associated with the bursts (Scholz et al., 2017; Acciari et al., 2018).
The only reliable method so far is direct interferometric localization of the burst itself, as demonstrated for FRB 121102 (Chatterjee et al., 2017; Marcote et al., 2017). But for FRBs with small extragalactic contributions to their DMs, the number of candidate host galaxies in the error circles with large diameters (e.g. multiple arc minutes) may be small enough for identification of the FRB’s host (see, e.g. Mahony et al., 2018).
3.6 Energetics
With peak flux densities similar to those of pulsars, FRBs originating from Gpc distances compared to kpc pulsar distances imply energy densities at the source and total burst energies that are larger by factors to . For a flux density in a bandwidth , the energy density scaled to a distance from the source is
[TABLE]
The equivalent magnetic energy requires a field strength,
[TABLE]
that would be encountered, for example, at a distance from a magnetar with a surface field G and radius cm,
[TABLE]
Expressed in terms of the velocity of light cylinder radius of a spinning object with period ,
[TABLE]
To match or exceed the radiation energy density with a particle energy density , electrons would have to be highly relativistic even with a large electron density. For example, a Lorentz factor (with ) requires an electron density cm*-3* for the same parameters as in the above equations. The single-particle or particle-bunch radiation is therefore highly beamed into a solid angle . However, the total solid angle for an FRB is much larger than this because bursts are incoherent sums of many individual coherent units of radiation (Cordes & Wasserman, 2016).
Isotropic emission implies a total emitted energy obtained by integrating over a spherical shell of thickness . Correcting for the beaming solid angle gives the burst energy Small beam solid angles can therefore substantially alter burst energies.
3.7 Are Bursts From Rotation, or Temporal Modulation?
If a rotating beam causes observed burst widths with duty cycle , the beam solid angle (in units of ) satisfies . Small duty cycles imply , thus reducing energetic requirements for a burst. For this to be the case, pulse widths ms require the spin period to exceed to reduce the solid angle significantly. The total radiated energy also depends on the duration of radiation in the rotating beam. To avoid seeing multiple, periodic bursts, the duration must be less than a spin period, as for the repeating FRBs, indicating that there is substantial modulation of coherent radiation in the rotating frame. This also suggests that the observed burst durations themselves may be from temporal modulation rather than from a rotating beam. In this case, the beam solid angle cannot be constrained directly from observations.
3.8 Fast Transients, Brightness Temperatures, and Coherent Radiation
The radiation brightness temperature is often used to characterize radio emission from astrophysical objects and it is particularly useful for distinguishing incoherent and coherent emission. It is the effective blackbody temperature based on the Rayleigh-Jeans portion of the Planck spectrum , where is Boltzmann’s constant and is the wavelength. For a transient burst of duration and peak flux density , the specific intenisty is where is the observed solid angle of the source. A burst source of size at distance subtends , giving a brightness temperature . A 1 Jy FRB of millisecond duration yields K, compared to K for a Galactic pulsar at a kpc distance.
Thermal sources (stars, HII regions) yield brightness temperatures equal to their physical temperatures. Non-thermal but incoherent emission such as synchrotron emission from active galactic nuclei (AGNs) yields as large as K indicating electron energies MeV. AGN radio emission is limited to about this brightness temperature by inverse Compton scattering.
Figure 5 shows the location of FRBs in the phase space for radio transients with a luminosity-like quantity444 is usefully called the pseudo luminosity in pulsar contexts to emphasize that the measured flux density is influenced by both the angular width of the beam and its direction with respect to the line of sight. in Jy kpc2 plotted against the dimensionless duration in gigahertz-seconds; these axes allow lines of constant brightness temperature to be drawn. The region of coherent sources is designated to the left of the K line that represents the approximate synchrotron-self-Compton limit for AGNs.
FRBs and pulses from pulsars necessarily involve coherent radiation and display propagation effects, including dispersive propagation, as described above, and DISS — the analog to optical scintillation of stars due to turbulence in Earth’s atmosphere — caused by turbulence in the interstellar electron density. Dispersion and scintillation are co-features because coherent sources are typically compact, allowing radiation to have short-enough durations to show dispersive propagation as well as scintillations555Interstellar scintillation requires sources to be more compact than a critical (isoplanatic) angle in the same way that stars twinkle but planets do not, typically. Instead, pulsars and FRBs scintillate, but AGNs do not.. Coherent radiation mechanisms involve large numbers of particles () emitting with a distinct phase relationship, yielding collective power rather than for incoherent radiation. This can be through an antenna type mechanism with charge bunching in coordinate space or through a plasma maser involving a non-monotonic charge distribution in momentum space.
The signal processing of fast transients includes dedispersion that removes frequency-dependent delays to improve burst detection probabilities and to potentially restore bursts to their emitted shapes. Two dedispersion algorithms are used. The first, ‘post-detection’ dedispersion, is approximate and shifts intensities by the dispersion delay for the center frequency of each channel of a digital filterbank. The best time resolution obtainable with this method at GHz is for (Cordes & McLaughlin, 2003), which is insufficient for probing burst time structure. The second method is coherent dedispersion (Hankins & Rickett, 1975) that applies an exact matched filter to ‘voltage’ data proportional to sampled electric fields. It corrects the phase factor imposed by propagation and can provide sub-microsecond resolution.
4 THE ASTRO-OPTICS OF FRBs
The detectability of FRBs and their observed properties are strongly affected by propagation through intervening plasmas and mass assemblies. We summarize propagation phenomena that affect FRB surveys and also how they can be used to probe FRB sources, their environments, and the IGM, including dark matter.
4.1 Galactic Propagation
Electron density variations in the ionized ISM cause three important effects: angular broadening (‘seeing’), pulse broadening due to angular broadening, and intensity scintillations from both refraction and diffraction. Length scales smaller than the Fresnel scale km diffract radiation while refraction, caustics, and multiple images from larger scales can strengthen and dim bursts and affect arrival times. For reviews see Rickett (1990); Narayan (1992).
An extragalactic burst viewed through the Galaxy’s ISM is broadened into an angular diameter and temporally smeared by , where is the distance of the scattering layer from the observer, approximately the Galactic scale height kpc of free electrons. The upper envelope of values and the latitude dependence of in Figure 4 correspond to a Galactic seeing diameter, , where the exponents are for a medium with a Kolmogorov wavenumber spectrum for . Galactic seeing is important for any gravitational ‘nanolensing’ of FRBs (e.g. Eichler, 2017) because it may exceed the Einstein radius for dark-matter objects and contaminate gravitational time delays.
Intensity scintillations (DISS) are correlated over a bandwidth related to by an ‘uncertainty’ relation (Cordes & Rickett, 1998; Lambert & Rickett, 1999). These scintillations are accompanied by refractive scintillation (RISS), though typically DISS is more important. In the strong scintillation regime where , DISS is 100% modulated with an exponential gain PDF, where is the Heaviside function (0 for , 1 otherwise).
4.2 Propagation Model for Bursts
The simplest model for an individual burst relates the emitted (pseudo) luminosity to the measured flux density using the distance , a propagation modulation , and a composite delay primarily from dispersion, scattering, and refraction,
[TABLE]
Many of the observed properties of FRBs are likely a combination of the intrinsic (to the source) and the extrinsic but their relative contributions have not yet been disentangled satisfactorily. The modulation has both short term and long term contributions from Galactic DISS (minutes to hours) and Galactic RISS (hours to months), respectively. Plasma lensing in host galaxies and gravitational microlensing will have similarly long time scales. The episodic bursting of FRB 121102 is naturally explained if bursts are heavily modulated by even if is a process with fixed mean rate (Poissonian or otherwise). Variability of the the total delay could potentially account for the observed aperiodicity for a source that is intrinsically periodic. Of course these features might also be intrinsic.
4.3 Scattering in Host Galaxies, Intervening Galaxies, and the Intergalactic Medium
The broadening times measured for FRBs (figure 4) are extragalactic and highly likely to be from scattering in host galaxies. However there is debate about the relative roles of host-galaxy scattering and contributions from the IGM (e.g. Macquart & Koay, 2013; Luan & Goldreich, 2014; Cordes et al., 2016; Xu & Zhang, 2016). Scattering near FRB sources yields a broadening time , where is the scale height or source-scattering layer distance and is the range of angles over which radiation is scattered. However, the scattering diameter seen by an observer is much smaller (and typically unmeasureable), , where is the source-observer distance.
Intervening galaxies are likely only for z\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}1. They will contribute to the total DM (perhaps modestly) but may broaden bursts by scattering by large amounts because of the long path lengths. The Euclidean expression holds in flat CDM space where , and are angular diameter distances; increases by a factor of while decreases by (for a plasma). The seeing disk diameter for a face-on Milky Way galaxy will be mas, giving a very large scattering time for distances in Gpc that will render undetectable all but the strongest bursts.
In principle the IGM can contribute to the scattering of FRBs if long path lengths compensate for the tenuous electron density. The scattering time per unit length depends on the square of the electron density and thus with a proportionality constant dependent on the length scales of density fluctuations and on the filling factor of larger-scale density concentrations. Luan & Goldreich (2014) and Macquart & Koay (2013) argue that the diffuse IGM has properties that yield negligible scattering. This conclusion is consistent with the lack of any obvious correlation of the scattering time with the extragalactic DM (Cordes et al., 2016, see also Section 7.3).
IGM structures including Lyman- clouds, damped Ly- systems, and intracluster media will have larger electron densities, different filling factors, and smaller length scales than the diffuse IGM, so scattering in those regions may be significant (Macquart & Koay, 2013) (but see Prochaska & Neeleman, 2018). At present there is no evidence for scattering from such regions. In fact, for a few FRBs, fine scale spectral structure is consistent with Galactic DISS and requires that the extragalactic scattering originate from near the FRB source (within a galaxy radius) (e.g. Masui et al., 2015).
4.4 Propagation Factors that Affect FRB Detections
The amplitudes of bursts may be influenced strongly by lensing, scintillation, and absorption. Such effects need to be considered in analyses of both surveys and follow-up observations.
4.4.1 Scintillation modulations and quenching
DISS typically reduces the burst amplitude but occasionally can boost it by a large amount for large, less probable gains on the tail of the exponential distribution, . The role of such modulations in burst detections (or missed detections) depends on the number of statistical trials in an FRB survey. This in turn depends on the size of the burst source population and the number of bursts emitted per source. If many trials are done, detected bursts may have been boosted significantly by DISS (or lensing, as discussed below), with the corallary that repeat bursts will also have low probability.
{textbox}
[h]
5 Scintillation Source Size Requirements
DISS has extraordinary resolving power because it is quenched for sources larger than about a microarcsecond. Waves from a source of angular size have a coherence length on a Galactic scattering screen. The coherence length must exceed the patch size on the screen that contributes to measured flux densities, or . For Galactic scattering with kpc and mas the isoplanatic angle is . Pulsars easily satisfy this constraint as do FRBs, which are intrinsically smaller in angular size by a factor given their millisecond durations and gigaparsec distances. However, scattering in host or intervening galaxies reduces the coherence length and can quench scintillations. Let and be the scattering diameters produced by extragalactic and Galactic screens at distances and from the source and observer, respectively, and the corresponding broadening times; then the requirement becomes (for in GHz, in kpc, and in Gpc),
[TABLE]
Host-galaxy scattering can also quench gravitational microlensing, as discussed in § 8.
However, DISS modulations are reduced if observations are made with bandwidths much larger than their correlation bandwidth or if the effective source size is larger than a critical amount. A finite bandwidth () reduces the RMS modulation of from unity to for a correlation bandwidth . Figure 6 (left panel) shows the correlation bandwidth for a few frequencies vs. Galactic latitude, demonstrating that plummets to very small values at low latitudes and that DISS is largely quenched (for large observing bandwidths), disallowing large scintillation boosts.
Similarly, a finite source size reduces the modulation to , where is a critical (isoplanatic) angular scale (see the sidebar titled Scintillation Source Size Requirements). Sources of millisecond bursts are necessarily small enough to show fully modulated, Galactic DISS. However any extragalactic scattering can make the apparent size larger than and thus quench DISS. In a few cases, Galactic DISS has been identified in FRB spectra, indicating that the extragalactic scattering also seen must occur in or near their host galaxies (Masui et al., 2015; Ravi et al., 2016; Gajjar et al., 2018; Spitler et al., 2018). Figure 6 (right panel) shows the distance constraints on a scattering screen in order for DISS to be manifest. The occurrence of Galactic DISS is therefore a useful probe of the host galaxies and environments of FRB sources.
5.0.1 Reduction in survey sensitivity from free-free absorption and pulse broadening
Dispersing and scattering electrons will also absorb FRBs. Apart from directions through the inner Galaxy at low frequencies, free-free absorption will only be important for any dense gas in host galaxies and for low frequency observations (\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}300 MHz). The emission measure is related to the DM and path length of the host along with parameters and that quantify electron density fluctuations (Cordes et al., 2016),
[TABLE]
corresponding to an optical depth (Draine, 2011)
[TABLE]
While negligible at 1 GHz for the nominal , the optical depth can exceed unity for larger host-galaxy DMs and lower frequencies. Free-free absorption may therefore affect detection rates of low-frequency surveys and may provide an additional probe of source environments.
Pulse broadening, when either or is comparable or larger than the intrinsic burst width , reduces detection numbers in surveys. It conserves fluence, so the matched-filter output amplitude is reduced by a factor,
[TABLE]
The scattering time and intrinsic width are implicitly frequency dependent and is strongly direction dependent, as implied in Figure 6 and using . The scattering factor undoubtedly plays a prominent role in low-frequency ( GHz) surveys and surveys of the inner Galaxy at low latitudes.
5.0.2 Aggregate frequency-dependent factors relevant to FRB detection
Figure 7 presents the aggregate effects from propagation of FRBs through ionized gas as a function of frequency. The left panel shows bandwidth and source-size quenching. The bandwidth reduction factor in the upper frame is evaluated for six different directions and for 10% receiver bandwidths. The bottom frame shows the source-size reduction factor caused by extragalactic scattering. The pulse-broadening time due to scattering is held fixed to ms at 1.5 GHz and scales as and the apparent angular size of the source is calculated assuming a 10 kpc separation of the scattering region and source. The conclusion is that if Galactic DISS is important in survey detections of FRBs, by either boosting or suppressing burst amplitudes, it will be much less important (if not negligible) at low frequencies. Suppression of FRB amplitudes is shown in the right panel of Figure 7. The top frame shows the suppression factor due to pulse broadening for four values of the ratio referenced to 1 GHz. Suppression of the signal-to-noise ratio occurs at low frequencies even if scattering is not evident at 1 GHz. The bottom frame shows the attentuation from free-free absorption , that can, but need not, be important at low frequencies.
5.0.3 Plasma and gravitational lensing
Refraction and especially lensing from discrete structures causes multiple imaging from the Crab pulsar (Graham Smith et al., 2011), strong enhancements of pulse amplitudes from the bow shock produced by a millisecond pulsar (Main et al., 2018), fringes in the dynamic spectra of pulsars (Wolszczan & Cordes, 1987), and events in the radio light curves of AGNs (Fiedler et al., 1987; Bannister et al., 2016). The strongly episodic burst detections from the repeating FRB 121102 may be explained most easily from plasma lensing and the overall detection rate could also be affected. Plasma lensing involves diverging or converging rays from refraction by electron density enhancements or deficits, respectively. These can produce strong dimming or large amplifications from caustics along with arrival time and DM variations (Cordes et al., 2017). See also Katz (2014b).
A Gaussian lens with a dispersion measure profile \rm DM$$(x)=\rm DM_{\ell}$$e^{-x^{2}/a^{2}} produces multiple images and caustics for lens-observer distances larger than a a frequency-dependent focal distance . The focal distance is Gpc for a modest lens with and AU at, say, a 1 pc distance from an FRB source at 1 Gpc from the Earth. Amplifications as large as are plausible. Equivalently, caustics will be seen for frequencies less than a focal frequency GHz for the same nominal parameters.
The lens gain and the number of images are strong functions of frequency as well as observer location. The dependence of the lens gain on the observer’s location and frequency is shown in Figure 8 for a one-dimensional Gaussian lens perturbed with 10% oscillations. Numerous caustics occur in this case and the gain is strongly peaked in frequency for some observer locations while at others, the gain . The observer’s effective location can change due to motion of the source or lens (as well as the observer’s), serving as a possible explanation for the absence of bursts from the repeating FRB at some epochs.
Gravitational lensing can also amplify FRBs and impose delays between multiply imaged bursts, which may also produce interference effects in dynamic spectra. Sources with projected sizes and impact parameters much smaller than the Einstein radius, , can show double images with large amplifications for durations for an effective transverse speed . The probability of amplifications greater than is for a population of lensing masses with a number density in a region of depth .
Lensing from a stellar population in a host galaxy with has Einstein radius , duration for km s*-1*, and . Microlensing might enhance a few bursts out of a much larger number of unlensed events from many host galaxies. However, given the small , microlensing is inconsistent with the episodic detections of FRB 121102 unless a particular geometry allows repeated lensing.
If it occurs for any FRBs, gravitational lensing is a unique diagnostic for dark matter comprising primordial black holes or other discrete objects, including those in binaries (Wang & Wang, 2018). Point-mass lensing yields a differential delay between a dual-imaged burst, for (Zheng et al., 2014; Muñoz et al., 2016). This may be detectable as an oscillation in dynamic spectra for bursts that are coherently dedispersed, providing a fringe pattern of the form with an amplitude related to the image amplification ratio (Zheng et al., 2014; Eichler, 2017). Objects with masses \mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}0.1M_{\odot} are within reach. At present, none of the spectral features seen in FRBs is clearly associated with a fringe pattern but more detailed analyses, particularly with wideband spectrometers, are needed. Primordial black holes (PBHs) with masses may be strongly constrained with large FRB samples if they extend to z\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}0.5 because the event probability can be large enough () if PBHs comprise a significant fraction of dark matter (Muñoz et al. (2016) ). Lensing from intervening galaxies (Li et al., 2018b) has been discussed as a means for determining cosmological parameters, including and the spatial curvature . Such lensing will be sustained for long times and cannot account for the episodicity of the repeater FRB 121102.
6 THE REPEATING FRB 121102
The detection of FRB 121102 (Spitler et al., 2014) in observations acquired at the Arecibo observatory on 2012 November 2 (Figure 1) laid to rest any residual concerns about site-specific interference at the Parkes observatory (Petroff et al., 2015c) and confirmed the astrophysical nature of the FRB phenomenon. As with other FRBs, the measured DM of significantly exceeded the predicted line-of-sight maximum electron density contribution from the Milky Way (), although the location of the source at a low Galactic latitude in the Galactic anticenter () added significant uncertainty, requiring extensive multiwavelength investigation to place deep limits on Galactic H 2 regions along the line of sight (Scholz et al., 2016).
The detection of additional bursts from FRB 121102 (Spitler et al., 2016) was an unexpected pay-off to routine follow-up observations (Figure 3). The overlapping sky position uncertainty regions and the consistent value of DM unambiguously identified FRB 121102 as a repeating source and ruled out cataclysmic and explosive models as the source of (at least) that particular set of FRB events666It also introduced a point of confusion in the nomenclature, since prior usage had made no distinction between the burst event and its source. At present, there are a handful of examples of repeating sources, and the confusion remains unresolved except by context..
The repetition of the bursts, though sporadic (see §§6.2), enabled a targeted observation campaign with the Karl G. Jansky Very Large Array, where interferometric visibilities were acquired at high resolution in both time and frequency ( ms, MHz over a bandwidth of GHz, limited by the maximum data rate of MB s*-1*). In 83 hours of observations over six months, nine bursts were detected, leading to a precise source localization on the sky ( with an uncertainty of ; Chatterjee et al. 2017). The detections used complementary approaches, de-dispersing the visibilities at the known DM of the FRB and then searching for a transient source in a sequence of -ms images (e.g., Law et al., 2015), as well as phasing and summing visibilities to create time-frequency dynamic spectra over a grid of sky positions and searching those for single dispersed pulses.
Chatterjee et al. (2017) identified a variable radio source coincident with the sky position of the bursts (Figure 9), with a mean flux density of Jy; the nature of this persistent radio source (hereafter PRS) remains enigmatic and is discussed further below (§§6.1). Building on the initial localization, Marcote et al. (2017) used very long baseline interferometry with Arecibo and the European VLBI Network to detect bursts, localize them with milliarcsecond precision, and confirm their spatial coincidence with the PRS. Chatterjee et al. (2017) also identified a faint optical counterpart to the bursts, with SDSS -band magnitude AB mag. With optical imaging and spectroscopy at the 8-m Gemini North telescope, Tendulkar et al. (2017) classified the counterpart as a low-metallicity star-forming dwarf galaxy and measured a redshift , corresponding to a luminosity distance of 972 Mpc (Figure 10). With high-resolution optical and infra-red imaging using the Hubble Space Telescope and the Spitzer Space Telescope, Bassa et al. (2017) further showed that the emission is dominated by a bright knot of star formation in the irregular dwarf galaxy with a half-light diameter of 1.4 kpc compared to 5–7 kpc for the galaxy itself, and this knot coincided (within the astrometric frame-matching uncertainties) with the PRS. With its high specific star-formation rate, low metallicity, and prominent emission lines, the host galaxy resembles the preferred hosts of long duration gamma-ray bursts and superluminous supernovae (e.g., Fruchter et al., 2006; Perley et al., 2013; Vergani et al., 2015, and others), as discussed further below (§7).
Unlike gamma-ray bursts and supernovae, though, the bursts from FRB 121102 show no afterglows, and have been observed to repeat at short enough intervals that no plausible explosive mechanism (i.e., one that destroys the central engine) could power them. For example, Gajjar et al. (2018) report 18 bright bursts detected by the Green Bank Telescope at 4–8 GHz within just a 30-minute span (and many more faint ones were identified by Zhang et al. (2018) in the same span of data). Additionally, simultaneous coverage in X-rays (Scholz et al., 2017) and high-energy gamma rays (Acciari et al., 2018) as well as optical wavelengths reveals no other coincident electromagnetic emission with bursts from FRB 121102.
However, the well-localized sky position and DM allow coherently dedispersed observations of FRB 121102 over a broad range of radio frequencies and a long period of time. Such broadband, coherently dedispersed observations have enabled the detection of bursts from FRB 121102 at frequencies as high as 8 GHz (Law et al., 2017; Gajjar et al., 2018; Spitler et al., 2018), and revealed unexpected richness of time-frequency structure in the bursts (see, e.g., Figure 3).
Coherently dedispersed observations by Michilli et al. (2018) at Arecibo at 4.1–4.9 GHz also revealed that the bursts had nearly 100% linear polarization (Figure 11) and stacking of the bursts revealed a very high and variable rotation measure of to rad m*-2* over a seven-month period. Such a high rotation measure had previously only been observed in the environment of Sgr A* (Bower et al., 2003; Marrone et al., 2007), the supermassive black hole in our Galactic center. Further, the large changes in the value of the RM without comparable changes in the burst DM require significant changes in the line-of-sight projected magnetic field. That rules out, for example, an H 2 region along the line of sight as the source of the high RM and implies that the source is embedded in an extreme magneto-ionic environment (Michilli et al., 2018). In what we suggest may not be a coincidence, such changes in RM without accompanying changes in DM have only been seen before for the Galactic center magnetar J17452900 (Desvignes et al., 2018). The implications of the constraints from the DM, RM, and EM are discussed further below.
6.1 The Persistent Radio Counterpart Associated with FRB 121102
The nature of the PRS associated with FRB 121102 remains enigmatic. The source is compact and barely resolved with very long baseline observations, with a source size of 2–4 mas at 1.7 GHz and 0.2–0.4 mas at 5 GHz (Marcote et al., 2017). The radio spectrum of the source (Figure 9) is non-thermal and inconsistent with a single power law (Chatterjee et al., 2017), and the flux density at 2–4 GHz is variable on day timescales, ranging between Jy over observations from 2016 to 2018 (Figure 9). Chatterjee et al. (2017) show that of the 69 sources detected within a 5*′* radius, 9 (including the PRS) show significant variability as defined by a reduced metric (), and that the variability is uncorrelated with the detection of bursts in the uniform VLA dataset (point biserial correlation coefficient , exceeded by chance 75% of the time).
Were it not for the knowledge that the PRS is associated with fast radio bursts, we would readily conclude that it is consistent with a weak active galactic nucleus. Indeed, given the inference of an extreme magneto-ionic environment associated with the burst source (Michilli et al., 2018), and its similarity to the Galactic center magnetar J17452900, the AGN model remains an attractive explanation for the PRS. An alternative model presented by, e.g., Metzger et al. (2017) and Margalit & Metzger (2018) is that the PRS is a magnetized electron-ion nebula powered by the termination shock of a relativistic magnetar wind, which implicates a very young magnetar as the source of the bursts from FRB 121102.
6.2 Burst Periodicity and Sporadicity
Bursts from FRB 121102 have been detected with separations as small as 22.7 seconds (Scholz et al., 2016, Arecibo, 1.4 GHz), at an epoch when 6 bursts were detected in a contiguous 1002 second observation. At the GBT at 4–8 GHz, Gajjar et al. (2018) have reported at least 18 bursts in a 1800 second scan, with bursts as close together as 11.3 seconds, although there may be even smaller separations, depending on the threshold for believable bursts (Zhang et al., 2018). These detections have been searched for periodicity using Fourier techniques, Fast-Folding analyses, and brute force trials, with no significant detection of a period longer than 100 ms. Phase-coherent trials are not feasible over widely-spaced epochs, and the false alarm probability is too high for periods much shorter than 100 ms. An underlying period (due to source rotation, say) could also be masked by an accelerated binary orbit, a wide rotational phase window for the burst emission, or by plasma lensing effects that result in variable path lengths even for closely-spaced bursts.
Meanwhile, the bursts are also sporadic in nature: as shown in Figure 9, comparable VLA observations led to no burst detections in the first 21 epochs (1 hr each) in 2016 April–May, followed by the detection of 9 bursts over the next 16 epochs in 2016 August–September (Chatterjee et al., 2017). With GBT observations, Gajjar et al. (2018) report 18 bursts in 30 minutes, 21 bursts in the first hour, and no further comparably bright detections in the remaining 4 hours (although Zhang et al. 2018 report fainter bursts). Such sporadicity is consistent with time-variable focusing or lensing effects, and if such a situation holds for other FRB sources as well, there are severe implied difficulties in placing meaningful constraints on the absence of repeat bursts.
6.3 Scattering of FRB 121102
There is no evidence for extragalactic scattering (pulse broadening), even at the lowest frequency at which bursts have been detected (1.2 GHz). Early detections in the 1.2-1.6 GHz band also showed no scintillation structure from either Galactic or extragalactic scattering. However, higher frequency observations (Gajjar et al., 2018; Spitler et al., 2018) and coherently dedispersed 1.4 GHz measurements reveal narrow scintillation structure. A multifrequency fit to the published data yields a frequency scaling that is consistent with plasma scattering and the prediction (within a factor of two) with the NE2001 model (Cordes & Lazio, 2002). Similarly, the (deconvolved) angular diameters of the burst source and the PRS, mas and -4 mas at 1.7 GHz, respectively (Marcote et al., 2017) are also consistent with Galactic scattering and the relation between angular and temporal broadening. The consistency with the NE2001 model contrasts with the YMW16 model (Yao et al., 2017), which does not model scattering explicitly but instead evaluates the scattering time using empirical relation between and DM based on Galactic pulsars. This overpredicts the scattering by a factor of 30.
6.4 Constraints on the Magnetoionic Circumsource Medium
The measurements of DM and RM, the absence of detectable extragalactic scattering, and possible plasma lensing provide empirical constraints on the source environment. We attribute a nominal {\rm DM_{\rm RM}}\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}100~{}{\rm pc~{}cm^{-3}} to the circumsource Faraday region. Using a nominal host-galaxy contribution , the parallel magnetic field is Equating to that expected for a region of thickness with plasma (thermal to magnetic energy) and a geometric factor we obtain
[TABLE]
The free-free optical depth through the region is (Draine, 2011, Eq. 10.22 with in GHz)
[TABLE]
A small optical depth at 1 GHz requires the composite gas factor , which increases the depth . If plasma lensing occurs for a transverse lens scale , requiring the focal distance d_{\rm f}\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}1 GHz at a frequency (section 5.0.3), defining the depth to be a multiple of , , and using in pc, in Gpc,
[TABLE]
The situation may be more complex, of course, with distinct Faraday and lensing regions, for example. However, there is sufficient latitude to account for the measured Faraday rotation as well as the lensing requirements. For a small , the Faraday region is very thin (l\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}1-10 AU), highly magnetized (B\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}1 G), and dense (n_{e}\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}10^{5} cm*-3*). The optical depth then need not be large, \tau_{\rm ff}\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}0.03 at 1 GHz, but will be optically thick at frequencies no lower than about 100 MHz.
7 HOST GALAXIES AND COUNTERPARTS
The identification of host galaxies is a key step to obtain FRB distances and energetics, and to identify the progenitor population. Efforts have included mapping of the beam shape to identify plausible sky regions and candidate hosts based on multi-beam detections (Ravi et al., 2016), as well as the mis-identification of a variable radio source as an “afterglow” (Keane et al., 2016b). As pointed out by Williams & Berger (2016), Vedantham et al. (2016b), and others, radio variability is commonplace and cannot be relied on as a sole indicator for an FRB host galaxy. However, the persistent radio source (PRS) associated with FRB 121102 is variable, along with several other sources in the field (§§6.1), and selecting luminous radio sources associated with galactic disks, after excluding AGN and background sources, may offer a reasonable sample for a targeted FRB search (Ofek, 2017). Rapid multiwavelength follow-up to detect the analog of GRB afterglows has not been fruitful either (e.g. Petroff et al., 2017a; Tominaga et al., 2018), and the absence of high energy emission associated with FRB 121102 (Scholz et al., 2017) makes such routes less promising for host identification. At present, therefore, the only reliable method demonstrated is the direct interferometric localization of the burst itself. Eftekhari & Berger (2017) show that 1*′′* localizations are required for unique host galaxy identifications, although if all FRBs are associated with PRS like FRB 121102, Eftekhari et al. (2018) show that the localization requirements are much less stringent, at the 10*′′* level.
The one uniquely-identified host galaxy for FRB 121102 is an irregular low-metallicity star-forming dwarf with a strong resemblance to the hosts of long duration GRBs and SLSNe (§6), leading to a unified model for the source of the repeating bursts and the PRS as a young millisecond magnetar embedded in a nebula powered by its relativistic wind (Metzger et al., 2017; Margalit & Metzger, 2018). If most FRBs come from repeating sources, Nicholl et al. (2017) find that a source association with GRBs or SLSNe and a burst emission lifetime of 30–300 years makes for a self-consistent picture. While such a model has many attractive features, the PRS does resemble a typical AGN, and it has been established that dwarf galaxies can have massive black holes (Reines et al., 2011; Seth et al., 2014). The high (and time-varying) RM of the bursts, without a correspondingly large change in DM, argues for an extreme magneto-ionic environment similar to our Galactic center (Michilli et al., 2018). Of course, one could require both circumstances (a very young magnetar in the environment of a massive black hole) for (repeating) FRBs, a proposition difficult to rule out given a sample of one (as of February 2019).
Even in the absence of a specific host galaxy identification, the very low DM of FRB 171020 (114 ; Shannon et al. 2018) leads to a very restrictive upper limit on the distance to a host, and Mahony et al. (2018) identify ESO 601G036, a Sc galaxy at a redshift as the most plausible host galaxy. However, the candidate host is not associated with a PRS, and nor is there a candidate PRS within z\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}0.06, suggesting that it may not be a generic feature for (all classes of) FRB emission. We discuss possible central engine models further below; further host identifications are the most urgent observational priority for FRB science.
8 SURVEYS AND POPULATIONS
8.1 The Fluence - DM Distribution
Measured FRB fluences are lower bounds in many cases (currently) due to uncertainties in location within telescope beams but they also show the wide range expected from a spatially distributed population having a wide intrinsic luminosity function777Also, beamed radiation introduces the unknown angle between the beam axis and the line of sight that further increases the range of apparent luminosities. If the extragalactic portion of the dispersion measure is a proxy for distance, the distribution of vs should provide some insights.
Figure 12 shows this distribution for FRBs detected in the GHz band from the Arecibo, ASKAP, and Parkes surveys (along with other FRBs). Broad conclusions that can be made include the following:
- •
The ASKAP and Parkes surveys yield fluences that are largely independent of .
- •
The mean is larger for ASKAP than Parkes by a factor , which is of order the sensitivity ratio of the 64-m Parkes telescope and ASKAP’s 12-m antennas (for the fly’s eye mode used by Shannon et al. 2018).
- •
The scatter in fluence \sigma_{\log{\mathcal{F}}}\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}0.5 for the two surveys.
- •
The repeating FRB 121102 by itself shows a large scatter (by ) between burst amplitudes, indicating intrinsic variance that is not unlike that seen from individual pulses of pulsars.
A simple analysis is instructive for estimating some rough numbers. The (pseudo) luminosity defined earlier is if is a proxy for the source-observer distance . This gives . We show in the bottom panel of Figure 12. Standard candles and a constant width would imply constant, while scatter in and imply vertical scatter in the - distribution. Cosmic variance and errors in estimating give horizontal scatter that combines with the variations of the true extragalactic DM. The clear difference in average for the ASKAP and Parkes samples demonstrates vividly that FRBs are not standard candles, as pointed out by Shannon et al. (2018). Only a subset of the Parkes FRBs shown in the figure come from the uniform set of surveys listed in Table 1. These are the events with . For this subset, compared to 2.5 for the ASKAP sample. The corresponding fluences have and 1.9, respectively.
The systematic rise in scales roughly as for both the ASKAP and Parkes samples and is to be expected for threshold-limited surveys. However, scatter about this trend is also expected when there are significant host-galaxy contributions to . The apparent flattening (beware small number statistics!) for may result from host-galaxy DMs.
It is also instructive to compare the number of burst detections in the ASKAP and Parkes surveys. Let be the distance out to which only a single burst event is expected for an exposure time per sky position, where is the burst rate per source and is the number density of sources. The number of events occurring out to an arbitrary distance is . Only a fraction of these events is detectable. Assume that burst detection corresponds to peak flux densities exceeding a threshold .
The detection number is , where is the maximum distance that a burst with luminosity could be detected. Noting that both and are survey dependent, the ratio of the ASKAP to Parkes survey yields is (using values in Table 1),
[TABLE]
By comparison, the actual numbers are in the ratio . Clearly, the wider field and longer dwell time for the ASKAP survey more than compensate for the sensitivity difference.
8.2 Some Population Numbers
A simple analysis of the events in Figure 12 illustrates some constraints that can be made on the event rate density . We assume that the lowest FRB in a survey is also at the lowest distance with d_{1}\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}\widehat{d}, which constrains , the distance out to which only one burst occurs in a survey. Using the mean IGM electron density to estimate and knowing the survey parameter (Table 1), the likelihood function for is where
[TABLE]
The source number density is not known empirically but has been estimated by Nicholl et al. (2017) as Gpc*-3* for dwarf galaxies that harbor SLSNe. Combined with Gpc*-3* d*-1*, we obtain the mean burst rate per source d*-1*. This average rate is exceeded by a large factor by the repeater FRB 121102 at some epochs but may be consistent with overall average FRB detection statistics.
8.3 Modulated Luminosity Functions and Detection Numbers
We now consider the effects of scintillations and lensing on FRB detection rates. We assume that all individual FRB sources emit bursts according to the same luminosity distribution . The overall population luminosity function is the combination of individual luminosity distributions weighted by the number of sources per unit volume. Our analysis is primarily in Euclidean space and we extend to cosmological contexts as needed. A more detailed analysis will be published elsewhere. Cosmological effects are discussed by Cordes & Wasserman (2016) and Macquart & Ekers (2018a).
The number of detections in the absence of propagation effects is
[TABLE]
With scintillations or lensing (or absorption) characterized with a PDF , the modified number of detections is
[TABLE]
By inspection, for a fixed gain , a modulation effectively lowers the threshold to or it effectively increases luminosities to . When varies over an ensemble of events with unit mean (appropriate for scintillation and lensing) some nearby events become undetectable while other more distant events become detectable.
8.3.1 Standard candles and power-law luminosities
A toy model comprising standard candles illustrates salient points that also apply to more realistic luminosity functions. Using , the maximum detection distance is . Figure 13 shows survey volumes for two cases, one where the detection distance exceeds and the other where no sources can be detected without lensing of DISS. The differential detection number is nonzero only for
[TABLE]
and its ratio to the differential number of events is
[TABLE]
All events from distances smaller than are detected but none for larger distances. Inclusion of a constant lens gain in a ‘standard lensing’ model increases the detection distance to and the total number of detected events from to .
If the burst rate density is large enough so that , some bursts will be detected without any lensing boost but the total number will dramatically increase with . Episodes of lens dimming () reduce the number. In the opposite case of a sparse rate density, detections require strong lensing. Figure 14 shows the differential ratio from Equation 21 for standard candles on the left and for a power-law case on the right, with regions indicated where detection numbers are enhanced or diminished by scintillations of lensing.
With scintillations included, the number of detections becomes
[TABLE]
where and are the incomplete gamma functions. For fully modulated DISS with , , and the number of detections at distances nearer than is reduced to of the original number because of scintillations but now a larger total number is detected, owing to scintillation boosts of sources beyond .
9 THE FRB DISTANCE SCALE
Measurement of the redshift of a securely associated galaxy is the only reliable method for determining FRB distances and that is likely to remain the case. Repeated bursts from the source of FRB 121102 were key to enabling its sub-arcsec localization that led to the redshift of the dwarf host galaxy. Absent a radio localization from the first (and perhaps only) burst from an FRB source, host galaxy associations are likely only for nearby, low-DM FRBs where a small number of galaxies is in the positional error box. For most bursts, which tend to be one-offs or at least very infrequent repeaters, localizations need to be done at the time of discovery using interferometric arrays. Until such arrays operate routinely, approximate distance estimates will be obtained from DMs. Here we summarize DM-based methods and their issues.
It is useful to consider the total DM and pulse broadening time together. Measured values include contributions from the host, the IGM (including cosmic variance), and the Milky Way along with other contributions that can arise frome the circum-source environment, intervening galaxies, galaxy clusters, or unmodeled HII regions in the MIlky Way,
[TABLE]
9.1 Deconstructing Dispersion Measure
The general approach so far has been to estimate the IGM’s contribution by subtracting estimates for the host galaxy and the Milky Way while ignoring other terms,
[TABLE]
Estimates for the MW term comes from the NE2001 and YMW16 models and inclusion of a Galactic halo contribution . Host galaxy contributions are often fixed to low constant values such as (Shannon et al. 2018) or based on the (questionable) assumption that the host contributions arise solely from Milky Way-type ISMs averaged over inclination angles. While MW models have systematic errors due to unmodeled HII regions (‘interstellar variance’), the uncertainties in are probably smaller than typical host-galaxy contributions, particularly for high-latitude FRBs.
The only empirical constraint on host-galaxy contributions comes from the repeating FRB for which Balmer-line based estimates of the emission measure translate into -200 . The assumption of generally small host-galaxy contributions runs counter to FRB models involving young supernovae (Piro, 2016), whose expanding shock fronts imply very large DM values that can hinder detection of bursts at early times, or models involving AGNs (e.g. Zhang, 2017) in the centers of galaxies. Without other constraints, it must be allowed that a circum-source contribution could be a large fraction of the DM for even the largest measured (FRB 160102). Consequently, the error on any given estimate for may be very large.
9.2 Dispersion Measure–Redshift Relation
Reionization at z\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}10 has rendered most of the baryons in the universe to a largely invisible status in the IGM, often referred to as the missing baryons (Nicastro et al., 2018). Measurements that constrain the IGM are therefore valuable for understanding the distribution and temperature-density phase structure of the ionized gas. Future FRBs may provide much of that information once host-galaxy redshifts are measured routinely in large numbers and host-galaxy contributions are better estimated. For now, IGM considerations have largely concerned the reciprocal problem of using to estimate the redshifts of FRBs. Published analyses of the DM- relation that conclude dominance by the IGM border on the procrustean because they attribute rather small values of the host galaxy contribution in the absence of any direct measurement (other than for FRB 121102). Assumption of small runs counter to viable models involving young NS where significant circumsource contributions to DM are expected.
Invariance of the electromagnetic phase, (Jackson, 1962) implies
[TABLE]
For a galaxy at redshift with dispersion measure , an observer measures while an arbitrary distribution of gives
[TABLE]
where in flat CDM spacetime . For the IGM, where expresses the degree of ionization of hydrogen and helium, and the local () mean electron density yields the mean DM,
[TABLE]
We use the Planck 2015 cosmological parameters (, , and ) to obtain and evaluate the fiducial dispersion measure, .
Cosmic variance yields significant variations about the mean from that are estimated from cosmological simulations by several authors and expressed in the form of a standard deviation vs. redshift, . The fractional RMS decreases with larger but fairly slowly. Consolidating the results of Ioka (2003); Inoue (2004); McQuinn (2014); Dolag et al. (2015); Shull & Danforth (2018) we show in Figure 15. For fixed the DM distribution is asymmetric with large positive excursions expected when the line of sight intersects dense halos (rich galaxy clusters) or individual galaxies for , as noted by Dolag et al. (2015). Intersections with massive halos become highly probable for (Voit et al., 2001; McQuinn, 2014; Cordes & Wasserman, 2016), so redshifts derived from FRBs with large DMs must be regarded with suspicion if intersections are ignored. Future analysis can look for correlations of large FRB DMs with proximity to galaxy clusters as both the FRB sample and cluster catalog increase in size. If DMs are IGM dominated, such a correlation should be found; conversely, the absence of a correlation is expected if FRBs are typically at and DMs receive large host-galaxy contributions.
In addition to cosmic variance, errors in due to uncertainties in and in the Galactic and host-galaxy contributions compound the difficulty of estimating redshifts. The resulting implies [using as the inverse of and using to denote cosmic variance in the - relation],
[TABLE]
MW contributions are estimated using Galactic electron density models, such as NE2001 (Cordes & Lazio, 2002) and YMW16 (Yao et al., 2017), which have inherent errors due to complex Galactic structure that is not well modeled.
From Figure 15, so each 100 of error on gives . What errors on can be expected? Differences between the NE2001 and YMW16 models at low Galactic latitudes suggest RMS values exceeding 100 (Tendulkar et al., 2017; Spitler et al., 2018) but high latitudes have errors a factor of 5 to 10 smaller. for the repeating FRB likely exceeds 100 and some authors argue that host galaxy contributions will be no larger than this, based on the notion that the host contribution comes from a galaxy disk. However, FRBs may generally be embedded in star forming regions, in galactic centers, or in a circumsource nebula that can provide much larger values. Consequently, redshift errors may be several tenths or more for .
9.3 The –Dispersion Measure Relation
Lines of sight to FRBs span plasmas with radically different properties, including the ISM, the IGM, the host galaxy’s ISM, and the circumsource medium (contributions from the interplanetary medium and ionosphere are minor for FRB studies888 We note however that any FRBs discovered in directions close to the Sun will likely be affected by interplanetary scintillation.. Turbulence will differ greatly between them just it does between intra-Galactic components.
To assess whether extragalactic scattering stems from the IGM or host galaxies, we compare the -DM relation for Galactic pulsars with FRB scattering in Figure 16. For a fixed DM, Galactic pulsars show more than an order of magnitude variation in . Figure 16 shows the fit to the data of the empirical model (Ramachandran et al., 1997), with roughly 5% errors on each parameter and a spread about the mean (data and fit in Cordes et al., 2016, update in preparation). Values for FRB broadening time measurements as well as upper limits are shown in the figure. When measurable, FRB scattering is comparable to burst widths but clearly is biased below the pulsar band.
To interpret FRB scattering, the extreme heterogeneity of the mean scattering strength per unit DM needs to be accounted for. Galactic pulsars at large DMs sample the inner Galaxy in the spiral-arm and thin-disk components of the NE2001 electron density model. Scattering per unit length is significantly larger in those regions than in the outer Galaxy or in the thick disk component, thus causing the larger slope of the –DM distribution in Figure 16 for \rm DM\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}50~{}{\rm pc~{}cm^{-3}}. FRBs have been seen mostly at high Galactic latitudes and in the Galactic anticenter direction, which sample the more weakly scattering gas also indicated in the figure. The measured scattering of FRBs must be extragalactic in origin, as demonstrated in Figure 4 of this review. However, for the corresponding DMs, the scattering is weaker than it would be for lines of sight through the disk of the Milky Way.
However, the scattering must be compared with only the extragalactic component of DM, which has contributions from the IGM and the host galaxy in a ratio that is unique to each FRB. We define the extragalactic contribution to DM as , where the estimated Galactic contribution is the sum of the NE2001 model integrated to its edge and a halo contribution, taken as a uniform value pc cm*-3* (Dolag et al., 2015). Similarly we write , where we exclude a halo contribution because it is likely much smaller than the Galactic disk contribution to that is itself small for the known FRBs. We then redraw the -DM relation in the right-hand panel of Figure 16, which shows the broadening time vs. DM using only the extragalactic components of both quantities.
In the figure we also show the Galactic pulsar -DM relation under the assumption that extragalactic scattering comes from only the host galaxy. To compare extragalactic with Galactic scattering, we need to compensate for geometrical differences between the spherical waves from nearby sources and plane waves from/to distant sources/observers. The scattering time is thus a factor of three larger for scattering in the host galaxy than implied by the Galactic –DM relation. The figure therefore shows the Galactic –DM band after shifting the Galactic scaling law of Figure 16 upward by a factor of three.
10 SOURCES, RADIATION PROCESSES, AND CENTRAL ENGINES
The aggregate properties of FRBs, to the extent that they are now known, require explanations for the bursts themselves — duration, time-frequency structure, polarization, energetics, and, for repeating FRBs, their low duty cycle, absence of periodicity, and rate variability — as well as their population properties, including the sky rate vs. fluence distribution, which are linked to their spatial distribution and beaming properties. All of these contribute to a determination and physical understanding of the underlying sources.
10.1 Radiation Processes and Beaming
Emission processes for FRBs are probably most closely related to those for radio pulsars, for which there is a vast literature too large to be reviewed here. Similarities with coherent cyclotron radiation from planets and brown dwarfs may also be related at least by analogy.
Empirically, bursts necessarily comprise coherent, polarized shot pulses whose short durations (\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}ns) must be on the order of the reciprocal of the spectral width (GHz) and combine incoherently in large numbers, with either a shot-rate variation or amplitude variation, to form the much longer burst durations ms. Individual shots like those seen from the Crab pulsar (Hankins & Eilek, 2007; Jessner et al., 2010) are prototypes for FRB shot pulses (Cordes & Wasserman, 2016). A feature of modulated shot noise is that bursts with multipeaked structure are a natural outcome, as are spectral modulations on the reciprocal time scale (s ms*-1* = kHzMHz; Cordes et al., 2004).
Relativistic beaming with large Lorentz factors is certainly involved with the emission process given the burst energetics discussed in §3.6 but it is not clear if beaming plays a role in burst durations and morphology. Figure 17 shows three beaming configurations. First is a non-rotating ‘jetted’ beam that might arise from magnetic reconnection (and would be two sided) or from a jet aligned with the spin axis of a compact object. Its orientation might change only slowly so burst durations and substructure would be associated with temporal modulations of the particle flow or of the radiation coherence. The middle frame shows a rotating pulsar-like beam that sweeps through more solid angle than that of the beam itself and might produce polarization changes like those seen from pulsars. Last is quasi-isotropic radiation involving local coherent beams associated with regions where coherent emission can be established, such as by particle beams injected into shocked gas. In this case the total solid angle is multiplied by a sub-beam filling factor. Other physical processes may also be described with these rotating vs. non-rotating paradigms.
The emitted luminosity of an individual source is determined by the radiation physics but the measured flux density (and luminosity defined earlier) depends on beam orientations. Individual pulsars, for comparison, show significant variability of pulse shapes and amplitudes indicating stochasticity of the radiation process that should also be anticipated for FRBs and is seen in the repeater FRB 121102. The population luminosity function is a combination of these factors with the spatial distribution of sources. For pulsars, spans at least five decades due to the combination of radiation stochasticity, beaming geometry, and spatial distribution (e.g. Arzoumanian et al., 2002) along with scintillations, so will span an even greater range for the more widely distributed FRBs.
Radiation coherence makes particles radiate with times the single-particle emission and is responsible for the high efficiency that is needed given the large energy in radio emission alone. The underlying particle acceleration may be linear (e.g. field-aligned electrostatic waves) or transverse (curvature and gyro-synchrotron radiation) but a coherence mechanism must also operate. An antenna mechanism involves particle bunches in size (modulo beaming) with many charged particles. Maser mechanisms require special distributions in momentum space to provide amplification. A maser (Luo & Melrose, 1992, e.g.) has the advantage of cumulative growth of radiation amplitudes over a region , which may alleviate energy requirements that challenge coherent curvature radiation from bunches (Cordes & Wasserman, 2016; Lu & Kumar, 2018; Ghisellini & Locatelli, 2018). Nonetheless, emission is limited to the energy carried by particles, which are likely to be strongly dissipated by radiation reaction from radio emission alone.
Polarization may provide some clues. As mentioned in § 3.4 for FRB 121102 and several other FRBs, the approximate constancy of the position angle across bursts contrasts with that often seen in pulsars, suggesting a non-rotating beam (as mentioned earlier) or a grazing beam where a magnetic axis does not make a close approach with the line of sight (e.g. Backer et al., 1976; Beskin & Philippov, 2012). The 100% linear polarization of bursts from FRB 121102 is similar to the polarization of some pulsars but pulsars often show some circular polarization.
The spectral islands seen from several FRBs with 0.1–0.5 GHz widths are distinct from Galactic scintillations and suggest a bandlimited emission process, such as one where the local plasma or cyclotron frequency (or their harmonics) are involved. The electron-cyclotron maser process is well established for planetary emission, including the Earth’s auroral kilometric radiation (AKR) (Treumann, 2006; Vorgul et al., 2011) and solar bursts (Chen et al., 2017), and produces 100% circular polarization, contrary to FRB emission. An plasma would show no net circular polarization in the simplest case but allows linear polarization. Measured radiation might be, however, a combination of emission with normal EM modes that are linearly polarized in the magnetosphere followed by maser amplification without any polarization conversion. A cyclotron frequency GHz corresponds to G that is encountered at a radius cm for a magnetar with a surface field of G. This exceeds or is a good fraction of the light-cylinder radius for modest but would require a very large to be within the light cylinder of a millisecond magnetar. This context is similar to that for pulsars, which show polarization transfer effects and differential refraction (Barnard & Arons, 1986; Wang et al., 2010), so similar complexity and diversity is to be expected from FRBs. A distinction from pulsars is the variability of the spectral islands, suggesting ‘retuning’ of the emission process between bursts (if intrinsic) that might be accompanied by beam wandering (e.g. Katz, 2017).
The absence of an observed periodicity in FRB 121102 may indicate a non-rotating object but it is easy to destroy periodicities by chaotic precession from a star with a stochastic moment of inertia tensor (e.g. crustquakes) or from lensing that produces multiple bursts with rapidly changing delays. The epoch dependent burst rate may have similar intrinsic or extrinsic causes. An additional extrinsic variability mechanism is triggering by injection of asteroids into a magnetosphere (Huang & Geng, 2016; Dai et al., 2016). Asteroids are difficult to inject in rapid rotators (\mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}0.5 s periods), however, because they are evaporated well before they reach the light cylinder (Cordes & Shannon, 2008).
10.2 Source Models
The number of proposed source models has long exceeded the number of detected FRBs. Fortunately, the current rapid increase in burst numbers is not accompanied by a proportionate number of models. In fact most (but certainly not all) attention is now paid to two paradigms, those involving isolated or binary compact objects (WD, NS, and BH) and AGNs, perhaps interacting with neutron stars. The much larger slate of models has included technomarkers from extragalactic civilizations (Lingam & Loeb, 2017), superconducting cosmic strings (Yu et al., 2014; Thompson, 2017a, b), exploding black holes (Barrau et al., 2014), reconnection in magnetars triggered by axion quark nuggets (Van Waerbeke & Zhitnitsky, 2019), WD-NS binaries (Gu et al., 2016), NS-NS mergers (Yamasaki et al., 2018), WD-BH mergers that create reconnecting magnetic blobs (Li et al., 2018a), collapse of supramassive NS (Falcke & Rezzolla, 2014), novae of exotic objects (quark or axion stars), accretion or interaction of asteroids with compact objects (e.g. WD, NS, BH Mottez & Zarka, 2014), mergers of compact objects, births of neutron stars or black holes, as well as AGN-NS interactions and energetic activity (flares and starquakes) from magnetars. Some of these produce GRBs from which associated prompt radio bursts have long been looked for. However, unless beaming radically increases the prompt radio burst rate, the GRB rate is too small by a factor - to account for FRBs. Models have been suggested for intermittent pulsars and RRATs (e.g. Luo & Melrose, 2007) that might be relevant to FRBs but the vastly different energetics may make these models less relevant.
It is not our goal to review this rich diversity, especially given page and reference list limits. More details about the the wide range of models may be found in other reviews (Katz, 2016a; Popov et al., 2018). Instead we build upon the fundamental quantities summarized in §2 on burst rates, repeatibility, and energetics to suggest that compact objects and especially neutron stars are prime candidates for the underlying engines of many or most FRBs because they exist in sufficient numbers in the universe (a NS born roughly every second in a Hubble volume) and possess sources of free energy (rotation, magnetic) that can account for burst energetics. Other objects may of course also generate radio bursts but perhaps at much lower rates.
While energy reservoirs are available, channeling it into high brightness, coherent pulses with millisecond durations is more challenging, particularly since pulses are isolated, without obvious pre or post cursors and they certainly do not occur as an ongoing, high duty-cycle process. This is in contrast to coherent solar bursts and radio flares, for example.
10.3 Demographics
Paradoxically, familiar objects in the universe are too numerous to account for the very large all-sky FRB rate ( d*-1*), even if the beaming fraction is small. Special objects or special circumstances are needed. NSs are a good reference population because they can provide free energy from rotation, magnetic fields, and gravity. In the Universe there are NSs in a Hubble volume (see the sidebar titled Neutron Star Populations in the Universe). Most pass through the pulsar channel involving birth spin rates ms, electromagnetic radiation across the entire spectrum including prominent coherent radio emission, spindown, and termination of pair production and thus also the radio emission after 10–100 Myr. If all NS in a Hubble volume are linked to FRBs, only about one event per NS is needed to account for the sky rate. Clearly, only a tiny subset of NS can be involved given the events seen from FRB 121102.
{textbox}
[h]
11 Neutron Star Populations in the Universe
Extragalactic NS formed over cosmological time are potential sources of super-strong bursts whose number per NS, , may be large or small (where = burst rate per NS during a burst phase of duration ). The aggregate burst rate follows the NS birth rate, . Scaling from the Galactic NS formation rate per unit stellar mass, (e.g. one NS every 100 yr per in stars), and the stellar mass density where is the closure density and (Read & Trentham, 2005), about NS are produced in a Hubble volume for a Hubble distance Gpc and a typical galaxy age Gyr. A higher star formation rate at redshifts increases the number by about a factor of ten (Nicholl et al., 2017, and references therein). The aggregate NS birth is then - and the corresponding burst rate is . For burst detections out to a distance (modulo a proper cosmological integration), , illustrating the tradeoff between and in matching to the empirical FRB rate, .
FRB directions appear to be isotropic. That the first FRB localization was to a dwarf, star forming galaxy rather than a massive L* type galaxy suggests that FRBs do not follow star formation generally but reside in host galaxies that are themselves special. This ‘sample of one’ situation may change with subsequent localizations, but the simplest provisional conclusion is that FRBs are from special galaxies that produce appropriate central engines.
The magnetar channel accounts for % of NS (e.g. Popov et al., 2010). About 1% of NS remain in binaries and become millisecond pulsars through accretion-driven spinup with radio lifetimes greater than about a gigayear. Another % are in NS-NS binaries that ultimately merge, producing short-hard GRBs and chirped gravitational waves in the kHz band, like GW 170817 (Abbott et al., 2017).
If FRBs are largely one-off events per source, rendering repeaters such as FRB 121102 outliers, FRBs could be associated with NS birth events or a highly unusual crustquake, accretion event, or magnetospheric discharge that occurs only once per NS and perhaps not to every NS. The aggregate event rate is then tied to the NS birth rate , which is within a factor of ten of the empirical FRB rate, . For this to be the case, FRB events would be associated with a sizable fraction of all NS, perhaps only the magnetar channel or some kind of rare event that happens to nearly all NS. This scenario seems implausible because spin and magnetic energies of the different NS differ by many orders of magnitude, implying that FRBs would be insensitive to this range, while the radio emission itself as extreme. Moreover, it seems premature to dismiss repeating FRBs as outliers because, as discussed earlier, spectrotemporal structure of some non-repeating FRBs is similar to that of FRB 121102. One might dismiss this similarity as a feature of the radiation process rather than of the underlying engine, but there is currently no support for that view. Consequently, NS models can plausibly imply that most or all FRBs repeat, albeit at potentially different rates that have obscured the observational situation about repetitions.
11.1 Young, Rapidly Rotating Neutron Stars
Young, high-field NS have been a particular focus of models since the early days of FRBs and a self consistent picture is emerging in favor of these models for at least the repeating FRB 121102 and its associated PRS. Broad features include a high magnetic field ( G), rapid rotation (spin period ms), and a young age ( 10 - 100 yr). The object must be old enough so that radio pulses are not free-free absorbed and young enough so that it can provide the luminosity of the PRS. Unresolved issues include whether the objects are magnetically powered or rotation powered and whether the coherent bursts themselves originate from the magnetosphere of the spinning object (i.e. within the light cylinder radius ) as giant pulses in a pulsar-like model or from synchrotron maser activity in a distributed region well outside . Other differences between models concern the mass in the supernova and pre-SN ejecta.
11.1.1 Giant Pulse Models
Analogs to giant pulses (GPs) from the Crab pulsar (Connor et al., 2016b; Lyutikov et al., 2016; Popov & Pshirkov, 2016; Cordes & Wasserman, 2016) scale burst amplitudes from the wide GP fluence distribution and from the spindown rate of the Crab pulsar. Coherent curvature radiation may underly Crab GPs but whether it can provide \mathbin{\lower 3.0pt\hbox{\hbox to0.0pt{\raise 5.0pt\hbox{}\hss}\mathchar 29208\relax}}10^{6} larger fluences for FRBs is challenging though may be helped by local maser amplification or extrinsic lensing. One avenue of exploration is a monitoring program to probe the extent of the long tail of Crab GPs. Constraints on GPs from neutron stars likely apply to other central engines, including exotic sources, because the issues in generating powerful fast bursts are generic.
11.1.2 Magnetar models and superluminous supernovae
Magnetar (and similar) models for FRBs were suggested prior to the discovery of repeat bursts from FRB 121102 and its association with a persistent radio source in a star-forming galaxy (e.g. Popov & Postnov, 2010; Thornton et al., 2013; Lyubarsky, 2014; Kulkarni et al., 2015; Pen & Connor, 2015; Katz, 2016b; Murase et al., 2016; Piro, 2016; Cordes & Wasserman, 2016). Subsequent work has identified a consistent picture for FRB 121102 where the bursts and persistent source originate from the same structure, although details differ between different models (Waxman, 2017; Kashiyama & Murase, 2017; Margalit et al., 2018; Margalit & Metzger, 2018). Figure 18 illustrates the features of the Margalit & Metzger (2018) model. It is by no means clear that a magnetar model underlies all FRBs but the case for the repeating FRB is strong because the model can account for many features of the bursts and the PRS. Even in the magnetar paradigm a great deal of diversity of FRB sources is expected from a range of ages, environments, and initial conditions of the sources.
Waxman (2017) used the radio light curve, angular broadening from VLBI, and radio spectrum to show consistency of the persistent source with a compact (-1 pc) region emitting non-self-absorbed synchrotron radiation from gas heated by semi-relativistic shells plowing into ambient gas. Other, highly relativistic shells produce FRBs from synchrotron maser emission at GHz frequencies determined by the local plasma and cyclotron frequencies. Negative absorption from this process is confined to roughly a 40% band. The age of the source is less than a few hundred years and the dense outer shell that confines the persistent emission provides only a small DM while providing an RM similar to the measured values. This analysis reached conclusions similar to those by Lyubarsky (2014), although the former paper assumes an e-p plasma and the latter a pair plasma produced in magnetar flares. Beloborodov (2017) made a similar analysis but invoked specific properties of magnetars to develop a flare-driven model, also with FRBs produced by synchrotron maser emission and a similar persistent source size.
The association of FRBs and persistent source(s) with SLSNe and long GRBs (Metzger et al., 2017) ties together the physics of central engines and circumsource media with the demographics of SLSNe in dwarf, star-forming galaxies. Though much of this hinges on FRB 121102, another source similar to its PRS has been identified (Law et al., 2018), and finding such sources may be a productive avenue for finding burst sources and testing the model and even for finding bursts. Omand et al. (2018) propose that high-frequency observations with the Atacama Large Millimeter/Submillimeter Array and the Jansky Very Large Array (VLA) can detect persistent sources at earlier, optically thin epochs than at -10 GHz. A recent ALMA observation of FRB 121102 placed an upper on any persistent continuum emission that was consistent with extrapolation of the low-frequency spectrum.
Other tests for general consistency with an central engine/outburst model include the epoch dependences of DM and RM along with the flux density of the PRS. If burst rates at present are enhanced by plasma lensing, then it too should vary. X-rays may discriminate between models where FRBs dominate the EM budget (e.g. Waxman, 2017) compared to those where high-energy emission dominates, though absorption may prevent this for young objects (Margalit et al., 2018).
11.2 AGNs interacting with NS
AGNs and NS are both abundant in the universe and NS populations bound to AGNs are likely common. But rare interacting NS-AGN configurations may provide an appropriately sized population that yields low duty cycle bursts. Zhang (2017, 2018) presents a specific picture where AGN outbursts trigger bursts from a NS; this is also suggested by Cordes & Wasserman (2016). A galaxy center is an alternative environment for providing a large RM, as demonstrated by the (old) Galactic center magnetar J1745-2900 (Desvignes et al., 2018) with that is time variable. The model implies that bursts should show periodicity at the NS orbital period and associates burst polarization with the magnetic field that interacts with the AGN’s jet flow. If a young magnetar is required to provide bright FRBs, it is not clear whether an external trigger or external magnetic field is really needed.
12 FRBs AS TOOLS FOR ASTROPHYSICS AND FUNDAMENTAL PHYSICS
Radio bursts are obvious probes of magnetized plasma of all kinds and those originating at extragalactic distances give unique opportunities remote sensing of the extreme environments around burst sources, their host galaxies, and the IGM, as discussed at length already. Continued monitoring of repeaters provides the means for testing models for central engines via epoch dependences of DM, RM, etc. Numerous papers have outlined the program for using FRBs to quantify the ionized IGM (as already summarized) and its large scale structure (e.g. Masui & Sigurdson, 2015). In the latter case DMs of FRBs may yield a significant clustering signal under the assumption that local (host galaxy and circumsource) DM contributions are small (Zhou et al., 2014). Currently, only the repeating FRB has relatively good constraints on local DM (and RM) contributions, but that will change as the FRB sample continues to grow rapidly. Probing cosmological magnetic fields using large FRB samples has been outlined by Vazza et al. (2018).
A large sample of FRBs is needed to fully ascertain the range of local DMs and contributions from galaxy clusters. Electron density models for the Milky Way are uncertain even with thousands of DM (and other) measurements because the number of lines of sight is too small to sample all prominent HII regions. Local DMs of FRBs may span a similar large range among the many host galaxies involved in a large FRB sample Yang et al. (2017). Indeed, young-NS models imply that DM, RM, and free-free absorption will be large in the early days of a source and that FRB detections will occur only after they have declined sufficiently (e.g. Pen & Connor, 2015; Connor et al., 2016b; Margalit & Metzger, 2018). High- FRBs benefit from having their local DMs reduced by a factor so the cosmology program may rely on identifying any large redshifts directly, which may be a challenge if only dwarf galaxies harbor FRB sources. Large scale magnetic fields in the IGM (Zheng et al., 2014; Vazza et al., 2018) will benefit from large FRB numbers and will complement RM measurements from AGNs already available (Kronberg et al., 2008).
As previously mentioned, FRB constraints on microlensing and dark matter objects will improve greatly with both large numbers and detailed analyses of burst spectra that may be influenced by interference effects. Finally, FRBs place limits on the photon mass (Bonetti et al., 2016; Wu et al., 2016; Shao & Zhang, 2017) but require independent redshifts and determinations of because a non-zero photon mass contributes an arrival time delay degenerate with that of plasma dispersion.
13 PROSPECTS for FUTURE WORK
The investigation of FRBs as a novel phenomenon has followed an explosive growth trajectory in its early phase, as measured by detections, theoretical models, publications, and citations. In the near term, increasing numbers of detections are assured. The Australian Square Kilometre Array Pathfinder (ASKAP) in its fly’s-eye mode has shown remarkable success with large fields of view at low sensitivity (Bannister et al., 2017; Shannon et al., 2018), and the Canadian Hydrogen Intensity Mapping Experiment (CHIME), which views the whole sky daily as it passes overhead, has detected FRBs in its initial operations (CHIME/FRB Collaboration et al., 2019b, a). However, neither telescope is likely to produce sufficiently precise localizations in the absence of new modes of operation or outrigger telescopes. The upgraded Molonglo telescope (UTMOST) has detected several FRBs (e.g., Caleb et al., 2017; Farah et al., 2018) but with limited localization precision in one dimension, joining blind surveys at single dish telescopes with improved instrumentation (e.g., the ALPACA phased array feed at Arecibo) to increase the FRB sample.
Reliable measurements of FRB distances and energetics require host galaxy identifications through better than arcsecond localizations. The realfast project (Law et al., 2015) should yield more such blind localizations at the VLA, as should surveys with the upgraded APERTIF at Westerbork (e.g., Oostrum et al., 2017), as well as MeerKAT. New telescope projects like the 110-dish Deep Synoptic Array (DSA-110) and the Hydrogen Intensity and Real-time Analysis experiment (HIRAX) also promise a future yield of blind detections with precise localizations. A complementary approach is the targeted follow-up of blind FRB detections at higher sensitivity (e.g., with the Arecibo or FAST telescopes) in order to identify other repeating sources that can then be subjected to intensive interferometric campaigns, as done for FRB 121102 (Chatterjee et al., 2017; Marcote et al., 2017).
The detection of rare weak bursts in massive volumes of survey data is a difficult problem, made more challenging by the steadily worsening radio frequency interference (RFI) environment. Machine learning techniques have been proposed Connor & van Leeuwen (2018) and have already demonstrated dramatic results (Zhang et al., 2018), and cross-disciplinary collaboration will continue to bear fruit. Manifestation of the cosmologically nearby FRB population is probably limited by the low burst rate per source, but sufficient dwell times on galaxy clusters (Fialkov et al., 2018, e.g.) may provide detections of nearby galaxies that are easier to characterize than more distant ones. If our Galaxy (or a neighboring one) hosts an FRB source, we might experience rare but extraordinarily bright bursts with (relatively) low pulse DM. Such bursts would be difficult to distinguish from RFI, but may be detectable with all-sky dipole antennas or as a citizen science project using mobile phone receivers (e.g. Katz, 2014a; Maoz & Loeb, 2017).
Eventually, efficient petascale computation may allow next-generation projects like the DSA-2000 (a proposed 2000-dish successor to DSA-110) and the full Square Kilometre Array (e.g. Macquart et al., 2015) to continuously image large swathes of the sky at high enough time resolution to routinely detect and localize large samples of FRBs. Rather like the LSST event streams, the primary challenge will be the efficient allocation of foillow-up resources to extract scientific value from those detections — no doubt a much better problem to have than the current situation.
DISCLOSURE STATEMENT
The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.
ACKNOWLEDGMENTS
We thank our colleagues and collaborators for discussions and help, as well as access to some results in advance of publication. An incomplete list includes Matthew Bailes, Keith Bannister, Cees Bassa, Nick Battaglia, Edo Berger, Geoff Bower, Patrick Boyle, Sarah Burke-Spolaor, Manisha Caleb, Fernando Camilo, Liam Connor, Adam Deller, Klaus Dolag, Jean Eilek, Ron Ekers, Wael Farah, Griffin Foster, Dale Frail, Bryan Gaensler, Vishal Gajjar, Avishay Gal-yam, Tim Hankins, Gregg Hallinan, Jason Hessels, Assaf Horesh, Simon Johnston, David Kaplan, Vicky Kaspi, Jonathan Katz, Evan Keane, Michael Kramer, Shri Kulkarni, Casey Law, Avi Loeb, Duncan Lorimer, Ryan Lynch, JP Macquart, Elizabeth Mahoney, Benito Marcote, Maura McLaughlin, Daniele Michilli, Chiara Mingarelli, Ben Margalit, Brian Metzger, Eran Ofek, Stefan Oslowski, Zsolt Paragi, Emily Petroff, Vikram Ravi, Paul Scholz, Andrew Seymour, Ryan Shannon, Andrew Siemion, Lorenzo Sironi, Laura Spitler, Shriharsh Tendulkar, Shen Wang, Ira Wasserman, Eli Waxman, Robert Wharton, Barak Zackay, Bing Zhang, Yunfan (Gerry) Zhang, and Weiwei Zhu. The authors acknowledge support from the National Science Foundation (AAG 1815242), and are members of the NANOGrav Physics Frontiers Center, which is supported by the National Science Foundation award number 1430284.
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