6. POPULATION PROPERTIES

Here we describe the properties of FRBs as an ensemble. Such considerations inform how we can optimize future FRB searches, whether there are observational sub-classes, and are a critical input for constraining theory.

6.1. FRB polarization and rotation measures

Currently only 9 of the more than 60 cataloged FRBs have polarimetric data available. From this subset, we already see a heterogeneous picture emerging (Fig. 12): some FRBs appear to be completely unpolarized (e.g. FRB 150418), some show only circular polarization (e.g. FRB 140514), some show only linear polarization (e.g. FRBs 121102, 150215, 150817, 151230), and some show both (e.g. FRBs 110523, 160102). A recent overview can be found in Caleb et al. (2018b, see their Table 1 and references therein). In one case, an FRB candidate (FRB 180301) has shown frequency-dependent polarization properties (Price et al., 2019), which may be indicative of a non-astrophysical progenitor if they cannot be explained through propagation effects (e.g. Gruzinov and Levin, 2019, Vedantham and Ravi, 2019). These varied polarization properties do not necessarily reflect different physical origins, however. In analogy with pulsars, which show a wide variety of polarization fractions between sources, as well as individual pulses, a single type of emitting source could be responsible for the observed range of FRB polarization properties. The heterogeneity in FRB polarization properties could thus arise from time-variable emission properties, different viewing geometries, or different local environments.

Figure 12. Polarization profiles for FRB 140514 (left), the first FRB with measured circular polarization (Petroff et al., 2015a), and FRB 110523 (right), the first FRB with measured linear polarization (Masui et al., 2015). The Stokes parameters for total intensity I (solid), Q (dashed), U (dot-dashed), and V(dotted) are plotted for each burst. FRB 140514 profile from Fig. 1 of Petroff et al. (2015a); FRB 110523 profile from Fig. 3 of Masui et al. (2015).

By measuring polarization angle as a function of frequency, Faraday rotation can be quantified (see Section 3.4). Here too, the known FRB population has presented a heterogeneous picture: while some FRBs have rotation measures (RMs) ∼10 rad m⁻² that are consistent with that expected from the Galactic foreground (e.g. FRBs 150215, 150807), others have much higher RMs, which point to a dense and highly magnetised local environment. Masui et al. (2015) presented the first detection of linear polarization from an FRB, and the derived RM = − 186.1 ± 1.4 rad m⁻² led them to conclude that the source is in a dense environment or surrounded by a nebula. Recently, FRB 160102 has also been found to have a relatively large RM (−220 ± 6.4 rad m⁻²) (Caleb et al., 2018b). Most strikingly, the repeating FRB 121102 was found to have an extremely high RM ∼ 10⁵ rad m⁻² (see Section 5.4 and Fig. 6 for more details). Such high RM values are difficult to detect given the limited frequency resolution in most FRB search experiments, and thus FRBs with apparently no linear polarization could potentially be high-RM sources de-polarized by intra-channel Faraday rotation smearing. This could be the case for FRB 140514, which was the first FRB with detected polarization (∼30% circular; Petroff et al., 2015a).

Conversely, some FRBs show high linear polarization fraction, but low RM. Petroff et al. (2017a) showed that FRB 150215 (43 ± 5% linearly polarized) has an RM in the range −9 < RM < 12 rad m⁻² (95% confidence level), i.e. consistent with zero and demonstrating a low Galactic foreground contribution. Likewise, Ravi et al. (2016) found RM = 12.0 ± 0.7 rad m⁻² for FRB 150807 (80 ± 1% linearly polarized), and used this to constrain the magnetic field of the cosmic web to < 21 nG (parallel to the line-of-sight). In both cases, the low RM points to negligible magnetization in the circum-burst plasma.

It is clear that measuring the RM provides an important way of characterizing FRB local environments, and may lead to clarity on whether there are multiple sub-classes of FRB. The increasing use of real-time triggering and full-polarization (or even voltage) data dumps should mean that a larger fraction of future FRB discoveries will have known polarimetric properties. Even the preservation of full-Stokes data for upcoming surveys with relatively narrow frequency channels may be sufficient to recover polarization profiles for many FRBs.

6.2. Multi-wavelength follow-up of FRBs

Despite multi-wavelength searches, to date prompt FRB emission has only been convincingly detected at radio frequencies between 400 MHz (CHIME/FRB Collaboration et al., 2019b, CHIME/FRB Collaboration et al., 2019a) and 8 GHz (FRB 121102; Gajjar et al., 2018, Michilli et al., 2018a). Prompt emission outside of the radio band has so far only been claimed in one source, FRB 131104, in a study by DeLaunay et al. (2016) who searched archival Swift data around the times of several known FRB events. These authors claimed the detection of a gamma-ray transient associated with FRB 131104. However, given the low significance of the X-ray signal (3.2σ), the association is arguably tenuous (for a discussion, see Shannon and Ravi, 2017). Further progress in this area can be made by dedicated experiments. One such study, currently in progress with a 20-m telescope at the Green Bank Observatory shadows the Swift daily source list for FRBs in the field of view (Gregg et al. in preparation).

For longer-term emission akin to afterglows in GRBs, we note that since the FRB isotropic energy is about 10 orders of magnitude smaller than GRBs, the predicted FRB multi-wavelength afterglow is much fainter (see, e.g., Yi et al., 2014). In spite of these challenges, it is of great importance to continue to search for longer-term emission. In one such study, Keane et al. (2016) mounted an unprecedented multi-wavelength follow-up campaign triggered by FRB 150418. This revealed a fading radio counterpart in the positional uncertainty region of the FRB. Assuming an association with the FRB 150418, this led to the identification of a candidate host galaxy and its redshift. However, this association has been disputed because of the non-negligible chance of a variable radio source in the field (Bell et al., 2015). Williams and Berger (2016) conducted additional radio follow-up and found that the candidate radio counterpart was continuing to vary and even re-brightened to the same levels as in the days following FRB 150418. They concluded that the source was a variable active galactic nucleus and could not be conclusively linked to the FRB source. Eftekhari and Berger (2017) and Eftekhari et al. (2018) discuss the challenges of identifying FRB counterparts and show that, for FRBs and hosts out to redshifts of ∼ 1, positional determinations at the level of at least 20 arcseconds (and in some cases much better) are required in order to provide robust associations.

The repeating FRB 121102 has provided a great practical advantage for multi-wavelength follow-up (as described in detail in Section 5.4). Other repeating FRB sources will be discovered in the future and followed-up in similar ways. Importantly, the increasing use of real-time searches will also allow near-real-time triggering of multi-wavelength instruments to look for afterglows through machine-parsable automated mechanisms such as VOEvents (Petroff et al., 2017b). Several experiments are also using multi-telescope shadowing, which could lead to the detection of multi-wavelength prompt emission – e.g., the MeerLicht optical telescope shadowing radio searches with MeerKAT (Bloemen et al., 2016).

Recently, ever more detailed follow-up efforts have been undertaken after the discovery of new FRBs. Bhandari et al. (2018) undertook follow-up for FRBs 151230 and 160102 from X-ray to radio wavelengths including some of the first searches for associated neutrino emission with the ANTARES neutrino detector. Ultimately, without a precise localization of the sources from their radio bursts and the unknown multi-wavelength nature of FRB emission, it is difficult to pinpoint the location of an FRB from follow-up but these observations place limits that are useful for future targeted searches.

6.3. Properties of the FRB population

In Section 6.4, Section 6.5, and Section 6.6 we consider the specific distributions of FRBs over the sky, in DM, and in pulse duration. First, however, we consider some of the two-dimensional distributions of the population as a function of various parameters. These are shown for some subsets of the known population in Fig. 13.

Figure 13. The properties of the catalogued FRB population. (a) The pulse duration (width) versus DM. Solid lines represent temporal broadening from DM smearing in an individual frequency channel combined with the sampling time for different telescopes. In the case of FRBs from CHIME, plotted widths have been obtained through modeling and are not the observed FRB widths from the instrument. (b) Scattering timescale versus DM for all FRBs where scattering has been measured. The curve shows the DM-scattering relation for pulsars in the Galaxy derived by Bhat et al. (2004). FRBs are under-scattered relative to Galactic pulsars of similar DMs. (c) A histogram of the DM excess compared to the expected Galactic maximum along the line of sight. (d) A histogram of the pulse durations. For panels (a) and (b) colors correspond to the Parkes (black), ASKAP (blue), Arecibo (green), UTMOST (red), GBT (aqua) and CHIME (pink) telescopes.

In Fig. 13a we show the pulse widths of FRBs versus their measured DM. Over-plotted are the curves per telescope showing the effects of instrumental smearing from Eq. 23, combined with survey sampling time as a function of DM. Some FRBs from each observing instrument closely follow this line, meaning that their intrinsic widths may in fact be much lower. In the range 500 cm⁻³ pc < DM < 1500 cm⁻³ pc pulse duration does seem to increase with DM, but this trend does not hold at the higher DMs where most FRBs are found with durations < 10 ms.

Fig. 13b plots the scattering timescales, where measured for individual FRBs, versus their DMs. While currently only roughly 20 FRBs have published scattering timescales, the shape of this distribution may change as a larger population have measured scattering parameters. The existing data, however, do provide an intriguing picture of limits on radio-wave scattering for FRBs. Most notably, unlike the well-known correlation seen for Galactic pulsars (see, e.g., Bhat et al., 2004), there does not appear to be a similar trend in the FRB distribution. As remarked by a number of authors (see, e.g., Lorimer et al., 2013, Cordes et al., 2016) for cases where most of the scattering is produced at the source, a lever-arm effect tends to minimize scatter broadening. The lack of any correlation with DM also suggests that the IGM plays a very minor role in pulse broadening for FRBs (Cordes et al., 2016, Xu and Zhang, 2016).

Fig. 13c plots a histogram of FRB DMs in excess of the modeled Galactic contribution (see Section 6.5) and Fig. 13d plots a histogram of the FRB pulse durations (see Section 6.6).

6.4. The sky distribution

The sky distribution of all published FRBs is shown in Fig. 14. Early non-detections of FRBs at intermediate and low Galactic latitudes by the Parkes telescope led Petroff et al. (2014) to conclude that the FRB detection rate is greater at high Galactic latitudes. They found the HTRU results to be incompatible with an isotropic distribution at the 99% confidence level based on 4 FRB detections at high Galactic latitudes and no detections at intermediate latitudes (|b| < 15^∘) in a longer observing time. This was further supported by analysis from Burke-Spolaor and Bannister (2014), upon the discovery of FRB 010125, which concluded that the high and low latitude FRB rates were strongly discrepant with 99.69% confidence, although this confidence level may have been overstated even at the time (Connor et al., 2016a). Macquart and Johnston (2015) attributed the observed disparities found in these works to diffractive scintillation at higher Galactic latitudes, which boosts FRBs that might otherwise not be detected (see also Section 3.2). The scintillation bandwidth is much wider along high latitude sight lines, and comparable to the observing bandwidth used by most surveys at Parkes. Conversely, in their study of the FRB rate, Rane et al. (2016) found no evidence to support a non-isotropic sky dependence of the distribution.

Figure 14. An Aitoff projection map of the sky positions of all published FRBs as a function of Galactic longitude and latitude. As in Fig. 13, colors correspond to the Parkes (black), ASKAP (blue), Arecibo (green), UTMOST (red), GBT (aqua) and CHIME (pink) telescopes.

Recent studies have been somewhat more successful at higher Galactic latitudes, and some searches, such as the ASKAP Fly's Eye pilot study, have purposely concentrated their time on sky at high latitudes to maximize detections (Bannister et al., 2017, Shannon et al., 2018). As the population of FRBs grows, however, the statistical significance of the latitude-dependent detection rate has gotten much weaker and early indications of anisotropy may have been an artifact of small number statistics. Using 15 FRBs detected at Parkes in the HTRU and SUPERB surveys Bhandari et al. (2018) find no significant deviation of the sample from an isotropic distribution above the 2 σ level.

As with many aspects of the FRB population, studies of the FRB sky distribution have been limited due to the small available FRB sample. With the new ultra-wide-field capabilities of CHIME as well as large-scale surveys from telescopes such as APERTIF, ASKAP, and UTMOST it may be possible to answer this question in the near future.

While the extragalactic nature of at least one FRB has been confirmed beyond doubt, a large and statistically isotropic population of FRBs would provide further weight behind the argument that FRBs are indeed extragalactic and possibly cosmological, similar to the early studies of GRBs (Meegan et al., 1992, Kouveliotou et al., 1993, Kulkarni, 2018). With a large enough population of FRBs it may also be possible to determine if there is any clustering on the sky associated with nearby galaxy clusters, if FRBs are extragalactic but non-cosmological.

6.5. The DM distribution

A histogram of DM_excess for all FRBs is plotted in Fig. 13c. The true minimum and maximum values of dispersion measure possible for FRBs remain unknown; however, at the moment DM is one of the primary criteria that we use to distinguish an FRB from a Galactic pulse. Most searches for FRBs place a strict cut on DM. Real-time searches at the Parkes telescope only consider bright bursts with a DM value 1.5 × DM_Galaxy or greater (Petroff et al., 2015a) and deeper, offline searches may consider pulses with DMs > 0.9 × DM_Galaxy. This requirement that the DM be larger than the expected contribution from the Milky Way makes it difficult to conclusively identify the minimum possible excess DM of an FRB. However, FRBs that occupy this border region between potentially galactic and extragalactic sources are beginning to be found (Qiu et al., 2019). This dilemma will likely only be resolved once we have a more physical definition of an FRB that does not rely on DM.

Thus far, the lowest DM measured for an FRB is 109.610 ± 0.002 cm⁻³ pc for FRB 180729.J1316+55 from the CHIME telescope (CHIME/FRB Collaboration et al., 2019b). In the context of the entire FRB population an FRB may be considered to have a low DM if DM_excess ≲ 350 cm⁻³ pc. There are now > 15 FRBs in this category. Relative to the population discovered with each detection instrument, the low-DM FRBs tend to have higher peak flux densities and larger fluences than the overall sample, for example FRBs 110214 (DM_excess = 130 cm⁻³ pc), 150807 (DM_excess = 230 cm⁻³ pc), 180309 (DM_excess = 218 cm⁻³ pc), and 010724 (DM_excess = 330 cm⁻³ pc) are the four brightest FRBs detected at the Parkes telescope thus far, all with S_peak > 20 Jy (Petroff et al., 2018, Oslowski et al., 2018, Ravi et al., 2016, Lorimer et al., 2007).

DM is often used as a rough proxy for distance (see Section 2) thus the maximum DM possible for an FRB is of great interest as it could tell us about the maximum possible redshift out to which we can see FRBs. High DM FRBs at z > 3 may even probe Helium reionization in the Universe (Zheng et al., 2014, Macquart, 2018). The maximum DM pulse detectable by a telescope is dependent on several aspects of the observing configuration, including the time and frequency resolutions and the dedispersion algorithm used (see Section 4.1). Thus far, the largest DM observed for an FRB is from FRB 160102 with DM = 2596.1 ± 0.3 cm⁻³ pc, found using the Parkes telescope (Bhandari et al., 2018). If all the excess dispersion originates in the IGM, this FRB would be at a redshift z = 2.10, i.e. a comoving distance D_L = 16 Gpc. A larger sample will determine whether even higher-DM FRBs exist.

6.6. The pulse width distribution

The observed FRB pulse width distribution is plotted in Fig. 13d. As with DM, the true minimum and maximum possible widths for FRBs are not yet known. However, the observed width distribution already spans several orders of magnitude. The known distribution peaks at a few milliseconds. The narrowest FRB single pulse yet measured is from FRB 121102 observed by Michilli et al. (2018a) to have a width of ≲ 30 s, although a sub-pulse of FRB 170827 revealed through voltage capture was measured to be 7.5 s in duration (Farah et al., 2018). The widest pulse reported in the literature is currently FRB 170922, which was detected with the UTMOST telescope at 835 MHz with W = 26 ms (Farah et al., 2017). The width of an FRB can be heavily affected by scattering in the intervening medium, which broadens the pulse and reduces the peak flux density (see Section 3.3). Thus, very wide, low peak flux density FRBs, even with equal fluence to short-duration easily detected FRBs, could exist but may be easily missed.

Notably, FRBs are under-scattered compared with Galactic pulsars of comparable DM (see Fig. 13b and Ravi, 2019). This could be due to the significantly different relative distances between observer, scattering screen, and burst source. In a simple one-screen toy model, scattering is maximized when the screen is half-way between source and observer. In the case of FRBs, if the dominant scattering screen is in the host galaxy or Milky Way, then the temporal broadening of the signal will be comparatively modest. Though FRBs may be less scattered compared to pulsars with similar DM, scattering may still be relevant for understanding the lack of FRBs detected at low frequencies (e.g. Karastergiou et al., 2015).

The minimum pulse width of an FRB is of interest as it probes the minimum physical scale on which these pulses can be generated. The ≲ 30 s pulse from FRB 121102 already puts an upper limit on the emitting region for this burst at ≲ 10km (in the absence of relativistic beaming effects). The maximum pulse width of an FRB would potentially tell us less about the emitting region and more about the propagation effects at play, as the widest pulse we detect is likely to be wide due to scatter broadening. Scattering has a larger effect at lower frequencies and FRBs found at lower frequencies (< 600 MHz) may be dominated by scattering effects. Recently reported FRBs between 400 and 800 MHz from CHIME show more scattering than might be explained by the normal ionized medium in a host galaxy, and CHIME/FRB Collaboration et al. (2019b) suggests that these bursts comes from special over-dense regions in their host galaxies, such as supernova remnants, star-forming regions, or galactic centers. However, other FRBs in the new CHIME sample exhibit very narrow pulse widths, such as a reported pulse duration of 0.08 ms for FRB180729.J0558+56.

Finding the narrowest FRBs remains an instrumentation challenge, as narrow frequency channels (or coherent dedispersion) and fast time sampling are required to probe these regimes. Some FRBs detected at telescopes such as Parkes are unresolved in width due to insufficient frequency and time resolution and only upper limits can be placed on their intrinsic pulse duration (Ravi, 2019). In the future, voltage capture systems on radio telescopes, either collected continuously as with Breakthrough Listen (Gajjar et al., 2018) or triggered collection as with UTMOST (Farah et al., 2018), will help us probe this region of the FRB parameter space – especially if we can observe at higher radio frequencies, where scattering is minimized.

6.7. Repeating and non-repeating FRBs

Clearly, an important diagnostic is whether an FRB has shown multiple bursts. Conversely, it is less informative if an FRB has not yet been seen to repeat, because one can always argue that the burst rate is simply very low.

In the current population, only two FRB sources have been seen to repeat (see Section 5.4 and Section 5.5). For these sources, only non-cataclysmic theories are viable, and it has been argued that perhaps all FRBs are capable of repeating. The locations of other FRBs have been re-observed to search for repeating pulses. Some FRBs have little to no follow-up published in the literature (e.g. FRB 010125; Burke-Spolaor and Bannister, 2014) and others have been followed up for over 100 hours within ± 15 days of discovery (e.g. FRB 180110 with > 150 hours in the 30-day window around the FRB; Shannon et al., 2018). With only two repeaters in the FRB sample there are many outstanding questions about the potential for repetition from other FRBs. The repeat rate of FRB 121102 is highly non-Poissonian (Oppermann et al., 2018) with epochs of high and low activity; FRB 180814.J0422+73 has not been studied sufficiently to constrain its repeat rate as a function of time. With the detection of more repeating FRB sources it may become clear that repeating FRBs come from an entirely different source class or progenitor channel compared to non-repeaters (see Section 6.8 and Section 9), but more data is needed and this issue may only be settled definitively with a very large sample of sources (hundreds to thousands).

FRB 121102 is currently the only repeater that has been studied in great detail, but only a few of its properties are distinctive compared to the rest of the population: it has the highest observed rotation measure (∼ 10⁵ rad m⁻²) of any FRB by several orders of magnitude, and it is capable of emitting bursts at a high rate (sometimes tens per hour), so it is clearly far more active compared to other sources. Some of the repeating pulses from both repeaters show complex frequency and time structure (Michilli et al., 2018a, Hessels et al., 2018, CHIME/FRB Collaboration et al., 2019a) but this may not be a distinctive trait to “repeaters”. This structure may also be present in some one-off FRB detections with sufficient temporal and spectral resolution (see Fig. 15; Farah et al., 2018, Ravi, 2019). The pulses of FRB 121102 and FRB 180814.J0422+73 vary enormously in width (from ∼ 30 s to ∼ 10 ms for FRB 121102 and ∼ 2 ms to ∼ 60 ms for FRB 180814.J0422+73) but in both cases the discovery pulse was not unusual in its duration (Spitler et al., 2014).

Figure 15. De-dispersed pulse profiles and dynamic spectra of several FRBs. FRB 170827 (top, left) from Farah et al. (2018) detected with UTMOST at 835 MHz, FRB 110220 (top, middle) from Thornton et al. (2013) detected with Parkes at 1.4 GHz, FRB 110523 (top, right) from Masui et al. (2015) detected with GBT at 800 MHz, FRB 180110 (bottom, left) from Shannon et al. (2018) detected with ASKAP at 1.3 GHz, a pulse from FRB 121102 (bottom, middle) from Michilli et al. (2018a) detected with Arecibo at 4.5 GHz, and a pulse from FRB 180814.J0422+73 (bottom, right) from CHIME/FRB Collaboration et al. (2019a) detected with CHIME at 600 MHz.

However, for FRB 121102, the discovery peak flux density at discovery was much lower compared to previously discovered FRBs. Palaniswamy et al. (2018) argue that there is a growing body of evidence suggesting that FRB 121102 is fundamentally different compared with the other (so-far)non-repeating FRBs. However, it may simply be an exceptionally active example, and not fundamentally different in physical origin.

More observations of FRB 180814.J0422+73 – including RM measurements, and identification of its host galaxy – will elucidate further whether both repeaters have similar properties. Additionally, even a few more repeating FRBs might help distinguish sources that are observed to repeat from those that remain one-off events. It is expected that ongoing CHIME observations, which sample the sky with daily cadence, will provide a much clearer picture of the population of repeating FRBs.

6.8. Sub-populations emerging?

With two repeating FRBs now known, both showing similar spectro-temporal structure, it may soon be possible to identify sub-populations in the overall distribution of FRBs. However, as both Ravi (2019) and Caleb et al. (2018a) conclude, besides the uniqueness of repeating pulses from FRB 121102 (before the publication of FRB 180814.J0422+73), the current sample offers no clear dividing lines over any other observed parameters. While FRB 121102 has a larger RM compared to measured values from other FRBs, RM has not been measured for the entire sample, making it difficult to draw definitive conclusions. The population of FRBs found with ASKAP are brighter than those at Parkes (see Fig. 16) but this is due to the different detection thresholds of these instruments. The majority of FRBs have durations < 5 ms, with a tail in the distribution towards longer pulse durations. However, no clear trends (such as the presence of a distinct short- and long-duration population) have yet emerged.

With a larger population of FRBs, multi-modality in some observed parameters may indicate sub-populations in the way that a bi-modal duration distribution of short and long gamma-ray bursts became apparent as the population grew (Kouveliotou et al., 1993). Some parameters may be more promising than others for investigation along these lines. Pulse duration (analogous to GRBs) may reveal information about the progenitor or emission mechanism, and the RMs of future FRBs may provide information about their origins in a dense and turbulent or clean and sparse local environment. The relationship between parameters such as fluence and DM (see Section 7) may also provide valuable clues.

However, once FRBs are more routinely localized to host galaxies, the types of galaxies and the specific regions thereof in which they reside may provide some of the most important clues for identifying sub-populations. The repeating FRB 121102 resides in a low-metalicity dwarf galaxy, and searches for galaxies of similar type have been done for other FRBs (Mahony et al., 2018). If some FRBs are found to reside in larger galaxies, or at different radii from their host galaxy centers, such as for GRBs (Kulkarni, 2018), this may provide a valuable tool for distinguishing between types of FRB sources.