The prevalence of repeating fast radio bursts

TL;DR

This paper analyzes the occurrence and nature of fast radio bursts, suggesting most originate from sources capable of emitting multiple bursts over their lifetimes, based on recent detection rates and dispersion measure data.

Contribution

It provides evidence that most fast radio bursts are from sources that emit multiple bursts, challenging the idea they are predominantly one-off events.

Findings

The volumetric rate of non-repeating FRBs exceeds that of cataclysmic progenitors.

Most FRBs likely originate from sources capable of multiple emissions.

Detection of low dispersion measure bursts supports multiple-burst source models.

Abstract

Fast radio bursts are extragalactic, sub-millisecond radio impulses of unknown origin [1,2]. Their dispersion measures, which quantify the observed frequency-dependent dispersive delays in terms of free-electron column densities, significantly exceed predictions from models [3] of the Milky Way interstellar medium. The excess dispersions are likely accrued as fast radio bursts propagate through their host galaxies, gaseous galactic halos and the intergalactic medium [4,5]. Despite extensive follow-up observations of the published sample of 72 burst sources [6], only two are observed to repeat [7,8], and it is unknown whether or not the remainder are truly one-off events. Here I show that the volumetric occurrence rate of so far non-repeating fast radio bursts likely exceeds the rates of candidate cataclysmic progenitor events, and also likely exceeds the birth rates of candidate compact-object sources. This analysis is based on the high detection rate of bursts with low dispersion measures by the Canadian Hydrogen Intensity Mapping Experiment [9]. Within the existing suite of astrophysical scenarios for fast radio burst progenitors, I conclude that most observed cases originate from sources that emit several bursts over their lifetimes.

Equations

$${\mathrm{DM}}_{\mathrm{X}}=\mathrm{DM}-{\mathrm{DM}}_{\mathrm{MW}}={\mathrm{DM}}_{\mathrm{MWhalo}}+{\mathrm{DM}}_{\mathrm{IGM}}+{\mathrm{DM}}_{\mathrm{host}},$$

Full text

Title: The prevalence of repeating fast radio bursts

Authors: Vikram Ravi1,2,3,∗.

1 Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge MA 02138, USA.

2 Cahill Center for Astronomy and Astrophysics, MC 249-17, California Institute of Technology, Pasadena CA 91125, USA.

3 E-mail: vikram@caltech.edu.

**Fast radio bursts are extragalactic, sub-millisecond radio impulses of unknown origin1,2. Their dispersion measures, which quantify the observed frequency-dependent dispersive delays in terms of free-electron column densities, significantly exceed predictions from models3 of the Milky Way interstellar medium. The excess dispersions are likely accrued as fast radio bursts propagate through their host galaxies, gaseous galactic halos and the intergalactic medium4,5. Despite extensive follow-up observations of the published sample of 72 burst sources6, only two are observed to repeat7,8, and it is unknown whether or not the remainder are truly one-off events. Here I show that the volumetric occurrence rate of so far non-repeating fast radio bursts likely exceeds the rates of candidate cataclysmic progenitor events, and also likely exceeds the birth rates of candidate compact-object sources. This analysis is based on the high detection rate of bursts with low dispersion measures by the Canadian Hydrogen Intensity Mapping Experiment9. Within the existing suite of astrophysical scenarios for fast radio burst progenitors, I conclude that most observed cases originate from sources that emit several bursts over their lifetimes. **

Thirteen fast radio bursts (FRBs) were published by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) collaboration, including one repeating source (FRB 180814.J0422$+$73) that I exclude from my analysis8,9 (see Methods). These events were detected during a pre-commissioning phase when the instrument was not operating with its full sensitivity and field of view. The survey was conducted over less than $7.82\times 10^{-5}$ sky-years, implying an all-sky FRB rate floor of 300 day*-1* in the 400$-$800 MHz CHIME frequency band. Despite the systematic uncertainties, this is an order of magnitude greater than the rate of bright FRBs detected with the Australian Square Kilometre Array Pathfinder (ASKAP)10. Additionally, although the ASKAP FRBs typically have lower excess dispersion measures (DMs) than FRBs detected with the more sensitive Parkes telescope, CHIME has a more than ten times higher detection rate than ASKAP at low excess DMs (Figure 1). This motivated the present analysis of the volumetric occurrence rate of FRBs.

The paucity of direct distance measurements for FRBs, based for example on observations of FRB host galaxies, has meant that FRB volumetric-rate estimates have relied on ascribing dominant fractions of the excess DMs to the intergalactic medium (IGM)1,11. I define the extragalactic DM, ${\rm DM}_{\rm X}$, as the difference between FRB DMs and predictions from models3 of the Milky Way interstellar medium ($\mathbf{\mathbf{\rm DM}_{\mathbf{\rm MW}}}$). If FRB ${\rm DM}_{\rm X}$ values were entirely built up from a homogeneous IGM comprising all cosmic baryons, the ${\rm DM}_{\rm X}$ range of the CHIME sample of 79–979 pc cm*-3* would correspond to a comoving distance range of $0.34-2.52$ Gpc [4]. This assumption, together with a host-galaxy contribution to ${\rm DM}_{\rm X}$ of 100 pc cm*-3*, was previously applied to an early sample of four FRBs from the Parkes telescope to derive a volumetric rate of $2.4\times 10^{4}$ Gpc*-3* yr*-1* [1,11]. Substantial, hard to quantify uncertainties affect this estimate, including the sample completeness at different distances, the host-galaxy ${\rm DM}_{\rm X}$ contributions and the effects of cosmological evolution in the FRB population.

Here I derive a robust lower limit on the FRB volumetric rate using the CHIME sample of low-${\rm DM}_{\rm X}$ bursts. For each FRB, I consider the following components of ${\rm DM}_{\rm X}$:

[TABLE]

where ${\rm DM}_{\rm MW}$ is estimated from the NE2001 model for the Milky Way ionised interstellar medium3, ${\rm DM}_{\rm MWhalo}$ arises in the Milky Way hot gaseous halo5, ${\rm DM}_{\rm IGM}$ arises in the IGM4, and ${\rm DM}_{\rm host}$ arises in FRB host galaxies. I adopt a relation between ${\rm DM}_{\rm IGM}$ and cosmological distance that incorporates the primordial helium fraction and an IGM baryon fraction of 0.84 [12], with a normally-distributed scatter of 10 pc cm*-3* [4]. Recent observations of ultraviolet and X-ray quasar absorption lines associated with the Galactic halo imply the presence of a substantial gas mass at temperatures between $10^{4}-10^{7}$ K, in agreement with observations of other galaxies and cosmological simulations, that contributes between $50-80$ pc cm*-3* out to the Milky Way virial radius5. I therefore assume that ${\rm DM}_{\rm MWhalo}$ can have any value between $50$ pc cm*-3* and the minimum of $80$ pc cm*-3* and $({\rm DM}_{\rm X}-{\rm DM}_{\rm host})$ with equal probability. I perform the analysis below for different characteristic values of ${\rm DM}_{\rm host}$. These features imply a probability distribution, $P(<{\rm DM}_{\rm X}\,|\,d)$, for an FRB to have an extragalactic DM that is less than the expectation given a $d$ (see Supplementary Figure 1).

A comparison of the ${\rm DM}_{\rm X}$ distributions of FRB samples from ASKAP and Parkes suggests that ASKAP is increasingly incomplete at higher values of ${\rm DM}_{\rm X}$ because of its insensitivity to the faint, high-${\rm DM}_{\rm X}$ FRBs observed by Parkes10. This effect, together with a possible correlation between FRB temporal widths and ${\rm DM}_{\rm X}$ [2,9], and additional unknown systematics in the CHIME observations9, strongly suggests that CHIME is also increasingly incomplete at higher values of ${\rm DM}_{\rm X}$. I mitigate this unknown incompleteness by deriving a lower limit on the FRB rate, $R$, within a limited volume bounded at $d=d_{\rm limit}$ that contains the lowest-${\rm DM}_{\rm X}$ CHIME FRBs. I choose a $d_{\rm limit}$ such that $P(<{\rm DM}_{\rm X}\,|\,d)$ is essentially unity for the lowest-${\rm DM}_{\rm X}$ FRB (180729.J1316$+$55, ${\rm DM}_{\rm X}=78.610$ pc cm*-3*), and 0.95 for the FRB with the second lowest ${\rm DM}_{\rm X}$ (FRB 180810.J1159$+$83, ${\rm DM}_{\rm X}=122.134$ pc cm*-3*); for no ${\rm DM}_{\rm host}$ contribution, $d_{\rm limit}=426$ Mpc. I also consider the case where $P(<{\rm DM}_{\rm X}\,|\,d)$ is essentially unity for the two aforementioned FRBs, and 0.95 for the event with the third lowest ${\rm DM}_{\rm X}$ (FRB 180814.J1554$+$74; ${\rm DM}_{\rm X}=197.32$ pc cm*-3*; $d_{\rm limit}=739$ Mpc). When $P(<{\rm DM}_{\rm X}\,|\,d)\sim 1$, the probability of having observed the FRB within a volume bounded by $d$ is likely to also be approximately unity.

Assuming that the so far non-repeating FRBs are independent events associated with distinct sources, their observed occurrence within the bounded volume can be modelled as a Poisson process. Lower limits on $R$ can then be derived from the number of observed events using the Poisson probability mass function (see Methods)13. For the two cases of $d_{\rm limit}$ described above, I assume that two and three FRBs were observed respectively, and calculate corresponding conservative 90%-confidence lower limits on $R$. Direct statistical inference on $R$ cannot be performed without specifying a model for the unknown incompleteness of the CHIME observations. Besides this incompleteness, the lower limits quoted below are conservative because they do not account for possible angular beaming of FRBs and cosmological time-dilation.

I evaluate $d_{\rm limit}$ and the 90%-confidence lower limit on $R$ for different values of ${\rm DM}_{\rm host}$, and the results are shown in Figure 2. The lower limit on $R$ is less constraining for $d_{\rm limit}$ corresponding to three observed FRBs than for $d_{\rm limit}$ corresponding to two observed FRBs. The lower limits on $R$ decrease as $d_{\rm limit}$ is increased to include more CHIME FRBs, which may indicate increasing incompleteness at higher values of ${\rm DM}_{\rm X}$. In the remainder of the text, I quote lower limits on $R$ for $d_{\rm limit}$ corresponding to two observed FRBs. For no assumed ${\rm DM}_{\rm host}$, $R>2.1\times 10^{4}$ Gpc*-3* yr*-1*, and for ${\rm DM}_{\rm host}=50$ pc cm*-3*, $R>2.4\times 10^{5}$ Gpc*-3* yr*-1*. Despite these lower limits being conservative, they are comparable to the estimate of $R\sim 2.4\times 10^{4}$ Gpc*-3* yr*-1* from the initial sample of four Parkes FRBs where ${\rm DM}_{\rm host}=100$ pc cm*-3* was assumed1,11. This may be explained by the uncertainties noted above in the latter, such as incompleteness in the Parkes sample given the large $d_{\rm limit}$ that was adopted. I note that such a large ${\rm DM}_{\rm host}$ would be in tension with the lowest-${\rm DM}_{\rm X}$ CHIME FRBs.

The FRB rates derived herein can be compared with predictions for non-repeating FRB progenitors, and with the estimated birth rates of FRB sources (see Figure 2). All astrophysical FRB progenitors (excluding those attributed to new physics) are expected to be contained within galaxies, in many cases in regions with atypically dense interstellar medium14. Simulations of the ${\rm DM}_{\rm host}$ values corresponding to typical locations within inclination-averaged early-type and dwarf galaxies suggest ${\rm DM}_{\rm host}=23$ pc cm*-3*, and ${\rm DM}_{\rm host}=35$ pc cm*-3* is likely characteristic of typical locations within face on late-type galaxies15,16. Substantially larger values of ${\rm DM}_{\rm host}$ of a few hundred pc cm*-3* were recently inferred for the ASKAP FRB sample based on a comparison between FRB DMs from ASKAP, Parkes, and CHIME, and a tentative correlation between the ASKAP FRB sky-locations and catalogs of nearby galaxies17.

Models for non-repeating FRB progenitor events rely on the destruction of highly magnetised white dwarfs (WDs) or neutron stars (NSs). These events are, however, likely too rare to produce FRBs at the observed rate. For example, FRBs may be produced upon the merger of two WDs18, the merger of two NSs19, or the collapse of an NS to a black hole20. Gravitational-wave observations have demonstrated that NS-NS mergers occur at less than a quarter of the FRB volumetric-rate limit21. Binary WDs most likely trace stellar mass with a possible preference for galactic disks, making it unlikely that all WD-WD mergers are found in under-dense regions of their host galaxies22, as is required for this FRB progenitor channel23. Further, only NS-NS mergers and the accretion-induced collapse (AIC) of white dwarfs24,25 can form massive, rotationally supported NSs that rapidly collapse to black holes in sufficiently sparse environments for FRB radiation to escape11.

Predictions for the birth rate of stellar-mass compact objects that can produce FRBs are also inconsistent with the FRB volumetric rate, if FRB sources do not repeat. Core-collapse supernovae ($\sim 10^{5}$ Gpc*-3* yr*-1*) [26] are likely the most common channel for compact-object production, and are consistent with the FRB volumetric-rate limit for low ${\rm DM}_{\rm host}$. However, their young stellar progenitors are commonly associated with star-forming regions of galaxies27, and their compact-object remnants would need to migrate into less dense regions and age prior to FRB production to avoid tension with the FRB volumetric rate due to a high ${\rm DM}_{\rm host}$ [16]. The magnetar birth rate is at most half the core-collapse rate28, and active magnetars in the Milky Way are only found close to the Galactic plane. Other channels for compact-object production (e.g., NS-NS and WD-WD mergers, AIC of WDs) have even lower volumetric rates.

If FRBs are associated with stellar-mass compact objects produced through the standard astrophysical channels summarised in Figure 2, the high FRB volumetric rate implies that the majority of FRB sources repeat. Most FRB progenitor channels require specially configured compact objects, such as young magnetars and NSs in unusual environments14. The precise repetition rates of individual FRB sources will depend on the birth rates of the specific progenitor objects, and the lifetimes over which FRBs can be emitted. Recent analyses of the population of FRB sources similar to the repeating FRB 121102 suggest that this object is atypical of the so far non-repeating FRB population29,30. However, for example, even an FRB production rate of $\sim 10^{2}$ events per Hubble time per source would be sufficient to resolve the present tension with many of the models discussed here. Ongoing observations with CHIME will provide unprecedented sensitivity to the range of possible FRB repetition rates, together with a larger sample of low-${\rm DM}_{\rm X}$ FRBs to refine the present analysis. The localization of a large sample of FRBs to regions within their host galaxies will enable quantitative tests of population synthesis models for astrophysical FRB progenitors, and estimates of the progenitor ages that will in turn better quantify the expected repeat rates. If the sample completeness can be quantified, FRB distance measurements based on observations of host galaxies will enable a direct measurement of the FRB volumetric rate.

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Correspondence and requests for materials should be addressed to V. Ravi.

Acknowledgements. I thank E. Thomas, C. Bochenek and J.-P. Macquart for useful discussions. This work made use of the astropy (http://www.astropy.org) python package. V.R. is supported by a Clay Postdoctoral Fellowship of the Smithsonian Astrophysical Observatory.

Author contributions V.R. was the sole contributor to this submission.

Competing interests. The author declares that they have no competing financial interests.

Data availability statement. The datasets analysed during the current study are available from the FRB Catalogue, http://frbcat.org/.

Code availability statement. Custom code used in this study is available at

https://github.com/VR-DSA/frb_rate.

Methods

The choice of the lowest possible $d_{\rm limit}$ values to contain either two or three FRBs does not upwardly bias the lower limit on the FRB rate. I demonstrate this through a simulation. Consider FRBs that are uniformly distributed in space, with a rate of one event per unit time per unit volume. I simulated $10^{4}$ samples of $10^{3}$ events, where in each sample the actual number of events was drawn from a Poisson distribution with a rate parameter of $10^{3}$. I then recorded the distances to the nearest three FRBs in each sample ($d_{1}$, $d_{2}$, and $d_{3}$ respectively). 90%-confidence lower limits on the volumetric rate were calculated as in the main text13: $R_{1}=0.105\times[(4/3)\pi d_{1}^{3}]^{-1}$, $R_{2}=0.532\times[(4/3)\pi d_{2}^{3}]^{-1}$ and $R_{3}=1.102\times[(4/3)\pi d_{3}^{3}]^{-1}$ for each sample. Histograms of $R_{1}$, $R_{2}$ and $R_{3}$ are shown in Supplementary Figure 2, and the 90th percentiles of the samples are indicated. In each case, the 90th percentiles are very close to the true rate of unity. This exercise was also carried out for $10^{4}$ samples of Poisson-distributed events with an expectation of 12, with identical results.

The use of a low $d_{\rm limit}$ is also motivated by the observations. Figure 1 of the main text shows the empirical cumulative distributions of FRB ${\rm DM}_{\rm X}$ values from ASKAP and CHIME, quantified as all-sky detection rates using the survey extents. I also show curves of predicted FRB all-sky detection rates assuming various comoving volumetric rates and no observational incompleteness, ${\rm DM}_{\rm MWhalo}=50$ pc cm*-3*, ${\rm DM}_{\rm host}=0$ pc cm*-3*, and assuming the same DM-distance relation (with no scatter) as in the main text. Cosmological time-dilation effects are included. The shallowness of the CHIME (and ASKAP) empirical distribution of ${\rm DM}_{\rm X}$ values in comparison with the predicted curves suggests incompleteness that increases with ${\rm DM}_{\rm X}$. A similar argument was made in Ref. [33] (e.g., their Figure 1). This effect is also evidenced by the decrease in the lower limits on the FRB rate, $R$, for increasing values of $d_{\rm limit}$. For example, the 90% confidence lower limits on $R$ for $d_{\rm limit}$ corresponding to four and five FRBs are $R>8.9\times 10^{3}$ Gpc*-3* yr*-1* $R>4.8\times 10^{3}$ Gpc*-3* yr*-1* respectively, for ${\rm DM}_{\rm host}=0$ pc cm*-3*. These arguments only hold as long as ${\rm DM}_{\rm X}$ values are typically dominated by ${\rm DM}_{\rm IGM}$. However, if this were not the case, the conclusions reached in the main text would only be strengthened.

The repeating CHIME FRB 180814.J0422$+$73 was not included in the present analysis despite its low ${\rm DM}_{\rm X}=102.4$ pc cm*-3* [8]. This is partly because of the evidence that several properties of the first repeating FRB 121102, some of which (e.g., the observed repetition, and the burst time-frequency structure) are inconsistent with the population of FRBs that have not been observed to repeat2,29,30. Additionally, although the ${\rm DM}_{\rm X}$ of FRB 180814.J0422$+$73 is lower than that of FRB 180810.J1159$+$83, the conclusions reached in the main text are independent of its inclusion in the analysis.

The results presented in the main text are robust to the choice of model for the DM contribution from the Milky Way ionised interstellar medium (${\rm DM}_{\rm MW}$). For example, if the YMW1734 model is used instead of the NE2001 model, the lower limit on the FRB rate, $R$, derived for $d_{\rm limit}$ corresponding to two FRBs and ${\rm DM}_{\rm host}=0$ pc cm*-3* changes from $R>2.1\times 10^{4}$ Gpc*-3* yr*-1* to $R>1.8\times 10^{4}$ Gpc*-3* yr*-1*.

Nicholl, M. et al. Empirical Constraints on the Origin of Fast Radio Bursts: Volumetric Rates and Host Galaxy Demographics as a Test of Millisecond Magnetar Connection. Astrophys. J. 843, 84 (2017). 2. 2.

Yao, J. M., Manchester, R. N. & Wang, N. A New Electron-density Model for Estimation of Pulsar and FRB Distances. Astrophys. J. 835, 29 (2017).