Associating Fast Radio Bursts with Extragalactic Radio Sources: General Methodology and a Search for a Counterpart to FRB 170107

Fast radio bursts (FRBs) are extremely bright, millisecond-duration pulses of coherent radio emission, with large dispersion measures (DMs) that exceed typical Galactic values, hence pointing to an extragalactic origin. Since the discovery of the first FRB in archival data (Lorimer et al. 2007), roughly 30 additional FRBs have been detected, both in archival and real-time searches (Keane et al. 2012; Thornton et al. 2013; Spitler et al. 2014; Champion et al. 2016; Petroff et al. 2016; Caleb et al. 2017). Despite a growing number of FRB detections, the lack of precise localizations (typically ∼10³ arcmin²) has led to a wide range of suggested progenitor systems: giant pulses and magnetar flares (Popov & Postnov 2013; Lyubarsky 2014; Cordes & Wasserman 2016; Lyutikov et al. 2016), mergers of compact objects (Wang et al. 2016; Zhang 2016), the collapse of supramassive neutron stars to black holes (Falcke & Rezzolla 2014), and emission from rapidly spinning magnetars (Kumar et al. 2017; Metzger et al. 2017).

The discovery of the repeating FRB 121102 (Spitler et al. 2014, 2016) led to the first precise localization (Chatterjee et al. 2017) and the identification of a low-metallicity dwarf star-forming host galaxy at z = 0.193 (Tendulkar et al. 2017), with properties remarkably similar to the host galaxies of both long-duration gamma-ray bursts (LGRBs) and hydrogen-poor superluminous supernovae (SLSNe) (Metzger et al. 2017). Radio observations with the European VLBI Network (EVN) (VLBI: very longbaseline interferometry) revealed the presence of a compact, persistent radio source with a projected linear size of ≲0.7 pc, co-located with the bursts to ≲12 mas (Marcote et al. 2017). The large angular offset between the radio source and the optical center of the galaxy (170–300 mas; Tendulkar et al. 2017) generally argue against an active galactic nucleus (AGN) origin, although this premise is less clear in the case of dwarf galaxies. Similarly, the resulting ratio of radio-to-optical brightness for the persistent source and host galaxy (L_rad/L_opt ≈ 104) is much larger than expected for a star formation origin. This has led to the suggestion that the radio source may be a nebula associated with FRB 121102 (Metzger et al. 2017). More recently, the discovery of a large rotation measure with ∼10% variations on half-year timescales suggests the presence of a dynamic and highly magnetized environment surrounding the source of the FRB (Michilli et al. 2018).

The properties of the host galaxy, the repeating nature of the bursts, and the persistent radio source are consistent with a model in which FRBs are powered by young, millisecond magnetars (Metzger et al. 2017; see also Piro 2016; Murase et al. 2016), the same engines that have been argued to power SLSNe and perhaps LGRBs (Nicholl et al. 2017a, 2017b). In this model, individual bursts are emitted via the dissipation of rotational or magnetic energy, while the quiescent radio emission is due to the magnetar wind nebula or the shock interaction between the supernova ejecta and the surrounding circumstellar medium (Beloborodov 2017; Metzger et al. 2017).

In this broad scenario, we expect that FRBs should be located preferentially in dwarf galaxies (Nicholl et al. 2017c) and be coincident with quiescent radio sources similar to that observed in FRB 121102 (Metzger et al. 2017). Nicholl et al. (2017c) demonstrate that ≲10 FRB localizations will be sufficient to test various formation channels. Given the high event rate for FRBs (∼600 sky⁻¹ day⁻¹ above 1 Jy; Lawrence et al. 2017) and the improved sensitivities of upcoming telescopes and surveys, the number of detected bursts is expected to increase drastically over the next few years as new radio facilities come online. However, due to a wide range of localization capabilities, precise localizations will continue to be a challenge.

In Eftekhari & Berger (2017; hereafter, Paper I), we explored how robustly FRBs with different localization regions can be associated with host galaxies based on the optical brightness of the galaxy. Due to the large areal number density of faint optical sources, we showed that sub-arcsecond localizations are required for confident associations with dwarf galaxies at z ≳ 0.1, whereas localizations of up to 3'' may suffice if the hosts are instead generally L* galaxies, where L* denotes the characteristic luminosity of a bright galaxy.

Here we explore the likelihood of constraining similar associations with radio sources, motivated by the persistent radio source associated with FRB 121102 and assuming that all FRBs are coincident with such sources, potentially with a resulting high radio-to-optical flux ratio. We also explore what limits can be placed on the presence and luminosity of a persistent radio source (as a function of localization area) even in the absence of a robust association. We assess our results in the context of existing and upcoming radio facilities. As an example of our method, we present radio (Very Large Array (VLA)) and optical (Magellan) observations of the localization region of the ASKAP FRB 170107 (Bannister et al. 2017). We search for radio counterparts in the region using the radio-to-optical flux ratio to identify potential candidates.

The paper is structured as follows. We begin by using radio source number counts to determine the probability of chance coincidence for an FRB and a persistent radio source as a function of localization region and persistent source flux density (Section 2). In Section 3 we use these results to constrain the upper limit on the radio luminosity of a source in the absence of a robust association. In Section 4, we discuss various techniques which may further aid in the identification of associated counterparts. We present an example of our approach in Section 5, using radio and optical observations of the localization region of FRB 170107. Finally, we discuss our results in the context of existing and planned FRB search facilities in Section 6.

We assess the likelihood that an FRB is associated with a persistent radio source by calculating the probability of chance coincidence for a source of a given brightness within a localization region. We use the 1.4 GHz Euclidean-normalized differential source counts presented in Condon et al. (2012) to calculate the number density of radio sources above some limiting flux density, n(≥S); see the top left panel of Figure 1. These source counts are measured over the range 10 μJy–100 Jy and extrapolated to lower flux densities, imposing an evolutionary model for the spectral luminosity function of extragalactic radio sources (Condon 1984a, 1984b). The source counts are comprised of both AGN and star-forming galaxies, with the latter dominating the counts below ∼0.1 mJy (Padovani et al. 2015), although radio-quiet AGN have been shown to comprise a sizable fraction of the sub-mJy population (Fomalont et al. 2006; Padovani et al. 2007, 2015; Smolčić et al. 2008). We assume a Poisson distribution of radio sources across the sky and calculate the chance coincidence probability as:

$$\begin{eqnarray}&&{P}_{\mathrm{cc}}=1-{e}^{-\pi {R}^{2}n(\geqslant S)}.\end{eqnarray} \tag{ 1 }$$

The localization region, R, is parameterized by R = 2R_FRB, where R_FRB is the 1σ localization radius of the FRB.¹

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Using the integrated source counts, we plot in the top right panel of Figure 1 the number of radio sources above some limiting flux density [i.e., πR_FRB²n(≥S)] as a function of R_FRB. We plot the results over the range S = 1 μJy to 1 Jy, in order of magnitude increments. We find an expectation value of about one source at S ≈ 100 mJy within the typical localization regions of single-dish telescopes (R_FRB ≈ 10'). Conversely, at the faint end (≈0.1 mJy), we expect one source within R_FRB ≈ 1'.

We plot the resulting chance coincidence probability contours as a function of flux density and R in the lower panel of Figure 1. We denote the contours corresponding to P_cc = 0.01 and 0.1. We also show the flux density of the persistent radio source associated with FRB 121102 over the redshift range z ≈ 0.1–1, as well as the nominal sensitivities for a number of existing and future radio observatories. We note that the FRB 121102 persistent source falls well below P_cc = 0.01. While most existing facilities are sensitive to FRB 121102-like persistent sources across a range of redshifts (z ≈ 0.1–1; see Table 1), detecting such a source at z ∼ 1 (with an expected flux density of a few μJy) is challenging even with the VLA. On the other hand, the advent of the ngVLA and SKA will push the achievable sensitivity to sub-μJy levels, and hence the detection of such persistent sources to z ≳ 1.

At ≲1 mJy (i.e., FRB 121102-like persistent sources at z ≳ 0.1), confident associations (P_cc ≲ 0.01) require localizations of R ≲ 20''. At higher redshifts (z ∼ 1), localizations of R ≲ 1'' are required. While this level of localization is not feasible for most FRB search telescopes, it can be achieved using the VLA in an extended configuration, or with VLBI, as in the case of FRB 121102, which was localized to ≲12 mas (Marcote et al. 2017). However, a number of facilities, including the VLA, MeerKAT, ASKAP, and DSA-10, will be able to provide the ≲20'' localizations required for robust associations with sub-mJy sources at moderate redshifts (z ∼ 0.5). Conversely, at R ≳ 1', confident associations with sub-mJy sources are not feasible. This corresponds to the localization regime for CHIME, UTMOST-2D, and Apertif (as well as single-dish telescopes). These facilities can provide robust associations only if the counterparts generally have flux densities of ≳1 mJy, but this would require some of the persistent radio counterparts to be much more luminous than the source associated with FRB 121102. Finally, the poor localizations from single-dish telescopes are insufficient for robust associations with all but the brightest (∼Jy) sources. Although these telescopes may reveal additional bursts from FRBs in the case of repetitions, they will not be able to directly provide localizations that will lead to associations with persistent radio sources at any reasonable confidence level.

In Table 1, we list a number of radio facilities designed to detect FRBs. We sort these by anticipated or known localization capability. We also list the flux density of a radio source in the respective localization region that would have P_cc = 0.01 and 0.1, as well as the maximum redshift z_max out to which an association with an FRB 121102-like persistent source can be made. These values are extracted directly from the probability contours in Figure 1. We find that while the VLA, ASKAP, DSA-10, and MeerKAT are capable of probing these sources out to z ∼ 1 (and z > 1 for VLBI), the large flux densities required for P_cc ≈ 0.01 for facilities with localizations of R ≳ 1' preclude associations with these sources at z ≳ 0.1. Given the expectation from radio source number counts and the sensitivity of current instruments, localizations below 3'' will not improve the association confidence markedly, as existing facilities cannot achieve the μJy levels required for P_cc ≲ 0.1.

We note that for the same localization requirement of R ≲ 20'', optically based host galaxy associations are impractical, requiring host luminosities several times brighter than L* at redshifts below z ≲ 0.1 (Paper I). Assuming that FRB 121102 is representative of the FRB population as a whole, and that we can expect continuum radio sources coincident with FRBs, the lower areal number density of radio sources on the sky enables more robust associations at a given localization precision; we demonstrate this further using optical and radio observations of the localization region of FRB 170107 in Section 5.

We use the results of Section 2 to investigate upper limits on the radio luminosity of an associated persistent source in the absence of a robust association. For a given localization radius, we determine the typical brightest source expected within the region (using the top right panel of Figure 1). For a given intergalactic DM value (excluding the host and Milky Way contribution), we then estimate z_max, using the DM–redshift relation of Deng & Zhang (2014; see also Ioka 2003) and incorporating the uncertainty due to intergalactic medium inhomogeneities as parameterized by McQuinn (2014). We follow the procedure described in detail in Paper I. In Figure 2, we plot the maximum luminosity of a radio source as a function of R for a range of DM values. As in Figure 1, we overlay the localization capabilities of the various FRB search facilities for reference. We also denote lines corresponding to the luminosity of star-forming galaxies with star formation rates of 1 and 100 M_⊙ yr⁻¹, and we indicate the dividing line above which radio sources are almost exclusively AGN (L ≈ 10³¹ erg s⁻¹ Hz⁻¹). Finally, we mark the achievable luminosity limits as a function of redshift for several facilities (ATCA, VLA, and the SKA/ngVLA).

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The results suggest that for DM ≈ 1000 pc cm⁻³, an upper limit comparable to the luminosity of the FRB 121102 persistent radio source (L ≈ 2 × 10²⁹ erg s⁻¹ Hz⁻¹; Marcote et al. 2017) can be placed if R ≲ 10''. These limits would also rule out star formation at the level of ≈100 M_⊙ yr⁻¹. A similar localization in the optical would only constrain the host galaxy luminosity to ≈L* (see Paper I and Figure 3). However, these limits are below the nominal sensitivities for existing radio telescopes. For example, although the VLA can provide the required localization precision, the 3σ limiting flux density at 6 GHz corresponds to a luminosity upper limit of L ≈ 6 × 10²⁹ erg s⁻¹ Hz⁻¹. For lower DMs, similar constraints on the luminosity of a quiescent radio source can be placed for larger localizations, i.e., R ≲ 30'' for DM ≈200 pc cm⁻³.

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Although the upcoming SKA and ngVLA will provide the sensitivities required for meaningful upper limits, similar limits can be placed with existing facilities, only for lower DM values (DM ≲ 500 pc cm⁻³).

While the probability of chance coincidence analysis in Section 2 provides a direct measure of the confidence level of associating an FRB with a persistent radio source, we are also interested in exploring additional ways of rejecting spurious associations with unrelated radio emission due to AGN or star-forming galaxies (i.e., the sources that make up the extragalactic radio source counts). First, we discuss a number of methods that can be used to identify radio emission due to star formation and separate these sources from FRB host candidates. Next, we discuss the distinction between AGN and putative FRB hosts, which is generally more complicated due to the wide range of AGN radio properties.

4.1. Rejecting Star-forming Galaxies

4.2. Rejecting AGN

FRB 170107 (Bannister et al. 2017) was the first FRB detected by the Australian Square Kilometer Array Pathfinder (ASKAP; Johnston et al. 2008; Schinckel et al. 2012) using the phased array feed system. This led to the detection of the pulse in three separate beams, allowing for a localization region smaller than the size of an individual beam: the 90% confidence ellipse has semimajor and semiminor axes of 53 × 42 with a position angle of 52°. Motivated by the smaller size of the localization region compared to previous FRBs and the analysis presented above, we obtained radio and optical follow-up observations shortly after publication of the event to search for a host galaxy via a radio source with a large radio-to-optical flux ratio.

5.1. Radio Observations

We obtained radio observations with the Karl G. Jansky VLA² on 2017 June 2, 146 days after the FRB. The observation lasted 30 minutes and the pointing center was R.A. = 11:23:10, decl. = −05:01:00, matching the FRB position centroid reported by Bannister et al. (2017). The correlator was configured in the standard "C band" wideband continuum mode using the 3-bit samplers, covering the full bandwidth of 4–8 GHz. Standard calibration techniques were used. The bandpass and flux density calibrator was 3C 286 and the complex gain calibrator was the blazar PKS J1131−0500.

After this observation was conducted, we were provided with an updated localization probability map with a new centroid that differed from the published position (R. Shannon and K. Bannister, 2017, private communication). On 2017 June 22 we conducted a second observation using the improved pointing center of R.A. = 11:23:21, decl. = −04:58:38. The two positions were separated by almost exactly the half-width at half power of the VLA at 6 GHz. The other characteristics of this observation were identical to those of the first.

We calibrated and imaged both observations within the CASA software environment (McMullin et al. 2007) using standard techniques. We imaged the fields separately, creating images of 1024 × 1024 pixels at a scale of 1'' per pixel using multi-frequency synthesis (Sault & Wieringa 1994) and w-projection with 128 planes (Cornwell et al. 2008). The images of the first and second pointing centers achieved rms values of 8 and 10 μJy at the pointing center, respectively.

We visually identified radio sources and measured their flux densities following a primary beam correction. Due to the decrease in sensitivity away from the pointing center, we imposed a 75 μJy threshold and found five radio sources above this limit. The radio image from our second observation (2017 June 22) is shown in Figure 4 and the identified sources are listed in Table 2.

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Table 2.  Radio Sources in the FRB 170107 Localization Region

R.A.	Decl.	Flux Density	mi	r
		[μJy]
11:23:14.739	−04:58:20.47	86 ± 15	20.4	0.5
11:23:24.431	−04:59:33.21	112 ± 15	21.4	1.0
11:23:20.400	−05:00:38.59	76 ± 14	22.0	1.1
11:23:11.227	−04:57:14.38	129 ± 23	>24.3	>2.3
11:23:26.385	−04:57:41.65	158 ± 16	>24.3	>2.4

Note. Optical non-detections are listed as the 3σ limiting magnitude.

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5.2. Optical Observations

5.3. Candidate Sources

Motivated by the persistent radio source associated with the repeating FRB 121102, we explored the likelihood of identifying persistent radio sources associated with FRBs as a function of their flux density and the FRB localization radius, assuming that all FRBs are associated with such sources. We also quantified the limits that can be placed on a radio counterpart in the absence of a robust association. Finally, we applied our analysis to the case of FRB 170107. Our main results can be summarized as follows.

• 1.  
  Localizations of R ≲ 20'' are required for robust associations (P_cc = 0.01) with sub-mJy radio sources at z ≈ 0.1. At higher redshifts (z ≈ 1), smaller localizations of R ≈ 1'' are needed. A number of radio facilities, including the VLBA, EVN, VLA, MeerKAT, ASKAP, and DSA-10 will be capable of providing such FRB localizations. For large localizations (≈300''), only bright sources (≈10–100 Jy) lead to P_cc ≲ 0.01. However, such sources are not obviously expected given the luminosity of the FRB 121102 counterpart and the expected extragalactic redshifts. Nevertheless, several radio facilities, including Apertif, CHIME, and UTMOST-2D will be able to achieve this level of accuracy.
• 2.  
  Radio sources with luminosities similar to the FRB 121102 persistent source beyond z ∼ 0.5 are not easily detectable with existing facilities, since they will have flux densities of only a few μJy. However, the upcoming SKA and ngVLA will be sensitive to such sources beyond z ∼ 1.
• 3.  
  In the absence of a robust association, an upper limit can be placed on the radio luminosity of an associated radio source. These limits are particularly interesting for localizations of R ≲ 10'' (for DM ≈ 1000 pc cm⁻³) or R ≲ 30'' (for DM ≈ 200) where the luminosity is comparable to that of the FRB 121102 persistent source. Conversely, in the optical, a 10'' localization does not place a particularly meaningful constraint on the host galaxy luminosity (upper limit of L* for DM ≈ 1000 pc cm⁻³; Paper I). These limits are below the imaging capabilities of existing facilities, however, except for low DM values (DM ≲ 500 pc cm⁻³).
• 4.  
  A number of multi-wavelength techniques can be used to reject spurious associations with unrelated radio sources, namely AGN and star-forming galaxies. The radio-to-optical flux ratio can be used to reject star-forming galaxies as FRB host candidates, imposing a threshold of r ≳ 1.4 for FRB counterparts. Although the rejection of AGN is generally more challenging, optical emission lines and X-ray observations can be leveraged to determine whether a source is consistent with an AGN.
• 5.  
  Using a combination of radio and follow-up observations, we identified five radio sources above 75 μJy within the FRB 170107 localization region. Two of these sources share properties consistent with the FRB 121102 persistent source, namely a high radio-to-optical flux ratio, a comparable radio luminosity, and a low-luminosity optical counterpart. We find that the range of allowed radio luminosities (1 × 10²⁹–4 × 10³⁰ erg s⁻¹ Hz⁻¹) is comparable to that of the FRB 121102 persistent source (2 × 10²⁹ erg s⁻¹ Hz⁻¹). Similarly, the optical limits (m_i > 24.3 mag) are consistent with the dwarf host galaxy of FRB 121102 (m_r ≈ 23.3 mag).

Combined radio and optical follow-up observations of FRB localization regions can provide a powerful tool for identifying host associations. If FRB 121102 is representative of the FRB population, candidate sources can be identified on the basis of their radio-to-optical flux ratio, and targeted follow-up observations can be used to search for repetitions directly from these sources. Although continued monitoring with ASKAP or single-dish telescopes may reveal additional bursts from FRBs, these will not provide unambiguous host identifications. Detections of additional bursts with targeted phased-array observations with the VLA would not only demonstrate repetitions, confirming the existence of a class of repeating FRBs, but would also immediately lead to a host identification. This technique may therefore provide a novel framework for identifying counterparts and localizing future FRBs. However, in the absence of repetitions or very precise localizations, definitive associations remain challenging, particularly due to the broad region of parameter space occupied by AGN.

We thank the referee for helpful comments. The Berger Time-Domain Group at Harvard is supported in part by the NSF through grant AST-1714498, and by NASA through grants NNX15AE50G and NNX16AC22G. This research has made use of the FRB Catalog (http://www.astronomy.swin.edu.au/pulsar/frbcat/) and NASA's Astrophysics Data System.

Software: CASA (McMullin et al. 2007), pwkit (Williams et al. 2017).

In Section 2, the chance coincidence probability is calculated assuming uniform sensitivity over a region with a 1σ localization radius given by R_FRB. However, in typical radio observations, sensitivity is not spatially uniform. Consequently, the number density of detectable point sources decreases. In the common case of a Gaussian primary beam, the limiting flux density is given by ${S}_{\mathrm{lim}}=S\cdot {e}^{-{r}^{2}/2{\sigma }_{\mathrm{PB}}^{2}}$, where r is the distance from the pointing center, σ_PB ≈ θ_PB/2.4, and θ_PB refers to the full-width at half power of the primary beam. For a given localization radius R and flux density S, the resulting chance coincidence probability P_cc therefore increases. In this scenario, the chance coincidence probability is given by:

$$\begin{eqnarray}&&{P}_{\mathrm{cc}}=1-{e}^{-{\int }_{0}^{R}2\pi rn(S\cdot {e}^{-{r}^{2}/2{\sigma }_{\mathrm{PB}}^{2}}){dr}}.\end{eqnarray} \tag{ 2 }$$

We illustrate the effects of accounting for the primary beam response in Figure 5. Namely, we recalculate the chance coincidence probability using Equation (2), where we use, as an example, θ_PB = 10 arcmin (representative of the VLA at 4.5 GHz). We find that in this regime, an accurate characterization of the beam produces results that are comparable to the uniform sensitivity case across the extent of the primary beam (R = 300''). For example, at R = 300'', using Equation (1), we find that a 1% chance coincidence probability occurs for a source flux density of ≈250 mJy. Conversely, in the case of a Gaussian beam, the same flux density corresponds to a ≈1.2% chance coincidence probability, where P_cc = 1% requires S ≈ 300 mJy. We therefore conclude that our simplified beam-model analysis in Section 2 is sufficient in terms of characterizing P_cc and identifying the required localization precision for confident associations.

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