THE REPEATING FAST RADIO BURST FRB 121102: MULTI-WAVELENGTH OBSERVATIONS AND ADDITIONAL BURSTS

We observed FRB 121102 with the 305 m William E. Gordon Telescope at the Arecibo Observatory (AO) using the single-pixel L-Wide receiver (1150–1730 MHz) and the Puerto-Rican Ultimate Pulsar Processing Instrument (PUPPI) backend. We used PUPPI's coherent filterbank mode, in which each of seven 100 MHz bands are sampled with 10.24 μs time resolution and 64 spectral channels. Each of the spectral channels was coherently dedispersed at DM = 557.0 pc cm⁻³. As such, the recorded signals do not suffer significantly from intra-channel dispersive smearing (unlike the ALFA observations presented in Spitler et al. 2016, which use the Mock spectrometers¹⁷ and incoherent dedispersion). Observing sessions ranged from roughly 1–2 hr in length (FRB 121102 is only visible to Arecibo for ∼2 hr per transit), and typically we observed a 2 minute scan on a test pulsar, followed by a single long pointing at the best known position of FRB 121102. On a few occasions we observed alternate pointing positions consistent with the 2015 May/June detection beams reported by Spitler et al. (2016)—i.e., positions offset by a few arcminutes with respect to the average position quoted above. All scans were preceded by a 60 s calibration observation of a pulsed noise diode. The details of each session are given in Table 2.

We observed FRB 121102 with the 110 m Robert C. Byrd GBT using the Green Bank Ultimate Pulsar Processing Instrument (GUPPI) backend and the 820 MHz and 2 GHz receivers. The 820 MHz observations used a 200 MHz bandwidth and recorded spectra every 20.48 μs. The 2 GHz observations have 800 MHz of nominal bandwidth (RFI filters reduce the usable bandwidth to about 600 MHz), and the spectra were recorded every 10.24 μs. Note that the GBT beam has an FWHM of ∼6' at 2 GHz and thus comfortably encompasses the conservative positional uncertainty of FRB 121102 despite the higher observing frequency. In each case, the data were coherently dedispersed at the nominal DM of FRB 121102, and 512 spectral channels were recorded with full Stokes parameters. During a single observing session, we observed FRB 121102 typically for 50 minutes using each receiver. We also observed a pulsed noise diode at the start of each scan for use in absolute flux calibration. A detailed description of each session is given in Table 2.

We observed the position of FRB 121102 with the Lovell Telescope at the Jodrell Bank Observatory on seven separate epochs (see Table 2) for a total of 14 hr. Spectra were recorded with a total bandwidth of 400 MHz over 800 channels with a center frequency of 1532 MHz, at a sampling time of 256 μs. Unlike for the Arecibo and GBT observations, the spectral channels were not coherently dedispersed. The data were RFI-filtered using a median absolute deviation algorithm before applying a channel mask, which results in typically ∼20% of the band being removed.

We observed the position of FRB 121102 with the Effelsberg 100 m Radio Telescope using the S60mm receiver, which covers the frequency range 4600–5100 MHz, and the Pulsar Fast-Fourier-Transform Spectrometer (PFFTS) search backend. The FWHM of the Effelsberg telescope at 5 GHz is 24. As such, the high-frequency Effelsberg observations covered only the central region of the positional error box given in Spitler et al. (2016). The PFFTS spectrometers generate total intensity spectra with a frequency resolution of 3.90625 MHz and time resolution of 65.536 μs.

We observed the FRB 121102 field at 1.6 GHz for 10 hours with the Karl G. Jansky VLA in D-configuration (Project Code: VLA/15B-378) to better localize the FRB position and to set limits on the distribution of free electrons along the line of sight (see Section 5). The 10 hr were split into ten 1 hr observations occurring every few days from 2015 November 25 to 2015 December 17. Each 1 hr observation consisted of a preliminary scan of the flux calibrator J0542+4951 (3C147) followed by three 14 minute scans on the FRB field bracketed by 100 s scans on the phase calibrator J0555+3948.

Data were collected in the shared-risk fast-sample correlator mode (see, e.g., Law et al. 2015) with visibilities recorded every 5 ms. The bandwidth available in this mode is currently limited by the correlator throughput to 256 MHz, which we split into two 128 MHz sub-bands. The sub-bands were centered on frequencies of 1435.5 MHz and 1799.5 MHz to avoid known RFI sources. By observing in the fast-sample mode, we are able to produce channelized time-series data for any synthesized beam within the ∼05 primary field of view (28' across) in addition to the standard interferometric visibilities. If a pulse is detected in the time-series data, it will localize FRB 121102 to within one synthesized beam (about 30''–45'' in D-configuration at 1.6 GHz, depending on hour-angle coverage and visibility weighting in the image). The results of the time-domain burst search will be presented in a subsequent paper (B. S. Wharton et al. 2016, in preparation). The analysis of these data is described below in Section 4.1. Here we present only the imaging results.

We performed observations with the Swift X-ray Telescope (Burrows et al. 2005), which is sensitive to X-rays between 0.3–10 keV, on 2015 November 13, 18, and 23 (Obs IDs 00034162001, 00034162002, 00034162003). The observations were performed in Photon Counting (PC) mode, which has a time resolution of 2.5 s and had exposure times of 5 ks, 1 ks, and 4 ks, respectively. We downloaded the Level 1 data from the HEASARC archive and ran the standard data reduction script xrtpipeline using HEASOFT 6.17 and the Swift 20150721 CALDB.

On 2015 November 23, Chandra X-ray Observatory observations were performed using ACIS-S in Full Frame mode, which provides a time resolution of 3 s and sensitivity to X-rays between 0.1 and 10 keV (Obs ID 18717). The total exposure time was 39.5 ks. The data were processed with standard tools from CIAO 4.7 and using the Chandra calibration database CALDB 4.6.7. Note that we also performed a simultaneous 1.5 hr GBT observation during the Chandra session (see Section 2.2) but detected no radio bursts in those data.

For both the Swift and Chandra observations, we corrected the event arrival times to the solar system barycenter using the average FRB 121102 position from Spitler et al. (2016). The analysis of these X-ray observations is described below in Section 4.2.

To search for bursts from FRB 121102, we used standard tools from the PRESTO software suite (Ransom 2001).¹⁸ We first identified RFI-contaminated frequency channels and time blocks using rfifind. Those channels and blocks were masked in subsequent analysis. We performed two searches: we first searched using the full instrumental time resolution (see Section 2) in a narrow DM range and then a coarser search where the data were downsampled to 163.84 μs in a DM range of 0–10,000 pc cm⁻³.

We performed a search for bursts in the DM range of 0–10,000 pc cm⁻³ on data that were downsampled to 163.84 μs. Dedispersed time series were produced with a step size depending on the trial DM and selected it to be optimal given the amount of interchannel smearing expected based on the time and frequency resolution of the data. For each time series, we searched for significant single-pulse signals using single_pulse_search.py. For the Effelsberg, Jodrell, and GBT observations, we have searched down to an S/N threshold of seven. For Arecibo, which suffers from much stronger and persistent RFI, we have an approximate S/N ∼ 12 threshold. More sophisticated RFI excision could lead to the identification of additional weak bursts in these data sets. A deeper search of the data can also be guided by the possible future determination of an underlying periodicity.

In addition to the 11 bursts detected using the Arecibo ALFA receiver and reported by Spitler et al. (2014, 2016), we have detected a further six bursts: five in GBT GUPPI observations with the S-band receiver and one in an Arecibo PUPPI observation using the L-wide receiver (see Table 2). All five GBT bursts were found at 2 GHz; no bursts were found in the GBT 820 MHz observations. Further, four of them were found within a ∼20 minute period on 2015 November 19. No bursts were found at DMs significantly different from the DM of FRB 121102.

The detection of a burst using the L-wide receiver suggests that the source is localized within the beam width of the receiver. We therefore quote two uncertainty regions: a conservative one with a diameter of 6' (as in Spitler et al. 2016) and a 31 region corresponding to the L-wide FWHM.

In Figure 2 we show each burst as a function of observing frequency and time. Each burst has been dedispersed to a DM of 559 pc cm⁻³. The data have been corrected for the receiver bandpass, which was estimated from the average of the raw data samples of each channel. That average bandpass was then median filtered with a width of twenty 1.6 MHz channels to remove the effects of narrow-band RFI. Frequency channels identified as containing RFI by PRESTO's rfifind were masked. The data were downsampled to 32 frequency channels and a time resolution of 1.3 ms. The top panel for each burst plot shows the frequency-summed time series and the side panel shows the spectrum summed over a 10 ms window centered on the burst peak. We continue the burst numbering convention used in Spitler et al. (2016) whereby bursts are numbered sequentially in order of detection. The first GBT burst is thus designated "burst 12," as the bursts presented in Spitler et al. (2016) were numbered from 1 to 11. We choose this approach in order to avoid conflict with the burst identifiers used in Spitler et al. (2016), but caution that there may be weaker pulses in these data which can be identified by future, deeper analyses.

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In Figure 3 we highlight frequency-dependent profile evolution in bursts 8, 10, and 13. As observed in Spitler et al. (2016), the ALFA-detected bursts 8 and 10 show evidence for double-peaked profiles. Here we show that the double-peak behavior is apparent at high frequencies, but the two peaks seem to blend into a single peak at lower frequencies. For burst 13, which is detected in only the top three sub-bands shown in Figure 3, the burst in the 1.8–2 GHz sub-band is wider than in the two higher frequency sub-bands, causing a bias in the DM measurement (see below). To our knowledge, this is the first time frequency-dependent profile evolution (not related to scattering) has been observed in an FRB.

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For each burst we measured the peak flux, fluence, and burst width (FWHM). Before measuring these properties we normalized each burst time series using the radiometer equation where the noise level is given by

$$\begin{eqnarray}&&\displaystyle \frac{{T}_{\mathrm{sys}}}{G\sqrt{2{{Bt}}_{\mathrm{int}}}},\end{eqnarray} \tag{ 1 }$$

where T_sys is the system temperature of the receiver, 20 K for GBT 2 GHz observations and 30 K for Arecibo L-wide; G is the gain of the telescope, 2 K/Jy for GBT and 10 K/Jy for Arecibo; B is the observing bandwidth; and t_int is the width of a time-series bin. The peak flux is the highest 1.3 ms-wide bin in this normalized time series. The fluence is the sum of this normalized time series. To measure the width we fit the burst with a Gaussian model. The peak time is the best-fit mean in the Gaussian model.

In Table 3 we show the above measured properties for each burst. The GUPPI bursts have peak flux densities in the range 0.02–0.09 Jy at 2 GHz assuming the bursts are detected on axis. These are similar to the range of peak flux densities found for the ALFA-detected bursts presented by Spitler et al. (2016), 0.02–0.3 Jy. The PUPPI-detected burst had a peak flux density of 0.03 Jy, again assuming a perfectly on-axis detection, similar to the faintest bursts seen by Spitler et al. (2016).

We measured the DM of each burst except burst 15, which was detected over too narrow a frequency range to make a reliable DM measurement. For each burst, time series were generated in sub-bands by averaging over blocks of frequency channels. The number of sub-bands depended on the S/N of the burst, and sub-bands with too little signal (S/N < 2) or too contaminated by RFI were excluded. Times of arrival (TOAs) for each frequency sub-band were calculated using a Gaussian template. The width of the Gaussian template was chosen to match the burst width measured from the whole band, as described above. TEMPO2¹⁹ (Hobbs et al. 2006) was used to find the best-fit DM from the TOAs. The results are given in Table 3.

Several of these bursts (13 and 14) have formal DM measurements that are larger than the mean by a statistically significant margin. We argue that this reflects unmodeled frequency-dependent profile evolution (see Figure 3) and not a measurement of time-variable DM. Our simple Gaussian template assumes a constant burst shape and width across the band. If the burst shape varies across the band, then the TOA will shift to reflect the shift in the concentration of the flux density (Hassall et al. 2012).

We explored this in depth for burst 13, which has a higher S/N than burst 14. The value of 565.1 ± 1.8 pc cm⁻³ quoted in Table 3 was calculated by dividing the full bandpass into eight sub-bands but only including the TOAs from the top five sub-bands in the fit (i.e., excluding data below 1900 MHz due to low S/N). If instead we include TOAs above ∼1700 MHz, the value drops to 560.0 ± 1.2 pc cm⁻³. Similarly, calculating TOAs for four sub-bands instead of eight and including only the TOAs above 1800 MHz gives a value of 569.2 ± 1.8 pc cm⁻³. The spread in these fitted values is larger than the formal uncertainties reported by TEMPO2 by a factor of ∼3. Clearly there are systematic effects in the burst profiles that are not accounted for by the TEMPO2 uncertainties.

Spitler et al. (2016) estimated the systematic uncertainty for bursts 1–11 by calculating the ΔDM that results in a DM delay across the band equal to half the burst width. This has been calculated for each GUPPI- and PUPPI-detected burst and is the second uncertainty value given in Table 3. Adding the systematic uncertainties to the statistical uncertainties brings the DMs into agreement at the level of 1.5σ. Thus, there is currently no strong evidence for variations in the DM between bursts. The weighted average of the 15 bursts with measured DMs, excluding bursts 13 and 14 due to the above-mentioned profile variations, is 558 ± 0.8 pc cm⁻³.

Additionally, we measured the frequency index of the DM delay, i.e., Δt_DM ∝ ν^−ξ, for the brightest of the GUPPI bursts (burst 16). We expect ξ = 2 for the propagation of radio waves through a cold, ionized plasma. The consistency of the observed frequency sweep of FRBs with ν⁻² has been used to argue their astrophysical origins, as it would be highly unlikely that RFI would mimic the dependence so exactly.²⁰ The DM index was measured using a least-squares fitting code, which is described in detail by Spitler et al. (2016). The measured index for burst 16 is −1.997 ± 0.015, consistent with −2. Although the PUPPI-detected burst (burst 17) is also seen at high S/N, a large fraction of the band is masked due to RFI, making estimating a dispersion index difficult. The DM index has also been measured for both the discovery burst from FRB 121102 (Spitler et al. 2014), as well as the brightest of the bursts reported by Spitler et al. (2016), and all are consistent with −2.

In Figure 2, we show the spectrum of each burst as a solid black line in the right panel of each burst sub-figure. The gray lines show the spectrum of the noise extracted from an off-pulse region that is the same width as the on-pulse region (a 10 ms time window). Due to low S/N, it is difficult to say anything about the GUPPI-detected burst spectra except for the brightest bursts (bursts 13 and 16). Burst 17, the PUPPI-detected burst, is also seen at high significance, but much of the band is corrupted by RFI. Because of this, we do not attempt to fit any models to the spectra, and only describe them qualitatively here. Both bursts 13 and 16 have bandwidths of ∼600 MHz and drop off in S/N at the edge of the 1.6–2.4 GHz band. It is clear that, as with the ALFA-detected bursts at 1.4 GHz (Spitler et al. 2016), the bursts detected at 2 GHz are not well described by a broadband power-law spectrum and their spectra vary from burst to burst.

Each GUPPI- and PUPPI-detected burst was extracted in the PSRFITS format using dspsr ²¹ , retaining all four Stokes parameters and the native time and frequency resolution of the raw data. These single pulses were calibrated with PSRCHIVE tools using the pulsed noise diode and the quasar J1442+0958 as a standard flux reference. No linear or circular polarization was detected. We searched for Faraday rotation using the PSRCHIVE²² rmfit routine in the range $\mathrm{RM}\leqslant | 20000| \,\mathrm{rad}\,{{\rm{m}}}^{-2}$ but no significant RM was found. It should be noted that most of the GBT pulses are in a relatively low S/N regime, and a small degree of intrinsic polarization cannot be ruled out.

In Spitler et al. (2016), we searched for an underlying periodicity in the burst arrival times by attempting to fit a greatest common denominator to the differences in time between the eight bursts that arrived on 2015 June 2 (bursts 4–11), but we did not detect any statistically significant periodicities. Here, we apply an identical analysis to the four bursts detected on 2015 November 19 (bursts 13–16) and found that it was not possible to find a precise periodicity that fit all of the bursts detected. We note that the minimum observed time between two bursts is 22.7 s (between bursts 6 and 7), so if the source is periodic, the true period must be shorter than this. As we concluded from the ALFA-detected bursts, more detections are necessary to determine whether any persistent underlying periodicity to the bursts is present.

In addition, we conducted a search for a persistent periodicity on dedispersed Arecibo and GBT observations using a fast-folding algorithm (FFA).²³ Originally designed by Staelin (1969), this algorithm operates in the time domain and is designed to be particularly effective at finding long-period pulsars (Lorimer & Kramer 2005; Kondratiev et al. 2009). The FFA offers greater period resolution compared to the FFT and has the advantage of coherently summing all harmonics of a given period, while the number of harmonics summed in typical FFT searches such as those performed by conventional pulsar search software, like PRESTO, is restricted, typically to ≤16. This makes the time-domain analysis more sensitive to low rotational-frequency signals with high harmonic content, i.e., those with narrow pulse widths, which are often obscured by red noise (e.g., Lazarus et al. 2015).

Prior to searching for periodic signals, RFI excision routines were applied to the observations. Such routines include a narrow-band mask generated by rfifind, in which blocks flagged as containing RFI are replaced by constant data values matching the median bandpass. Bad time intervals were removed via PRESTO's clipping algorithm (Ransom 2001) when samples in the DM = 0 pc cm⁻³ time series significantly exceeded the surrounding data samples. Moreover, a zero-DM filtering technique as described in Eatough et al. (2009) was also applied to the time series by removing the DM = 0 pc cm⁻³ signal from each frequency channel.

In this periodicity analysis, we searched periods ranging from 100 ms to 30 s. Below 100 ms, the number of required trials becomes prohibitive. Re-binning was performed such that the FFA search was sensitive to all possible pulse widths, ranging from duty cycles of 0.5% up to 50%.

For every ALFA, PUPPI, and GUPPI observation (see Table 2), candidates were generated by the FFA from the dedispersed, topocentric time series. Approximately 50 of the best candidates for each time series were folded using PRESTO's prepfold and then inspected by eye. No promising periodic astrophysical sources were detected.

The VLA data were processed with the Common Astronomy Software Applications (CASA; McMullin et al. 2007) package using the computing cluster at the Domenici Science Operations Center in Socorro, New Mexico. For the imaging analysis presented here, each observation was downsampled to increase the sampling time from 5 ms to 1 s. We then flagged the data and performed standard complex gain calibration of the visibilities using our flux and phase calibrators. Using the seven brightest sources in the field, we ran three rounds of phase-only self-calibration followed by one round of amplitude self-calibration.

The flagged and calibrated data were imaged using CLEAN deconvolution (Schwab 1984). The two brightest sources in the field are located beyond the half-maximum point of the primary beam at 1.6 GHz. Since the primary beam width gets narrower with increasing frequency, these sources have very steep apparent spectral indices. To account for the spectral shape of these sources, we used the multi-frequency synthesis mode of the CASA CLEAN implementation (Rau & Cornwell 2011) and approximated the sky brightness as a first-order polynomial in frequency. As a result, we get both an image and a spectral index map for each of the 10 single-epoch observations.

We combined all the single-epoch observations into one multi-epoch data set and performed a single round of amplitude-only self-calibration to correct any amplitude offsets in the visibility data between scans. The combined data were then imaged using the same procedure as the single-epoch imaging, producing by far the deepest radio continuum image to date for this field (see Figure 4(a)). No obvious new sources (see below) are seen in our FRB detection overlap region. The central 5' × 5' region of the image has an rms noise of σ = 60 μJy beam⁻¹, with pixel values ranging from −156 to 209 μJy beam⁻¹. These results set a 5σ upper limit on the flux density of any point source of S_max = 0.3 mJy, a factor of ∼10 deeper than previous images of the field (from the NRAO VLA Sky Survey, NVSS; Condon et al. 1998).

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While no obvious new sources fall within the FWHM of the two ALFA beams of the re-detections, there are two previously identified sources within the 28 sq. arcmin conservative uncertainty region: J053210+3304 (α=05^h32^m1008(3), δ = 33°04'055(3)) and J053153+3310 (α = 05^h31^m5391(2), δ = 33°10'202(2)). These sources were termed VLA1 and VLA2 by Kulkarni et al. (2015), who presented an analysis of archival data from NVSS (Condon et al. 1998). J053210+3304 is consistent with a two-component AGN with the brighter component having a multi-epoch average flux density of S₁ = 3.2 ± 0.1 mJy and spectral index α_1.6 = −1.1 ± 0.1. J053153+3310 has a multi-epoch average flux density of S₂ = 3.0 ± 0.1 mJy and spectral index of α_1.6 = +1.7 ± 0.1. Imaging each of the 10 epochs separately, we see that J053153+3310 is variable on timescales of a few days to a week, which is consistent with typical AGN variability timescales and amplitudes (e.g., Ofek et al. 2011). No other transient sources were detected in the single-epoch images within the conservative positional uncertainty region for the FRB.

We searched the Chandra image (Figure 4(b)) for sources using the CIAO tool celldetect. Table 4 shows the coordinates and number of counts in a circular extraction region with a 1'' radius (∼90% encircled power) for each detected source. There are five sources within the conservative 6' diameter uncertainty region shown as a solid circle in Figure 4(b). Only one of these X-ray sources, CXOU J053156.7+330807 (No. 1 in Table 4 and Figure 4(b)), is within the 31 1.4 GHz beam FWHM of our Arecibo PUPPI burst detection (see Section 3.1). We also searched the Swift observations using the HEASARC tool ximage and found no sources within the more conservative 6' uncertainty region.

We cannot assume that CXOU J053156.7+330807, or any of the other four sources in the more conservative uncertainty region, is a counterpart of FRB 121102. The Chandra image has seven detected sources within a 64 arcmin² field of view. Given this source density, the number of expected sources in any given 9 arcmin² (the FWHM area of an Arecibo 1.4 GHz beam) region is ∼1.

If we assume that CXOU J053156.7+330807 is associated with FRB 121102, and that the hydrogen column density, N_H, is correlated with DM according to the prescription of He et al. (2013), then the N_H toward the source would be ${1.7}_{-0.5}^{+0.7}\times {10}^{22}$ cm⁻² (significantly higher than the predicted maximum Galactic N_H of 4.9 × 10²¹ cm⁻²; Kalberla et al. 2005). Assuming this N_H, the best-fit power-law index for a photoelectrically absorbed power-law model of the X-ray spectrum is $3.3\pm {0.4}_{-0.5}^{+0.7}$ and the 1–10 keV absorbed flux is $(9\pm {3}_{-0.5}^{+0.7})\times {10}^{-15}$ erg s⁻¹ cm⁻², where the first errors on the index and flux are statistical uncertainties and the second are systematic uncertainties from the spread in the N_H–DM relation of He et al. (2013). We note that these values are heavily dependent on the assumed N_H.

We also searched for variability during the 39.5 ks observation by making time series for each detected source with time resolutions of 3, 30, and 300 s. We then compared the predicted number of counts in each time bin with the average count rate. No significant deviations from a Poisson count rate were found for any of the sources.

The field of FRB 121102 is in the anti-center region of the Galactic plane, and has been covered by several optical and infrared surveys. We have examined archival images from the Spitzer GLIMPSE 360 survey, the 2 Micron All-Sky Survey (2MASS), and the Second Palomar Observatory Sky Survey (POSS II), among others. Due to the large beams of single-dish radio telescopes in comparison to the density of sources found in optical and infrared surveys, there are many sources within the positional uncertainty region of FRB 121102.

The Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) space telescope covered the entire sky at multiple infrared bands (3.4, 4.6, 12, and 22 μm wavelengths). Several objects are present in the 3.4 (W1), 4.6 (W2), and 12 μm (W3) images of the field around FRB 121102. The ALLWISE catalog (Cutri et al. 2013) lists 182 sources consistent with the best position of FRB 121102 (6' diameter), of which 23 have detections in the W1, W2, and W3 bands. Nikutta et al. (2014) find that the W2–W3 color is a reliable indicator to distinguish between stars and galaxies. They suggest using the criterion W2–W3 > 2 for separating galaxies from stars. Using this indicator, we find that 9 of the 23 objects can be classified as being galaxies. In Figure 4(c) we show the 4.6 μm (W2) image and mark the nine sources identified as galaxies. We treat this number of galaxies as a lower limit, as many WISE sources are not detected in the W3 band. Further, there are undoubtedly many galaxies that would not be detected in any WISE band. For this reason, it is extremely difficult to identify a host galaxy without further localization of the FRB source.

Alternatively, in order to further investigate the possibility of a Galactic origin, here we report on the two most constraining archival observations in terms of testing for the existence of a hypothetical Galactic H ii region that could provide the excess dispersion of FRB 121102 compared with the maximum line of sight value expected from the NE2001 model.

The WISE 22 μm band images, with 12'' resolution and a sensitivity of 6 mJy, have been used by Anderson et al. (2014) to catalog Galactic H ii regions with a high degree of completeness in conjunction with radio continuum imaging. We have extracted WISE 22 μm data in the region of interest from the NASA/IPAC Infrared Science Archive and find no sources within FRB 121102's positional uncertainty region, down to the sensitivity limit of the Anderson et al. (2014) survey.

The Isaac Newton Telescope Photometric H-Alpha Survey (IPHAS; Drew et al. 2005; Barentsen et al. 2014) provides optical survey images of the Galactic plane in our region of interest with a median seeing of 12 and a broadband magnitude limit of ∼20 or better at the SDSS r' band, as well as narrow-band Hα observations that are typically a magnitude brighter in limiting sensitivity. Since the field of interest is in the Galactic anti-center, the images are relatively uncrowded for the low Galactic latitude, and the Hα image is devoid of any extended emission. No evidence is seen for a planetary nebula or a supernova remnant within the region.

In combination with our VLA 1.6 GHz (20 cm) observations, the non-detections at the 22 μm and Hα bands place a stringent limit on any Galactic H ii regions or other sources that might contribute to FRB 121102's high DM, as discussed further in Section 5 (see also Kulkarni et al. 2015).

We can also look for optical and IR counterparts of the Chandra sources (Table 4 and Figure 4(b)) in the WISE and IPHAS source catalogs. For each Chandra source, we looked for sources in the IPHAS catalog that are within 2'' of the Chandra position and for sources within 10'' from the WISE catalog. In Table 4 we show whether each source has an IPHAS or WISE counterpart. The source CXOU J053207.5+330936 has both an IPHAS and WISE counterpart and is coincident with the star TYC 2407-607-1 (Høg et al. 2000). The source CXOU J053203.5+330446 has an IPHAS optical counterpart (r' = 15.6, i' = 15.0) but no WISE counterpart (note that this source is outside our conservative uncertainty region). The source CXOU J053156.7+330807, the only source within the 1.4 GHz FWHM region of FRB 121102, does not have an optical counterpart in IPHAS, but does have a WISE counterpart (one of the nine WISE sources classified as galaxies above as shown in Figure 4(c)). Given this galaxy classification and the fact that the vast majority of faint Chandra X-ray sources are AGN (Bauer et al. 2004) this source is most likely an AGN. Indeed, the expected number of AGNs in the FWHM region of FRB 121102 at the X-ray flux level of CXOU J053156.7+330807 is ∼1 (Bauer et al. 2004). Note that at this point the suggested AGN nature of this source does not preclude it from being the host galaxy of FRB 121102.

An examination of the transient catalogs from Swift BAT, Fermi GBM, MAXI, and INTEGRAL reveals that no hard X-ray/soft γ-ray bursts have been reported within ∼1° of FRB 121102's position. In principle, high-energy counterparts to the radio bursts may be below the significance threshold necessary to trigger a burst alert. To explore this possibility, we retrieved the Fermi GBM daily event data from all 12 detectors to check for any enhancement in count rate during the times of the FRB bursts. We find that the event rates within ±10 s of the radio bursts (after correcting for dispersive delay between radio and gamma-ray arrival times) are fully consistent with that of the persistent GBM background level. The absence of soft γ-ray emission associated with the FRB 121102 radio bursts rules out a bursting magnetar within a few hundred kiloparsecs (Younes et al. 2016).

In the Fermi LAT 4-year Point Source Catalog (3FGL; Acero et al. 2015) there are no γ-ray sources positionally coincident with FRB 121102. This is confirmed by a binned likelihood analysis, which shows no γ-ray excess at FRB 121102's position that may arise due to a persistent source. This is not surprising, given the Galactic latitude of b = −02, where the diffuse γ-ray background is high. On the other hand, if the γ-ray emission is also transient, the source may be evident in the Fermi LAT light curve. To this end, we generated exposure-corrected light curves using aperture photometry with a circle of radius 1° binned at 1, 5, 10, and 60 day intervals. None of these exhibit any statistically significant increase in flux, including around the times of the radio detections. In addition, within 1° of FRB 121102, none of the individual γ-rays detected arrive within 10 s of the arrival time of the radio bursts.

The 11 bursts discovered in ALFA data presented by Spitler et al. (2016) displayed significant spectral variability. The bursts were observed with both rising and falling spectra, and some were found with spectra peaking in the band. Overall, the spectral behavior could be described as consisting of a feature with bandwidth comparable to the 322 MHz ALFA band that varied in peak frequency from burst to burst. It is not clear whether the behavior is caused by a single feature or a broadband spectrum that is strongly modulated at a frequency scale of 100–1000 MHz. The spectral behavior of the GBT bursts presented here in our 2 GHz observations seems to be consistent with what we see at 1.5 GHz, implying that the unusual spectral behavior persists to at least the higher GBT frequency.

We can rule out DISS as the cause of the observed spectral structure on frequency scales Δν ∼ 600 MHz at both 1.5 and 2 GHz. The frequency scale expected for DISS differs markedly from what is observed. The NE2001 estimate for the DISS bandwidth is only 57 kHz at 1.5 GHz and 200 kHz at 2 GHz, more than 10³ times smaller than the observed spectral structure (assuming an extragalactic origin). Unlike for DISS, the scale of the observed structure does not appear at least qualitatively different between 1.5 and 2 GHz. In addition, the DISS timescale estimated by the NE2001 model (Cordes & Lazio 2002) is ∼4 minutes at 1.5 GHz²⁵ , whereas we see extreme variation in spectral shape between bursts separated by as little as 1 minute.

Empirically, we find no evidence for DISS in the burst spectra on any frequency scale, provided the source is not nearby. Two effects can generally account for the absence of DISS: either finite source-size smearing of the diffraction pattern, which occurs at an angular size of ≳1 μas at 1.5 GHz, or the DISS bandwidth is too small to be resolved with our channel bandwidth Δν_ch = 0.33 MHz. However, for the source size to be >1 μas, ${\rm{\Delta }}{\nu }_{d}$ would need to exceed Δν_ch, which is only the case if the source is closer than about 2 kpc (the distance at which the integration of the NE2001 model yields ${\rm{\Delta }}{\nu }_{d}={\rm{\Delta }}{\nu }_{\mathrm{ch}}$). Since the source appears to be unavoidably extragalactic, as discussed in Section 5, it must be the case that ${\rm{\Delta }}{\nu }_{d}\ll {\rm{\Delta }}{\nu }_{\mathrm{ch}}$.

It is also possible that the observed frequency structure is intrinsic to the source. Observations of giant pulses of the Crab pulsar at 1.4 GHz have shown extreme spectral variability with spectral indices ranging from −15 to +15 (Karuppusamy et al. 2010). At higher frequencies (5–10 GHz), banded frequency structure has been observed with similar bandwidths to those we observe in FRB 121102 (∼300–600 MHz; Hankins & Eilek 2007). The center frequencies of these Crab giant pulse bands also seem to vary both during the microsecond-duration pulses and from pulse to pulse.

We have now observed FRB 121102 for over 70 hr using radio telescopes, with the majority of observations resulting in non-detections (note, however, that the 70 hr is spread over telescopes with different sensitivities and these observations were performed at several different radio frequencies; see Table 1). Of the 17 bursts found, six were found within a 10 minute period on 2015 June 2 and an additional four were found in a 20 minute period on 2015 November 19. The arrival time distribution of the detected bursts is therefore clearly highly non-Poissonian. We discuss here two possibilities for such variation: propagation effects due to the interstellar medium and variations intrinsic to the source.

DISS is highly unlikely to play any role in the intensity variations of the bursts from FRB 121102. Bandwidth averaging of DISS yields a modulation index (rms relative to mean intensity) that is only ${m}_{d}\sim 1/\sqrt{0.3B/{\rm{\Delta }}{\nu }_{d}}\sim 2.5 \%$ at 1.5 GHz with the ALFA system (bandwidth 322 MHz). The burst amplitudes therefore will be largely unaffected by DISS.

However, refractive interstellar scintillation (RISS) may play an important role in the observed burst intensity variations on timescales of weeks to months as its characteristic bandwidth is Δν_r ∼ ν ≫ B. Using expressions in Rickett (1990), we estimate the RISS modulation index to be m_r ∼ 0.13 based on the scaling for a Kolmogorov wavenumber spectrum for the electron density. We note, however, that measured modulation indices are often larger than the Kolmogorov prediction (Rickett & Lyne 1990; Kaspi & Stinebring 1992).

The timescale for RISS is uncertain in this case, and the observed episodic timescales are certainly within the range of these uncertainties. We estimate the characteristic timescale for RISS as follows. The length scales in the spatial intensity patterns of DISS and RISS, l_d and l_r, are related to the Fresnel scale ${r}_{{\rm{F}}}=\sqrt{\lambda L/2\pi }$ according to ${l}_{r}{l}_{d}={r}_{{\rm{F}}}^{2}$, where L is the effective distance to the Galactic scattering screen. In the NE2001 model, scattering in the direction of FRB 121102 is dominated by the Perseus spiral arm at L ∼ 2 kpc, giving r_F ∼ 10¹¹ cm. The diffraction length scale is related to the DISS bandwidth as ${l}_{d}\sim \lambda \sqrt{d{\rm{\Delta }}{\nu }_{d}/4\pi c}$ (Equation (9) of Cordes & Rickett 1998) from which we estimate l_r ∼ 4 × 10¹³ cm. The corresponding timescale for RISS depends on the characteristic velocity for motion of the line of sight across the Galactic plasma. Using a nominal velocity of 100 km s⁻¹, we obtain Δt_r ∼ 40 days. However, it is not clear what velocity to use because, unlike pulsars, the source motion is not expected to contribute. If the motions are only from Galactic rotation with a flat rotation curve, the scattering medium and the Sun move together with zero relative velocity. However, non-circular motions, including the solar system's velocity relative to the local standard of rest (∼20 km s⁻¹) and the Earth's orbital velocity, will contribute a total of a few tens of km s⁻¹, yielding a RISS timescale longer than 40 days. Given the uncertainties in estimating RISS timescales, it is possible that Δt_r ranges from tens of days to 100 days or more at 1.5 GHz. RISS times scale with frequency as Δt_r ∝ ν^−2.2, so higher frequencies vary more rapidly.

Although variability intrinsic to the source appears to dominate on timescales of minutes to hours, RISS could be important for intensity variations on timescales of weeks to months. If we use m_r = 0.13 (allowing for the modulation index to be larger than predicted by a factor of 2) at 1.5 GHz and consider ±2m_r variations, the maximum and minimum range of the RISS modulation is g_r,max/g_r,min = 1.7. If the burst amplitude distribution is a power law ∝S^−α, as seen in the Crab pulsar's giant pulses (for which 2.3 ≲ α ≲ 3.5; e.g., Mickaliger et al. 2012), RISS will cause the apparent burst rate above a detection threshold to vary by an amount ${({g}_{{\rm{r}},\max }/{g}_{{\rm{r}},\min })}^{\alpha -1}\sim 2\mbox{--}4$ for α = 2.3 to 3.5. But note again that modulation indices have been observed to be higher than predicted, so the burst-rate variation could be still higher (e.g., for ${m}_{r}=0.4,{({g}_{{\rm{r}},\max }/{g}_{{\rm{r}},\min })}^{\alpha -1}\sim 20\mbox{--}200$). Keeping in mind these uncertainties, it is clear that RISS could cause large variations in the observed burst rate. This issue is being considered in detail in a separate article (J. M. Cordes et al. 2016, in preparation).

For intrinsic phenomena that might cause the episodic behavior, we look at examples from pulsars within our Galaxy, as supergiant pulses from pulsars and magnetars (Pen & Connor 2015; Cordes & Wasserman 2016) are a viable model for repeating bursts. First, the time separations in Crab giant pulses do not show a deviation from a random process (Lundgren et al. 1995). However, a subset of young Galactic pulsars display a phenomenon known as nulling in which they emit pulses only a fraction of the time. The nulling fractions of these pulsars can be quite high, the most extreme emitting pulses <5% of the time (Wang et al. 2007). Some Rotating Radio Transients, a class of Galactic radio pulsar that emit infrequent, bright millisecond-duration radio pulses, also show episodic behavior in their pulses (Keane et al. 2010). It is therefore possible that, if the bursts from FRB 121102 originate from a rotating neutron star, a similar process is causing the episodic behavior in FRB 121102.

Another example of young neutron stars in our Galaxy emitting bursts in episodes are X-ray bursts from magnetars. Magnetar X-ray bursts have timescales from milliseconds to seconds and are emitted in clusters during periods of outburst (e.g., Göğüş et al. 2001; Gavriil et al. 2004; Scholz & Kaspi 2011). Lyutikov (2002) suggests that these X-ray bursts may have accompanying radio emission. To date, no radio counterpart to a magnetar X-ray burst has been observed (e.g., Tendulkar et al. 2016), but the possibility remains that it is what we are observing for FRB 121102.

Here we compare some of the properties of FRB 121102's 12 Arecibo-detected bursts against equivalent properties from the 15 FRBs so far reported from Parkes observations (see FRBCAT). We limit ourselves to the 1.4 GHz-detected bursts, so that we are comparing bursts from the same frequency range to each other.

Based on the telescope gain and system temperatures of the Arecibo ALFA receiver and the Parkes multibeam receiver, Arecibo is about a factor of 10 more sensitive to FRBs than Parkes (see Table 1) at 1.4 GHz. The limiting peak flux density (using a 1.3 ms timescale as used in Section 3.2 to measure the peak fluxes of our bursts and an S/N ratio of five) of the Parkes multibeam receiver is 0.15 Jy. Of our 12 1.4 GHz Arecibo detections of FRB 121102, only burst 11 is brighter than this limit (Spitler et al. 2016). So, if Parkes had undertaken a comparable follow-up campaign for FRB 121102, it may not have found repeat bursts.

The peak flux densities of all but one of the Parkes-detected FRBs are within an order of magnitude of the brightest FRB 121102 burst, making the above comparison valid. The notable exception is FRB 010724 which is, with a peak flux density of >30 Jy, by far the brightest FRB detected to date and, as it was the first discovered, the most followed-up, with nearly a hundred hours of telescope time spent checking for repeat bursts (Lorimer et al. 2007). This seems to argue against the nature of FRB 010724 being similar to FRB 121102. Note however that the episodic behavior displayed by FRB 121102 makes this comparison difficult. The underlying origin and timescales of this behavior remains uncertain and the duty cycle could vary from source to source. If active periods of repeating FRB emission come and go, the follow-up observations of FRB 010724, performed six years after the initial burst, could plausibly have resulted in non-detections if its periods of activity are sufficiently rare.

We can also compare the widths of the FRB 121102 bursts to those of the Parkes FRBs. Three of the Parkes FRBs, including the first reported (Lorimer et al. 2007), were detected with an analog filterbank system, with 3 MHz-wide frequency channels. These cause an intra-channel dispersion smearing time, Δt_DM, eight times larger than the equivalent for the other Parkes FRBs, detected with the BPSR backend (with 0.39 MHz channel width), or for the ALFA observations of FRB 121102 (0.34 MHz width).

The 12 Arecibo FRB 121102 pulses have measured widths spanning 3–9 ms (Spitler et al. 2016). Given that Δt_DM for the bursts detected with ALFA at 1.4 GHz is 0.7 ms and zero for the PUPPI-detected burst (as it was coherently dispersed), and that no scattering tail is observed in the pulses, the observed widths must be the intrinsic width of the emission.

Two of the 15 Parkes FRBs have two-component profiles (as do some of the FRB 121102 pulses, although their shape is varied and not obviously comparable to those of the Parkes events), and we neglect them here. The observed widths of the remaining 13 FRBs span 0.6–9 ms, apparently comparable to the widths of FRB 121102 bursts. However, at least two (see Thornton et al. 2013; Ravi et al. 2015), and possibly four (see Lorimer et al. 2007; Petroff et al. 2015a) of the Parkes FRBs display significant evidence of multi-path propagation/scattering, which can make their observed widths larger than their intrinsic widths. In addition, two Parkes FRBs have Δt_DM = 7 ms, comparable to their observed widths (Keane et al. 2011; Burke-Spolaor & Bannister 2014).

After accounting for all instrumental and measurable propagation effects, none of the 13 Parkes single-component FRBs is wider than ∼3 ms. Indeed, several of the Parkes FRBs are temporally unresolved, e.g., FRB 130628 has an observed width of 0.6 ms and Δt_DM ∼ 0.6 ms (Champion et al. 2015).

In summary, it appears that the intrinsic widths of the 12 FRB 121102 bursts from Arecibo (3–9 ms) are significantly longer than the intrinsic widths of the 13 single-component Parkes FRBs (≲3 ms).

We can also compare the spectra of the FRB 121102 bursts with those of Parkes FRBs. The collection of FRB 121102 bursts has spectra that in some cases can be approximated by power laws with indices spanning $-10\lt \alpha \lt +14$. In some instances, the spectral behavior is more complex and cannot be approximated by a power law (Spitler et al. 2016, Figure 2).

Only 9 of the 15 Parkes FRBs have sufficiently well-described spectral properties to allow at least qualitative judgements on their spectra. In most such cases, the original references do not provide quantitative spectral information, but a "waterfall" plot (showing a grayscale of the pulse flux density as a function of observing frequency, as in Figure 2) is available with sufficient S/N in these nine cases. Note that the waterfall plots for FRBs 090625, 110703, and 130729 are not published in the refereed literature but are available at FRBCAT.

For seven of the Parkes FRBs, within the available S/N, the spectrum appears consistent with showing roughly monotonic flux density frequency evolution and qualitatively consistent with mildly negative spectral indices as for ordinary radio pulsars (e.g., Manchester & Taylor 1977). A closer look shows possible departures from this general trend (e.g., for FRB 110220; see Figure S4 of Thornton et al. 2013), but likely propagation effects need to be accounted for when considering this issue in detail. Two Parkes FRBs have published spectral indices: Ravi et al. (2015) report a marginally inverted spectrum for FRB 131104, with α = 0.3 ± 0.9, but caution that this value could be different depending on the true position of the FRB within the telescope beam pattern. Keane et al. (2016) report α = 1.3 ± 0.5 for FRB 150418, but a similar caveat applies in that they assume the position of the possibly coincident variable source detected in a galaxy within the Parkes beam pattern (but see Vedantham et al. 2016; Williams & Berger 2016).

In summary, the largely qualitative spectra inferred for nine Parkes FRBs may show in a few cases departure from standard pulsar-like spectra, but even in the best such counterexamples, a possibly uncertain FRB position renders such conclusions tentative. In contrast, the collection of Arecibo spectra from FRB 121102 bursts displays intrinsic variability that includes examples with very positive and very negative spectral indices, not represented in the Parkes collection.

Two other useful quantities to compare are the observed peak flux density S_peak and fluence F of the various FRBs. Arecibo detections of FRB 121102 have 0.02 < S_peak < 0.3 Jy and 0.1 < F < 1 Jy ms. For the most part, the Parkes FRBs have S_peak and F an order of magnitude larger than the Arecibo FRB 121102 values: 0.2–2.2 Jy and 1–7 Jy ms, respectively. The one exception is FRB 010724 (Lorimer et al. 2007), which is yet another order of magnitude brighter (S_peak ∼ 30 Jy and F ∼ 150 Jy ms).

The Arecibo ALFA system, used to detect the FRB 121102 bursts near 1.4 GHz, is ∼10 times more sensitive than the multibeam receiver system used to detect all Parkes FRBs. It is thus not surprising that the faintest Arecibo FRB detections have flux densities an order of magnitude smaller than those of the faintest Parkes FRBs. That the strongest FRB 121102 detections are one to two orders of magnitude below the strongest Parkes FRB detections could reflect a luminosity distribution favoring fainter bursts. Indeed, there are more FRB 121102 bursts near the Arecibo detection limit than high S/N bursts. The lack of repeated burst detections to date from Parkes FRBs might be due to the Parkes telescope's lower sensitivity not probing as deeply into the flux density distribution for putative repeating FRBs.

In any case, it is possible that with more time on source, some of the Parkes FRBs will be found to be repeating. Based on current observations, however, we cannot exclude the possibility that Parkes FRBs represent a non-repeating population, and thus are fundamentally different from FRB 121102. The differing pulse widths and spectra as discussed above may provide modest support for this idea.