FAST RADIO BURST DISCOVERED IN THE ARECIBO PULSAR ALFA SURVEY

Radio pulsar surveys sample the sky at high time resolution and are thus sensitive to a range of time variability and source classes. Over the last decade, there has been renewed interest in expanding the purview of pulsar search pipelines, which traditionally exploit the periodic nature of pulsars, to also search for single dispersed pulses. This led to the discovery of rotating radio transients (RRATs; McLaughlin et al. 2006), which are believed to be pulsars that are either highly intermittent in their radio emission or have broad pulse-energy distributions that make them more easy to discover using this technique (Weltevrede et al. 2006). Of the now nearly 100 known RRATs,¹⁹ the vast majority emit multiple detectable pulses per hour of on-sky time, though a few have thus far produced only one observed pulse (Burke-Spolaor & Bailes 2010; Burke-Spolaor et al. 2011b). The dispersion measures (DMs) of the RRATs are all consistent with a Galactic origin, according to the NE2001 model for Galactic electron density (Cordes & Lazio 2002).

Single-pulse search methods have also discovered a new class of fast radio bursts (FRBs) in wide-field pulsar surveys using the 13-beam, 1.4 GHz receiver at the Parkes radio telescope (Lorimer et al. 2007; Keane et al. 2012; Thornton et al. 2013). Most have been found far from the Galactic plane and have DMs that are anomalously high for those lines of sight. Lorimer et al. (2007) reported the first such burst with a Galactic latitude of b = −42° and DM = 375 pc cm⁻³. The expected DM contribution for that line of sight from the ionized interstellar medium (ISM) in our Galaxy is only 25 pc cm⁻³ according to the NE2001 model. The DM excess has been interpreted as coming from the ionized intergalactic medium (IGM) and led to the conclusion that FRBs are extragalactic.

More recently, Thornton et al. (2013) reported four FRBs with Galactic latitudes of |b| > 40° and DMs ranging from 521 to 1072 pc cm⁻³. The expected Galactic DM contribution along the lines of sight of these bursts is 30–46 pc cm⁻³, i.e., only 3%–6% of the observed DM can be attributed to our Galaxy. An additional FRB candidate was reported by Keane et al. (2012) and is at a lower Galactic latitude (b = −4°) than the other five reported Parkes FRBs. This source could be of Galactic origin given that the measured DM = 746 pc cm⁻³ is only 1.3 times the maximum expected DM from NE2001 along this line of sight. The dispersion delay of all of the published FRBs are consistent with the expected ν⁻² dispersion law. Additionally, the burst reported by Lorimer et al. (2007) showed frequency-dependent pulse broadening that scaled as ν^{−4.8 ± 0.4}, consistent with the expected value of −4.0 to −4.4 (Lambert & Rickett 1999) for scattering by the ISM. The brightest burst reported by Thornton et al. (2013) showed a clear exponential tail and a pulse duration that scaled as ν^{−4.0 ± 0.4}. This provides additional credence to the interpretation that the signal is of astrophysical origin.

Generally, FRBs have been found in minute- to hour-long individual observations; multi-hour follow-up observations at the same sky positions have thus far failed to find repeated bursts. Thus, FRBs are considered a different observational phenomenon from RRATs based on DMs in excess of the predicted Galactic contribution and the fact that none of the FRBs has been seen to repeat. At this point, however, we cannot be certain that the bursts are non-repeating. Detecting an astrophysical counterpart will be an important step in determining whether we expect repeated events.

The progenitors and physical nature of the FRBs are currently unknown. The FRBs have brightness temperatures well in excess of thermal emission (T_b > 10³³ K) and therefore require a coherent emission process. One possible source of repeating, extragalactic FRBs is extremely bright, rare Crab-like giant pulses from extragalactic pulsars, which repeat over much longer time scales than currently constrained. Similarly Popov & Postnov (2007) propose hyperflares from extragalactic magnetars. Proposed extragalactic sources of non-repeating, fast radio transients include evaporating primordial black holes (Rees 1977), merging binary white dwarf systems (Kashiyama et al. 2013), merging neutron stars (Hansen & Lyutikov 2001), collapsing supramassive neutron stars (Falcke & Rezzolla 2014), and superconducting cosmic strings (Cai et al. 2012). Alternatively, Loeb et al. (2014) suggest a repeating, Galactic source—flares from nearby, magnetically active stars, in which the DM excess is due to the star's corona. In this scenario, additional pulses could also be observed and potentially at a different DM. Localizing FRBs with arcsecond accuracy is technically challenging but will help identify potential host galaxies, or stars, and multi-wavelength counterparts.

In any pulsar survey, the vast majority of statistically significant signals are due to man-made radio frequency interference (RFI), which can originate far from the telescope or be locally generated. RFI can also mimic some of the characteristics of short-duration astronomical signals. Thus, care is needed when interpreting whether a particular signal is astronomical in origin, and claims of a new source class require due consideration and skepticism. The situation is further complicated by the discovery of "perytons" (Burke-Spolaor et al. 2011a). Perytons are short duration radio bursts observed in pulsar surveys over a narrow range of DMs but have patchy spectra and are observed in many beams simultaneously. The fact that FRBs have so far been observed with only the Parkes telescope has raised some concern—even though the observed brightness distribution and event rate can explain why other experiments have so far not detected any similar signals.

In this article, we report the discovery of an FRB with the Arecibo Observatory. The FRB was found as part of the Pulsar ALFA (PALFA) survey of the Galactic plane (Cordes et al. 2006). This detection, made with a different telescope at a different geographic location, bolsters the astrophysical interpretation of a phenomenon seen until now only with Parkes. The outline for the rest of this paper is as follows. In Section 2, we describe the PALFA survey and the observations that led to the discovery of the new FRB. The burst's properties are discussed in Section 3, and the implied FRB event rate is described in Section 4. A discussion of the possible origin of this FRB, both astrophysical and otherwise, is outlined in Section 5. In Section 6, we discuss the implications of our discovery for FRBs in general and present our conclusions.

PALFA is a pulsar survey of the Galactic plane that uses the 305 m Arecibo telescope and the Arecibo L-band Feed Array²⁰ (ALFA; Cordes et al. 2006). ALFA is a seven-beam feed array with a single center pixel (beam 0) surrounded by a hexagonal ring of 6 pixels (beams 1–6) that spans the frequency range 1225–1525 MHz. The FWHM of each beam is approximately 35, and the beams are separated from each other by roughly one beam-width on the sky. (See Figure 1 for a map of the power pattern.) A tessellation of three pointings is required to sample the sky to the half-power point. The system temperature (T_sys) is 30 K. The on-axis gain of beam 0 is 10.4 K Jy⁻¹, and the average on-axis gain of the other six beams is 8.2 K Jy⁻¹. The peak gain of the sidelobes (about ∼5' from the beam centers) is 1.7 K Jy⁻¹, over twice as high as the on-axis gain of the Parkes beams. The 7 pixels yield an instantaneous field of view (FOV) of 0.022 deg² within the FWHM, though the effective FOV is larger as the sidelobes have enough sensitivity to detect FRBs.

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The survey began in 2004 and targets low Galactic latitudes (|b| ⩽ 5°) in two ranges of Galactic longitude: inner Galaxy (30° < l < 78°) and outer Galaxy (162° < l < 214°). Initially the PALFA survey data were recorded with the Wideband Arecibo Pulsar Processors (Dowd et al. 2000), and the single-pulse analysis of these data is presented in Deneva et al. (2009). In March of 2009, PALFA began observing with the Mock/PDEV²¹ spectrometers (hereafter Mock spectrometers). The Mock spectrometers cover the entire ALFA frequency range in two frequency subbands, which are separately recorded as 16-bit data. The 16-bit subband data are converted to 4-bit data to reduce storage requirements. The subbands are merged prior to processing and the resulting data have 322.6 MHz of bandwidth, 960 frequency channels, and a time resolution of 65.5 μs. For a more detailed description of the Mock data, see, e.g., Lazarus (2013).

The time-frequency data are processed with a PRESTO²²-based pipeline to search for single dispersed pulses. The raw data are cleaned of RFI using the standard PRESTO RFI excision code (rfifind). The raw time-frequency data are dedispersed with 5016 trial DMs ranging from DM = 0–2038 pc cm⁻³; the maximum DM searched is roughly twice as high as the maximum Galactic DM contribution expected for any line of sight covered in the survey. Single pulse candidates are identified in each dedispersed time series using a matched filtering algorithm (single_pulse_search.py). This algorithm increases the sensitivity to pulses wider than the original time resolution of the data by convolving each dedispersed time series with a series of boxcar matched filters (for a general discussion of this technique, see Cordes & McLaughlin 2003). After matched filtering, pulse candidates are identified by applying a threshold signal-to-noise ratio (S/N) > 5. The spectral modulation index statistic was calculated for each event to identify those caused by narrowband RFI (Spitler et al. 2012). Candidate pulses are identified by inspecting a standard set of single-pulse diagnostic plots (e.g., Figures 5 and 6 in Cordes & McLaughlin 2003). In practice, an isolated pulse needs an S/N somewhat above the threshold (S/N ≳ 7) in order to verify that it is astrophysical. A repeated source of pulses found at an S/N close to the threshold, for example, from an RRAT, could be recognized as astrophysical because of the underlying periodicity.

The analysis presented here includes data recorded with the Mock spectrometers from beginning with their deployment in 2009 March through 2012 December, for a total of ∼5045 pointings in the outer Galaxy. The distribution in Galactic latitude of the pointings is fairly uniform so far; the number of pointings in 1° bins from |b| = 0°–5° is 8134, 5926, 7252, 7476, and 6279, respectively. For this analysis we do not consider the inner Galaxy pointings because the larger DM contribution makes finding extragalactic bursts more difficult. The outer Galaxy observations are conducted in piggy-back mode with our commensal partners, and pointing duration varies depending on their requirements. Roughly 70% of the pointings have a duration of 176 s, and 30% have a duration of 268 s. The total observing time of all the pointings is 283 hr, or 11.8 days.

A single, dispersed pulse with an S/N = 14 was observed in ALFA beam 4 on 2012 November 2 (MJD = 56233.27492180) at 06:35:53 UT in a 176 s survey pointing toward the Galactic anticenter. Because we do not know for certain where in the beam the burst occurred, we give the position to be the center of beam 4 (b = −0223, l = 17495). The burst occurred 128 s into the observation. The burst properties are summarized in Table 1. Following the naming convention introduced by Thornton et al. (2013), we henceforth refer to this event as FRB 121102. A frequency versus time plot of the pulse, a dedispersed pulse profile, and the spectrum of the pulse are shown in Figure 2.

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Table 1. Observational Parameters of FRB 121102

Parameter	Value
Date	2012 Nov 2
Time	06:35:53 UT
MJD arrival timea	56233.27492180
Right ascensionb	05h32m096
Declinationb	33$^{\circ }05^{^{\prime }}13{\buildrel{\prime\prime}\over{.}} 4$
Gal. long.	17495
Gal. lat.	−0223
DM (pc cm−3)	557.4 ± 2.0
DMNE2001, max (pc cm−3)	188
Dispersion index,c β	−2.01 ± 0.05
Pulse width (ms)	3.0 ± 0.5
Pulse broadening (ms),d τd	<1.5
Flux density (Jy),e S	$0.4_{-0.1}^{+0.4}$
Spectral index range,f α	7 to 11

Notes. ^aBarycentered arrival time referenced to infinite frequency. ^bThe J2000 position of the center of beam 4. ^cDispersive time delay ∝ν^β. ^dAt 1 GHz. ^eFlux estimation at 1.4 GHz assumes a sidelobe detection and a corresponding gain of 0.7 ± 0.3 K Jy⁻¹. ^fS(ν)∝ν^α.

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The DM of the pulse was calculated using a standard analysis technique also employed in pulsar timing. The data were divided into 10 frequency subbands and times of arrival were determined from the five highest frequency subbands. The lower five subbands were not included because the S/N was too low. The best-fit DM is 557.4 ± 2.0 pc cm⁻³. The NE2001 model predicts a maximum line of sight Galactic DM of 188 pc cm⁻³, i.e., roughly one-third of the total observed column density. For comparison, PSR J0540+3207 has the larger DM of the two known pulsars within 5° of FRB 121102 with a DM of 62 pc cm⁻³ (Manchester et al. 2005) and a DM-derived distance of 2.4 kpc.

We also explored the possibility of a sweep in frequency that deviates from the standard ν⁻² expected from dispersion in the ionized ISM, i.e., ν^β, where β is the DM index. The DM-fitting analysis described above determined a best fit for the DM index of β = −2.01 ± 0.03. Also, a least-squares fit for deviations from the ν⁻² law verified that a variation in β from −2 of up to 0.05 can be tolerated given the time resolution of the data. We also note that the value of DM is for β = 2 because the units are otherwise inappropriate. As such, we report a final value of DM index of β = −2.01 ± 0.05.

The remaining burst properties were determined by a least-squares fit of the time-frequency data with a two-dimensional pulse model doing a grid search over a range of parameters. The model assumes a Gaussian pulse profile convolved with a one-sided exponential scattering tail that is parameterized by a 1/e temporal width τ_d. The amplitude of the Gaussian is scaled with a spectral index (S(ν)∝ν^α), and the temporal location of the pulse was modeled as an absolute arrival time plus dispersive delay. For the least-squares fitting the DM was held constant, and the spectral index of τ_d was fixed to be −4.4. The Gaussian FWHM pulse width, the spectral index, Gaussian amplitude, absolute arrival time, and pulsar broadening were all fitted. The Gaussian pulse width (FWHM) is 3.0 ± 0.5 ms, and we found an upper limit of τ_d < 1.5 ms at 1 GHz. The residual DM smearing within a frequency channel is 0.5 ms and 0.9 ms at the top and bottom of the band, respectively. The best-fit value of the spectral index was α = 11 but could be as low as α = 7. We note that the fit for α is highly covariant with the Gaussian amplitude.

Every PALFA observation yields many single-pulse events that are not associated with astrophysical signals. A well-understood source of events is false positives from Gaussian noise. These events are generally isolated (i.e., no corresponding event in neighboring trial DMs), have low S/Ns, and narrow temporal widths. RFI can also generate a large number of events, some of which mimic the properties of astrophysical signals. Nonetheless, these can be distinguished from astrophysical pulses in a number of ways. For example, RFI may peak in S/N at DM = 0 pc cm⁻³, whereas astrophysical pulses peak at a DM >0 pc cm⁻³. Although both impulsive RFI and an astrophysical pulse may span a wide range of trial DMs, the RFI will likely show no clear correlation of S/N with trial DM, while the astrophysical pulse will have a fairly symmetric reduction in S/N for trial DMs just below and above the peak value. RFI may be seen simultaneously in multiple, non-adjacent beams, while a bright, astrophysical signal may only be seen in one beam or multiple, adjacent beams. FRB 121102 exhibited all of the characteristics expected for a broadband, dispersed pulse, and therefore clearly stood out from all other candidate events that appeared in the pipeline output for large DMs.

We also performed a thorough periodicity search on the discovery observation. We created a set of trial dedispersed time series around the burst DM, using an rfifind mask to excise RFI. Each trial DM was searched for periodicities using PRESTO's accelsearch and all candidate signals with an S/N greater than 3σ were folded and inspected by eye. This closer inspection, in addition to the blind periodicity search that had already been done as part of the normal survey processing, also failed to reveal any periodic candidates.

Reobservations of the source position showed no additional pulses at the discovery DM. First, the same seven-beam ALFA survey pointing direction was repeated in a 176 s observation on 2012 November 4. Second, targeted follow-up was done using the L-wide single-pixel receiver and the PUPPI spectrometer on 2013 July 7, during which the position of beam 4 was observed continuously for 1.66 hr. The L-wide receiver has a frequency range of 1.15–1.73 GHz and an FWHM of 35, while PUPPI provides a time resolution of 40.96 μs and a bandwidth of 800 MHz, which was divided into 2048 frequency channels. These data were processed using the single-pulse search algorithms and a narrow range of DMs spanning the burst's DM.

Finally, because the uncertainty on the position of FRB 121102 is larger than the FWHM of the ALFA beams, we performed a dense sampling of the region around the original beam 4 pointing center using three interleaved ALFA pointings of 2600 s each and recorded with the Mock spectrometers on 2013 December 9–10. Combined, these covered a circular area with an approximate diameter of 17'. An additional 2385 s observation was conducted on 2013 December 10 using the Arecibo 327 MHz receiver and the PUPPI backend with the telescope pointed at the center of the beam 4 position from the discovery observation. The FWHM of the beam of the 327 MHz receiver is 14', so this observation covered both the position of the main beam and sidelobe of ALFA. The lower frequency observation was performed in the event that the single bright burst seen at 1.4 GHz was part of a broad distribution of pulses emitted from a source with a steep negative spectral index, as expected for pulsar-like coherent radiation. These observations were searched for single pulses over a narrow DM range and also for periodic signals at the burst's DM. No additional bursts or periodic astrophysical signals were found.

One peculiar property of FRB 121102 is the observed positive apparent spectral index of α = 7–11. If the coherent emission process for FRBs is similar to that of pulsars, we would expect an intrinsically negative spectral index or a flat spectral index in the case of magnetars. The spectral indices of the Thornton et al. (2013) bursts are consistent with being flat. We therefore suspect that the observed positive spectral index is caused by frequency-dependent gain variations of ALFA. To explore this possibility, we developed a model for the receiver using an asymmetric Airy function and coma lobes but no correction for blockage from the feed support structure. The left panel of Figure 1 is a map of ALFA's power pattern using this model. We also generated a map of the induced spectral index at the center frequencies of the two Mock subbands. The spectral index map is shown in the right panel of Figure 1. Most positions within the beam pattern, including the entire main beam, impart a negative spectral index. However, the rising edge of the first sidelobe can impart a positive spectral index bias of 0 ≲ α ≲ 10. We therefore conclude that the burst was likely detected in the sidelobe and not the main beam. Note that we see no evidence for the burst in the co-added dedispersed time series from pairs of neighboring beams (beams 0 and 3 and beams 0 and 5) with S/N > 4.

It is also possible that the observed spectrum is additionally biased by RFI. Indeed, the lower of the two Mock subbands is significantly more affected by RFI contamination compared with the upper subband, which may contribute partly to the observed positive spectral index. In summary, given the uncertainty in the exact position, as well as the exact beam shape and other extrinsic effects, it is unfortunately impossible to adequately constrain the true spectral index of the burst.

Nonetheless, the sidelobe detection hypothesis allows us to better constrain both the position and flux of the burst. Conservatively, we consider a range of gain corresponding to the inner edge of the sidelobe of 0.4–1.0 K Jy⁻¹ for a mean gain of 0.7 K Jy⁻¹. Estimating the peak flux density (S) from the radiometer equation, we have $S = 0.4_{-0.1}^{+0.4}$ Jy, where we have assumed S/N = 14, T_sys = 30 K, a bandwidth of 300 MHz, and a pulse duration of 3 ms. If instead FRB 121102 was detected on axis, the flux density is ∼40 mJy, which is an order of magnitude weaker than any other known FRB.

We can estimate the occurrence rate of FRBs from our single FRB discovery, the total observing time included in this analysis, and the instantaneous FOV of ALFA. The gain variations of the receiver (see Figure 1) complicate the definition of the instantaneous FOV, but a practical definition is the region enclosed by a minimum system gain threshold. We calculate the rate using two different assumptions for minimum gain. The first is the area enclosed by the FWHM level of the seven beams (Ω_FWHM), and because the sidelobes of Arecibo have comparable sensitivity to Parkes, we also assume a lower minimum gain that encompasses the main beams and first sidelobes (Ω_{MB + SL}). We use the numerical model of the ALFA beam pattern shown in Figure 1 to calculate the instantaneous FOV and a FOV-averaged system equivalent flux density S_sys.

The FWHM FOV is defined to be the area with a gain greater than half the peak gain of the outer beams, i.e., where G > 4.1 K Jy⁻¹. This corresponds to Ω_FWHM = 0.022 deg² and an FOV-averaged S_sys = 5 Jy. Using the radiometer equation, a fiducial pulse width of 1 ms, a bandwidth of 300 MHz, two summed polarizations, and S/N = 10, we get that S_min = 65 mJy. For 11.8 days of observing, the event rate is then $R_{S>65\; \rm mJy} = 1.6^{+6}_{-1.5} \times 10^5$ sky⁻¹ day⁻¹. The uncertainty interval represents the 95% confidence interval assuming the occurrence of FRBs is Poisson distributed.

The main beam and sidelobe FOV was defined as the region with G > 0.4 K Jy⁻¹. This value of gain was chosen because it corresponds to the average FWHM sensitivity of the Parkes multibeam receiver. The instantaneous FOV is Ω_{MB + SL} = 0.109 deg², and the FOV-averaged S_sys = 27 Jy. Using the same parameters as above yields a minimum detectable flux density of S_min = 350 mJy. The corresponding event rate is then $R_{S>350\; \rm mJy} = 3.1^{+12}_{-3.1} \times 10^4$ sky⁻¹ day⁻¹.

Thornton et al. (2013) have the most robust event rate of FRBs published to date with $R_{\rm S 3\; Jy} = 1^{+0.6}_{-0.5} \times 10^4$ day⁻¹ sky⁻¹ for a 1 ms burst. To determine whether this rate is consistent with our inferred rates, one must consider the relative volumes probed given each survey's S_min. If the FRBs do come from a population of sources at z ≳ 1, one must also account for cosmological effects, i.e., simple Euclidean geometry is no longer valid. Lorimer et al. (2013) introduce a model for the FRB population that properly handles the effect of cosmology on the detection rate, and for concreteness, they scale their predictions to the Thornton et al. (2013) FRB properties. Scaling our event rates using this prescription, we find that our inferred rates are roughly consistent with the cosmological model, but we caution that the model is predicated on a large number of uncertain assumptions. In particular, the distance (or redshift) of a burst is estimated from the observed DM and requires making an assumption about the contribution of the host Galaxy, which is highly uncertain. Furthermore, the intrinsic emission properties of the FRBs (e.g., spectral index, beaming fraction) is also known.

In this section, we describe three possible origins for FRB 121102: terrestrial, Galactic, or extragalactic. To avoid confusion, we adopt different nomenclature for the two astrophysical possibilities, namely, FRBg and FRBx for FRBs originating from Galactic and extragalactic sources, respectively.

5.1. Terrestrial

5.2. Galactic

Because the observed DM is only three times the predicted DM from the NE2001 model (188 pc cm⁻³), it is conceivable that FRB 121102 is an FRBg, and the DM excess is caused by localized density enhancements along the line of sight. We have investigated the possibility of unmodeled gas by checking Hα and H ii survey catalogs. The position of FRB 121102 was mapped by the Wisconsin Hα Mapper Northern Sky Survey (Haffner et al. 2003) with 1°spatial resolution (see also Finkbeiner 2003). The emission measure (EM) inferred from the Hα intensity is EM =28 pc cm⁻⁶ using the expression from Haffner et al. (1998; assuming T = 10⁴ K, I_Hα ≈ 10 R, and no extinction). For this line of sight, the NE2001 model predicts EM = 15–70 pc cm⁻⁶ assuming an outer scale for the electron-density spectrum of 10–100 pc, which is appropriate for the thick disk in the outer Galaxy. The consistency between the measured EM and predicted EM suggests that NE2001 is correctly modeling the electron content for line of sight, and therefore the predicted DM is also accurate.

We also checked for H ii regions along the line of sight by searching through two complementary catalogs. Paladini et al. (2003) compiled a catalog of 1442 H ii regions from 24 previously published radio surveys, and Anderson et al. (2014) produced a catalog of over 8000 known and candidate H ii regions using infrared images from the Wide-Field Infrared Survey Explorer and archival radio data. The closest H ii region in either catalog was greater than 1°away from the position of FRB 121102. In conclusion, we find no evidence for previously unmodeled dense gas along the line of sight that would explain the excess DM.

Figure 3 illustrates the Galactic DM excess for pulsars and FRBs quantified by the DM ratio, r_DM = DM_obs/DM_{NE2001, max}, where DM_obs is the observed DM for a source and DM_{NE2001, max} is the DM expected for the source's line of sight integrated through the entire Galaxy. Four classes of sources are included: Galactic pulsars, RRATs, pulsars in the Small and Large Magellanic Clouds (SMC and LMC), and FRBs. The data for the Galactic, SMC, and LMC pulsars are from the ATNF Pulsar Catalog²³ (Manchester et al. 2005). The RRAT data are from the RRATalog, and the FRB data are from this paper, Lorimer et al. (2007), Keane et al. (2012), and Thornton et al. (2013).

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Galactic pulsars have r_DM < 1, except for a few pulsars whose observed DM is likely enhanced due to unmodeled local excesses in the ISM (e.g., H ii regions). While this may suggest the DM excess of FRB 121102 could also be due to uncertainties in the NE2001 model, our analysis of Hα and H ii data described above makes this highly unlikely. The six known pulsars within ∼100 pc of the Galactic center (GC) are clustered at DM ∼1000 pc cm⁻³ and r_DM ∼ 0.2–0.4 and are offset in DM from the rest of the pulsar population due to the increased density of the ionized ISM in the GC. RRATs have DM ratios consistent with Galactic pulsars. The pulsars in the LMC and SMC have r_DM = 1 to 5, reflecting the additional contribution of the ionized electrons in the LMC, SMC, and possibly from the local IGM. The FRB from Keane et al. (2012) has the lowest DM ratio, which is lower even than some of the Galactic pulsars, suggesting this burst could be Galactic. In fact Bannister & Madsen (2014) infer that this FRB is Galactic with a 90% probability from an EM determined using optical spectroscopy. The five, high-Galactic-latitude bursts from Lorimer et al. (2007) and Thornton et al. (2013) have DM ratios greater than even the Magellanic Clouds, which makes a Galactic interpretation difficult. The LMC and SMC pulsars and high-Galactic-latitude FRBs fall long a line because the maximum Galactic DM contribution at high Galactic latitudes is roughly constant (DM ∼ 50 pc cm⁻³). The DM ratio of FRB 121102 is larger than all of the Galactic pulsars, but only just. We also note that the inferred extragalactic DM contribution for FRB 121102 is ∼ 370 pc cm⁻³, which is larger than for the FRB from Lorimer et al. (2007).

If the burst is an FRBg, the most likely source is an RRAT. RRATs have been observed with only one pulse in an epoch (Burke-Spolaor & Bailes 2010; Burke-Spolaor et al. 2011b). However, our lack of a detection in the 327 MHz follow-up observations suggests that FRB 121102 is not simply an unusually bright pulse of an otherwise weak pulsar. While we cannot completely rule out that this burst is an FRBg, it is highly unusual for Galactic sources.

5.3. Extragalactic

Under the assumption that FRB 121102 is extragalactic in origin, and following Thornton et al. (2013), we can estimate the redshift, z, of the burst based on the observed total dispersion delay across the bandpass, which is fortuitously for ALFA ∼1 ms for each 1 pc cm⁻³ of DM, i.e., Δt_obs = 552 ms (Figure 2). The contributions to Δt_obs are from (1) free electrons in the Galactic ISM (Δt_ISM); (2) the IGM (Δt_IGM); (3) the putative host galaxy (Δt_Host). Adopting the NE2001 electron density for this line of sight, we find Δt_ISM ≃ 184 ms. To be consistent with the estimates presented in Thornton et al. (2013), we make the same assumptions about Δt_IGM and Δt_Host as presented in their Figure S3. Using the model DM scaling relationship for the IGM model of Ioka (2003) and Inoue (2004), we find Δt_IGM ≃ 1200 z ms. For a host galaxy DM contribution of 100 pc cm⁻³, Δt_Host ≃ 100 ms/(1 + z)². The condition Δt_obs = Δt_ISM + Δt_IGM + Δt_Host is met when z = 0.26. The redshift value can be taken as an upper bound because it is plausible that a host galaxy can contribute more to the total delay than we have assumed. As was the case for the redshift estimates presented by Thornton et al. (2013; z = 0.45–0.96), the contributions to Δt_obs are highly model dependent, and therefore the z value should be used with caution.

With these caveats in mind, the implied co-moving radial distance at z = 0.26 would be D ∼ 1 Gpc. The FRB pseudo-luminosity SD² ∼ 1 × 10¹² Jy kpc² and energy output is ∼10³⁸ erg for isotropic emission and ∼10³⁷ erg for emission beamed over 1 sr. Both values are consistent with the FRBs from Thornton et al. (2013). Using this estimate of the co-moving distance, we can also constrain the brightness temperature, i.e., $T_b \sim 1 \times 10^{34}\; D_{\rm Gpc}^2\; \rm K$, where D_Gpc is the source distance in units of Gpc. This unphysically large brightness temperature requires a coherent emission process.

All of the FRBs observed to date show less temporal scattering than pulsars with similar DMs. Using a population of pulsars at low Galactic latitudes, Bhat et al. (2004) determined an empirical relation for pulse broadening timescale versus DM and observing frequency. For example, the predicted pulse broadening timescales for DM = 500–1000 pc cm⁻³ are 2–2000 ms at 1.4 GHz, albeit with a large scatter in the observed distribution. By comparison, only FRB 110220 has a measurable scattering timescale of ∼5 ms with DM = 910 pc cm⁻³ (Thornton et al. 2013), roughly a factor of 200 less than predicted by Bhat et al. (2004). Using this single FRB scattering measurement, Lorimer et al. (2013) scale the Bhat et al. (2004) relation. The scaled relation predicts a scattering timescale for FRB 121102 of ∼0.04 ms, which is shorter than the time resolution of the data. If this relation can in fact be applied broadly to FRBs, then it is not surprising that we detected no scattering. Lorimer et al. (2013) point out that for a given scattering screen, the largest observed scattering occurs when the screen is near the mid-point between the source and observer, due to geometric effects. This suggests that the IGM or an intervening galaxy located midway along the line of sight would be the most important contribution to the scattering of FRBs. However, Cordes & McLaughlin (2003) show that for a source imbedded in a region of high scattering, for example near the center of the host galaxy or for a line of sight that passes through the host's galactic disk, the observed scattering can still be dominated by the host galaxy even at large distances. Observations of scattering along extragalactic lines of sight by Lazio et al. (2008) and more theoretical calculations by Macquart & Koay (2013) suggest that scattering in the IGM is several orders of magnitude lower than in the ISM, which is consistent with the observations of FRBs.

One caveat to the conclusions of this paper is that the search presented here, and all searches for dispersed radio bursts, are optimized for signals with a ν⁻² dispersive time delay. This simple approach introduces a selection effect in what signals breach the S/N threshold used to identify candidates, and thus which signals are deemed worthy of close inspection. We note, however, that this selection effect is not severe in our case as the fractional bandwidth we have used here (20%) is just barely sufficient to see the quadratic curvature of the burst delay.

Although the poor localization of FRB 121102 prevents a detailed search for a multi-wavelength counterpart, we searched for any major high-energy events that were both contemporaneous and co-located on the sky. We checked the Gamma-ray Coordinates Network archive of γ-ray bursts and found no potential association with FRB 121102. There are no plausible associations with X-ray transients detected by current all-sky monitors, and there are no observations of the field of FRB 121102 (within a 20' radius) with X-ray telescopes. There is no source associated with the position of FRB 121102 in either the ROSAT All Sky Survey Catalog or the Fermi Source Catalog.

In summary, we have described the Arecibo discovery of FRB 121102, a single, highly dispersed pulse in the PALFA survey. This is the first claimed FRB detection that has been found with a telescope other than Parkes. The large DM excess, roughly three times what would be expected from the Galactic ISM along this line of sight, the absence of repeat bursts, and the low measured interstellar scattering suggest that this is an FRBx and not a Galactic emitter such as an RRAT. Using the event rate inferred from the PALFA discovery, there is the potential in the coming years to find two to three more FRBs in the remaining outer Galaxy survey region.

We thank the referee for extensive comments that significantly improved the clarity of this paper. We thank M. Kramer, B. Stappers, and R. Ekers for useful discussions. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968), and in alliance with Ana G. Méndez-Universidad Metropolitana, and the Universities Space Research Association. These data were processed on the ATLAS cluster of the Max-Planck-Institut für Gravitationsphysik/Albert-Einstein Institut, Hannover, Germany. L.G.S. and P.C.C.F. gratefully acknowledge financial support by the European Research Council for the ERC Starting grant BEACON under contract No. 279702. J.W.T.H. acknowledges funding for this work from ERC Starting grant DRAGNET (337062). Work at Cornell (J.M.C., S.C.) was supported by NSF grant 1104617. V.M.K. holds the Lorne Trottier Chair in Astrophysics and Cosmology and a Canadian Research Chair in Observational Astrophysics and received additional support from NSERC via a Discovery Grant and Accelerator Supplement, by FQRNT via the Centre de Recherche Astrophysique de Québec, and by the Canadian Institute for Advanced Research. Pulsar research at UBC is supported by NSERC Discovery and Discovery Accelerator Supplement Grants as well as by the CFI and CANARIE. P.L. acknowledges the support of IMPRS Bonn/Cologne and FQRNT B2.