A Fast Radio Burst Discovered in FAST Drift Scan Survey

The Commensal Radio Astronomy FAST Survey (CRAFTS;¹³ Li et al. 2018) is a multi-purpose all-sky survey designed to obtain data streams for pulsar searching, transients searching, H i imaging and H i galaxies simultaneously. The survey began testing in 2017 August, initially using a single-beam wide-band receiver covering 270–1620 MHz. After 2018 May, the survey started using the FAST L-band Array of Nineteen Beams (FLAN), which covers 1050–1450 MHz band with a system temperature of about 20 K (Li et al. 2018). The drift scan survey typically happens at night (from 21.00 to 8.00 CST), during which time no other observations are scheduled. A total of 138 nights of observations were conducted, and ∼1500 hr of 19-beam observations were taken from 2018 May to 2018 November, when the burst event was discovered. Data taken subsequently are still being processed. While we report on FRB searches here, we note that the CRAFTS survey has already discovered over 100 new pulsars¹⁴ (Qian et al. 2019; Zhang et al. 2019a).

The original FAST data were written in PSRFITS format (Hotan et al. 2004) with two polarizations and 8 bit sampling at 196.608 μs intervals and with 4096 spectral channels between 1000 and 1500 MHz. Due to the large data volume, we sum the two polarizations and compress the data to 1 bit before further processing. In the following sections, the signal searching and significance calculations are both based on the single bit summed data, and we include a degradation factor of 33% to account for the loss in signal-to-noise during data compression. The resulting system parameters that we adopt are an average system temperature of 23 K including contributions from the cosmic microwave background, the foreground sky, earth atmosphere, and radiation from the surrounding terrain and an effective telescope gain of 10 K Jy⁻¹ for beam 17 (15 K Jy⁻¹ before digitization loss; Jiang et al. 2019, 2020).

FRB 181123 was identified by a novel GPU-based single pulse search system that integrates the PICS AI software (Zhu et al. 2014) for selecting single pulse candidates with the FAST multibeam data. This system uses GPUs to dedisperse the original data streams from each beam into eight sub-bands for 4096 trial DMs in the range 8.7–9211 pc cm⁻³. The DM step ΔDM is determined by

$$\begin{eqnarray}&&C\,{\rm{\Delta }}\mathrm{DM}\left(\displaystyle \frac{1}{{\nu }_{\min }^{2}}-\displaystyle \frac{1}{{\nu }_{\max }^{2}}\right)={\rm{s}}\sqrt{{\tau }_{\mathrm{samp}}^{2}+{\tau }_{\mathrm{pulse}}^{2}+{\tau }_{\mathrm{smear}}^{2}},\end{eqnarray} \tag{ 1 }$$

here the left-hand side is the pulse broadening across the whole band due to one DM step, the right-hand side is the pulse broadening in the lowest channel composed of sample time τ_samp = 196.608 μs, an assumed minimal pulse width τ_pulse = 0.5 ms, and the inter-channel DM smearing ${\tau }_{\mathrm{smear}}\,=2C\delta \nu /{\nu }_{\min }^{3}$, where δν = 0.122 MHz is the channel width. Here C = 4148.808 MHz² pc⁻¹ cm³ s is the dispersion constant, s = 2 is a manually chosen sparseness parameter, ν_max = 1500 MHz, and ν_min = 1000 MHz. The dedispersed time series in each sub-band are downsampled by a small factor (usually 8) in the GPUs to match the expected typical pulse width of ∼1 ms. The code outputs the dedispersed time series in each sub-band for each DM trial to memory. We then search for threshold-crossing burst events in a summed time series combining all sub-bands in CPUs with multiple levels of possible burst widths. While searching for bursts, the code uses multi-level wavelets¹⁵ (Lee et al. 2019a) to reduce red noise and search for significant bursts that pass a threshold of 7σ. This burst search normally results in thousands of detections in each data set. The code then takes the detected signal position in time and DM for each candidate and extracts from the dedispersed sub-band time series a segment of data that contains the burst signals. This segment of data contains eight frequency sub-bands and time bins chosen such that the data segment contains 32 times the burst width of data. We refer to these segments as dedispersed snapshots of the burst. Despite some exceptions, most pulsar-like bursts are wide-band signals, their snapshots often contain a full or partial vertical line, which is distinguishable from that of narrow-banded radio frequency interference (RFI). We then employ the CNN classifier in PICS (Zhu et al. 2014) that was trained using the frequency-versus-phase subplot of the PRESTO¹⁶ (Ransom 2011) candidate plots.

The image pattern of a real pulse in our snapshots resembles those in the frequency versus phase subplot in pulsar candidates, i.e., a vertical line. Our experiments show that the PICS-CNN classifier was able to rank the most pulsar-like burst snapshot to the top of all snapshots. We pick only the top candidates from these snapshots (usually with a zero-to-one score >0.96, as determined by experiments) to form the final output candidate list. These candidates were subsequently plotted and inspected by eye. This GPU single pulse search system (enabled by PICS) helped in the discovery of over 20 new pulsars in the FAST drift scan survey, including those reported in Qian et al. (2019) and Zhang et al. (2019a). This PICS-aided search system uses non-standard ranking criteria. Although successful in finding some pulsars, it does not necessarily detect all pulses that cross the event threshold. A careful study of the recall of this system will be presented in a later contribution (W. W. Zhu et al. 2020, in preparation). For now, we assume that this system does not find all true signals that cross the threshold. Meanwhile, we also searched the data using the more standard HEIMDALL¹⁷ (Barsdell et al. 2012) pipeline and will report the results in future publication.

FRB 181123 was detected with a significance of 19σ in beam 17 of the multibeam receiver on MJD 58445. More detailed parameters with uncertainties are summarized in Table 1. We searched time series from other beams that are dedispersed with the same DM but found no signal above 3σ during the same time. From the logged position of the receiver cabin at the time, we infer that the FRB came from the direction of l = 18406, b = −1347 with a positional uncertainty of 3' based on the full width of the FAST beam at the center frequency of 1250 MHz. The observed DM for this FRB (1812 pc cm⁻³) is substantially greater than the maximum DM expected from the Galaxy in this direction ∼150 pc cm⁻³ (Yao et al. 2017).

Table 1.  Observational Parameters of FRB 181123

Parameter	Valuea
Date (UTC)	2018 Nov 23
Time (UTC)	17:49:09
MJD arrival timeb	58445.74246675
R.A.c	05h06m0676
Decl.c	18°09'357
Gal. long.	184.06
Gal. lat.	−13.47
DM (pc cm−3)	1812(2)
P1 pulse arrival timed(s)	2.64422(4)
P1 pulse height (mJy)	65(3)
P1 pulse width (ms)	1.05(6)
P2 pulse arrival timed (s)	2.6499(1)
P2 pulse height (mJy)	24(3)
P2 pulse width (ms)	0.6(2)
P3 pulse arrival timed (s)	2.6538(1)
P3 pulse height (mJy)	19(2)
P3 pulse width (ms)	1.2(2)
P1 spectral indexe	−3.3(5)
P2-P3 frequency drift ratef	≲−140 MHz ms−1

Notes.

^aNumber in parentheses indicates 1σ uncertainty in the least significant digit. ^bThe topocentric arrival time of the first peak (P1) in MJD. ^cCoordinates obtained from the position of the receiver cabin when P1 arrived. We assume a position error circle of 3' radius. ^dPulse arrival time at the top edge of the band (1500 MHz) since the start of the particular data file. ^eS(ν) ∝ ν^α. ^fMeasured in the observer's frame.

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Figure 1 shows a more detailed look at the time–frequency spectrum of FRB 181123, along with the dedispersed pulse profile. The burst shows a multi-peak pulse profile with three distinguishable peaks separated by few milliseconds (labeled as P1, P2, and P3). The measured parameters of these peaks are presented in Table 1. From Gaussian fits to the pulse profiles, we infer that P2 arrives about 5.6 ms after P1, and P3 arrives about 4 ms trailing P2 in the observer's frame, these correspond to 1.9 ms and 1.4 ms delays in the rest frame of the FRB. Using the radiometer equation to convert our data to a Jansky scale, we measure the specific peak flux to be 65 mJy for P1 and find a specific fluence of 0.2 Jy ms for all three peaks. FRB 181123's flux and multi-peak pulse profile resemble those from some previously discovered FRBs (Champion et al. 2016). In particular, the two smaller peaks, P2 and P3, show narrow-band features that resemble the down-drift pattern seen in the repeating bursts of FRB 121102 (Gajjar et al. 2018; Hessels et al. 2019; D. Li et al. 2020, in preparation).

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Hessels et al. (2019) presented a detailed analysis of the complex time–frequency structures seen in the repeating bursts of FRB 121102. We followed their approach and estimated the drift rate between FRB 181123's P2 and P3 to be ≲−140 MHz ms⁻¹ (Figure 1, right panel) in the observer's frame and ≲−400 MHz ms⁻¹ in the rest frame of the FRB; the estimated drift rate has significant uncertainty, and it could be underestimated because we only see part of the spectrum of P2 and P3. Nevertheless, our estimated drift rate of ≲−400 MHz ms⁻¹ fits well to the range measured in FRB 121102 (Hessels et al. 2019) around the rest-frame emission frequency of 3–4.4 GHz, enhancing the similarities between FRB 181123 and FRB 121102.

Figure 2 shows the results of a fine frequency-time structure analysis applied to FRB 181123, following the approach in Hessels et al. (2019). We found significant fine structures, characterized by the square of Gaussian-smoothed forward-difference time derivatives (i.e., the changes between every consecutive time bins), in the dedispersed bursts around the position of P1 and minor structures in P2 and P3. These fine structures allow us to derive the optimal DM as 1812 ± 1 pc cm⁻³. This estimation is consistent with, and slightly more constrained than, what we we derived from using the signal-to-noise ratio (S/N). Unlike Gajjar et al. (2018) and Hessels et al. (2019), we did not observe FRB 181123 in a coherent-dedispersion mode, thus the intra-channel smearing due to a DM of ∼1812 is 0.5–2 ms in our observing band. Hence, DM smearing will not allow us to resolve structure finer than 0.5 ms despite our 0.196608 ms sampling interval. The measured widths of P1, P2, and P3 are consistent with this DM-smearing width and show no significant evidence of scattering tails.

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As can be seen in the frequency structure plot in Figure 1, P1 of FRB 181123 is brighter at the lower frequency part of the band. From P1's on-pulse minus off-pulse spectrum shown in the middle panel of Figure 1, we find that the best-fit FRB spectrum index is −3.3 ± 0.5. Spitler et al. (2014) detected the first burst of FRB 121102 in the sidelobe of the Arecibo beam. They argue that the sidelobe position varied with frequency and caused the detected burst spectrum to be steep and up-swinging (with spectral index 7–11). The same argument could be applied conversely to FRB 181123, in which case the FRB is likely detected by the main beam instead of the sidelobe. In contrast to the original observation of FRB 121102 (Spitler et al. 2014), FRB 181123 is detected in a drift scan where the beam was moving across the sky while the burst arrived, further changing the observed burst spectral index. We use a theoretical antenna power pattern to evaluate how these two factors change the FRB's spectral shape (Figure 3). The antenna power pattern of a uniformly illuminated dish,

$$\begin{eqnarray}&&P(x,y,\nu )={\left[2{J}_{1}(u)/(u)\right]}^{2},\end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray}&&u=\pi \sqrt{{x}^{2}+{y}^{2}}D\nu /c.\end{eqnarray} \tag{ 3 }$$

Here x and y represent the source position with respect to the beam center, D is the dish diameter, ν is the observing frequency, c is the speed of light, and J₁(u) is a Bessel function of the first kind (Wilson et al. 2012). We integrate P along the drifting path of the FRB

$$\begin{eqnarray}&&I=\int G(\nu ){\left(\nu /{\nu }_{0}\right)}^{2}P(x(t),y,\nu (t)){dt},\end{eqnarray} \tag{ 4 }$$

to get an approximated power for two sub-bands: the bottom band (1000–1250 MHz) and the top band (1250–1500 MHz), here G(ν) is the gain of the telescope as a function of frequency ν, and (ν/ν₀)² is a normalizing factor with ν₀ = 1250 MHz. For convenience, we assume G(ν) to be flat while in practice it varies slightly with ν (Jiang et al. 2020). The result of this integration depends on the assumed starting position of the FRB (i.e., its position at 1500 MHz), and the FRB's DM value. We then use the ratio between the integrated power in the top and bottom band to derive an approximation for the extra spectral index: ${\rm{\Delta }}\gamma \sim \mathrm{log}({I}_{\mathrm{top}}/{I}_{\mathrm{bottom}})/\mathrm{log}({\nu }_{\mathrm{top}}/{\nu }_{\mathrm{bottom}})$, where ν_top = 1375 MHz and ν_bottom = 1125 MHz. As shown in Figure 3, if FRB 181123 were detected in the sidelobe, its spectrum would likely have been significantly impacted. But, we observed a relatively flat burst spectrum, and the main peak P1's signal persists across the whole band. This suggests that FAST likely caught the FRB in the main lobe. Admittedly, the observed antenna pattern of FAST (Jiang et al. 2020) may be quantitatively different from a theoretical one, but our conclusion should still be valid.

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The observed DM of FRB 181123 (1812 ± 2 pc cm⁻³) includes contributions from the intergalactic medium (IGM)—DM_IGM, from the Galaxy—DM_Gal and from the host galaxy of the FRB—DM_host. We assume DM_Gal ∼ 149.5 based on Yao et al. (2017) and DM_host ∼ 40/(1 + z) pc cm⁻³ (Xu & Han 2015; Yang & Zhang 2016), where z is the redshift of the host galaxy. Zhang (2018) derived how one could estimate the upper limit of FRB luminosity based on its observed DM. They also derived a DM–z relation that correctly accounts for the integrated dispersion effect for objects in cosmological distances assuming homogeneous IGM, and provided an approximated formula z ∼ DM_IGM/855 pc cm⁻³ for z < 2. We follow their calculations closely and solve for the redshift z of FRB 181123 using the equation ${\mathrm{DM}}_{\mathrm{obs}}-{\mathrm{DM}}_{\mathrm{Gal}}\,=(855z+40/(1+z))$ pc cm⁻³. The best solution is z ≲ 1.93 and DM_IGM ≃ 1650 pc cm⁻³. Note that we kept three significant digits for z and DM_IGM to show the exact solution to the above equation.

To quantify the uncertainties on the above z estimate, we now step through the relevant contributions. We note that the estimated DM_Gal has ∼50% uncertainty (Yao et al. 2017), DM_host may contain ∼100% uncertainty, together they contribute 5% relative uncertainty to the estimated DM_IGM. Furthermore, due to inhomogeneity in the IGM, objects from the same DM_IGM could be from different z (Pol et al. 2019), according to Walker et al. (2018), this could increase the uncertainty in our estimated z by an additional factor of 10%. In the above derivations, we assumed probable distributions of DM_Gal and DM_host, but we could still underestimate them substantially and thus overestimate DM_IGM and z. Therefore, we treat the FRB's derived redshift, luminosity, and energy as upper limits.

Assuming the ΛCDM cosmological parameters with H₀ = 67.8 ± 0.9 km s⁻¹ kpc and Ω_M = 0.308 ± 0.012 (Planck Collaboration et al. 2016), the luminosity distance of a z = 1.93 object is ≃15.3 Gpc.¹⁸ Based on Equation (8) and (9) in Zhang (2018), FRB 181123's peak luminosity is ≳2 × 10⁴³ erg s⁻¹ and the isotropic energy ≳2 × 10⁴⁰ erg, both limits contain relative uncertainties of ∼15%. These values are comparable to those derived in Table 1 of Zhang (2018) from previously discovered FRBs.

The PICS-aided GPU searching system is an experimental pipeline, therefore it probably does not find all events that cross the 7σ threshold. A more thorough search is currently being conducted using standard software such as HEIMDALL. With one detection from a pipeline of recall <1, we can only calculate a lower bound on the FAST event rate for the given detection threshold of 7σ, i.e., 25 mJy ms for 1 bit polarization-summed data. Assuming that the FRB events follow a Poisson distribution, the probability density distribution of the first detected event should follow an exponential distribution, i.e., Poisson distribution of zero events until the first detection. In this case, the cumulative distribution function of an exponential distribution follows F(x) = 1 − e^−kx, where k is the event rate, and x is the time to the first detection. Here we would like to find the 95% confidence limits for the event rate k giving one event in 1500 hr. We find that F(1500 hr) > 0.05 when k > 0.034 event per 1000 hr (i.e., 0.3 event per year). Considering that our search system does not have a 100% recall rate, no upper bound can be set. Due to small number statistics, the lower limit of k > 0.034 event per 1000 hr is not yet constraining to most theoretical predictions (Li et al. 2017; Luo et al. 2018, 2020).

Nevertheless, this first detection attests to FAST's potential to systematically detect FRBs in the future, and such detections will put far more stringent constraints on the FRB-rate at high DM. Lorimer (2018) and Zhang (2018) showed that the FAST event rate, especially the rate of high-DM FRBs, would help determine the luminosity function of FRBs. Detection of very high DM (>6500 pc cm⁻³) could probe FRB at more than z = 10 (Zhang 2018), and help shed light on the cosmological distribution of the FRBs.