CHIME/FRB Detection of the Original Repeating Fast Radio Burst Source FRB 121102

The CHIME/FRB instrument has been described in an overview paper in which the CHIME telescope, FRB detection instrument, and pipeline are described in detail (CHIME/FRB Collaboration et al. 2018). During the interval from 2018 July 25 to 2019 February 25, CHIME was in a commissioning state in which various components of the instrument were being tested, with software and calibration systems being updated and improved frequently. Although the CHIME/FRB system was operational starting 2018 July 25, the beam configuration for the months of July and August rendered FRB 121102 undetectable as it did not transit within the FWHM region of any of the fast Fourier transform (FFT)-formed beams at 600 MHz. Following a system reconfiguration on 2018 September 4, we were sensitive to FRB 121102 for a total of 11.3 hr, as shown in Figure 1. We truncate our reported exposure on 2019 February 25, when we brought the CHIME/FRB system down for pipeline updates and testing. The telescope sensitivity was known to be varying from day to day during the interval due primarily to changing gain calibration strategies, but also due to a variety of issues that, once recognized, were rectified. Overall, we determine the median sensitivity to be ${7}_{-4}^{+7}\,\mathrm{Jy}\,\mathrm{ms}$, for a burst width of 34 ms (see Section 2.3), during on times shown in Figure 1. Further details regarding the sensitivity estimate are provided below (see Section 2.5).

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The burst was detected and associated with FRB 121102 by our automated FRB detection pipeline on 2018 November 19, at 09:38:47.706 UTC (topocentric, 600 MHz), when our threshold for saving buffered intensity data was signal-to-noise ratio (S/N), S/N = 10. The nominal pipeline detection S/N for the event was 23.7, and so intensity data were saved. The event was detected in a single beam whose central pointing position is consistent with the known position of FRB 121102 (Chatterjee et al. 2017), as shown in Figure 2. This, and the similarity in nominal pipeline DM of 565 pc cm⁻³ to previously published values (∼559 pc cm⁻³; Scholz et al. 2016), assured us of the event's identification.

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The saved intensity data, having 16k frequency channels each at 0.983 ms time resolution, allowed us to produce a "waterfall plot," as shown in Figure 3. A complex burst morphology is seen, both in time and in radio frequency. Note that correcting for CHIME's bandpass response is a work in progress, and is complicated by a declination-dependent ∼30 MHz ripple due to multiple reflections, declination-specific ∼7 MHz ripple due to FFT beamforming (Ng et al. 2017), as well as additional rippling due to the use of a polyphase filterbank algorithm and FFT upchannelization for defining our frequency channels (CHIME/FRB Collaboration et al. 2018). Bandpass-calibrated data are shown in the bottom subplots of Figure 3. The conversion from instrumental units to fluence is discussed in Section 2.4. Emission is clearly detected down to ∼600 MHz, by far the lowest yet seen for this source. Moreover, it also appears to be band-limited, with no emission seen below this value, in spite of good sensitivity down to 400 MHz.

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The CHIME X-Engine, in addition to supplying data to the CHIME/FRB instrument as described in CHIME/FRB Collaboration et al. (2018), also provides tied-array formed-beam data products to a separate backend that is used for targeted observations of pulsars and other known radio transients. This instrument, CHIME/Pulsar, is described in detail in Ng et al. (2018). CHIME/Pulsar has been monitoring the position of FRB 121102 reported in Chatterjee et al. (2017) since 2018 November 3. Each observation tracks the position of the source for about 19 minutes as it drifts over the meridian FOV of CHIME. All together, 23.86 hr were spent on source, covering a total of 81 days of transits up until 2019 March 1. The data were coherently dedispersed to a DM¹⁷ of 558.1 pc cm⁻³ then saved as a total-power filterbank time series, with a time resolution of 327.68 μs and 1024 frequency channels each with a width of 390 kHz. Offline, a PRESTO-based (Ransom 2011) single-pulse search was conducted on these data. Throughout this period, only one burst was observed, on 2018 November 19, for which the CHIME/FRB has a simultaneous detection. The waterfall plot of this burst is shown in Figure 3. This burst was detected with an S/N of 17 using the CHIME/Pulsar instrument, and shows temporal structure similar to previous bursts of FRB 121102. We note that the S/N reported from the Pulsar backend is lower than that from the FRB backend. The difference is likely due to imperfect scaling from floating point precision to the 4-bit integer VDIF output in the early commissioning data of the Pulsar backend. For this reason, we restrict further analysis and rate estimates to the FRB backend, where defining a fluence completeness limit throughout our quoted exposure is more tractable.

The observed burst morphology—broad pulse structure with several apparent components—might be caused by a combination of subburst drifting and scattering. To try to disentangle the two, we analyzed the CHIME/FRB intensity data first by assuming all morphology is caused by subburst drifting, and then by fitting a model burst that includes both subbursts and scattering.

To characterize subburst drifting in the burst, we optimized the DM for burst structure by finding the DM that maximizes the forward derivative of the dedispersed time series, following Hessels et al. (2019) and Gajjar et al. (2018), as shown in Figure 4. We calculated the DM transform for 400 steps ranging from 556 to 574 pc cm⁻³ and smoothed the transform with a 3 × 3 (2.8 ms × 0.135 pc cm⁻³) rectangular kernel to reduce the noise. Then, we calculated the forward derivative and smoothed the resulting image further by a 3 × 5 (2.8 ms × 0.225 pc cm⁻³) rectangular kernel. Finally, we summed the absolute value of the forward derivative to the power n ∈ (1, 2, 4) over the time axis. The approach of Gajjar et al. (2018) corresponds to n = 1, while Hessels et al. (2019) use n = 2. We find that higher values of n select for singular sharp rises in the pulse profile, while lower values may favor multiple lower-amplitude peaks. For a given n, the maximum of a high-order polynomial fit to the curve is taken as the structure-optimizing DM. To estimate uncertainties, we normalize the DM transform such that each pixel represents an S/N value, then perform a Monte Carlo simulation by perturbing the transform with normally distributed noise. For n = 4, we find a structure-optimizing DM of 563.6 ± 0.5 pc cm⁻³, while n = 2 gives 565 ± 1 pc cm⁻³. We adopt the former value as the curve for n = 4 has an unambiguous peak. This is several DM units higher than earlier reported DMs for this source (e.g., Spitler et al. 2016; Hessels et al. 2019) but is consistent with measurements of the structure-optimizing DM in Arecibo observations near 1.4 GHz from 2018 November (A. Seymour et al. 2019, in preparation).

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Using the structure-optimizing DM, we analyze the autocorrelation of the emission region in the dedispersed dynamic spectrum, as shown in Figure 5. To mitigate RFI masking effects, we limit the analysis to the relatively clean 580–725 MHz band, which contains the majority of the observed signal (see Figure 3). The 2D autocorrelation shows where the burst has the most self-similarity. A tilt in the ellipse reflects the subburst drift rate and here we find a rate −3.9 ± 0.2 MHz ms⁻¹. Assuming the pulse profile and spectral bandwidth of the burst envelope and subbursts are reasonably well described by Gaussian profiles, we measure their FWHMs from the standard deviation σ of a Gaussian profile fit to the summed autocorrelation over the respective axes.¹⁸ We find a burst envelope width of 33.7 ± 0.6 ms and a typical subburst width of 26.9 ± 0.3 ms. The total emission bandwidth is 87 ± 1 MHz and the subburst bandwidth 71 ± 2 MHz. We note that bandpass correction is a work in progress, imposes structure on comparable scales, but which is stable on the timescale of the burst. The 530–580 MHz range, excluded due to significant RFI contamination, may hide additional structure and lead to an underestimated envelope bandwidth and duration. This possibility is supported by the Gaussian fit to the full-band spectrum (see Figure 3), which is centered at 631 MHz. Note that due to the limited S/N of the detection, coupled with imperfect bandpass correction, the intrinsic structure of the burst remains mostly unresolved—despite time resolutions much finer than the envelope width.

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In order to quantify frequency-dependent scattering in the burst, we also applied an S/N-optimizing routine to our raw total-intensity data that uses a least-squares algorithm similar to that used in the analysis of the first 13 FRBs discovered by CHIME/FRB (CHIME/FRB Collaboration et al. 2019a). This algorithm was modified to allow for fitting an arbitrary number of Gaussian spectral components and their respective parameters against 16k-channelized dynamic spectra; per-component parameters include an arrival time, time/frequency Gaussian widths, signal amplitude, and central frequency of peak emission. The DM and scattering parameters are applied to all substructure components as "global" fit parameters.

We find that three Gaussian components are statistically favored for FRB 121102 when using the spectrum-fitting algorithm on our bandpass-calibrated data, and weighting spectra residuals by per-channel variances. In these fits, we hold the DM fixed to the structure-optimizing value of 563.6 pc cm⁻³, as well as the DM and scattering indices fixed to −2 and −4, respectively. We detect no significant scattering of the burst, with a 3σ upper limit on the scattering timescale of 9.6 ms at 500 MHz. Fit parameters are listed in Table 1.

The best-fit parameters of the three Gaussian components can also be used to constrain the subburst drift rate in time and frequency. Using these data, we find the drift rate between the three components to be −2.9 ± 1.0 MHz ms⁻¹ when using an orthogonal-distance-regression method for weighting fits by the uncertainties in spectral and temporal centroid positions of the three components. This rate is consistent with the estimate from the model-independent autocorrelation analysis.

We note that the S/N of our data and the complex bandpass function do not allow us to robustly search for evidence of diffractive scintillation in the spectrum.

The burst was detected during the commissioning phase of the CHIME/FRB system. We therefore adopt the same method to estimate its fluence as in CHIME/FRB Collaboration et al. (2019a). We used the observation of 3C 48 (which has a decl. within 01 of FRB 121102) on 2019 November 18 for calibration and obtained a flux conversion factor as a function of radio frequency to account for the telescope primary beam. We assessed the uncertainty on the fluence in the same way as described in CHIME/FRB Collaboration et al. (2019a). Here, we used nine bright sources within 1° (instead of 5°) elevation angle. Since we estimated an uncertainty on the flux as a function of frequency using the calibration sources, we have an upper and lower bound for each intensity value in the band-averaged profile, hence, an upper and a lower bound profile. We measured the uncertainty on the burst fluence by measuring the average area between the two profiles. Since we were operating in a commissioning phase, a large fraction of the bandwidth was unusable for estimating the fluence for the same reasons described in CHIME/FRB Collaboration et al. (2019a). Overall, we estimated the burst fluence to be 12 ± 3 Jy ms, measured over an effective total bandwidth of 255 MHz in the range 400–800 MHz. We stress that uncertainty in our fluence measurement is systematics dominated, and is expected to improve as our beam model and calibration techniques mature. The detection S/N (23.7σ) should be taken as the best representation of detection significance.

In determining sensitivity to FRB 121102 over the course of our exposure, we characterize three potential sources of variability: (i) day-to-day instrument gain variations, (ii) changing source position within the synthesized beams, and (iii) different emission bandwidths and frequency centers within the instrument bandpass.

To capture (i), the day-to-day gain variation, we identified Galactic radio pulsars within 5° decl. of the source, which were detected by CHIME/FRB on at least 20% of the days between 2018 July 25 and 2019 February 25. For the purpose of this analysis, we identify a pulsar detection as robust if at least five pulses with S/N > 8 were observed on each day within the FWHM region for the FFT-formed beams at 600 MHz. We use the distribution of measured S/N values for these pulses to estimate the rms radiometer noise, ${T}_{\mathrm{sys}}/(G\sqrt{{n}_{{\rm{p}}}{\rm{\Delta }}\nu {t}_{\mathrm{samp}}})$, where T_sys is the system temperature, G is the telescope gain, n_p is the number of summed polarizations, Δν is the bandwidth, and t_samp is the sampling time. In contrast to the approach used for estimating the rms noise in our previous work (CHIME/FRB Collaboration et al. 2019b), we do not directly compare the measured S/N for each pulsar with its cataloged flux density. This is to avoid underestimating the sensitivity in the presence of RFI excision algorithms that cause bright pulsars to be detected with reduced S/N or overestimating it for pulsars for which CHIME/FRB is sensitive only to the tail of the flux distribution and the cataloged flux density is not representative of that observed.

For each pulsar, we take the median of the measured S/N values on each day and account for the pulse width to estimate the ratio of the rms noise at the pulsar sky location and its flux density. Assuming that the flux distribution for each pulsar is stable in time, the daily variation in this ratio for each pulsar is due to the varying rms noise for its sky location. For each day, we normalize this ratio by dividing by its median over all days the pulsar was detected. We then perform a weighted average of the normalized ratios for all pulsars detected on each day to get the overall variation in rms noise. Performing a weighted average ensures that pulsars with less intrinsic variation dominate the resulting estimate.

For (ii), we use a beam model to estimate sensitivity variation across a single transit of FRB 121102 (see Figure 2). The frequency-dependent model includes an analytic description of the FFT-formed beams (Ng et al. 2017), as well as an approximated forward-gain description of the primary beam, which is based on ray-tracing simulations done for the CHIME Pathfinder (Bandura et al. 2014). The composite model is used to compute the band-integrated relative sensitivity between different locations within the transit.

For (iii), we recognize the significant effect of our bandpass on detectability of the variety of spectra seen in FRB 121102 bursts. To test our sensitivity to bursts with different spectral energy distributions (SEDs), we use the beam-former-to-Jansky conversion as a function of frequency that is generated from the calibration process. Multiplying this array with a simulated SED and summing across frequencies gives the expected recovered signal. We restrict this simulation to Gaussian spectral profiles, with which we convolve the conversion array to get relative S/N scale factors for different emission bandwidths and central frequencies.

We combine these three sources of variability in a Monte Carlo simulation, with each sample representing the fluence threshold for some possible burst within the defined exposure. To generate a sample, we first draw a date within the covered interval, where the probability for choosing each day is proportional to its exposure (see the upper panel of Figure 1). We then draw from a Gaussian distribution parameterized according to the relative sensitivity and uncertainty for the chosen day, as given by the pulsar study (see the lower panel of Figure 1). We then uniformly draw a position along the transit and within the FWHM at 600 MHz for the relevant beams (see Figure 2). Since our decreased exposure is caused by a node failure, the active beams, and therefore possible positions, depends on the chosen day. Once a location is chosen, we compare sensitivity to the detection location to get our second relative sensitivity factor.

Next, we uniformly draw an emission bandwidth Δν ∈ [Δν_fit/2, 2Δν_fit]. The bandwidth determines the range of central frequencies we consider: ν ∈ [400 MHz + Δν/2, 800 MHz − Δν/2]. The expected S/N for this SED is divided by the expected S/N for the detection-parameterized SED to get the final relative sensitivity factor (ν_fit = 631 MHz, Δν_fit = 100 MHz; see Figure 3).

The three factors are multiplied to get an overall relative sensitivity for the simulated sample. To translate this to a fluence threshold, we first draw an initial fluence threshold from a Gaussian distribution, which is parameterized according to the recovered S/N and measured fluence of our single detection. Scaling the fluence to a detection threshold based on the S/N assumes a linear relationship between the two, which we caution is not always a valid assumption. Finally, we divide the drawn initial fluence threshold by the overall relative sensitivity to get a fluence threshold for the simulated sample. We repeat this process a million times to build up a distribution of fluence thresholds. The median value with two-sided 90% confidence interval is ${7}_{-4}^{+7}\,\mathrm{Jy}\,\mathrm{ms}$. The medians and 90% confidence intervals for the three intermediate distributions of relative sensitivity are (i) 1 ± 0.2, (ii) 0.7 ± 0.3, and (iii) 0.9 ± 0.2.

Using the total estimated CHIME/FRB exposure time of 11.3 hr (see Section 2) to FRB 121102 and the 90% Poisson uncertainty on the single burst detected by CHIME/FRB of 0.05–4.7 bursts, we estimate an average rate in the CHIME band of 0.1–10 bursts per day for the interval 2018 July 25 through 2019 February 25. We note that the repetition of FRB 121102 is known to be non-Poissonian (e.g., Scholz et al. 2016; Oppermann et al. 2018) so this rate should be considered a rough approximation that is averaged over periods of likely variable activity.