Highest Frequency Detection of FRB 121102 at 4–8 GHz Using the Breakthrough Listen Digital Backend at the Green Bank Telescope

The DM of FRB 121102 has been previously reported to range between 553 and 569 pc cm⁻³ (Spitler et al. 2014, 2016; Scholz et al. 2016; Law et al. 2017) from lower-frequency observations. For each burst detected here, we measured the S/N as a function of DM, and found that individual bursts show slightly different peak S/N-maximizing DMs. These S/Ns correspond to the peak flux densities obtained after integrating the entire 4.5–8 GHz band. For bursts 11B, 11L, 11M, and 11R, which are confined to a limited fraction of the entire band, we have used only that portion of the band to better estimate S/N-maximizing DM uncertainties. Estimated S/N-maximizing DMs for all 21 bursts are listed in Table 1. To investigate further, we coherently dedispersed raw voltages from burst 11A across a range of DMs with a DM step of 5 pc cm⁻³. This investigation led to the discovery of detailed spectrotemporal structures (components, see Figure 1 and Section 3.2). It is likely that the differences between the DMs originate from how these components superimpose for different trial values of DM. Figure 1 shows burst 11A dedispersed and detected at three different DMs. While it is not clear if these components are intrinsic to the emission mechanism or due to propagation effects, their peculiar alignment provides enhanced S/N at higher DMs compared to previously reported DMs (Spitler et al. 2014, 2016; Scholz et al. 2016; Law et al. 2017).

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Assuming these components to be intrinsic, we optimized the S/Ns of individual components by maximizing the average absolute rate of change of the total flux density, which we call here a structure parameter, across the pulse window defined as,

$$\begin{eqnarray}&&\mathrm{Structure}\,\mathrm{Parameter}=\displaystyle \frac{1}{n}\displaystyle \sum _{i}^{n}\left|\displaystyle \frac{{S}_{i}-{S}_{i+1}}{{\rm{\Delta }}t}\right|.\end{eqnarray} \tag{ 1 }$$

Here, n is the number of on-pulse bins, S_i is the flux at the ith bin, and Δt is the time resolution. This structure-parameter-maximizing DM differs significantly from the S/N-maximizing DM (see Figure 1). Similar techniques have also been explored and will be reported in detail in J. W. Hessels et al. (2018, in preparation) at lower frequencies. Although an analysis of this type was not possible for most of our detected pulses due to either low S/N, fewer components, or both, we assumed a structure-maximizing DM of 565.0 pc cm⁻³ to be consistent for all our bursts and used that value in coherent dedispersion. We note that this estimate can be off by our DM resolution in Figure 1 from a "true" DM (i.e., ±5 pc cm⁻³).

We found highly variable temporal and spectral features in many of the bursts. Figure 2 shows dynamic spectra of all bursts after coherent dedispersion at a DM of 565 pc cm⁻³. Bursts 11A and 12B exhibit distinct components, while bursts such as 11E, 11K, and 11O show some indication of unresolved components. For bursts 11D and 11F, such components are not clearly visible but likely give rise to the slanted or curved features seen in the dynamic spectra. Each burst was modeled as a sum of multiple Gaussian components using the PSRCHIVE utility pass. The model was then used to derive average widths and fluences for all bursts (see Table 1). We note that the burst widths found here are relatively narrow compared to the burst widths seen at lower frequencies (<3 GHz)—as also noted for the Arecibo sample of 4.5 GHz bursts presented by Michilli et al. (2018).

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Bursts 11A and 12B clearly exhibit distinct components. The overall shape of burst 11A is strikingly similar to micro-structures seen for FRB 170827 at lower frequencies (Farah et al. 2018). We identify four components in burst 11A integrated across 4.5–8 GHz, with individual widths of 0.18, 0.10, 0.25, and 0.51 ms. from the leading component to the trailing component, respectively. For the fourth component, it was evident that a single Gaussian function did not represent its true shape, thus, we used a hybrid function, which is combination of a Gaussian and an exponential decay function, to estimate its width. It should be noted that this is just a mathematical representation of the shape and we are not inferring an exponential function as a scattering tail. These components show varying spectral extents, with the first two limited to higher frequencies and the last two at lower frequencies. Additionally, components three and four show a very sharp rise and gradual decay of the burst energy. Component four exhibits a gradual increase in burst width toward lower frequencies. To compare the width of the fourth component across the observed band, we extracted dynamic spectra with widths of 200 MHz centered around 6200, 5980, 5780, and 5460 MHz. An integrated profile of the fourth component at these frequencies was found to have widths of 0.22, 0.24, 0.34 and 0.41 ms, respectively. More detailed analyses of the progressive drift in pulse profile components, as seen at other radio frequency bands, are presented in J. W. Hessels et al. (2018, in preparation).

Burst 12B also exhibits two resolved components with widths of 0.29 and 0.30 ms, separated by ∼2 ms. As with 11A, the leading component spans higher frequencies, while the trailing component spans lower frequencies. In contrast to 11A, the trailing component of 12B does not show an increase in width at lower frequencies. While there may be a third component on the leading edge of the second component, the burst S/N is not sufficient for verification.

We determined the Faraday RM of the bursts by performing a brute-force search of the linear polarization fraction at different RM trials with the rmfit tool from PSRCHIVE. We developed a custom routine to correct for the initial RM values from rmfit and fit a quadratic function to the complex angles determined by the Stokes parameters. This technique refines the initial RMs and computes a polarization angle (PA) for each burst. A detailed description of this technique can be found in Michilli et al. (2018). This approach was motivated by the extremely variable spectral properties of the bursts. From the 13 brightest bursts that could be analyzed using this technique, we find a mean RM of 93589 ± 118 rad m⁻². The RMs found here differ by 9169 ± 122 rad m⁻² from the RMs of the bursts detected from Arecibo at 4.5 GHz by Michilli et al. (2018). After de-rotating the Stokes Q and U using the best-fit value of RM, all 13 bursts show a ∼100% linear polarization fraction and uniform PAs across the burst (Figure 2). We have only considered PAs from the phase bins with linear polarization above 3σ. The weighted mean PA for each burst, measured after weights calculated empirically from the variance in PAs across these phase bins, is listed in Table 1. The uncertainty on the weighted PA was measured as a sum of all weights for each burst. It should be noted that the PA is roughly uniform across the pulse phase; however, there are apparently significant variations (∼7°) in the average PA between all observed bursts at the ∼3σ level. For example, bursts 11A and 12B show slightly lower PAs compared to rest of the reported bursts. These differences in PAs could possibly arise from our uncertainties in the RM measurements, as these two quantities are covariant. No circular polarization was found for any burst and any undetected circular polarization is less than a few percent.

Figure 3 shows measured flux density as a function of observing frequency and time for the 17 brightest bursts. The peak flux frequency is not constant within the observed frequency band; similar spectral variation between bursts has also been reported by previous studies (Spitler et al. 2016; Law et al. 2017; Scholz et al. 2017; Michilli et al. 2018). These large-scale frequency features are approximately of the order of ∼1 GHz in extent. To estimate the average number of discrete large-scale structures, we divided the spectrum from each burst into multiple bins, each 94 MHz wide, and then calculated the total amount of spectral energy in each bin (Figure 4). The overall spectral energy distribution shows two approximately GHz wide peaks around 6 and 7.2 GHz, with a possible trough in the spectral energy between 6.5 and 7 GHz. It should be noted that this spectral behavior is based on our detections of only 21 bursts. It is possible that the detection of a larger sample of bursts might fill this trough.

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Figure 3 shows that bursts exhibit marked differences in their spectral extent and spectral peaks. Some bursts, such as 11A, show emission across the entire observed band; others, such as 11C, 11H and 11K, show emission only at the highest frequencies. Bursts 11G, 11N, and 12A show a concentration of emission in the lower half of the band. Bursts 11A to 11F exhibit a spectral peak around 7 GHz, which appears to then shift to lower frequencies in later bursts.

In order to assess the origin of large- and finer-scale frequency structures seen in Figures 2 and 3, we calculated the Galactic scintillation bandwidth across the observed band. We used the NE2001 model (Cordes & Lazio 2002), and estimated a Galactic scattering timescale τ_s = 20 μs ν^−α toward the direction of FRB 121102 (ν is the observing frequency in GHz, while α is the scaling parameter). Assuming a frequency scaling for a Kolmogorov spectrum with scaling parameter, x, between 4 and 4.4 (Cordes & Lazio 2002; Bhat et al. 2004), we estimate the expected diffractive interstellar scintillation bandwidth as (Lambert & Rickett 1999)

$$\begin{eqnarray}&&{\rm{\Delta }}{f}_{\mathrm{DISS}}=\displaystyle \frac{1.16}{2\pi {\tau }_{{\rm{s}}}}=\displaystyle \frac{1.16{\nu }^{x}}{40\pi }\,\mathrm{MHz}.\end{eqnarray} \tag{ 2 }$$

For the observed band (4.5–8 GHz), the predicted Δf_DISS varies from 7 to 87 MHz (assuming a scaling parameter of 4.4). Thus, the large-scale frequency structures (∼GHz wide) are likely to be intrinsic to the source and/or due to propagation effects in the source's local environment.

To compare these predicted values for Δf_DISS with fine-scale frequency structures from the detected bursts, we obtained spectra for each burst by selecting an appropriate on-pulse window. Following the procedure of Cordes et al. (1985) and Cordes (1986), we then computed auto-correlation functions (ACFs) for these spectra (Figure 5). As the spectral extent of a few bursts were significantly broad—spanning over 3 GHz—the ACFs over the entire spectra produce a multi-featured ACF with multiple widths. To measure the characteristic bandwidth for a given burst, we divided each spectrum into two or three parts, depending upon the spectral extent. We then fitted a Gaussian function to the ACF to obtain the half width at half maximum as a characteristic bandwidth for the given sub-spectra for each burst.

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We found that the ACFs showed different characteristic bandwidths in different sub-spectra in the 4.5–8 GHz band. Table 2 shows these characteristic bandwidths from 15 stronger bursts. The measured characteristic bandwidth follows the expected Δf_DISS across the 4.5–8 GHz band (see Figure 6), suggesting that the fine-scale frequency structures seen in each of these bursts are likely due to Galactic interstellar scintillation, with a few exceptions. For example, burst 11H does not appear to show characteristic bandwidth matching with the Δf_DISS at higher frequencies. However, this could be a statistical fluctuation, given the small number of scintiles in the burst.

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Our detection of 21 bursts within 60 minutes represents the highest number of bursts detected within a short interval (i.e., hour timescale), with 18 bursts occurring in the first 30 minutes. We did not detect any bursts during the following 4 hr of observations, which supports the idea that FRB 121102's bursting behavior is episodic. This could be due to intrinsic changes in the emission conditions or due to more favorable "plasma lensing" conditions (Cordes et al. 2017) during the first hour, potentially enhancing observed burst energies by an order of magnitude.

Our observations highlight the advantages afforded by wider instantaneous bandwidth. If our 4 GHz instantaneous bandwidths were halved, we would only have detected 10–12 bursts, mainly as the band-limited spectral structures they exhibit would have fallen out of the band (Figure 2). Law et al. (2017) have also pointed out similar limitations of narrow bandwidth observations.

The spectral peak variation of each burst and apparent band-limited characteristics indicate that further bursts may be detected by searching for pulses over subbands, particularly in observations over large fractional bandwidths. The existence of spectral structure may also impact the performance of single-pulse search pipelines, which are generally designed to search for broadband pulses.

We compared the average peak flux densities of all our bursts with previously reported observations at various lower frequencies, as shown in Figure 7(a). We found that statistically the distribution of peak flux densities across frequency is consistent with being flat across 1–8 GHz. It should be noted that these measurements were obtained from different telescopes at very different epochs, which might affect their intrinsic absolute scaling. The different sensitivities of different telescopes at various frequencies are also highlighted in Figure 7(a). We also compared the burst widths at various frequencies (Figure 7(b)) and highlight that bursts are relatively narrower at higher frequencies (>4 GHz).

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The apparently flat spectrum of FRB 121102 stands in contrast to the steep spectral indices observed for most neutron star emission. Giant pulses (GPs) from the Crab pulsar, for instance, typically exhibit a very steep spectrum with a power-law index α = −2.6 and a steep power-law distribution of rates at a fixed fluence (Meyers et al. 2017). Ordinary pulsars also show very steep spectra, with a mean index α = −1.4 (Bates et al. 2013). An important exception is the radio to millimeter spectrum of magnetars. The Galactic Center magnetar, SGR J1745−2900, has been observed to have a flat spectrum up to 291 GHz (Torne et al. 2017). The similarity in spectral index between FRB 121102 and radio magnetars suggests a common emission mechanism. It is likely that further high-frequency observations with better sensitivity, enabling the detection of weaker bursts, may provide better constraints on the steepness of the spectral index.

If the apparently flat spectral behavior of FRB 121102 is a common property for other FRBs, we suggest that future FRB surveys could be conducted effectively at higher frequencies, utilizing either a fly's eye mode or multiple beams to compensate for a smaller field of view. Higher-frequency observations may also have lower terrestrial radio interference and larger instantaneous receiver bandwidths—potentially beneficial for detecting more of these spectrally limited bursts. Similar suggestions were also made by Law et al. (2017).

The large-scale frequency structures are unlikely to be instrumental in nature and are likely intrinsic to the progenitor or propagation effects imparted in the source's local environment. We note the similarity of these structures to the banded structures seen for the Crab GPs at similar high radio frequencies reported by Hankins & Eilek (2007) and Jones (2010). We also found that burst-to-burst large-scale spectral properties change on the order of tens of seconds. If bursts from FRB 121102 have a physical origin similar to Crab GPs, then such changes are comparable to similar spectral feature variations between Crab GPs, although these manifest at a shorter timescale (few microseconds). The fine-scale structures appear to be due to the Galactic DISS. This is consistent with the angular diameter of the bursts measured at 1.7 GHz from VLBI (Marcote et al. 2017).

The high RM found here for FRB 121102 is almost 500 times greater than the RMs reported for any other FRB (e.g., Masui et al. 2015) and somewhat larger than the RM of the Galactic center magnetar SGR J1745−2900 (Eatough et al. 2013). Our measured RM is about 10% lower than the RM from bursts detected at 4–5 GHz, from data obtained seven months prior to the observations reported here. This change in the RM is already highlighted in Michilli et al. (2018). This is a significant change in the RM and further justifies regular monitoring to clarify how the RM varies with time. SGR J1745−2900 also shows changes in the RMs on a similar scale over four years of regular monitoring (Desvignes et al. 2018).

The high RM suggests an intense magnetic field, at least 1 mG, in the progenitor's environment. As noted in Michilli et al. (2018), plausible scenarios that could produce this RM include: the source being in the vicinity of an intermediate-mass or supermassive black hole, like SGR J1745−2900 (Eatough et al. 2013) or inside a powerful pulsar wind nebula, or a supernova remnant. Piro (2016) suggested that an expanding supernova shell could also cause the RM to decrease with time, as reported here. However, such changes can also cause the corresponding DM to decrease with time by a similar factor, which was not observed. Other FRBs might have similarly high RMs; however, measuring large RMs requires higher frequency resolution at lower frequencies (e.g., ≤3 GHz) to avoid intra-channel depolarization. For example, to search for RM up to 10⁵ rad m⁻², the required channel resolution is of the order of tens of kHz at 1 GHz. This again highlights the utility of high-frequency observations of FRBs, as intra-channel depolarization is inversely proportional to observational frequency to the third power.