Distinct Properties of the Radio Burst Emission from the Magnetar XTE J1810–197

The period-averaged flux density was estimated by using the "top-hat" equivalent width of the average intensity profile and the corresponding signal-to-noise ratio (S/N) in the radiometer equation (Lorimer & Kramer 2004). We assumed 60% aperture efficiency and receiver temperatures as per the observatory specifications. The sky background temperature (${T}_{\mathrm{sky}}$) toward the magnetar was estimated by scaling the corresponding estimate at 408 MHz (Haslam et al. 1982) to the center frequency of our observations. At 650 MHz, ${T}_{\mathrm{sky}}$ is estimated to be about 115 K. The temporal evolution of the 650 MHz flux density thus obtained is shown in the top panel of Figure 1.

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To obtain the spectrum, we used our 2018 December 18 (S1) observation to compute average profiles in four different 50 MHz wide sub-bands centered at 575, 625, 675, and 725 MHz. ${T}_{\mathrm{sky}}$ was estimated at each of these frequencies as mentioned above. The period-averaged flux densities at these sub-bands are shown in Figure 1 (bottom panel), along with those in the frequency range 768–3840 MHz measured by Dai et al. (2019) using the Parkes telescope on the same day. On 2018 December 21, we successfully detected the magnetar in the frequency range 300–500 MHz. Due to low S/N we could not estimate the spectrum in this frequency range; however, we have plotted the band-averaged flux density in Figure 1.

To understand the average properties of the bursty emission from the magnetar, we used single_pulse_search.py from PRESTO to first detect all the bright pulses above a detection threshold of 8σ. From our 650 MHz observations, we detected a total of 1856, 2662, 818, and 261 bursts from sessions S1, S2, S3, and S4_a, respectively. Additionally, we detected 219 bursts from the 1360 MHz observation (S4_b). The positions of these bursts, in terms of the magnetar's rotational phases, could provide crucial clues to the underlying emission mechanism. As shown in Figure 2 obtained from session S1, the number of detected bursts roughly follow the total intensity profile shape. A similar trend is noticed in the other observations as well. Unlike the giant pulse emission from several pulsars (e.g., B0531+21, B1937+21), these bursts are not confined in narrow rotation phases inside or outside the average emission window.

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The spiky emission from the magnetar is known to be much narrower than the individual components in the average profile. Our observations clearly show that the bursts have a characteristic width of some 1−4 ms at 650 MHz (see Figure 2). The characteristic width seems to become narrower (≲1 ms) at 1360 MHz. We note that the observed pulse-width is essentially the intrinsic pulse-width convolved with our sampling time. Peak of the 1360 MHz distribution around 1.3 ms may have been particularly affected by the coarse sampling time of 0.655 ms. Due to this coarse resolution, pulses intrinsically as narrow as 0.7 ms would also appear to be nearly 1 ms wide. Hence, the actual characteristic pulse-width at 1360 MHz would be of the order of 1 ms or smaller. As discussed later in this section, the increase of the pulse-width at lower frequencies is most likely caused by the propagation effects, and is not intrinsic.

Following the convention used by Serylak et al. (2009), we mark three components in the average profile: M1, M2, and M3 (see Figure 2). Component M3 is absent in session S1 (Figure 2), but it appears in the other sessions. However, even when M3 is visible, the number of spiky bursts detected under this component are only 1%–2% of the total number of bursts. So, we only consider the bursts detected under the components M1 and M2.

To determine the peak flux density (S_p) of the individual pulses (Cordes & McLaughlin 2003), we use the pulse-width and the peak S/N of the pulse corresponding to a smoothing optimum for its observed width, in the modified radiometer equation as described in Maan & Aswathappa (2014). The S_p distributions of the bursts under the two components, combined as well as component-separated, in individual observations are presented in Figure 3. We model the tails of the distributions using power-law statistics of the form $N({S}_{p})\propto {S}_{p}^{\alpha }$, where N is the number of pulses, and α is the power-law index. Furthermore, we used S_p = 500 mJy as a uniform lower cutoff to fit only the tails of the distributions. The fitted values of α for the overall burst distributions are presented in Table 1. The distributions in the last two observations appear to be slightly flattened when compared to those from the first two observations, which were much closer to the start of the outburst. Except for the session S2, the 650 MHz burst distributions under M1 have significantly steeper tails than those under M2 (Figure 3). As evident by a single point at the far-right tail of the distributions from sessions S4_a and S4_b, a very bright narrow pulse with peak flux densities of about 3.5 and 8.6 Jy was detected at 650 and 1360 MHz, respectively.

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The bursts from the magnetar show a variety of temporal and spectral characteristics and phenomenology. A representative set of bursts from our 650 MHz observations are presented in Figure 4. The first two panels in each of the rows show some of the narrowest bursts and their spectral structures in the respective sessions. Most of these bursts exhibit an exponential tail, indicating scatter broadening in the intervening propagation medium. To determine the intrinsic width and scatter-broadening timescale (${\tau }_{\mathrm{sc}}$), we modeled the first two bursts from session S2 shown in Figure 4 as a Gaussian convolved with a one-sided exponential function (Krishnakumar et al. 2019). Our model fits suggest the intrinsic widths of the two bursts to be 0.69 ± 0.05 ms and 0.53 ± 0.04 ms, and the corresponding ${\tau }_{\mathrm{sc}}$ to be 1.30 ± 0.06 ms and 1.05 ± 0.05 ms, respectively. Therefore, the apparent characteristic pulse-width of a few ms at 650 MHz is predominantly due to scatter broadening. The above intrinsic pulse-widths at 650 MHz are consistent with the characteristic pulse-width of less than 1 ms at 1360 MHz, as discussed earlier.

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The bursts also show significant spectral variations (Figure 4). Interstellar scintillation could induce such spectral structures. However, using the above measured ${\tau }_{\mathrm{sc}}$, the scintillation bandwidth is estimated to be less than a kHz. Both the popular electron density models, NE2001 (Cordes & Lazio 2002) and YMW16 (Yao et al. 2017), also suggest similar estimates. Hence, the observed spectral structures of several tens of MHz are intrinsic to the source. The structures are more prominently noticeable closer to the outburst onset (i.e., in sessions S1 and S2) and less so in the later observations. The frequency bandwidths of these structures seem to have narrowed down with time. The bursts in the later sessions appear to have more and more uniform and featureless spectra. The number of bursts that show prominent spectral variations, such as those in the first row, also appear to be much lesser in the later sessions. To quantify the spectral variations, we compute spectral modulation index, ${m}_{I}$, defined as ${m}_{I}^{2}=(\overline{{I}^{2}}-{\overline{I}}^{2})/{\overline{I}}^{2}$, where $\overline{I}$ and $\overline{{I}^{2}}$ are the first and second moments of the peak-intensity of a burst as a function of frequency (Spitler et al. 2012). For each of the sessions, we selected all the bursts narrower than 3 ms and with S/N > 10. We then computed ${m}_{I}$ for the dedispersed spectra corresponding to the peaks of the bursts after partially averaging in frequency to obtain 128 sub-bands across the bandwidth. The obtained ${m}_{I}$ are in the ranges 0.40−1.41, 0.49−2.46, 0.42−1.20, and 0.46−1.19, using 335, 660, 267, and 54 bursts from the sessions S1, S2, S3, and S4_a, respectively. The distributions of the obtained ${m}_{I}$ are shown in Figure 5. Note that the lowest values of ${m}_{I}$ in the above ranges correspond to the bursts where the spectral power is near uniformly distributed across the frequency band, and, as expected, these are indeed quite close to each other (0.40−0.49). A higher value of ${m}_{I}$ implies the spectral power to be localized in smaller sub-bands. As apparent from Figure 5, the sessions S1 and S2 have many more bursts with relatively higher ${m}_{I}$, and hence more spectral variations than the last two sessions. Moreover, in the last two sessions (S3 and S4_a), peaks of the distributions have shifted very close to the lowest observed ${m}_{I}$ values, indicating that the majority of the bursts in these sessions have close to uniform and featureless spectra.

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As apparent from the last panels in each of the rows in Figure 4, the bursts often tend to occur in succession. Sometimes even a quasi-periodic occurrence is noticeable, with separations in some 5−25 ms range. A more quantitative characterization of the quasi-periodicity, as well as the above spectral structures (e.g., measuring the structure bandwidths, and their evolution with time and frequency), will be reported elsewhere.

A working definition of giant pulses is that the flux density or pulse-energy of a averaged over the spin period is more than 10 times the corresponding mean quantity. The mean flux density of the bursts from the magnetar do not exceed this conventional threshold. Nevertheless, the peak flux densities of the bursts are very large in absolute terms. For example, the brightest pulses in session S3 and S4 are about 2.5 and 3.5 Jy, which is 40–60 times the mean S_p of the average profiles. These properties are rather reminiscent of the giant micropulses (Johnston et al. 2001) discovered from the Vela pulsar (B0833−45).

Much like the giant pulses, the giant micropulses add extended power-law tails to the single-pulse flux density distributions (Kramer et al. 2002). The peak flux densities are often averaged over the period before making the histograms (e.g., see Karuppusamy et al. 2010). We note that the distributions of the absolute (Figure 3) as well as those of the period-averaged (not shown but analyzed separately) peak flux densities exhibit tails that are very well fit with a power law.

Kramer et al. (2002) reported a characteristic relationship between widths of micropulses and the spin period. Using their Equation (1), the expected micropulse width for J1810−197 would be 2.8–5.6 ms. While this width is consistent with the characteristic width of the bursts that we measure at 650 MHz, we note that the intrinsic widths of the narrowest pulses are only about 0.5–0.7 ms, i.e., smaller by a factor of 4–5. However, the widths of the narrowest giant micropulses from the Vela pulsar are in fact also smaller than those of the average micropulses by a similar factor Kramer et al. (2002). In any case, given the scatter in the data used to derive the relationship between micropulse width and the spin period, the characteristic width of the magnetar's bursts is consistent with the expected micropulse width. The micropulses often exhibit an associated quasi-periodicity in their occurrences. While a detailed analysis of any underlying quasi-periodicity is under progress, Figure 4 shows some examples of a possible underlying quasi-periodicity in the magnetar's bursts.

The giant micropulses from Vela pulsar and the classical giant pulses from a handful of pulsars occur in narrow pulse phase ranges. However, the giant pulses from the Crab pulsar appear in significant parts of the pulse window. The bursts from the magnetar also do not have any favorable phase ranges, and their occurrence rate roughly follow the integrated profile shape.

While most FRBs are one-off events, a couple of these are known to repeat (FRB 121102 and FRB 180814.J0422+73; Spitler et al. 2016; CHIME/FRB Collaboration et al. 2019). Recently, Hessels et al. (2019) used high time-resolution observations to show complex time-frequency structures in the FRB 121102 bursts. Particularly, they showed that many of the bursts at 1.4 GHz show ∼250 MHz wide frequency bands that cannot be explained by scintillation in the interstellar medium (ISM). Similar structures have been seen in the second repeating FRB as well (CHIME/FRB Collaboration et al. 2019). Except for the high-frequency interpulse giant pulses from the Crab pulsar (Hankins et al. 2016), and in some faint emission components of PSR 1745-2900 (Pearlman et al. 2018), such frequency structures have not been seen from any known pulsar or magnetar. In Figure 4, we show that the spiky emission from J1810−197 also exhibits frequency structures that cannot be caused by the ISM scintillation. Hessels et al. (2019) also showed that the banded structures in many of the FRB 121102 bursts show a frequency drift, and the drift rates possibly decrease at lower frequencies. The relatively coarse time resolution of our observations and the smearing caused by the scattering at our observing frequency does not allow adequate probes of any underlying drifts at timescales shorter than a few ms. However, the frequency drifts of FRB 180814.J0422+73 are observed at much longer timescales of some 20–60 ms in the frequency range 400−800 MHz. We do not notice such long timescale drifts in the magnetar's bursts. In any case, high time resolution probes of the spiky emission from the magnetar at adequately high frequencies will clarify if the frequency structures indeed share some similarities with those from the repeating FRBs, for which magnetar origin is one of the popular models.

We note that the 1.36 GHz peak flux density of the brightest burst in our sample is about 9 Jy. This is about an order of magnitude larger than the peak flux density of the bright bursts from FRB 121102 at similar frequencies. However, FRB 121102 is nearly 2.8 × 10⁵ times more distant, implying a ∼10¹¹ times more luminosity, for similar emission solid angles. Nevertheless, the fact that the magnetar J1810−197 is only the third object after the repeating FRBs and the Crab pulsar that is found to exhibit frequency structures in its bursts so prominently might provide a phenomenological link between the underlying emission mechanisms.