An Insight-HXMT Dedicated 33 day Observation of SGR J1935+2154. I. Burst Catalog

The blind search is based on the signal-to-noise ratio (S/N) method that has been applied to the GRB search in the HE CsI detectors of Insight-HXMT (see Cai et al. 2021 for more details). This method is used to search for magnetar bursts in the HE NaI detectors of Insight-HXMT. In order to unveil the soft and faint bursts that might not be found with only HE detectors (which have a higher energy band than those of LE and ME), we use three telescopes (HE, ME, and LE) of Insight-HXMT to jointly search for bursts (e.g., Guidorzi et al. 2020a, 2020b), covering a series of timescales ranging from 5 to 40 ms, with two phase offsets (Cai et al. 2021). Given the limited counts for weak bursts, Poisson statistics is assumed (e.g., Younes et al. 2020).

To help to set the search strategies and to estimate the expected counts in LE, ME, and HE for substantially weak soft bursts, we simulate the Insight-HXMT observations of the SGR J1935+2154 bursts measured by NICER. The expected counts are calculated by multiplying the softest spectrum (burst #222) from NICER (see Table 2 in Younes et al. 2020, i.e., ${kT}={0.5}_{-0.1}^{+0.1}$ keV, ${R}^{2}={970}_{-560}^{+1300}$ km²) with the responses of LE, ME, and HE detectors. It results in 2 counts, 0 counts, and 0 counts in LE, ME, and HE, respectively, with a duration of about 0.2 s, which means that there is some signal in LE while there is no signal in ME and HE for such kinds of soft and weak bursts (flux of 10⁻⁹ erg cm⁻² s⁻¹ in 0.5–10 keV as measured by NICER). However, given the low background of LE (i.e., ∼1 counts in 0.1 s), LE could marginally detect such weak and soft bursts but with a low significance (less than ∼3σ). We note that the ratio of model predicted counts of LE and ME is roughly 1 for bursts with kT > 2.5 keV, which constitutes about 10% of the NICER samples (see Table 2 in Younes et al. 2020). However, the spectral parameters of NICER samples are derived from a relatively limited energy range of 1−10 keV.

According to the count ratios between the three telescopes (HE, ME, and LE) in the simulations shown above, some bursts with softer spectra are likely detected by LE only. However, the background of LE is very complicated, which is mainly composed of two parts: particle background (>7 keV) and the diffuse X-ray background (<7 keV) (Liao et al. 2020a), and the background count rate distribution (see Figure 1) is very wide and far deviating from a simple Poisson distribution. Therefore, it is not easy to identify the SGR J1935+2145 bursts, especially for weak bursts, only using the light curves of LE. We leave the detailed burst search with LE data only to future work.

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Therefore, in this paper, considering the quality of the burst sample and available data, we require that a burst should be observed by at least two telescopes during the burst search and verification; thus, three telescopes of Insight-HXMT could be divided into four combinations: HE&ME, HE&LE, ME&LE, and HE&ME&LE. Following the experience in previous search studies (Cai et al. 2021; Guidorzi et al. 2020a, 2020b), all unblinded detector units are summed together for ME and LE, respectively, while the 17 NaI units of HE are used separately.

The detailed search algorithms and trigger criterion are shown in Table 2, including different combinations of three telescopes, timescales, phases, the threshold of detector number of HE, and net counts of HE, ME, and LE. A burst candidate is found when the excess in the net counts of two or more telescopes exceeds a preset threshold of significance. Different polynomial fits are applied to the light curves of each telescope to estimate the background count rate within a 100 s time window centered on the searched time bin. Then, the background counts of each time bin are obtained through the interpolation of the background model.

The backgrounds of the three telescopes of Insight-HXMT are relatively complicated owing to their relatively large field of view. The LE background is mainly caused by the particles in orbit and the diffuse cosmic X-ray background (Liao et al. 2020a), while that of the ME is primarily contributed by the charged particles (Guo et al. 2020). The background of HE is more complicated than that of LE and ME, since it is dominated by the activated isotopes (with relatively longer decay time), which is related to the passages of SAA, together with other components including particles and albedo scattering (Liao et al. 2020b).

In order to set a proper search criterion and estimate the significance for each burst candidate, it is important to know how the backgrounds of the three telescopes vary with time and the distribution of background counts on those short timescales used in the SGR burst search. To study the background variation, calibrate our search algorithm, and derive the false-alarm probability, the same trigger criterion is used to search a group of blank-sky background observations (i.e., observations of the selected blank-sky regions without bright sources), which span from 2017-11-02T05:00:57.000 to 2018-03-27T05:24:47.000 (a total span time of 909 hr, or 78,537.6 ks), as listed in Table 1.

According to these blank-sky observations, there are significant extra-Poisson components in the background distributions of all three telescopes (see Figure 1), which are the imprint of the complicated background behaviors. Such complicated distributions of background indeed require one to derive the significance (i.e., false-alarm probability) of the searched burst candidate directly from the background data with real variations rather than from the S/N of the searched time bin (Cai et al. 2021).

We calibrate the trigger criterion by searching for any count excess in the blank-sky data with the same trigger threshold as used in the SGR burst search. Detailed results are listed in Table 2, including the common GTIs of different telescopes, total numbers of false triggers N_FT, and false-alarm probability P_FA of the blank-sky at four timescales. The false-alarm probability (P_FA) is defined as

$$\begin{eqnarray}&&{P}_{\mathrm{FA}}=\frac{{N}_{\mathrm{FT}}}{{N}_{S}},\end{eqnarray} \tag{ 1 }$$

where N_FT and N _S represent the number of false triggers and the number of searches of different timescales and different combinations of telescopes, respectively. The search number is calculated using the length of common GTIs divided by timescales and taking into account the phase shifts.

As shown in Table 2, based on the detailed calibration with blank-sky data, the search threshold for SGR bursts is generally equivalent to at least a 5σ detection (Gaussian).

In the preliminary analysis released on the website of Insight-HXMT, ⁹ we reported 133 burst candidates, which triggered the blind search with rough burst identification. In this work, we execute a refined analysis for each burst candidate with the careful removal of various false triggers (including instrumental effects and real bursts from other sources rather than SGR J1935+2154) and a comprehensive processing of all the data of the three telescopes.

Spikes are short and soft pulses in the HE light curve caused by fake events output by the readout electronics when there is a very large energy deposition in HE detectors. The presence of spikes in the HE data is a well-known instrumental effect and has been studied in detail (Wu et al. 2022). Here we find that the spike events cannot be removed completely by the current version (v2.04) of the HXMTDAS, which cause some false triggers, as shown in Figure 2.

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We identify each burst candidate carefully and filter out spike events based on the following features. The spikes usually occur on only one or a few adjacent NaI and CsI detectors (see the right panel of Figure 3) with low-energy events (i.e., the pulse height less than about channel 35; Wu et al. 2022), while the count increases of all nonblinded NaI detectors should be comparable for an SGR J1935+2154 burst (see the left panel of Figure 3) since the energy responses are similar for all nonblinded NaI detectors for the targeted source in the pointed observations. This is an important criterion to identify spikes. In addition, there is no spike event on LE and ME data, which can also be used to identify SGR J1935+2154 bursts mostly triggered by HE.

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Apart from the SGR bursts, the blind search could unveil various bursts from other sources, including GRBs and terrestrial gamma-ray flashes (TGFs). The typical duration of short bursts from SGRs ranges from 0.1 to 1 s (Collazzi et al. 2015; Lin et al. 2020b). In contrast, GRBs would appear in a much broader duration ranging from milliseconds to more than thousands of seconds. Indeed, Insight-HXMT/HE has served as a wide-field gamma-ray monitor for GRBs, mainly using the CsI detectors of HE (Zhang et al. 2020b; Cai et al. 2021). We find that some short GRBs (nominally with duration less than 2 s) would look similar to the SGR bursts in NaI detectors when they are incident to the HE telescope from the front side. Thus GRBs could be a potential contamination source to the SGR bursts. However, the spectra of GRBs usually extend from tens of keV up to several MeV, much harder than SGR bursts; thus, GRBs are mostly detected by CsI instead of NaI and leave many more counts in CsI than NaI detectors. This feature is opposite to the fact that SGR bursts are soft and mostly detected by NaI and barely leave signals in CsI detectors in this pointed observation of SGR J1935+2154. Therefore, we use the light curves of both NaI and CsI detectors to identify and remove GRBs from the burst candidates of SGR J1935+2154.

TGFs are short intense gamma-ray flashes produced in the lightning process in the atmosphere of Earth (Fishman et al. 1994; Enoto et al. 2017). Its duration ranges from submillisecond to several milliseconds with a hard spectrum in the energy range of hundreds of keV to tens of MeV (Nemiroff et al. 1997; Briggs et al. 2013). There are a wealth of TGF detections by Insight-HXMT (Q. B. Yi et al. 2022, in preparation). Similar to the case of GRBs, TGFs are hard in spectrum and leave more counts in CsI than NaI detectors. Moreover, TGFs are much shorter than typical SGR bursts. Based on these characteristics, it is convenient to identify TGFs out of the detected bursts.

In summary, we check each burst candidate found by the blind search and filter out the false triggers, including spikes, GRBs, and TGFs. We obtained a sample of 75 bursts that are confidently identified as from SGR J1935+2154, to our best knowledge. The durations of each burst are listed in Table 3. The burst samples are listed in Table 4, including FRB 200428−Associated Burst (i.e., burst #15).

We define the daily burst rate (R, in units of bursts per day, 24 hr) as

$$\begin{eqnarray}&&R=\displaystyle \frac{N}{P},\end{eqnarray} \tag{ 2 }$$

where N is the observed burst number per day and P represents the percentage of the effective observation time in a full day, excluding the time intervals of Earth blocking of the SGR J1935+2154 and SAA passages of Insight-HXMT, during which the instrument (observation) would be turned off.

Note that, due to the schedules of ToO observations, the observation coverage is incomplete in 3 days (i.e., 2020 April 28, 2020 April 29, and 2020 April 30), for which the burst rate (R) also accounts for the nonobservation time intervals.

As shown in Figure 5, the burst rate generally decreases with time during the 33 day evolution of burst activity, with a few small reactive peaks. This Insight-HXMT dedicated long ToO observation caught up with the later part of the most active phase and monitored the entire process from very active to inactive in the burst rate of SGR J1935+2154. Thanks to the broad energy band (1−250 keV) and high sensitivity, Insight-HXMT detected many more bursts than other instruments (e.g., Fermi/GBM), providing a unique valuable burst data set to the community.

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Following previous studies (Lin et al. 2013), the burst duration T_bb is calculated with the Bayesian blocks method (Scargle et al. 2013). We perform the Bayesian blocks to measure the duration for all bursts using the screened event data of the 10 s burst time window, including both pre-burst and post-burst regions. The blocks with a duration longer than 6 s are treated as background, while blocks with duration less than the spin period (i.e., 3.24 s) of SGR J1935+2154 are considered as part of the burst region (Lin et al. 2013). The background count rate is estimated with the mean rate of the background blocks. The burst blocks with less count rate than the background are excluded. Some bursts with multiple pulses (e.g., burst #49 in Figure 4) have at least two subsequent blocks, along with burst-free (or quiescent) intervals, so the burst duration is defined as the time length from the start of the first burst block to the end of the last block within the burst time window, which represents the entire burst duration. As an example of the definition of burst duration, light curves of burst # 56 are shown in Figure 6.

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The durations (T_bb) of each burst measured by the three telescopes of Insight-HXMT are listed in Table 4. The burst duration distributions of LE, ME, and HE are shown in the left panel of Figure 7. These distributions are well fit with lognormal functions, with the mean values of 130 ± 25 ms and σ = 0.62 ± 0.08 for LE, 86 ± 7 ms and σ = 0.61 ± 0.03 for ME, and 102 ± 11 ms and σ = 0.48 ± 0.04 for HE. ¹⁰ We define the common time interval (duration) of LE, ME, and HE, where the start time is the maximum start time, while the end time is the minimum end time of the three telescopes. The common duration is also listed in Table 4. For bursts detected by fewer than three telescopes, the common duration is obtained in the same manner. We also plot the distribution of common duration, which can be described with a Gaussian function of μ = 64 ± 8 ms and σ = 0.59 ± 0.05, as shown in the left panel of Figure 7.

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We also checked the evolution of the burst duration, as shown in the right panel of Figure 7. We find that longer bursts (with duration larger than 350 ms) mostly occurred during those time intervals with higher burst rate (i.e., the gray shaded regions).

We measure the waiting time (δ_t ) between successive bursts that fall within an uninterrupted GTI,

$$\begin{eqnarray}&&{\delta }_{t}={t}_{i+1}-{t}_{i},\end{eqnarray} \tag{ 3 }$$

where t_i+1 and t_i represent the trigger times of the (i + 1)th (latter) and ith (previous) bursts, respectively.

To obtain the continuous observation time intervals (i.e., without interruption) with Insight-HXMT, we exclude the time intervals when the satellite passes through SAA or SGR J1935+2154 is blocked by Earth. During those continuous observation time intervals, there are 21 waiting times δ_t . The distribution of these waiting times is shown in Figure 8, which ranges from 5.38 to 1935.94 s and could be fitted to a lognormal function with a peak of 572 ± 82 s and σ = 0.44 ± 0.06. The length distribution of the continuous observation time interval is also shown in Figure 8, which naturally provides the maximum value of the waiting time.

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The scatter plot of waiting time versus T_bb and fluence (see Paper II) is shown in Figure 9. We find that there is no significant correlation between the waiting time and the fluence or the burst duration either for the previous burst or for the latter burst.

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The net count of each burst is estimated as

$$\begin{eqnarray}&&{C}_{i}={S}_{i}-{B}_{i},\end{eqnarray} \tag{ 4 }$$

where S_i and B_i represent the total counts and background counts in the burst duration, respectively. The net counts are computed for HE, ME, and LE, respectively.

The hardness ratio is the ratio of the net count rates in different energy bands. We derive the hardness ratio between 10−30 keV and 1−10 keV with ME and LE data and the hardness ratio between 28−250 keV and 10−30 keV with ME and HE data. There are 60 bursts detected by all three telescopes of Insight-HXMT, which could be used for the hardness ratio study. The relationship between common burst duration and hardness ratio of these 60 bursts is shown in the left panel of Figure 10. Hardness ratios between 10−30 keV and 1−10 keV and between 28−250 keV and 10−30 keV of these bursts spread over a large range from 0.52 to 25.60 and from 0.32 to 3.86, respectively. There is no correlation between the duration and the hardness ratio. As shown in the right panel of Figure 10, there is also no significant trend in the evolution of the burst hardness across the observation time.

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Note that there are seven bursts (see Table 4) for which HE or LE data suffered from data saturation (Xiao et al. 2020). Thus, the hardness ratio calculation is not applicable for them. We report the detailed spectral analysis to study the hardness of the bursts in Paper II, considering the data saturation and dead-time effects.