Identification of a non-thermal X-ray burst with the Galactic magnetar SGR 1935+2154 and a fast radio burst with Insight-HXMT

Fast radio bursts (FRBs) are short pulses observed in radio band from cosmological distances, some of which emit repeating bursts. The physical origins of these mysterious events have been subject to wide speculations and heated debates. One class of models invoke soft gamma-ray repeaters (SGRs), or magnetars, as the sources of FRBs. Magnetars are rotating neutron stars with extremely strong magnetic field and can sporadically emit bursts from X-ray ($\sim$keV) to soft gamma-ray ($\sim$sub-MeV) with duration from $10^{-2}$~s to $10^2$~s. However, even though some bright radio bursts have been observed from some magnetars, no FRB-like events had been detected to be associated with any magnetar burst, including one giant flare, and no radio burst has been associated with any X-ray event from any magnetar. Therefore, there is still no observational evidence for magnetar-FRB association up to today. Recently, a pair of FRB-like bursts (FRB~200428 hereafter) separated by 30 milliseconds (ms) were detected from the general direction of the Galactic magnetar SGR~J1935+2154. Here we report the detection of a non-thermal X-ray burst in the 1-250 keV energy band with the Insight-HXMT satellite, which we identify as emitted from SGR~J1935+2154. The burst showed two hard peaks with a separation of $\sim30$ ms, consistent with the separation between the two bursts in FRB~200428. The delay time between the double radio and X-ray peaks is $\sim8.57$ s, fully consistent with the dispersion delay of FRB~200428. We thus identify the non-thermal X-ray burst is associated with FRB~200428 whose high energy counterpart is the two hard peaks in X-ray. Our results suggest that the non-thermal X-ray burst and FRB~200428 share the same physical origin in an explosive event from SGR~J1935+2154.

Fast radio bursts (FRBs) are short pulses observed in radio band from cosmological distances 1 , some of which emit repeating bursts 2 . The physical origins of these mysterious events have been subject to wide speculations and heated debates. One class of models invoke soft gammaray repeaters (SGRs), or magnetars, as the sources of FRBs 3 . Magnetars are rotating neutron stars with extremely strong magnetic field 4 and can sporadically emit bursts from X-ray (∼keV) to soft gamma-ray (∼sub-MeV) with duration 5 from 10 −2 s to 10 2 s. However, even though some bright radio bursts have been observed from some magnetars 6 , no FRB-like events had been detected to be associated with any magnetar burst, including one giant flare 7 , and no radio burst has been associated with any X-ray event from any magnetar. Therefore, there is still no observational evidence for magnetar-FRB association up to today. Recently, a pair of FRB-like bursts (FRB 200428 hereafter) separated by 30 milliseconds (ms) were detected from the general direction of the Galactic magnetar SGR J1935+2154 8,9 . Here we report the detection of a non-thermal X-ray burst in the 1-250 keV energy band with the Insight-HXMT satellite 10 , which we identify as emitted from SGR J1935+2154. The burst showed two hard peaks with a separation of ∼ 30 ms, consistent with the separation between the two bursts in FRB 200428. The delay time between the double radio and X-ray peaks is ∼ 8.57 s, fully consistent with the dispersion delay of FRB 200428. We thus identify the nonthermal X-ray burst is associated with FRB 200428 whose high energy counterpart is the two hard peaks in X-ray. Our results suggest that the non-thermal X-ray burst and FRB 200428 share the same physical origin in an explosive event from SGR J1935+2154.
SGR J1935+2154 was discovered when it went into outburst in 2014 11 . Since then and before 2020, the source experienced several activities in 2015 February, 2016 May to July and 2019 November. Between outbursts, isolated bright flares or short bursts in X-ray or gamma-ray have been detected from the source 12,13 . These make SGR J1935+2154 one of the most active magnetars. Starting from 2020 April 27 18:26:20 UT, a series of X-ray and gamma-ray instruments were triggered by multiple short bursts and a burst forest including hundreds of bursts from SGR J1935+2154 14,15 . Within thirteen hours, we started a long Target of Opportunity (ToO) observation of this source using Insight-HXMT with all its three collimated telescopes covering 1-10 keV (Low Energy X-ray telescope, LE), 5-30 keV (Medium Energy X-ray telescope, ME) and 20-250 keV (High Energy X-ray telescope, HE), respectively. This pointed ToO observation continued for 60 ks from April 28 07:14:52 UT to April 29 11:53:01 UT.
During the Insight-HXMT observation, a double-peaked and short radio burst, FRB 200428, from the general direction of SGR J1935+2154 was reported by CHIME/FRB 8 and STARE2 9 at April 28 UTC 14:34:33 (at 400 MHz) and 14:34:25 (at 1.4 GHz), respectively. The fluence of this radio burst recorded by STARE2 9 is > 1.5 MJy ms , which is over six magnitudes brighter than those radio bursts from XTE J1810-197 6 , which had been the brightest radio bursts from magnetars. This makes it the first possible magnetar radio burst detectable from an extra-galactic distance (e.g FRB 180916.J0158+65 at 149 Mpc 9 ), if FRB 200428 were emitted from SGR J1935+2154.
Insight-HXMT detected a series of 11 bursts within about 17 hours of exposure to SGR J1935+2154 (see Methods for description and burst list). It is mostly likely that most, if not all, of these bursts came from SGR J1935+2154, since it was the only active magnetar in this period and in the field of view of Insight-HXMT. The brightest burst with a trigger time (denoted as T 0 ) of April 28 14:34:24.0000 UT (satellite time) or 14:34:24.0114 UT (geocentric time) lasted for about 1 second in 1-250 keV and was seen clearly in all three telescopes. This burst is also the closest one in time to FRB 200428. With different orientations of the collimators, Insight-HXMT can localize the burst within its field of view, as shown in Figure 1. The burst is located at RA = 293.75 +0.06 −0.08 deg, Dec = 21.88 +0.06 −0.06 deg, ∼1.4 arcmin away from SGR J1935+2154 with 1σ error of ∼4 arcmin. We thus identify this burst as coming from SGR J1935+2154.
This burst was so bright that it saturated both LE and HE, and also caused moderate deadtime effects in ME. After correcting all these effects (see Methods), the lightcurves and hardness of the burst obtained by the three telescopes are presented in Figure 2. The full lightcurves of this burst consist of two major bumps separated by about 0.2 s, and a minor soft bump just before T 0 that is only present in LE and ME data, indicating overall spectral evolution as shown by the hardness evolution during the burst. The second major bump, which was also detected by INTEGRAL 16 and Konus-Wind 17 , is much brighter than the first one. In the lightcurves of both ME and HE, two narrow peaks are clearly seen (see Methods) during the second major bump. In the LE lightcurve, only the second narrow peak is visible significantly, indicating somewhat different broad band energy spectra between the two narrow peaks. The separation time between the two narrow X-ray  peaks (∼ 30 ms) is consistent with that of the two narrow peaks in FRB 200428, and the apparent time lag between X-ray and radio peaks (∼8.57 s) is in good agreement with the calculated dispersion delay (8.63 s) between X-ray and radio using the DM (∼333 pc/cm 3 ) measured by CHIME/FRB 8 and STARE2 9 . We thus identify the burst detected by Insight-HXMT is associated with FRB 200428 and both belong to a single explosive event from SGR J1935+2154.
The time-integrated spectrum of this burst (T 0 − 0.2 s to T 0 + 1.0 s) is derived jointly using HE, ME and LE data (Figure 3, see Methods for details of spectral fitting). The best fit and statistically acceptable model is a cutoff power-law (CPL) with neutral hydrogen column density n H = (2.79 +0. 18 −0.17 ) × 10 22 cm −2 , photon index Γ = 1.56 ± 0.06 and cutoff energy E cut = 83.89 +9.08 −7.55 keV. The unabsorbed fluence is (7.14 +0.41 −0.38 ) × 10 −7 erg cm −2 in 1-250 keV, corresponding to a total emission energy of ∼ 1 × 10 40 erg for the 12.5 kpc 18 distance of SGR J1935+2154. This burst is brighter than ∼ 84% of events collected from the source during 2014 − 2016 with Fermi/GBM 13 . We also fit the spectrum with several other spectral models, e.g., single power-law (PL), double blackbody (BB+BB) and blackbody plus power-law (BB+PL). The fit to the BB+PL mode is marginally consistent with data, with slightly higher column density (n H = (3.50 ± 0.17) × 10 22 cm −2 ) and larger photon index (Γ = 1.93 ± 0.04); the flux of the unabsorbed blackbody component with temperature of 11.32 +0.55 −0.56 keV is only 18% of the total flux in 1-250 keV. The other two models provide significantly worse fit and are thus rejected.
We conclude that the integrated spectrum is dominated by a power-law covering at least the 1-100 keV range, and thus this burst is primarily non-thermal in nature. It is also clear that the two narrow peaks separated by ∼ 30 ms must also be dominated by a non-thermal spectrum, since the hardness reaches its maximum during the peak of the second bump of the lightcurves where the two narrow peaks are found. It is interesting to note that the lower limit of the radio flux detected with STARE2 9 falls in between the extrapolated values from the non-thermal X-ray spectrum with the power-law parameters of the fits to the CPL and BB+PL models (see the panel (f) in Figure 3).
In summary, with the observation of Insight-HXMT we have identified that the short nonthermal X-ray burst was emitted by the Galactic magnetar SGR J1935+2154 and produced almost simultaneously with FRB 200428 in a single explosive event. In the literature, FRB emission has been interpreted as either coherent curvature radiation of electron-positron pairs from a neutron star magnetosphere [19][20][21] or synchrotron maser emission in a relativistic, magnetized shock 22, 23 . Since magnetar bursts are believed to be magnetosphere-related 24 , the fact that the narrow double peaks in both radio and X-ray are emitted around the same time, and hence, likely originate from the same emission region, lends support to the magnetospheric models of FRBs.
However, a thermal origin is preferred for normal short bursts from magnetars 25, 26 . We notice Figure 3: The spectrum observed with Insight-HXMT covers the 1-250 keV energy band. Data from the three telescopes of Insight-HXMT covering different energy bands are represented in different colors (LE: black, ME: red and HE: green). In the fitting process, we introduced a constant factor to offset the different saturation and deadtime effects in different detectors. Four models were considered, cutoff power-law (CPL), blackbody+power-law (BB+PL), power-law (PL), and blackbody+blackbody (BB+BB). The equivalent hydrogen column in the interstellar absorption model was free to fit. (a) The X-ray spectrum of SGR J1935+2154 described by CPL model. The inset (f) shows the comparison between the radio flux lower limit detected with STARE2 9 and extrapolations from the X-ray spectrum to the radio frequency range, where the green and orange regions are the 3σ error bands with the parameters of the CPL (below STARE2) and BB+PL (above STARE2) models, respectively. Panels (b)-(e) are the residuals of the data from the individual models, respectively. (see Methods for details of the spectral fitting and parameters derived.) that ∼ 6% of the bursts (7/109) from SGR J1935+2154 detected with Fermi/GBM between 2014 and 2016 can be best fit with a power-law model 13 . The fluence of these bursts is about one order of magnitude dimmer than this one associated with FRB 200428. We therefore set a conservative upper limit of 6% to the percentage of magnetar bursts which may have similar radio emission to FRB 200428. Actually, non-thermal X-ray bursts are very rarely observed from magnetars in general, which explains why events similar to FRB 200428 have not been seen previously.
If this burst were emitted from an extragalactic magnetar located at a distance of FRB 180916.J0158+65 at 149 Mpc 27 , and assume the distance of SGR J1935+2154 is 12.5 kpc 18 , then the observed fluence should be ∼ 4 ×10 −15 erg cm −2 in 1-250 keV, which is far below the sensitivity limits of the X-ray telescopes currently in orbit (or in the foreseeable future). This may explain the non-detection of the X-ray counterpart of any cosmological FRB so far. Nevertheless, identification of FRB 200428 with a magnetar means at least some of FRBs are produced by magnetars, thus FRBs can be used as an effective tool to study the extra-galactic magnetars, which are otherwise undetectable. On the other hand, giant flares from magnetars can have peak luminosity of 10 44−47 erg s −1 , about 4-7 orders of magnitude more luminous than this non-thermal X-ray burst, and thus might be detectable with the current X-ray telescopes in orbit or the future X-ray missions, such as eXTP 28 which has a much larger effective area in the X-ray band than those X-ray telescopes in orbit. Giant flares of magnetars might not be associated with FRBs by temporal coincidence, however, short X-ray transient events from the same directions of FRBs may be the peaks of magnetar giant flares and thus identified as the counterparts of these FRBs. Competing Interests The authors declare that they have no competing financial interests.
Author contribution CKL, LL and SLX are co-first authors and listed in alphabetical order. TPL, FJL and SNZ are co-corresponding authors and listed in alphabetical order. TPL was the initial proposer and PI of Insight-HXMT. SNZ is the current PI of Insight-HXMT, organized the observations, data analysis and presentation of the results, writing and editing of the paper. LL proposed the ToO observation, is a main writer of the paper and participated in discussions. SLX participated in organizing the observations, data analysis, discussion and paper writing. FJL is a leader in building Insight-HXMT and participated in organizing the data analysis, discussions and paper writing. CKL is the main contributor to the data analysis and participated in paper writing. BZ is responsible for theoretical interpretation, and participated in organizing the observations, discussions, and paper writing. MYG, YLT, XBL, YN, SX, YC, LMS, YT, XFZ, CZL, SMJ, JYL and BL participated in the data analysis and discussion. All other authors contributed to developing, building and operating the Insight-HXMT payloads and science data center.

Insight-HXMT observations and burst search
The Insight-Hard X-ray Modulation Telescope (Insight-HXMT) is China's first X-ray astronomy satellite 10,29,30 which was launched on June 15th, 2017. It has an altitude of 550 km and an inclination of 43 degrees. As a broadband X-ray (1-250 keV) observatory, Insight-HXMT consists of three telescopes, i.e., the High Energy X-ray telescope (HE) using 18 NaI(Tl)/CsI(Na) phoswich scintillation detectors for 20-250 keV 31 , the Medium Energy X-ray telescope (ME) using 1728 Si-PIN detectors for 5-30 keV 32 , and the Low Energy X-ray telescope (LE) using 96 Swept Charge Device (SCD) detectors for 1-15 keV 33 . All three telescopes use slat collimators to confine their Field Of Views (FOVs). In addition to the pointed or scanning observation with the collimators, Insight-HXMT can also monitor the all-sky in gamma-ray (0.2-3 MeV) using the CsI scintillation detectors of HE. More details about the Insight-HXMT can be found in 10 .
A dedicated and long Time of Opportunity (ToO) observation of Insight-HXMT was implemented for SGR J1935+2154 from 2020-04-28T07:14:51 to 2020-04-29T00:00:00, and a throughout search for X-ray bursts have been made. The trigger condition for the search is that the count rates of three or more NaI detectors of HE exceeds the background count rate, which is the mean count rate in the previous 10 s, with significance greater than 3σ at five time scales ( 0.05 s, 0.1 s, 0.2 s, 0.5 s and 1 s). This search results in 11 bursts. The starting time and other properties are listed in Table 1, where the fluence is obtained by fitting their spectra with simple spectral models (i.e. PL or CPL), as the fluence does not varies significantly with which spectral model is used. Saturation and deadtime corrections are made before spectral fitting, according to the procedures described below. More detailed analyses of these bursts will be presented elsewhere.
The rest of this Methods part is mainly dedicated to the burst at 2020-04-28T14:34:24.00 (UTC) that is associated with FRB 200428. Because of the extreme brightness, the Insight-HXMT data suffers substantial saturation and deadtime effects, which require dedicated corrections as detailed below.
Data analysis The timing and spectral results of the X-ray burst associated with FRB 200428 are obtained by analysing the Insight-HXMT 1L data with the Insight-HXMT Data Analysis Software package (HXMTDAS) version 2.02. Specifically, the steps are: (1) Use the commands hepical, mepical, lepical in HXMTDAS to calibrate the photon events from the 1L data according to the Calibration Database (CALDB) of Insight-HXMT. As for HE, the short spikes with known characteristics produced in the electronics are removed from the physical events. (2) Select the good time intervals (GTIs) from T 0 -0 to T 0 +1 s, where T 0 is 2020-04-28 14:34:24 UTC. (3) Extract the good events based on the GTIs using the commands hescreen, mescreen, and lescreen. (4) Generate the spectrum with the selected events using the commands hespecgen, mespecgen, and lespecgen. (5) Create the background spectrum from the events in the time interval T 0 −51 to T 0 − 1 s. (6) Generate the response matrix files required for spectral analysis using the commands herspgen, merspgen, and lerspgen. (7) Produce the raw ME and LE lightcurves using the commands, melcgen, and lelcgen.
Due to the strong saturation effect in both LE and HE data, the raw data in some time intervals were discarded on-board and their lightcurves need to be corrected as presented below.
Data saturation and deadtime correction Because of the extremely high flux of the burst, the detected events exceeded the storage limits of their on-board data buffer, and so the observed data suffered from saturation. The observational effect of saturation is that in some time intervals the events are lost. Besides the saturation effect, during the procession of an event by the frontend electronics, the detectors sharing the same Physical Data Acquisition Unit (PDAU) can not record any photons, and such an effect is called deadtime. As will be detailed below, both HE and LE suffered strongly from the saturation effects, while the deadtime effects are significant in the HE and ME data. Both the saturation and deadtime need to be corrected when we produce the lightcurves and spectra.
The 18 phoswich X-ray detectors of HE are divided into three groups, each contains six detectors that share one PDAU. Therefore, the three groups of detectors have different event-lost intervals, which are shown in Figures 1, 2 and 3. We correct for the saturation effects in the data of the three groups independently, and then combine them together when we produce the final lightcurve.
The steps of saturation correction for a group of HE detectors are listed as follows: (1) Find the start and stop time of the intervals in which the raw data are not lost. (2) Calculate the deadtime ratio of each detector as a function of time, the details of which can be found in Xiao et al. (2020) 34 .
(3) Screen the data in these time intervals to discard the CsI events (anti-coincident events), as well as the events whose energies are out of the selected energy band. Then, the number of NaI events can be obtained for each detector in the group. Using the time intervals selected in the first step and the deadtime ratio calculated in the second step, the true source count rate of each detector in the group can be obtained. (4) Merge the count rate of all detectors in each group and calculate the error of the merged rate. It should be noted that, for the third group (Group ID is 2), as the events of the blinded detector are not used, a factor of 6/5 is used to normalize its count rate, so that the count rates of the three groups can be compared at the same level and combined together to produce the overall HE lightcurve. ME does not suffer from the saturation effect and the raw data have no time gap. The dead-time of ME can be calculated with HXMTDAS v2.02. The number and ratio of the lost events in T 0 + 0.37 and T 0 + 0.62 s are also listed in Table 2. The lightcurves before and after deadtime corrections are shown in Figure 4. LE has three detector boxes and each box contains 32 SCD detectors. The data of each detector box can be processed independently. In the LE data, besides the normal physical events with energies above the on-board threshold, LE also has the forced trigger events, which record the amplitude of the noise or the pedestal offset for each SCD detector in every 32 ms 30 . The count rate of the forced trigger events in each detector box is 1000 counts per second if there is no saturation effect.
The LE lightcurves are then corrected for saturation using the count rate of the recorded forced trigger events. Since the three detector boxes have different saturated time intervals, we reconstructed the LE lightcurve with almost the full time coverage. The lightcurves before and after saturation correction are shown in Figure 5. The deadtime of LE caused by the force trigger events can also be calculated by HXMTDAS, which are listed in Table 2. It is a minor and negligible issue. Hardness ratio The hardness ratio evolution during the burst is studied by using all the HE, ME and LE data. We derive the 50-250 keV to 27-50 keV hardness ratio with the HE data, and the 10-30 keV to 1-10 keV hardness ratio with the ME and LE data.
To produce the 50-250 keV to 27-50 keV hardness ratio, we first extract photons in 50-Extended Data Table 1: Bursts detected by Insight-HXMT from 2020-04-28T07:14:51 to 2020-04-29T00:00:00. In the table, trigger time is the satellite time, the energy band for fluence calculation is 1-250 keV, duration is that covers 90% of the burst counts, and ∆t is the time difference between burst and FRB 200428. 37.6% 0.27 0.03% a N1 is the number of events lost due to saturation. b LR1 is the lost ratio of events due to saturation. c N2 is the number of events lost due to deadtime. For LE, the deadtime is induced by the forced trigger events. d LR2 is the lost ratio of events due to deadtime.   250 keV and 27-50 keV from the HE data to obtain two lightcurves, in which the bin size before T 0 + 0.38 s and after T 0 + 0.53 s is 60 ms, and the bin size in between is 1 ms. Since the background events contribute to the lightcurves (and so the hardness ratio), especially in the two wings of the burst, we subtract the background of each lightcurve by using the linear interpolation of the count rates in two time intervals before and after the peak, i.e., T 0 -4 s to T 0 -2 s and T 0 + 2 s to T 0 + 4 s. The errors of the hardness ratios are calculated with the standard error propagation formula.
The HE data are used in different ways when producing the hardness ratio in different time intervals. Before T 0 + 0.38 s and after T 0 + 0.53 s, the hardness ratio is given by the ratio of the combined lightcurve of the three detector groups, because there is no saturation effect and the count rates can be calculated in the same time bins. However, from T 0 + 0.38 s to T 0 + 0.53 s, the three detector groups have different data gaps caused by the saturation effect, and so the hardness ratio data points are calculated for each of the three group, respectively.
The hardness ratio between ME and LE is calculated by the ratio of the counts rate in 10-30 keV and 1-10 keV. The time bin width for the hardness ratio calculation in this energy band is 10 ms. A possible background contribution to the hardness ratio is also subtracted.
The two narrow peaks As shown in Figure 2, the lightcurve in each energy band roughly consists of two bumps located at around T 0 +0.2 and T 0 +0.45 s, and the HE and ME lightcurves show two narrow peaks on the second main bump. In order to estimate the significance and to get the exact time of each peak, the HE and ME lightcurves are fitted by five Gaussian functions, in which two of them are used to describe the two narrow peaks, where G(t, t p , σ p ) = 1 √ 2πσp exp(− (t−tp) 2 2σ 2 p ), N p1 and N p2 are the normalization, t p1 and t p2 are the arrival times of the two narrow peaks, σ p1 and σ p2 are the Gaussian widths of the two narrow peaks. R 3 = 5 i=3 G(t, t pi , σ pi )+l describes the three Gaussian functions for the broad components of the lightcurve, where l is the background level of the lightcurve. From the fitting results, the separation τ of the two narrow peaks is calculated from t p2 − t p1 .
As shown in Figure 6 (a) and (b), the lightcurves of HE and ME could be well fitted by equation 1. If the normalization of the two narrow components is set to 0, the reduced-χ 2 is 4.1 (d.o.f.=30) for the fitting to the data points in T 0 +0.35 to T 0 +0.43 s that contains the first narrow peak. Similarly, the reduced-χ 2 is 3.0 (d.o.f.=29) for duration T 0 +0.43 to T 0 +0.50 s that contains the second narrow peak. These large reduced-χ 2 values verify the high detection significance of the two narrow peaks.
As shown in Figure 6 (c), the lightcurve of LE can be well fitted by R = N p2 G(t, t p2 , σ p2 ) + R 3 . A narrow peak corresponding to the second narrow peak in HE and ME lightcurves is also visible, though not as significant as in HE and ME lightcurves. The red lines represent the sum of the three broad Gaussian functions. In panels (a) and (b), the green lines represent the fitted curves with the sums of the five Gaussian functions for ME and HE, in which two are for the two narrow peaks. In panel (c), the green line represents the fitted curve to the LE lightcurve with four Gaussian functions, in which one is for the narrow peak in coincidence to the second peak in HE and ME lightcurves. Spectral analyses and model comparison We extract the spectrum using data in a duration of 1.2 s, from T 0 -0.2 s to T 0 + 1 s. Deadtime correction is a built-in function of the HXMTDAS and has been considered in spectral analysis. However, the saturation correction is not implemented in spectrum generation but will be dealt with in spectral fitting process.
We use XSPEC version 12.10.0c to analyze the spectra. Four different models are used to fit the spectra, which are (1) single power-law (PL), (2) cutoff power-law (CPL) , (3) two blackbody (BB+BB) and (4) blackbody plus power-law (BB+PL). In addition, we use a constant (const) to represent the saturation effect in LE and HE and the wabs model to account for the absorption of the interstellar medium. Eventually, the four models are: wabs * cutof f pl * const, wabs * pow * const, wabs * (bb+bb) * const and wabs * (bb+pow) * const. The best-fit parameters and their uncertainties are listed in Table 4. The distribution of the fitted residuals is displayed in Figure 2 of the main article.
From Table 4 and Figure 2 of the main article we can easily reject the single power-law model and the two temperature blackbody model, but the cutoff power-law (CPL) and the blackbody plus power-law model (BB+PL) fit the burst spectra well, though the latter has relatively higher χ 2 values and slightly structured residual above 80 keV. Discussions about these models can be found in the main article.
Localization Although the three telescopes of Insight-HXMT point to the same nominal directions, the long axis directions of their Field Of Views (FOVs) are different, which could be used to locate the burst. Figure 7 shows the FOVs of the three telescopes of Insight-HXMT. Every telescope has three groups of FOVs whose long axis directions are 60 degree different from the neighbouring ones. When the direction of a source deviates from the center of the FOVs, the count rates on detectors with different FOVs decrease with different slopes, following the shapes of the Point Spread Functions (PSF) 35 , which allow us to fit the position of the source using the count rates of the burst on different detectors and their PSFs.
PSFs of all Insight-HXMT collimators have been calibrated 35 , which are then used to reconstruct the position of the source from the differences of the count rates between different FOVs. This localization method has been extensively tested and verified with Insight-HXMT observations 36, 37 .