Discovery of Three Candidate Magnetar-powered Fast X-Ray Transients from Chandra Archival Data

Our search for FXTs is part of our large program to investigate all the X-ray sources serendipitously detected by Chandra ACIS observations. In this program, we reduced each observation, carried out the source detection, performed multiwavelength cross correlation, and classified the sources largely based on the method from Lin et al. (2012). The details of this program will be reported in a future paper. In order to find magnetar-powered FXT candidates, we selected out sources that are variable according to the Chandra Interactive Analysis of Observations (CIAO) tool glvary (variability index ≥6) from all ACIS archival data up to 2019 December 31. Then we visually checked the light curves to identify the sources that showed a clear single flare in an observation. Most of these flaring sources are stars with low X-ray-to-IR flux ratios (Lin et al. 2012) and can be ruled out securely. Only about a couple dozen were left at this step, and they included many interesting flaring sources that had been reported before (Jonker et al. 2013; Glennie et al. 2015; Irwin et al. 2016; Bauer et al. 2017; Xue19). We will focus on the three relatively bright FXTs that show similar properties (the flare has a fast rise and a peak plateau) to CDF-S XT2 and have not been studied yet.

We analyzed not only the Chandra observations in which the three FXTs were discovered but also other archival Chandra, X-ray Multimirror Mission (XMM)-Newton, and Swift observations that happened to cover the fields of these FXTs (Table 2) in order to check whether flares were also detected in other observations and, if not, calculate the detection limit. We extracted the source and background light curves and spectra and created the corresponding response files for spectral fits with the latest calibration (as of 2019 May for Swift data, as of 2020 June for XMM-Newton observations and the calibration database (CALDB) version 4.9.1 for Chandra observations). Table 2 lists the size of the source extraction region used for each observation; the background spectra and light curves were extracted from a larger (by a factor of 6–90) background region near the source. We used the software packages CIAO 4.12, SAS 19.0.0 and FTOOLS 6.25 for analysis.

For the flares, we created energy spectra from the whole flare, from the peak, and from the decay separately, and fitted them with an absorbed single power law using the X-ray Spectral Analysis Package (XSPEC; Arnaud 1996). Due to the low counts, we rebinned the spectra to have at least one count in each bin (most bins have 1–3 counts after rebinning) and carried out the fits using the C statistic.

We also carried out the fits to the flare light curves with XSPEC. In order to do this, we created the "fake" spectra corresponding to the source and background light curves. Due to the low counts, we also fitted the light curves with the C statistic, with the light curves binned to have at least one count in each bin.

In order to search for the multiwavelength counterparts to the FXTs, we carried out the absolute astrometric correction to the X-ray positions. We adopted the method in Lin et al. (2016). The positions of the X-ray sources were obtained with the CIAO tool wavdetect, with the statistical errors calculated following Kim et al. (2007). The relative astrometry of the X-ray sources is corrected (about 05 for all cases) by matching with the IR sources from the Visible and Infrared Survey Telescope for Astronomy (VISTA) Hemisphere Survey (McMahon et al. 2013). In this step, we first identified candidate matches and then searched for the translation and rotation of the X-ray frame that minimize the total χ² value (χ is the ratio of the X-ray–IR separation to the total positional error) for 90% of the candidate matches (we allowed 10% of matches that have the largest χ values to be spurious or bad). The systematic positional errors from such an astrometric correction procedure were estimated based on 200 simulations. All the positional errors of the X-ray sources that we will report are the root sum squares of the statistical and systematic errors.

The field of XRT 170901 happened to be covered in the Hubble Space Telescope (HST) WFC3 Infrared Spectroscopic Parallel Survey (Atek et al. 2010), with two optical images (F606W and F814W, 2600 s each) taken on 2014 July 11 and two IR images (F110W and F160W, 1518 s and 759 s, respectively) taken on 2014 July 10. We produced the drizzled images with the DrizzlePac software package. The pixel size was set to be 003 for the optical images and 006 for the IR images. The astrometry of these HST images was aligned to that of the VISTA Hemisphere Survey by crossmatching the point sources detected in both frames.

We also obtained a deep Gemini Flamingos-2 K_s image (Program ID GS-2019B-FT-208) around the field of XRT 030511 in order to search for the counterpart. The IR filter was adopted because the counterpart might be very red if the FXT is associated with a high-redshift passive galaxy or with a very late-type star. Due to weather constraints, individual exposures ranging from 12 to 20 s were taken over several nights spanning about a month (2019 November 30–2020 January 01) under the best seeing conditions (average seeing 045) at the Gemini South observatory. We reduced the images using the Gemini Data Reduction for Astronomy from Gemini Observatory North and South (DRAGONS) software. The final stacked image obtained has a total exposure of 1926 s. The astrometry of the Gemini image was also aligned with the VISTA survey.

Table 1 lists the various properties of the three FXTs that we discovered. Figure 1 plots the background-subtracted light curves of the three FXTs from the Chandra observations in which they were detected. XRT 170901 was detected at 69 ks into the observation, and the observation was stopped before the flare ended. XRT 030511 was detected at the middle of the observation and seemed to end before the observation was stopped. XRT 110919 occurred at the beginning of the observation and probably began earlier than the observation. We calculated T₉₀, the time span from the 5%-th to 95%-th of the total detected counts, and obtained 4.1 ks, 6.6 ks, and 11.0 ks for XRT 170901, XRT 030511, and XRT 110919, respectively (Table 1). The value for XRT 170901 should be a lower limit because we missed the long faint decay for this FXT, and the value for XRT 110919 is most likely an upper limit because we probably missed the early bright phase of this FXT. No clear rising phase was detected in XRT 170901 and XRT 030511. We estimated the upper limit of the rise time for these two FXTs following Xue19, which assumed a linear rise profile and the nondetection of the rising period. We obtained a 1σ upper limit on the rise time of 42 s and 19 s for XRT 170901 and XRT 030511, respectively.

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Table 1. Properties of the Three New Chandra FXTs

	CXOU J234503.4−423841	CXOU J050706.7−315210	CXOU J010344.5−214845
	XRT 170901	XRT 030511	XRT 110919
X-ray position (J2000, astrometrically corrected):
R.A., decl.	23:45:03.44, −42:38:41.7	05:07:06.76, −31:52:10.8	01:03:44.59, −21:48:45.9
95% error (arcsec)	0.24	1.05	0.78
Detected Chandra observation:
ObsID	20635	4062	13454
Observation Start Date	2017-08-31	2003-05-10	2011-09-19
Exposure (ks)	74.2	46.2	91.8
Source region radius (arcsec)	2.1	13.7	6.9
Off-axis angle (arcmin)	2.8	10.7	7.2
t1st photon (UTC)	2017-09-01 13:26:47	2003-05-11 04:38:06	2011-09-19 20:02:49
Flare net counts a	164 ± 13	374 ± 20	88.2 ± 9.6
T90 (ks) a	>4.1 ± 0.1	6.6 ± 0.2	<11.0 ± 0.2
Candidate host galaxy photometry a :
Optical (AB mag)	F606W = 24.92 ± 0.01	g > 25.6, r > 24.7, i > 24.2	g > 25.2, r > 24.6, i > 24.2
	F814W = 25.00 ± 0.02	z > 23.9, Y > 22.8	z > 23.9, Y > 22.7
IR (AB mag)	F110W = 24.81 ± 0.01	J > 21.7	J > 22.1
	F160W = 24.64 ± 0.01	Ks = 24.5 ± 0.2	Ks > 20.1
Light-curve fits a :
Broken power law:
Initial index	${0.11}_{-0.13}^{+0.33}$	0.09 ± 0.08	0.03 ± 0.15
Break (ks)	${1.53}_{-0.59}^{+0.31}$	1.73 ± 0.13	${1.93}_{-0.31}^{+0.25}$
Second index	$-{1.63}_{-0.36}^{+0.53}$	−2.30 ± 0.16	$-{2.04}_{-0.30}^{+0.25}$
Magnetar model (free n):
τ (ks)	>24.0	>35.3	${11.6}_{-6.4}^{+46.6}$
n	<1.4	<1.2	1.7 ± 0.5
C-stat (dof)	155.6 (161)	319.8 (346)	93.6 (88)
Magnetar model (n = 3, fixed):
τ (ks)	3.0 ± 0.6	1.8 ± 0.2	2.2 ± 0.4
C-stat (dof)	162.6 (162)	379.0 (347)	99.1 (89)
Magnetar model (n = 5, fixed):
τ (ks)	1.0 ± 0.3	0.3 ± 0.1	0.4 ± 0.1
C-stat (dof)	170.1 (162)	508.6 (347)	117.7 (89)
Fits to the whole flare spectrum b :
Exposure (ks)	5.7	13.6	19.5
Single power law (z = 0)
NH,i (1021 cm−2)	${8.8}_{-3.3}^{+3.7}$	${0.8}_{-0.8}^{+1.3}$	0.0+0.6
Γ	2.16 ± 0.31	1.84 ± 0.27	1.88 ± 0.21
Single power law (z = 1.0)
NH,i (1021 cm−2)	${46.4}_{-19.4}^{+22.1}$	${3.6}_{-3.6}^{+6.3}$	0.0+2.8
Γ	2.12 ± 0.31	1.81 ± 0.25	1.88 ± 0.21
Joint fits to the plateau and decay spectra:
Plateau/decay exposures (ks)	2.0/3.7	1.7/11.9	2.2/17.3
Plateau/decay net counts	104/61	203/167	52/37
Single power law (z = 0)
NH,i (1021 cm−2)	${7.6}_{-3.2}^{+3.7}$	${1.0}_{-1.0}^{+1.3}$	0.0+0.9
Γ Plateau/decay	2.05 ± 0.20/2.29 ± 0.27	1.65 ± 0.21/2.17 ± 0.27	1.45 ± 0.27/3.05 ± 0.42
Single power law (z = 1.0)
NH,i (1021 cm−2)	${43.9}_{-19.3}^{+21.9}$	${4.2}_{-4.1}^{+6.5}$	0.0+3.5
Γ Plateau/decay	2.03 ± 0.21/2.27 ± 0.27	1.61 ± 0.21/2.13 ± 0.27	1.45 ± 0.27/3.05 ± 0.42
High-energy emission upper limit:
sGRB Fluence (10−7 erg cm−2)	5.8	5.1	5.3
lGRB peak flux (10−7 erg cm−2 s−1)	1.6	1.27	1.63

Notes.

^a Errors or limits are at the 1σ confidence level, except for the magnitude limits, which refer to the magnitude of the 90th faint source among the 100 nearest sources. ^b Errors are at the 90% confidence level.

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Figure 2 zooms in on the flares. The time axis is on a logarithmic scale with the time zero set at the start of the flares. The start times of the flares were estimated as follows. We first identified the first photon detected from each flare and then calculated the average waiting time dt of the next nine photons from the source region. We assumed the flare start time to be at dt/2 before the first detection. We estimated the chance probability p_bg that the first flare photon that we identified is in fact from the background as R_bgdt, where R_bg is the background count rate in the source region. We obtained p_bg ∼ 0.03%, 1.6%, and 0.8% for XRT 170901, XRT 030511, and XRT 110919, respectively. In comparison, the time gap between the assumed first flare photon and the photon immediately before it (also from the source region) for each case is large, 12 ks and 430 s, with p_bg ∼ 15% and 35%, for XRT 170901 and XRT 030511, respectively. They are most likely from the background. The first flare photon that we identified for XRT 110919 is the first photon of the observation in the source region. Therefore, our identification of the first flare photon is fairly secure.

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We first fitted the light curves with a broken power law as was done in Xue19. The results are given in Table 1 and shown in Figure 2. The fits started from the beginning of the flares until the end of the observation (for XRT 170901) or the end of the flares (for XRT 030511 and XRT 110919, at around 20 ks). The initial index was inferred to be consistent with zero in all three XRTs. The breaks are all between 1.5 and 2.0 ks. The second indexes were all consistent with −2.0. We note that for XRT 030511, which occurred at the beginning of the observation, the break could occur at a later time than that we inferred in Table 1, which assumed the flare started at the beginning of the observation.

We also fitted the light curves with the magnetar model F_X(t) ∝ (1 + t/τ)^4/(1−n), in which n is the braking index, and τ is the spin-down timescale of the magnetar. This model was commonly used to fit the X-ray afterglow of GRBs (e.g., Lü et al. 2019). The results are given in Table 1. For XRT 110919, we inferred n = 1.7 ± 0.5 and $\tau ={11.6}_{-6.4}^{+46.6}$ ks. However, for both XRT 170901 and XRT 030511, we obtained n very close to 1.0 and τ very large, which is caused by the degeneracy of these two parameters when n is very close to 1.0. In this case, the model becomes an exponential function $\exp (-t/\tau )$. We are most concerned about whether good fits can be obtained with the standard magnetar models of n = 3 (the magnetic-dipole braking dominated) or n = 5 (GW braking dominated). Therefore, we also fitted the models with n = 3 and 5 and compared with the fits with free n. The results are given in Table 1. The fits with n = 5 are strongly disfavored, with the C statistic values larger than those of the fits of free n by 14.5, 188.8, and 24.1 for XRT 170901, XRT 030511, and XRT 110919, respectively. The fits with n = 3 are much better, with the C statistic values larger than those of the fits of free n by 7.0, 59.2, and 5.5, respectively, but at least for the case of XRT 030511, the improvement is still not enough. Therefore, all three FXTs might prefer braking indexes smaller than 3, as was found in CDF-S XT2 (Xiao et al. 2019) and many GRBs (Stratta et al. 2018). This could imply the presence of other braking mechanisms such as fallback accretion onto the magnetar (Metzger et al. 2018).

The fits to the whole flare spectra with an absorbed single power law, assuming two cases of redshifts z = 0.0 and z = 1.0, inferred a photon index of ∼2.0 in all the three FXTs (Table 1). While no significant absorption was inferred in XRT 030511 or XRT 110919, XRT 170901 seems to be heavily absorbed (intrinsic absorption column density N_H,i = 0.9 ± 0.4 × 10²² cm⁻² and ${4.6}_{-1.9}^{+2.2}\times {10}^{22}$ cm⁻² when z = 0.0 and 1.0 was assumed, respectively). While the photon index inferred is fairly independent of the redshift assumed, the absorption column density inferred in XRT 170901 increased with the redshift assumed.

Figure 2 shows the temporal evolution of the hardness ratio for all three FXTs. We followed Xue19 to define the hardness ratio as (H − S)/(H + S), where S and H are the count rates from the soft energy band 0.5–2.0 keV and the hard energy band 2.0–7.0 keV, respectively. In order to have enough statistics, the hardness ratios were calculated with varying time bin size, requiring that each data point has at least 20 counts from the source region. The uncertainties of the hardness ratios were calculated with the Bayesian code BEHR (Park et al. 2006), due to the low statistics. We found that the hardness ratios in both XRT 030511 and XRT 110919 decreased significantly, indicating spectral softening, in the decay in these two FXTs. The hardness ratios in XRT 170901 seem to remain constant over time when the flare was observed.

In order to characterize the spectral variation further, we fitted the plateau and decay spectra simultaneously with N_H,i tied to be the same for each FXT. The fitting results are shown in Figure 3 and are given in Table 1. We note that the uncertainties in the photon indexes in the table were obtained after fixing N_H,i at the best-fitting value, which allows for easy tracking of the spectral evolution. The fits confirmed that the plateau spectrum had a smaller value of the photon index, thus is harder, than the decay spectrum at the confidence levels of 2.5σ and 3.2σ in XRT 030511 and XRT 110919, respectively. In XRT 170901, the photon index of the plateau spectrum is consistent with that of the decay spectra within 0.7σ. We note that we could not rule out that the spectral softening might also be present in XRT 170901 but was missed due to the early termination of the observation before the flare ended.

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Figure 4 plots the long-term X-ray flux curves of the three new FXTs from all the Chandra, XMM-Newton, and Swift observations (Table 2). No extra flares were detected. There was no significant persistent emission seen in any observation in all the three XRTs either. Combining all available observations, we obtained the most stringent constraint on the 0.5–7.0 keV persistent emission to be <6.3 × 10⁻¹⁶ erg s⁻¹ cm⁻², <1.0 ×10⁻¹⁴ erg s⁻¹ cm⁻², and <1.0 × 10⁻¹⁵ erg s⁻¹ cm⁻² (3σ upper limits) for XRT 170901, XRT 030511, and XRT 110919, respectively. Therefore, these FXTs have very large amplitudes, with the peak to the persistent X-ray flux ratio F_peak/F_persistent > 1320, >170, >430, respectively. Because only one flare was detected in each FXT, we estimated the upper limit of the duty cycle γ roughly as ≲1/T_tot, where T_tot is the total exposure time of all the Chandra, XMM-Newton, and Swift X-ray observations. We obtained γ ≲ 1.4 × 10⁻³ ks⁻¹, ≲1.4 × 10⁻² ks⁻¹, and ≲2.0 × 10⁻³ ks⁻¹, respectively.

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Table 2. X-ray Observation Log

Obs. ID	Date	Detector	OAA	Expo	rsrc	0.5–7 keV Count Rate	0.5–7 keV Flux
				(ks)		(10−3 counts s−1)	(erg s−1 cm−2)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
XRT 170901
Swift:
00038092001	2008-09-16	X-ray Telescope	109	2.7	20''	<0.99	<5.8e-14
00038092002	2008-09-17	X-ray Telescope	109	4.5	20''
00038092004	2008-11-06	X-ray Telescope	112	0.1	20''
00038092005	2008-11-09	X-ray Telescope	98	0.6	20''
00038092006	2009-03-29	X-ray Telescope	72	0.3	20''
00038092007	2009-03-31	X-ray Telescope	61	1.2	20''
00081309001	2020-05-04	X-ray Telescope	79	1.5	20''	<1.32	{<6.8e-14
00081309002	2020-05-05	X-ray Telescope	69	3.0	20''
XMM-Newton:
0693661801	2012-05-28	pn	59	8.9	15''	<2.4	<1.4e-14
0722700101	2013-11-22	pn	58	104.4	15''	<0.46	<3.2e-15
0722700201	2013-11-13	pn	58	81.5	15''	<0.41	<2.7e-15
Chandra:
13401	2011-09-19	ACIS-I	44	11.9	25	<0.66	<1.1e-14
16135	2014-08-18	ACIS-I	25	58.1	12	<0.10	<1.5e-15
16545	2014-08-20	ACIS-I	25	59.2	12	<0.10	<1.4e-15
19581	2017-08-23	ACIS-I	24	88.8	11	<0.07	<1.3e-15
19582	2017-08-28	ACIS-I	26	10.0	12	<0.59	<1.1e-14
19583	2017-09-14	ACIS-I	36	24.7	19	<0.31	<6.7e-15
20630	2017-08-21	ACIS-I	23	38.5	11	<0.15	<2.9e-15
20631	2017-08-27	ACIS-I	24	50.4	11	<0.12	<2.2e-15
20634	2017-08-29	ACIS-I	26	70.6	12	<0.14	<2.5e-15
20635	2017-08-31	ACIS-I	27	68.5	21	<0.16	<2.4e-15
20636	2017-09-04	ACIS-I	28	21.3	1 3	<0.28	<5.2e-15
XRT 030511
Swift:
00084253001	2015-04-27	X-ray Telescope	117	0.7	20''	<0.36	<2.0e-14
00084253002	2015-05-18	X-ray Telescope	103	2.0	20''
00084253003	2015-05-19	X-ray Telescope	102	1.3	20''
00084253004	2015-05-23	X-ray Telescope	108	0.7	20''
00084253005	2015-05-25	X-ray Telescope	78	3.4	20''
00084253006	2015-05-27	X-ray Telescope	74	0.6	20''
00084253007	2015-05-28	X-ray Telescope	78	0.5	20''
00084253008	2015-06-02	X-ray Telescope	94	0.5	20''
00084253010	2015-06-07	X-ray Telescope	90	2.9	20''
00084254001	2015-05-06	X-ray Telescope	116	0.6	20''
00084254002	2015-05-25	X-ray Telescope	87	0.2	20''
00084254003	2015-06-07	X-ray Telescope	90	5.0	20''
00084254004	2015-06-09	X-ray Telescope	85	4.8	20''
00084254005	2015-06-12	X-ray Telescope	95	1.2	20''
00084254006	2015-06-17	X-ray Telescope	114	1.4	20''
00084254007	2015-06-19	X-ray Telescope	108	0.9	20''
00084254008	2015-06-21	X-ray Telescope	113	0.9	20''
Chandra:
4062	2003-05-10	ACIS-S	10.7'	22.9	13 7	<0.72	<1.2e-14
XRT 110919
Chandra:
13447	2011-09-08	ACIS-I	52	69.1	32	<0.14	<2.0e-15
13448	2011-09-13	ACIS-I	72	146.0	57	<0.06	<1.8e-15
13454	2011-09-19	ACIS-I	72	72.2	6 9	<0.19	<3.2e-15
13455	2011-10-19	ACIS-I	68	69.6	53	<0.16	<2.5e-15
14343	2011-09-12	ACIS-I	72	35.3	57	<0.24	<6.4e-15
14346	2011-09-21	ACIS-I	72	85.3	57	<0.16	<3.0e-15

Note. Columns: (1) observation ID, (2) observation start date, (3) detector, (4) off-axis angle, (5) clean exposure time of the data used in the final analysis after excluding periods of strong background flares, (6) radius of the source circular extraction region, (7) 3σ upper limit net count rate, (8) 3σ upper limit of the 0.5–7 keV flux. The limits are either from individual Chandra and XMM-Newton observations or from combinations of Swift observations. The count rate upper limits were calculated with the CIAO task aprates, which uses the Bayesian approach. The flux upper limits were calculated, assuming an absorbed power-law spectrum inferred from the fit to the whole flare spectrum. For the three Chandra observations, 20635, 4062, and 13454, in which the FXTs were detected, the exposures, count rate, and flux upper limits refer to the persistent periods.

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Our three FXTs were not associated with a GRB in the catalog compiled by Jochen Greiner (https://www.mpe.mpg.de/jcg/grb110918A.html). The interplanetary network, which examines high-energy data from a group of spacecraft equipped with γ-ray burst detectors, such as International Gamma-Ray Astrophysics Laboratory (INTEGRAL), Swift, and Fermi, provided a rough fluence upper limit of 10⁻⁶ erg cm⁻² for all the three FXTs (K. Hurley, private communication).

There were Konus–Wind (KW) waiting mode data for all the three FXTs, and no high-energy counterparts were found from the +/−10 ks interval of each FXT (D. Svinkin, A. Ridnaia, D. Frederiks, private communication). Two upper limits were calculated following Kozlova et al. (2019) and Ridnaia et al. (2020): an upper limit on the fluence for a burst lasting less than 2.944 s and having a typical KW sGRB spectrum (an exponentially cutoff power law with α = −0.5 and E_p = 500 keV) and a limiting peak flux (2.944 s scale) for a typical lGRB spectrum (a Band function with α = −1, β = −2.5, and E_p = 300 keV). Both were calculated for the interval +/−100 s relative to the start time of each FXT and are in the 20–1500 keV band and at the 90% confidence level. The results are given in Table 1. The sGRB fluence upper limit was about 5.5 × 10⁻⁷ erg cm⁻², and the lGRB peak flux upper limit was about 1.5 × 10⁻⁷ erg cm⁻² s⁻¹ for all the FXTs. The fluence upper limit is a factor of 3 more than the GRB 170817A (1.8 × 10⁻⁷ erg cm⁻²; Goldstein et al. 2017). Therefore, the KW limits can exclude the association of our FXTs with bright GRBs but fail to exclude the association with faint GRBs or orphan afterglows (Yamazaki et al. 2002; Ghirlanda et al. 2015; Lazzati et al. 2017).

Figure 5 shows the HST images in four broad bands, two in optical (F606W and F814W) and two in IR (F110W and F160W), around the field of XRT 170901. The 95% X-ray positional error of this FXT overlaps with a highly elongated galaxy ("Gal1" in Figure 5). The chance probability to find XRT 170901 so close to a galaxy brighter than Gal1 in F160W (24.64 AB mag) was estimated to be very low, only 0.5%. Therefore, we consider it as a candidate host galaxy of XRT 170901. This galaxy might be irregular, with the emission peaking to the west and slightly outside the 95% positional error circle of XRT 170901. The optical and IR colors of this galaxy are somewhat blue (Table 1), indicating a late-type galaxy with possibly strong star-forming activity. The other closest galaxy is "Gal2" in Figure 5, ∼1'' away from XRT 170901. Because it is well outside the 95% positional error circle of XRT 170901, it is very unlikely to host this FXT. We note that Figure 5 shows that there might be a cluster of galaxies, with both Gal1 and Gal2 being its members.

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Figure 6 shows the Dark Energy Survey (DES; Abbott et al. 2018) r-band and Gemini K_s-band images around the field of XRT 030511. There are DES and VISTA images in other filters around this FXT, but we saw no clear host galaxy in any DES or VISTA image; Table 1 lists the detection limits of these images. In the very deep Gemini K_s-band image, there might be a very weak source (a 1'' aperture magnitude of 24.5 ± 0.2 AB mag) within the 95% positional uncertainty of XRT 030511. Deeper images are required to confirm this candidate counterpart.

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Figure 7 shows the DES r-band and VISTA K_s-band images around the field of XRT 110919, and no clear host galaxy is seen in them. There are also DES and VISTA images in other filters around the field of this FXT, without a clear host galaxy seen in them either. Table 1 lists the detection limits of various images. The ground-based images around the fields of XRT 030511 and XRT 110919 are not deep enough (e.g., r > 24.7 AB mag, J > 22.0 AB mag) to rule out faint hosts as seen in XRT 170901 and CDF-S XT2 (m_F606W = 25.35 AB mag, m_F160W = 23.85 AB mag; Xue19).

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We have shown that the three new FXTs that we discovered also from the Chandra archival data are similar to CDF-S XT2 in many aspects, especially the flare light-curve profile: a fast rise to a plateau lasting 1–2 ks, followed by a steep decay of approximately t⁻². Therefore, these three new FXTs and CDF-S XT2 might have the same origin. The intriguing explanation that Xue19 proposed for CDF-S XT2, i.e., a magnetar-powered X-ray transient resulted from a BNS merger, could then be applied to our three FXTs. In the case of CDF-S XT2, the supporting evidence for the magnetar explanation includes not only the unique light-curve profile but also the host properties. Xue19 found that the combined properties of the host galaxy of CDF-S XT2 (stellar mass, star formation rate, metallicity, offset, and galaxy size) are much more commonly seen in sGRBs than in lGRBs. The redshift and thus the distance of its host galaxy are known (z = 0.738). Therefore, Xue19 could obtain the peak X-ray luminosity of CDF-S XT2 to be 3 × 10⁴⁵ erg s⁻¹, much lower than those seen in the X-ray afterglows of sGRBs. Therefore, CDF-S XT2 is consistent with an off-axis jet configuration. For our FXTs, only the host of XRT 170901 was detected, thanks to the deep HST images. Although its host might be a late-type galaxy of a modest star formation rate, given the blue HST colors, this FXT is most likely not in the star-forming region, with a significant offset from the peak emission of the host. Therefore, this FXT is probably also of compact-star merger origin. Our three FXTs had similar peak fluxes as CDF-S XT2 (∼10⁻¹² erg s⁻¹ cm⁻²). Therefore, they would have similar peak luminosity and are also more likely in an off-axis jet configuration if they are all at similar redshifts as CDF-S XT2.

The X-ray light curves of lGRBs and sGRBs typically include an initial very steep decay, which is most likely the tail of the prompt emission, and a long-lasting afterglow, which is caused by the forward shock from the interaction of the jet with the external medium (Nousek et al. 2006; Berger 2014). However, they often also show many complicated features that can signify the presence of the magnetar central engine (e.g., Dai et al. 2006; Berger 2014; Bernardini 2015): a plateau phase, precursors, and flares. The plateau phase, following the initial steep decay, is very common in both lGRBs (up to ∼80%, e.g., Evans et al. 2009; Margutti et al. 2013; Melandri et al. 2014) and sGRBs (∼50%, e.g., Rowlinson et al. 2013; D'Avanzo et al. 2014). The main argument to attribute this phase to the spinning-down energy of a newly born magnetar instead of a forward shock is that the plateau in some cases in both lGRBs and sGRBs was followed by a sudden drop (Rowlinson et al. 2013), which is hard to explain with a forward shock model but can be naturally explained by the collapse of a supramassive magnetar to a BH (Lyons et al. 2010; Rowlinson et al. 2013). The magnetic field strength and the spin period inferred from the magnetar model for the plateaus seen in lGRBs and sGRBs are around B ∼ 10¹⁵ G and P ∼ 1 ms (Rowlinson et al. 2014).

Our three FXTs and CDF-S XT2 are most similar to the plateau component in the X-ray light curves of GRBs. An alternative explanation for the low levels of the peak X-ray flux and the high-energy emission in these FXTs, compared with typical GRBs, is that they are distant GRBs, but this is very unlikely because an initial steep component associated with the prompt emission was not present in at least three of these four FXTs (except XRT 110919) whose early phases were fully covered by the X-ray observations.

If all these four FXTs are magnetar-powered, then there is the question of whether the newly born magnetars in these systems are stable or not. Because their decays were all consistent with t⁻² within 2σ, as expected for the spin-down luminosity of a stable NS, it is more likely that a stable NS was formed in these systems (see however Lü et al. 2021).

There is a correlation between the spin-down luminosity and the spin-down timescale: ${L}_{\mathrm{sd}}{t}_{\mathrm{sd}}\propto {P}_{0,-3}^{-2}$, where P_0,−3 is the initial spin period in millisecond (Zhang 2013). Then we can infer a redshift of 0.60, 0.39, and <0.82 and a luminosity distance of 3.6 Gpc, 2.14 Gpc, and <5.2 Gpc, for XRT 170901, XRT 030511, and XRT 110919, respectively, if we assume that the magnetars in them have the same initial spin periods as in CDF-S XT2. The upper limit was obtained for XRT 110919 because we only obtained the lower limit on the spin-down timescale (the start of this FXT was missed by the observation).

Based on these distances, we obtain the luminosity curves in Figure 8 for these magnetar-powered FXT candidates. They look remarkably similar to each other. Such a similarity indicates that the beginning of XRT 110919 might not be missed much by the observation. The plot also includes sGRBs that have redshifts and were followed up by the x-ray telescope obtained from the Swift Burst Analyser (Evans et al. 2010). It shows that if the distances that we inferred for our FXTs are correct, their initial luminosities would be much lower than those seen in sGRBs, which would suggest the lack of prompt emission and thus indicate an off-axis jet configuration.

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We followed Bauer et al. (2017) to have a simple estimate of the event rate for these magnetar-powered FXT candidates. Because we considered only relatively bright FXTs ( ≳100 net source counts in each source; Table 1), we assumed that they can be detected and identified in any CCD of any ACIS observation longer than >5 ks. With four magnetar-powered FXTs discovered in our search (including CDF-S XT2), we obtained a rate of ${4.5}_{-2.1}^{+3.6}$ events deg⁻² yr⁻¹ (the error is 1σ, following Gehrels 1986). To convert it to a local volumetric rate density, we assumed that the maximum redshift the observations can reach is 1.0, and we obtained a rate density of ${150}_{-70}^{+120}$ Gpc⁻³ yr⁻¹. This is roughly consistent with that obtained by Bauer et al. (2017) for "CDF-S XT1"-like events and that by Xue19 for "CDF-S XT2"-like events and is also broadly consistent with the BNS merger event rate density (${1.5}_{-1.2}^{+3.2}\times {10}^{3}$ Gpc⁻³ yr⁻¹; Abbott et al. 2017b), given the large uncertainties of these estimates.

A definite signature for the BNS merger nature of these FXTs would be the simultaneous detection of both GW events and such kind of FXTs. We consider whether such a source could be detected by the Burst Alert Telescope (BAT) on board Swift. The BAT can reach a 5σ sensitivity (14–195 keV) of $2.9\times {10}^{-8}\sqrt{T/1{\rm{s}}}$ erg s⁻¹ cm⁻², where T is the integration time (Baumgartner et al. 2013). The duration of the plateau phase in the rest frame is about 1000 s for all these FXTs if they are at the redshifts inferred above, so assuming an integration time of T = 1000 s, the BAT can reach a sensitivity of 1.0 × 10⁻⁹ erg s⁻¹ cm⁻². The Advanced Ligo/Virgo can detect BNS mergers up to around 150 Mpc currently (Abbott et al. 2020). At this distance, CDF-S XT2 would have a peak flux around 1.0 × 10⁻⁹ erg s⁻¹ cm⁻² in the soft X-rays. Assuming a photon index of 2.0 (all our three FXTs and CDF-S XT2 have photon index in the plateau phase consistent with this value), these FXTs would have a BAT flux of also around 1 × 10⁻⁹ erg s⁻¹ cm⁻², which can be marginally detected if it is in the BAT field of the view. The BAT was not pointed toward GW170817 (Evans et al. 2017) or the second strong BNS GW event candidate GW190425 (at a distance of ${159}_{-71}^{+69}$ Mpc; Sakamoto et al. 2019) at the times when these GW events were triggered.

The X-ray Telescope on board Swift has also carried out a fast scan over the error regions of GW events that are good BNS merger candidates in order to search for the EM counterparts (Evans et al. 2016). The observations typically have an exposure time of 70 s each or sensitivity ∼1.0 × 10⁻¹¹ erg s⁻¹ cm⁻². Assuming a distance of 150 Mpc for the GW events, our FXTs and CDF-S XT2 can stay above the detection limit of these X-ray Telescope scans (3 × 10⁴³ erg s⁻¹) for up to ∼5 ks (rest frame). Therefore, the X-ray Telescope scans need to be carried out very quickly in order to detect magnetar-powered FXT signals from the BNS GW events. The X-ray Telescope observed the EM counterpart to GW170817 at 0.62 days after the GW trigger, with the 3σ upper limit of 5 × 10⁴⁰ erg s⁻¹ (Evans et al. 2017). Based on Figure 8, our three FXTs and CDF-S XT2 can still be detected at the luminosity around 1.0 × 10⁴¹ erg s⁻¹ at 0.62 days, marginally above the detection limit. The nondetection could be either because the magnetar had collapsed by 0.62 days, or the spectra were softened significantly and shifted out the X-ray bands, or a magnetar was simply not formed in this GW event.

An alternative explanation for our three FXTs and CDF-S XT2 is the shock breakout (SBO) of a core-collapse supernova (Waxman & Katz 2017; Levinson & Nakar 2020). SBOs are expected to produce short-lived X-ray bursts lasting for a few minutes. The best known example of SBOs is SN2008D (Soderberg et al. 2008), which lasted for about 400 s and exhibited a fast-rise-and-exponential-decay profile. Dedicated search over XMM-Newton archival data found a dozen SBO candidates (Alp & Larsson 2020; Novara et al. 2020). With very fast rise and a plateau in the X-ray light curves, our FXTs and CDF-S XT2 are distinct from these SBO candidates and should belong to a different class of objects.

Peng et al. (2019) considered CDF-S XT2 and CDF-S XT1 as accretion-driven flares from tidal disruption of white dwarfs by intermediate-mass BHs. For CDF-S XT2, Peng et al. (2019) inferred a viscous accretion timescale of 1.5 ks, which is rather long and requires a radiatively efficient and geometrically thin disk. However, CDF-S XT2 appeared highly super-Eddington at the peak, which then requires the presence of a significant beaming effect (a beaming factor of more than 1000) in the system, possibly in the form of a jet. Although it is hard to completely rule it out, we think this is very unlikely, given that we have discovered three more similar systems.

Finally, our three new FXTs are unlikely due to stellar flares. Figure 9 compares our FXTs with the stellar flares discovered in Lin et al. (2012) from the XMM-Newton catalog. These flares mostly have F_peak/F_persistent < 150 and the X-ray (peak) to IR flux ratio F_X,peak/F_IR < 1.6, while our FXTs have much higher amplitudes (>170–1320) and much higher peak X-ray flux relative to the persistent IR flux, with F_X,peak/F_IR > 4.5, ≈ 4.3, >1.9, for XRT 170901 (the presumptive stellar IR flux was estimated from the detection limit due to the lack of a point-like counterpart in the HST images), XRT 030511, and XRT 110919, respectively. Besides, if they are stellar flares, they would have to be very far away, >31 kpc, ≈15 kpc, and >5 kpc for XRT 170901, XRT 030511, and XRT 110919 even assuming a very faint, late-type star of M6 (Covey et al. 2007). This is very unlikely given their very high Galactic latitudes of b = −69°, −35°, and −84°, respectively.

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