NICER, NuSTAR, and Insight-HXMT Views to Black Hole X-Ray Binary SLX 1746–331

A low-mass black hole X-ray binary consists of a companion star with a mass less than 1 M_⊙ and a black hole. Due to the lower mass of the companion star, the accreted material is more easily able to fill the Roche lobe, allowing the black hole to accrete material from the companion star through the Roche lobe (Shakura & Sunyaev 1973).

The black hole X-ray transient binary remains in a long-term quiescent state with a relatively low accretion rate (Deegan et al. 2009). As the accreted material in the disk accumulates, it reaches a temperature at which hydrogen can be ionized. Due to thermal and viscous instabilities, the angular momentum transfers outward, the material falls inward, and the accretion rate increases, and an X-ray outburst is produced (Cannizzo et al. 1995; Lasota 2001; Belloni et al. 2011; Corral-Santana et al. 2016).

The outburst of a black hole X-ray binary generally undergoes several different spectral states, including the low/hard states (LHS), high/soft states (HSS), and intermediate states (IMS; Belloni et al. 2005; Motta et al. 2009), and these spectral states have distinct positions on the hardness–intensity diagram (HID). The trajectory of the black hole X-ray binary forms a "q" shape on the HID (Homan et al. 2001; Fender et al. 2004; Motta et al. 2012). In the LHS, the emission is primarily dominated by hard X-ray emission from the corona/jet. The locations of the accretion disks in the LHS are not clear, and for XTE J1118+480, McClintock et al. (2001) argued that its accretion disk is truncated in the LHS, while Reis et al. (2009) found a thermal component consistent with a disk at the innermost stable circular orbit (ISCO), suggesting that its accretion disk is not truncated in the LHS. NuSTAR results for some canonical sources such as GRS 1915+105 and Cygnus X–1 also show no evidence that the accretion disk is truncated in the LHS (Markwardt 2003; Parker et al. 2015). In the HSS, where thermal emission from the disk dominates and the contribution of nonthermal emission is relatively low (<25%), the disk has reached its ISCO (Esin et al. 1997; McClintock & Remillard 2006; Gierliński et al. 2008). The IMS can be further divided into the hard intermediate state (HIMS) and the soft intermediate state (SIMS), where the spectrum of SIMS is softer than that of HIMS (Homan & Belloni 2005).

Not all black hole X-ray transient binaries exhibit "q"-shaped trajectories on the HID, meaning that not all of them undergo a complete outburst from the LMS through the HIMS to the HSS and then back to the LMS through the SIMS. These outbursts are referred to as "failed outbursts," which are mainly classified into two categories: one category includes outbursts that have only evolved to the low hard state or intermediate state but not to the soft state, accounting for approximately 38% of all outbursts (Brocksopp et al. 2004; Capitanio et al. 2009; Tetarenko et al. 2016). And the other category is LHS only, which lacks the beginning of the outburst, which is relatively rare and was in 4U 1630–472, MAXI J0637–430, and SLX 1746–331 (Baby et al. 2020; Ma et al. 2022; Peng et al. 2024).

SLX 1746–331 was discovered with the Spacelab 2 X-ray telescope in 1985 August and detected by the RASS in 1990 (Warwick et al. 1988; Skinner et al. 1990). Skinner et al. (1990) discovered that it had a very soft spectrum that best fit thermal bremsstrahlung at a temperature of kT = 1.5 keV, leading to the suggestion that SLX 1746–331 might be a black hole candidate. SLX 1746–331 experienced outbursts in 2003 (Markwardt 2003; Remillard & Levine 2003), 2007 (Markwardt & Swank 2007), and 2011 (Ozawa et al. 2011). The observed peak fluxes of these outbursts were approximately 400, 100, and 40 mCrab, respectively. Dunn et al. (2011) used data from Rossi X-ray Timing Explorer (RXTE) and assumed a black hole mass of 10 M_⊙, a distance of 5 kpc, and an inclination angle of 60°. By using the $L\propto {T}_{\mathrm{in}}^{4}$ relation, they estimated that R_in is approximately 6.7 km, which is about 0.45 times the gravitational radius (R_g), suggesting this system is either located further away or hosts a black hole with a smaller mass. Yan & Yu (2015) estimated the distance of SLX 1746–331 to be about 10.81 ± 3.52 kpc using data from RXTE.

SLX 1746–331 entered the outburst in 2023 and has been observed by Neutron Star Interior Composition Explorer (NICER) 81 times since 2023 March 8, covering the entire outburst, and has been observed a total of 46 times by Insight-HXMT over 35 days, from 2023 March 14 to April 17. The previous research mainly based on the early released NICER observations revealed the outburst stayed around ISCO down to a luminosity of as low as 0.03 L_Edd (Peng et al. 2023). Nuclear Spectroscopic Telescope Array (NuSTAR) has three observations of SLX 1746–331, carried out during the peak and decay phases of the outburst. In this Letter, we perform a detailed spectral analysis by taking the NuSTAR, complete NICER observations, and the supplementary Insight-HXMT observations. We report the first measurements on the basic properties of the system, including the black hole spin, the inclination angle, and the update of the black hole mass. In Section 2, we describe the observations and data reduction. The detailed results are presented in Section 3. The results are then discussed, and the conclusions are presented in Section 4.

2.1. NICER

2.2. NuSTAR

2.3. Insight-HXMT

3.1. Light Curve and Hardness–Intensity Diagram

SLX 1746–331 entered the outburst on 2023 March 8. As shown in Figure 1, NICER began observing it on 2023 March 8 (MJD 60011), covering the entire outburst. The outburst manifests with a profile of "fast rise and slow decay," which is a typical characteristic of those outbursts observed in most black hole X-ray binary systems. The three short red lines in Figure 1 represent NuSTAR observations, and the yellow line denotes the Insight-HXMT observation (Table 1).

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We extract the 1–6, 6–10, and 1–10 keV light curves of NICER to construct the HID of SLX 1746–331. The hardness is defined as the count rate ratio of 6–10 to 1–6 keV, while the intensity is the count rate ratio of 1–10 keV. As shown in Figure 2, the red arrows in the HID represent the trajectory of SLX 1746–331, showing that the outburst of SLX 1746–331 commences and evolves to a soft state, with no trend for a transition to the hard state during the entire outburst.

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3.2. The Spectral Analysis

For the NICER data, we fit the 0.5–10 keV spectra using a model that includes tbabs to account for interstellar absorption (Wilms et al. 2000), considering photoelectric cross sections provided by Verner et al. (1996), and diskbb for the multitemperature blackbody of the accretion disk (Mitsuda et al. 1984). So our model M1 is tbabs∗diskbb and the flux of the disk in the 1–100 keV is estimated with cflux.

As shown in Figure 1 and Table 1, there are three NuSTAR observations of SLX 1746–331, all of which have nearly simultaneous NICER observations. Additionally, one of these observations also had nearly simultaneous observations from Insight-HXMT. Since the spectrum of SLX 1746–331 is soft and the high-energy photon counts are relatively low, we conducted spectral analysis of SLX 1746–331 using nearly simultaneous data from NICER in 0.5–10 keV, NuSTAR FPMA and FPMB in 3–50 keV, and Insight-HXMT LE in 2–8 keV and ME in 8–25 keV. The first trial for the spectral model is constant∗tbabs∗(ezdiskbb+powerlaw), where ezdiskbb is a model of multiple blackbody disks with a zero-torque inner boundary (Zimmerman et al. 2005). In order to take into account the differences between the different spectral indices of NICER and NuSTAR, we allowed the temperature of the disk and spectral index to vary. We find a poor-fitting result with χ²/(degrees of freedom (dof)) =3358.67/1345 = 2.5, and there is a significant reflection component in the residuals (Figure 3). So we replaced powerlaw with relxill to fit the reflection component in the spectrum (Dauser et al. 2016), which results in an improving but not yet perfect fitting with χ²/(dof)= 1896.32/1340 = 1.4. Then, we add the nthcomp model to improve the fit, where the Γ in relxill is linked to Γ in nthcomp. The reflection fraction is fixed to −1, so we only consider the reflection emission [χ²/(dof) = 1746.27/1338 =1.3]. Since the fit is not improved much, we replace relxill with relxillNS, where the reflection fraction is fixed to −1 and kT_bb in relxillNS linked to T_in in nthcomp. R_in is fixed to −1, i.e., the disk is in the ISCO, emission index, and truncation radius of 3 and 15, respectively. Finally, the fit is largely improved [χ²/(dof) = 1462.19/1339 = 1.09]. Therefore, our fitting model M2 is:constant∗tbabs∗(ezdiskbb+nthcomp+relxillNS). The flux of the disk in the 1–100 keV is estimated with cflux. Figure 4 shows the spectral fitting of SLX 1746–331, and the spectral parameters are shown in Table 2, where the black hole spin and the inclination angle of the system are measured for the first time with the averaged values of 0.85 ± 0.03 and 53° ± 05, respectively.

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Table 2. The Results of Spectral Fitting the NICER+NuSTAR+Insight-HXMT Data for Model M2

Model	Parameter	80802346002	80802346004	80802346006
tbabs	NH (1022 cm−2)	${0.76}_{-0.01}^{+0.01}$	${0.86}_{-0.01}^{+0.01}$	${0.88}_{-0.05}^{+0.01}$
ezdiskbb	${T}_{\max }$	${1.69}_{-0.02}^{+0.01}$	${1.52}_{-0.01}^{+0.01}$	${1.34}_{-0.01}^{+0.02}$
	norm	${17.8}_{-0.2}^{+0.1}$	${16.8}_{-0.2}^{+0.3}$	${17.4}_{-1.1}^{+0.5}$
	flux (10−8 erg s−1 cm−2)	${1.36}_{-0.02}^{+0.03}$	${0.73}_{-0.02}^{+0.01}$	${0.52}_{-0.02}^{+0.02}$
relxillNS	a	${0.82}_{-0.06}^{+0.07}$	${0.88}_{-0.05}^{+0.04}$	${0.85}_{-0.01}^{+0.03}$
	i (°)	${51.2}_{-1.3}^{+1.1}$	${52.6}_{-0.6}^{+0.5}$	${53.1}_{-0.7}^{+0.3}$
	logxi	${3.32}_{-0.03}^{+0.09}$	${3.05}_{-0.03}^{+0.05}$	${3.48}_{-0.03}^{+0.01}$
	Afe	${0.87}_{-0.04}^{+0.51}$	${0.86}_{-0.14}^{+0.15}$	1.3 a
	norm (10−3)	${3.1}_{-0.2}^{+0.3}$	${1.6}_{-0.2}^{+0.1}$	${1.2}_{-0.1}^{+0.0}$
nthcomp	Γ	${2.31}_{-0.03}^{+0.06}$	${3.27}_{-0.03}^{+0.02}$	${3.47}_{-0.07}^{+0.11}$
	kTe  (keV)	${17.40}_{-2.33}^{+3.79}$	${6.13}_{-0.88}^{+1.15}$	${13.87}_{-4.03}^{+10.29}$
	norm	${0.41}_{-0.04}^{+0.08}$	${0.81}_{-0.11}^{+0.14}$	${1.12}_{-0.16}^{+0.41}$
constant	con(LE)	⋯	${1.25}_{-0.05}^{+0.04}$	⋯
	con(ME)	⋯	${0.79}_{-0.11}^{+0.12}$	⋯
	con(NFPMA)	${1.45}_{-0.01}^{+0.01}$	${1.38}_{-0.04}^{+0.03}$	${1.31}_{-0.02}^{+0.04}$
	con(NFPMB)	${1.37}_{-0.02}^{+0.01}$	${1.31}_{-0.03}^{+0.03}$	${1.19}_{-0.04}^{+0.02}$
...	χ2/(dof)	1.09	1.07	1.24

Note.

^a We fixed the iron abundance by the results of the joint fit to 1.3.

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We also try to fit the energy spectrum by replacing ezdiskbb with kerrbb, because kerrbb has spin, inclination, and other parameters. We link the spin and inclination with those of the relxillNS model and fix the distance to 10, the mass to 5, and according to the requirements of the model, fix the norm to 1. We find that the spin and inclination obtained in the fit are the same as those obtained with the model we used previously. We find that the spin and inclination are basically the same as what we obtained with model 2. To obtain more robust results, we jointly fit the spectra from the three separate days, with parameters of black hole spin, inner disk inclination, and iron abundance linked among these observations, and obtain spin, inclination, and iron abundance as ${0.86}_{-0.02}^{+0.03}$, ${54.4}_{-1.1}^{+0.8}$, and ${1.31}_{-0.04}^{+0.07}$, respectively. These parameter estimations are consistent with previous results.

The disk flux versus the inner disk temperature (T_in) is plotted in Figure 5, and a fit with a power law results in α around 3.974 ± 0.003. This finding suggests that the disk is around the ISCO during the whole outburst. The highest and lowest fluxes of the disk differ by a factor of 500.

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3.3. Estimating the Mass of Compact Objects

We have joint spectral analyses of the 2023 SLX 1746–331 outburst using data from NICER, NuSTAR, and Insight-HXMT, which have been carried out, and for the first time, the spin and inclination of SLX 1746–331 are measured approximately as 0.85 ± 0.03 and 53° ± 05, respectively. By taking a peak outburst flux of 0.3 L_Edd and the measured inclination, the mass of the compact object is derived as 5.5 ± 3.6M_⊙. Additionally, with the complete NICER observations, we also updated that during the entire outburst, it is found to have its inner disk staying around ISCO even at the later decay phase.

The previous outburst of SLX 1746–331 exhibited characteristics that were identified as a black hole transient X-ray binary (Skinner et al. 1990; White & van Paradijs 1996; Homan & Wijnands 2003). Yan & Yu (2015) reported a distance of about 10.81 ± 3.52 kpc using RXTE data, and Peng et al. (2024) estimated a lower limit of 3.3 ± 2.1M_⊙ for the mass of the compact object by assuming 0.3 L_Edd of the outburst peak flux, and 5.2 ± 4.5M_⊙ from an empirical correlation between disk temperature and black hole mass. The large mass uncertainty is due to the shortage of precise measurements of the inclination of the system and the distance. By performing the joint spectral fittings with NICER, NuSTAR, and Insight-HXMT, the disk inclination is first precisely measured, which results in an updated mass measurement of 5.5 ± 3.6M_⊙, well consistent with that derived from the previous empirical mass–temperature correlation (Peng et al. 2023). Obviously, mass can be further constrained in the future if the source distance can be more precisely measured.

For the 2023 outburst of SLX 1746–331, the analytical results of the spectrum of NICER and the HID indicate that it remained mostly in a soft state. However, we have observed a significant reflection component in the three NuSTAR observations, where the disk is most likely illuminated by itself at the inner part. In the meantime, the nonthermal emissions contribute about 20% to the total. It is generally believed that there is a hard component in the high soft state, but its proportion is relatively low (<25%). Liu & Taam (2009) argued that the evaporation rate that corresponds to the corona production is related to the distance of the inner disk for the central black hole. As shown in their evaporation curve, the distant disk can be truncated by evaporation due to insufficient mass supply. When the accretion rate increases to a maximum value (0.027 times the Eddington accretion rate), evaporation cannot evacuate any disk region because the mass flow in the disk is greater than the evaporation rate. As a result, the disk extends into the ISCO, and the corona covering the disk becomes very weak. For SLX 1746–331, no low hard state and intermediate states may mean the evaporation is very low during the entire outburst.

The 2023 outburst of SLX 1746–331 differs from those of normal black hole transient X-ray binaries in their evolution patterns in HID: instead of a low hard state toward a soft state, SLX 1746–331 stayed around the ISCO during the whole outburst. Although such an outburst phenomenon is relatively rare, we notice that so far a similar case was observed in the outburst of another black hole X-ray binary system, MAXI J0637–430 (Ma et al. 2022). Peng et al. (2023) compared SLX 1746–331 with MAXI J0637–430 and suggested that such a peculiar outburst could be related to the special configuration of the binary system. For example, a small compact object mass together with a rather tight orbital period could lead to a relatively smaller disk size, which could own a weaker large-scale magnetic field (Cao et al. 2021). As discussed in Peng et al. (2023) and Cao et al. (2021), a weak magnetic field born out of a smaller disk can in principle lead to the state transition toward HSS occurring at a lower luminosity level. Unlike MAXI J0637–430, which had a peak luminosity of about 0.08 L_Edd and a soft-to-hard transition at about 0.007 L_Edd, SLX 1746–331 remains in the soft state, with no state transition observed even at a luminosity <500 times lower than the peak luminosity of the outburst.

If we take the maximum luminosity of 0.3L_Edd for the outburst, the luminosity with which the disk remains around ISCO could be as low as 0.0006 L_Edd, lower than 0.001L_Edd established from previous numerical simulations and observations (Reynolds & Fabian 2008; Steiner et al. 2010; Salvesen et al. 2013). To further understand such a peculiar outburst, in the future, there are two key issues in probing this binary system, apart from the precise measurement of the source distance. One is the orbital period and the other is the state transitions. Since MAXI J0637–430 was already detected with, so far, the tightest orbital period of ${2.2}_{-0.6}^{+0.8}$ hr, given the nondetection of a return of the spectral state to the hard state for SLX 1746–331 during the outburst decay phase, we expect an orbit even tighter than that of MAXI J0637–430. To catch a state transition either toward HSS in the outburst rising phase or away from HSS in the decay phase would also be crucial to our pinning down the puzzle. Actually, such a task has already served as one of the key sciences of the Einstein probe, which was successfully launched on 2024 January 9 to discover and observe sources exhibiting activity at very low luminosity (Yuan et al. 2018).

This work is supported by the National Key R&D Program of China (2021YFA0718500), and the National Natural Science Foundation of China under grants Nos. 12333007, U1838202, U2038101, U1938103, 12273030, U1938107, and 12027803. This work made use of data and software from the Insight-HXMT mission, a project funded by China National Space Administration (CNSA) and the Chinese Academy of Sciences (CAS). This work was partially supported by International Partnership Program of Chinese Academy of Sciences (grant No. 113111KYSB20190020). This research has made use of software provided by data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center. L.D.K. is grateful for the financial support provided by the Sino-German (CSC-DAAD) Postdoc Scholarship Program (91839752).