NICER, NuSTAR and Insight-HXMT views to black hole X-ray binary SLX 1746–331

NICER was launched by the Space X Falcon 9 rocket on 3 June 2017 (Gendreau et al., 2016). NICER has a large effective area and high temporal resolution in soft X-ray band (0.2–12 keV), which may allow us to better study black body components at low temperatures.

NICER started to observe SLX 1746–331 on March 8, 2023, and covered the entire outburst of the SLX 1746–331. NICER observations till the MJD 600103 were analyzed and reported in Peng et al. (2023). More NICER observations beyond MJD 600126 allow for investigation of the outburst around its later decay phase.

We use NICERDAS 2022-12-16 V010a software with the latest CALDB xti20221001 for NICER data analysis. NICER data are reduced using the standard pipeline tool nicerl2¹¹1https://heasarc.gsfc.nasa.gov/lheasoft/ftools/headas/nicerl2.html. We extract light curves using nicerl3-lc²²2https://heasarc.gsfc.nasa.gov/docs/software/lheasoft/ftools/headas/nicerl3-lc.html in 1–6 keV, 6–10 keV and 1–10 keV. To extract the spectrum, we utilize nicerl3-spect³³3https://heasarc.gsfc.nasa.gov/docs/software/lheasoft/help/nicerl3-spect.html, employing the ”nibackgen3C50⁴⁴4https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/background/” model to estimate the background for spectral analysis. For spectrum fitting, we select an energy range of 0.5–10 keV. Additionally, nicerl3-spect automatically applies the systematic error using niphasyserr. In the energy range of 0.3-10 kev, the systematic error is about 1.5%.

NuSTAR is the first mission to employ focusing telescopes for high-energy X-ray (3 – 79 keV) imaging of the sky within the electromagnetic spectrum. It was launched on June 13, 2012, at 9 am PDT. (Harrison et al., 2013). As shown in Table LABEL:observ, NuSTAR conducted three observations of SLX 1746–331. For NuSTAR data analysis, we employ NuSTARDAS v2.1.2 software with the calibration database (CALDB 20230613). We extract NuSTAR-filtered data using the standard pipeline program nupipeline, The spectrum was extracted from a 120^′′ circle region centered on the source and the background was generated from a 60^′′ circle region away from the source. We utilized FPMA and FPMB 3–50 keV data for spectral analysis.

Insight-HXMT is the first Chinese X-ray astronomy satellite, which was successfully launched on 2017 June 15 (Zhang et al., 2014, 2018, 2020). It carries three scientific payloads: the low energy X-ray telescope (LE, SCD detector, 1–15 keV, 384 $\rm cm^{2}$, Chen et al. 2020), the medium energy X-ray telescope (ME, Si-PIN detector, 5–35 keV, 952 $\rm cm^{2}$, Cao et al. 2020 ), and the high energy X-ray telescope (HE, phoswich NaI(CsI), 20–250 keV, 5100 $\rm cm^{2}$, Liu et al. 2020).

Insight-HXMT started to observe SLX 1746–331 at the peak of its outburst on March 14, 2023 and continued until May 19, 2023. As shown in Table LABEL:observ, only the Insight-HXMT observations simultaneous with NICER and NuSTAR are adopted for joint spectral analysis. We extract the data from LE and ME using the Insight-HXMT Data Analysis software HXMTDAS v2.05. The data are filtered with the criteria recommended by the Insight-HXMT Data Reduction Guide v2.05 ⁵⁵5http://hxmtweb.ihep.ac.cn/SoftDoc/648.jhtml. Due to the count rate of high-energy photons in SLX 1746–331, the energy bands considered for spectral analysis are LE 2–8 keV and ME 8–25 keV. One percent systematic error is added to data (Liao et al., 2020), and errors are estimated via Markov Chain Monte-Carlo (MCMC) chains with a length of 20000.

SLX 1746–331 entered the outburst on March 8, 2023. As shown in Figure 1, NICER began observing it on March 8, 2023 (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 Insight-HXMT observation (Table LABEL:observ).

We extract the 1–6 keV, 6–10 keV, and 1–10 keV light curves of NICER to construct the Hardness-Intensity Diagram (HID) of SLX 1746-–331. The hardness is defined as the count rate ratio of 6–10 keV 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.

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 multi-temperature blackbodspy 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 LABEL:observ, 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 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 $\chi^{2}$/(d.o.f)=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 $\chi^{2}$/(d.o.f)=1896.32/1340=1.4. Then we add the nthcomp model to improve the fit, where the $\Gamma$ in relxill is linked to $\Gamma$ in nthcomp. The reflection fraction is fixed to -1, so we only consider the reflection emission [$\chi^{2}$/(d.o.f)=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 $kT_{\rm bb}$ in relxillNS linked to $T_{\rm in}$ 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 [$\chi^{2}$/(d.o.f)=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 LABEL:parameter, where the black hole spin and the inclination angle of the system are measured for the first time with the averaged values of $0.85\pm 0.03$ and $53\pm 0.5$°, respectively.

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 ($T_{\rm in}$) is plotted in Figure 5, and a fit with power law results in $\alpha$ around 3.974$\pm$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.

As shown in Figure 5, the disk flux is always proportional to the fourth power of the temperature of the inner disk during the 2023 outburst of SLX 1746–331. For the standard thin disk, $L_{\rm disk}\approx 4\pi R_{\rm in}^{2}\sigma T_{\rm in}^{4}$, where $R_{\rm in}$, $T_{\rm in}$, and $\sigma$ representing the inner radius, the temperature of the disk and Stefan-Boltzmann constant respectively. This indicates that the disk is around the ISCO. Note that the standard disk applies to a luminosity range of 0.001 $L_{\rm Edd}$ $\lesssim$ $L_{\rm disk}$ $\lesssim$0.3 $L_{\rm Edd}$ (Steiner et al., 2010; Salvesen et al., 2013; Garc´ıa et al., 2015; Draghis et al., 2023), where $L_{\rm Edd}$ is the Eddington luminosity ($L_{\rm Edd}=1.26\times 10^{38}\left(\frac{M}{M_{\odot}}\right)\text{erg/s}$). As shown in Figure 5, we find that the maximum flux for the disk is about 491 times greater than the lowest flux. This luminosity coverage exceeds that commonly associated with standard disks (0.001 $L_{\rm Edd}$ $\lesssim$ $L_{\rm disk}$ $\lesssim$0.3 $L_{\rm Edd}$). So we speculate that the peak flux most likely has reached a value around 0.3 $L_{\rm Edd}$, and hence we use the flux and luminosity conversion in X-ray binaries to estimate the mass of the compact object. For a disk blackbody emission, the luminosity of the disk can be approximated as $L_{\rm disk}\approx\frac{2\pi Fd^{2}}{\rm cos\theta}$, where the distance $d=10.81\pm$3.52 kpc (Yan & Yu, 2015), and thus a peak luminosity is $L_{\rm disk}=\frac{1.24\pm 0.81\times 10^{38}}{\rm cos\theta}$ erg/s. As shown in Table LABEL:parameter, the joint spectral fittings with NuSTAR, NICER, and Insight-HXMT, result in an average inclination angle $53\pm 0.5$°. Accordingly, the mass of the compact object could be estimated as $5.5\pm 3.6M_{\odot}$.

In section 3.2, we used the M1 model to fit the spectrum of NICER and obtained a normalization value of approximately $70\pm 10$ for the disk. For the normalization of the disk, $\text{norm}=\left(\frac{\text{Rin}}{\text{D}_{10}}\right)^{2}\cos\theta$, where $R_{\rm in}$ is the inner disk radius, $D_{\rm 10}$ is the distance of the source in units of 10 kpc (1.08 $\pm$ 0.352 kpc), and $\theta$ is the inclination angle ($53\pm 0.5$°). we estimate the inner disk radius $R_{\rm in}$ to be 11.7 $\pm$ 3.9 km. For M2 we estimate the inner disk radius $R_{\rm in}$ to be 5.8 $\pm$ 1.9 km. For a Kerr black hole, with a measured spin a=$0.85\pm 0.03$ and a mass of the compact object about $5.5\pm 3.6M_{\odot}$, $R_{\rm Isco}$ gives $21.3_{-14.5}^{+16.2}$ km. Within the error range, the inner disk radius is consistently estimated in two different manners.