NuSTAR and Swift Observations of the Extragalactic Black Hole X-ray Binaries

A stellar-mass black hole X-ray binary (BHXB) consists of a primary black hole of mass $M_{\rm BH}\sim 3-100$ $M_{\odot}$ and a normal companion star. A BHXB can be classified as a high mass black hole X-ray binary (HMBHXB) or low mass black hole X-ray binary (LMBHXB) depending on the mass of the companion star (Remillard & McClintock, 2006; Tetarenko et al., 2016). An HMBHXB consists of an O, B, or WR star, while an LMBHXB consists of an A-type or later star as a companion. Depending on the X-ray activity, a BHXB is classified as a persistent or transient source. A persistent source appears to be always active in X-rays with luminosity, $L_{\rm X}\geq 10^{35}$ erg s^-1 and easily detectable with the instruments on-board X-ray observatories. On the other hand, a transient source spends most of the time at the quiescent state ($L_{\rm X}\sim 10^{30-32}$ erg s^-1 ) with occasional outbursts when the X-ray luminosity increases to $L_{\rm X}\sim 10^{35-38}$ erg s^-1 .

The BHXBs show rapid variation and fluctuations in the spectral and timing properties. The X-ray spectrum of the source in these binaries can be described by a model consisting of a multi-colour thermal blackbody and a non-thermal hard power-law tail. The thermal multi-colour blackbody component is believed to originate from the standard thin disk (Shakura & Sunyaev, 1973; Novikov & Thorne, 1973), whereas the hard power-law tail is believed to be originated by the up-scattering of blackbody photons in the Compton cloud located close to the black hole (Sunyaev & Titarchuk, 1980, 1985; Haardt & Maraschi, 1993; Zdziarski et al., 1993; Chakrabarti & Titarchuk, 1995; Done et al., 2007). During the outburst period, a BHXB goes through different spectral states, namely, low hard state (LHS), hard-intermediate state (HIMS), soft-intermediate state (SIMS), and high soft state (HSS) (Remillard & McClintock, 2006; Jana et al., 2020). The LHS is dominated by the Comptonized hard photons with the power-law photon index $\Gamma\sim 1.5-1.7$ and disk temperature, $T_{\rm in}\sim 0.4-0.5$ keV, while the HSS is dominated by the thermal soft photons with $\Gamma\gtrsim 2.5$ and $T_{\rm in}\sim 1$ keV (for details, see Remillard & McClintock, 2006; Jana et al., 2021).

To date, over 100 stellar mass BHXBs have been discovered (Tetarenko et al., 2016). Among the known population, only five BHXBs, namely, LMC X–1, LMC X–3, IC 10 X–1, M33 X-7, and NGC 300 X–1 have an extra-galactic origin. Of these five sources, LMC X–1 and LMC X–3 are nearby sources and are located at a distance of $\sim 48.1$ kpc in the Large Magellanic Cloud (LMC), a satellite galaxy of Milky Way (Shattow & Loeb, 2009). LMC X–1 and LMC X–3 are the second and third black holes discovered after Cygnus X–1 (Cowley et al., 1983; Hutchings et al., 1983).

LMC X–1 is the first extra-galactic X-ray source discovered by UHURU (Mark et al., 1969; Price et al., 1971). It is a persistent X-ray source in an HMBHXB system containing an optical giant OIII star of mass $M_{*}=31.79\pm 3.48$ $M_{\odot}$ (Orosz et al., 2009). The black hole (BH) mass in this binary system is found to be $M_{\rm BH}=10.91\pm 1.41$ $M_{\odot}$ (Orosz et al., 2009). The orbital period, distance and the inclination angle of the binary system are reported to be $P_{\rm orb}\sim 3.909\pm 0.0005$ days, $d\sim 48.1$ kpc and $i=36^{\circ{}}.38\pm 1.^{\circ{}}92$, respectively (Orosz et al., 2009). The BH is found to be rapidly rotating with spin parameter of $a^{*}\geq 0.92$ (Gou et al., 2009; Mudambi et al., 2020; Bhuvana et al., 2021). LMC X–1 does not show any long-term variability, though short-term variabilities have been reported by Nowak et al. (2001). Consistent with the long-term light curve, the source is always found to be in the thermal dominated spectral state (Nowak et al., 2001). The power density spectra are similar to that of a high soft state (HSS) and can be described with a power-law model (Bhuvana et al., 2021).

LMC X–3 is a persistent HMBHXB consisting a BH of mass $M_{\rm BH}=6.98\pm 0.56$ $M_{\odot}$, and a B3 V companion star of mass, $M_{*}=3.63\pm 0.57$ $M_{\odot}$ (Orosz et al., 2014). The orbital period, distance and the inclination angle of the system are reported to be, $P_{\rm orb}\sim 1.7$ days, $d\sim 48.1$ kpc and $i=69^{\circ{}}.24\pm 0.72^{\circ{}}$, respectively (Orosz et al., 2014). The spin of the BH in LMC X–3 is reported to be low with $a^{*}\leq 0.3$ (Steiner et al., 2010, 2014; Bhuvana et al., 2021). LMC X–3 is found to spend most of the time in thermal dominated state with occasional transition to the LHS (Boyd et al., 2000; Wilms et al., 2001; Smale & Boyd, 2012). Occasionally, LMC X–3 is observed to be in anomalous low/hard state (ALS) with X-ray intensity reduced to $L_{\rm X}\sim 10^{35}$ erg s^-1 (Torpin et al., 2017).

In this paper, we present the results of spectral and temporal analysis of extra-galactic BHXBs LMC X–1 and LMC X–3, using data from the NuSTAR and Swift observations over a duration between 2014 and 2019. The paper is organized in the following way. In §2, we present the details of observations and data reduction processes. In §3, we present the result of timing and spectral analysis. In §4, we discuss our results and in §5, we summarize our findings from the study.

LMC X–1 was observed with NuSTAR at three epochs between 2014 and 2016, whereas LMC X–3 was observed at five epochs between 2015 and 2019. Though, LMC X–3 was observed again with NuSTAR twice in 2019, these observations were performed in calibration mode. Therefore, we did not use these observations in the present study. All eight epochs of NuSTAR observations (three for LMC X–1 and five for LMC X–3) were carried out simultaneously with Swift . The details of the observations are presented in Table 1.

We carried out timing and spectral analysis of LMC X–1 and LMC X–3 using data from multi-epoch simultaneous observations with NuSTAR and Swift observatories. As both the sources are weak in hard X-rays, data from the Swift /XRT and NuSTAR were used in $0.5-30$ keV range in our analysis. Simultaneous observations at three epochs between 2014 and 2016 for LMC X–1 and five epochs between 2015 and 2019 for LMC X–3 are analyzed in the present work.

LMC X–1 has always been found to be in the thermal dominated HSS (Nowak et al., 2001), whereas LMC X–3 shows state transitions (Torpin et al., 2017). However, LMC X–1 and LMC X–3 were caught in the HSS during all the epochs of observations used in the present work. Using background subtracted light curves, we estimated the fractional rms variabilities of both the sources during the observations and found to be $<2$%. The HID of individual observations did not show any systematic variation. The power in the PDS got diminished above $\sim 10$ Hz. We did not detect any signature of QPOs in the PDS of both sources during all the observations. The observed timing properties of both the sources are found to be similar to that during typical HSS of BHs (Remillard & McClintock, 2006).

Spectral analysis of data from all three observations of LMC X–1 revealed that the emission was dominated by thermal disc flux ($f_{\rm disc}>0.85.$) with low scattering fraction ($f_{\rm Scat}\sim 0.1$). This indicates insubstantial emission from Compton Corona. The reflection was found to be low with $R_{\rm refl}<0.1$ during all three epochs of observations. This could be associated with the fact that the Comptonized flux was very low. LMC X–3 also showed similar behaviour during the observations at all five epochs. We did not find any evidence of the reflection component in the $0.5-30$ keV spectrum from any of the five observations with $R_{\rm refl}<0.06$. This confirms that LMC X–3 was in the HSS during the observations used in the present work, though state transition has been observed in the past.

Spectral fitting of data from Swift /XRT and NuSTAR simultaneous observations allowed us to constrain the mass and spin of LMC X–1 and LMC X–3. The estimated mass of both the BHs agrees well with the earlier reported values. LMC X–1 is reported to be a high spinning BH. Gou et al. (2009) estimated the spin of LMC X–1 as $a^{*}=0.92^{+0.05}_{-0.07}$ from RXTE observations. Steiner et al. (2012) estimated the spin as $a^{*}=0.97^{+0.02}_{-0.25}$ from the reflection spectroscopy. Mudambi et al. (2020) and Bhuvana et al. (2021) estimated the spin of LMC X–1 as $a^{*}=0.93^{+0.02}_{-0.02}$ and $a^{*}\sim 0.82-0.92$, respectively, from the AstroSat observations. In this work, we obtained the spin of LMC X–1 in the range of $a^{*}\sim 0.92-0.95$ from NuSTAR observations. Our estimated values of the spin matches well with the previous observations. On the other hand, LMC X–3 is reported to host a low spinning BH with spin parameters, $a^{*}=0.25^{+0.20}_{-0.29}$ (Steiner et al., 2014). Recently, AstroSat observations revealed the spin of LMC X–3 in the range of $a^{*}\sim 0.22-0.41$ (Bhuvana et al., 2021). Our estimated value of the spin of the BH is in the range of $a^{*}\sim 0.19-0.29$.

From the diskbb normalization ($N_{\rm DBB}$), we can calculate the inner edge of the accretion disc. The disc normalization is given by, $N_{\rm DBB}=(r_{\rm in}^{2}/D_{\rm 10}^{2})\cos i$, where $D_{\rm 10}$ is the distance of the source in the unit of 10 kpc, $r_{\rm in}$ is apparent inner accretion disc radius in km, and $i$ is the inclination angle (Mitsuda et al., 1984; Makishima et al., 1986). The inner edge of the disc is given by, $R_{\rm in}=x\kappa^{2}r_{\rm in}^{2}$, where $x=0.41$ is the correction factor (Kubota et al., 1998) and $\kappa$ is the spectral hardening factor (Shimura & Takahara, 1995). From the spectral fittings, we observed that the inner edge of the disc for LMC X–1 varied in the range of $R_{\rm in}\sim 40-43$ km $\sim 2.5$ $R_{\rm g}$, considering $\kappa=1.55$ (see Sec. 3.3.1). For LMC X–3, we obtained the inner edge of the disc in the range of, $R_{\rm in}\sim 47-53$ km $\sim 4.5-5$ $R_{\rm g}$ for different epochs, considering $\kappa=1.7$ (see Sec. 3.3.2). Considering the spin, $a*\sim 0.9$, the ISCO is located at $R_{\rm ISCO}\sim 2.3$ $R_{\rm g}$ for LMC X–1. For LMC X–3, the ISCO is located at $R_{\rm ISCO}\sim 5$ $R_{\rm g}$, considering spin $a^{*}\sim 0.25$. Hence, for both LMC X–1, and LMC X–3, the inner edge of the disc ($R_{\rm in}$) is obtained to be consistent with the $R_{\rm ISCO}$.

We obtained the broad-band X-ray luminosity ($L_{\rm X}$) in the energy range of $0.1-100$ keV for LMC X–1 and LMC X–3. The luminosity is obtained to be in the range of $L_{\rm X}\sim 1.38-1.52\times 10^{38}$ erg s^-1 , which corresponds to the Eddington ratio, $L_{\rm X}/L_{\rm Edd}\sim 0.1-0.11$ for LMC X–1. Here, $L_{\rm Edd}$ is the Eddington luminosity and given by, $L_{\rm Edd}=1.26~{}\times~{}10^{38}~{}(M_{\rm BH}/M_{\sun})$ erg s^-1 . During our observations, the luminosity of LMC X–3 was estimated to be $L_{\rm X}\sim 1.46-4.06~{}\times~{}10^{38}$ erg s^-1 . The Eddington ratio for LMC X–3 was, $L/L_{\rm Edd}\sim 0.16-0.46$. From this, we conclude that during our observation period, LMC X–1 was stable while LMC X–3 showed variation in the mass accretion rate.

The accretion efficiency is given by, $\eta=L_{\rm X}/\dot{\rm M}c^{2}$, where $c$ is the speed of light. The mass accretion rate for LMC X–1 and LMC X–3 are derived to be $\dot{\rm M}\sim 1.06-1.31\times 10^{18}$ gm s^-1 , and $\dot{\rm M}\sim 4.05-9.24\times 10^{18}$ gm s^-1 , respectively. The accretion efficiency are obtained to be $\eta\sim 0.13$ and $\eta\sim 0.04$ for LMC X–1 and LMC X–3, respectively. The accretion efficiency is higher for LMC X–1. This is expected as LMC X–1 is a high spinning BH, while LMC X–3 is a low spinning BH.

We studied two extra-galactic black hole X-ray binaries LMC X–1 and LMC X–3 using data from simultaneous observations with the Swift and NuSTAR observatories. Following are the key findings from our analysis.

1. 1.

   Spectral and timing analysis of Swift /XRT and NuSTAR data revealed that both LMC X–1 and LMC X–3 were in the HSS during all the observations.

2. 2.

   We did not find any signature of QPO in the PDS of both the sources. Very weak variability was also observed in the PDS of each source with fractional rms amplitude $<2$%.

3. 3.

   The spectra of both the sources were associated with a disc of temperature $T_{\rm in}\sim 1$ keV and photon index, $\Gamma>2.4$. The thermal disc fraction was observed as $f_{\rm disc}\geq 80$% with a small scattering fraction, $f_{\rm Scat}\sim 0.1$.

4. 4.

   The Fe K$\alpha$ emission line was detected in the spectra of LMC X–1, whereas no such feature was present in the spectra of LMC X–3.

5. 5.

   The spin of LMC X–1 and LMC X–3 were estimated to be $0.92-0.95$ and $0.19-0.29$, respectively.

6. 6.

   The broadband X-ray luminosities were observed to be in the range of $L_{\rm X}\sim 1.38-1.52\times 10^{38}$ erg s^-1 , and $L_{\rm X}\sim 1.46-4.06~{}\times~{}10^{38}$ erg s^-1 , for LMC X–1 and LMC X–3, respectively. This corresponds to the Eddington ratio of $\sim 0.1-0.11$ and $\sim 0.16-0.46$ for LMC X–1 and LMC X–3, respectively.

7. 7.

   The values of accretion efficiency was obtained to be $\eta\sim 0.13$ and $\eta\sim 0.04$ for LMC X–1 and LMC X–3, respectively.

We acknowledge the anonymous reviewer for the helpful comments and suggestions which improved the paper. Work at Physical Research Laboratory, Ahmedabad, is funded by the Department of Space, Government of India. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Space Science Data Center (SSDC, Italy) and the California Institute of Technology (Caltech, USA). This work was made use of XRT data supplied by the UK Swift Science Data Centre at the University of Leicester, UK.

We used archival data of Swift, and NuSTAR observatories for this work.