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Home All issues Volume 669 (January 2023) A&A, 669 (2023) A57 Full HTML
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A&A
Volume 669, January 2023
Article Number A57
Number of page(s) 12
Section Astrophysical processes
DOI https://doi.org/10.1051/0004-6361/202244585
Published online 05 January 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The X-ray transient MAXI J1348–630 was discovered on January 26, 2019 with the Gas Slit Camera (GSC) of the Monitor of All-sky X-ray Image (MAXI) aboard the International Space Station (Yatabe et al. 2019) and with the Swift/BAT during its X-ray outburst. This outburst lasted for about four months. Further observations made it possible to associate it with an activity of a black hole (BH) located at a distance of 3–4 kpc from the Earth (Tominaga et al. 2020). The X-ray spectral and timing properties of this source estimates have been studied in detail. Combined source spectra in the range of 1–150 keV from Swift/XRT, Swift/BAT, and MAXI/GSC were analyzed by Jana et al. (2020; hereafter, J20). They appeared in the framework of a two-component advective-flow (TCAF) model wherby the source evolved from the low-hard state (LHS) and through the intermediate state (IS) to the high-soft state (HSS, see, for example McClintock & Remillard 2006; Titarchuk & Seifina 2009; Shaposhnikov & Titarchuk 2009, hereafter ST09, for definitions of spectral states). Spectral state evolution of MAXI J1348–630 during its outburst is also confirmed by NICER observations (Zhang et al. 2020, hereafter Z20), which is similar to that previously observed for other BH transients.

Two reflares of MAXI J1348–630 were detected, occurring at the end of the main outburst and exhibiting peak fluxes that were one and two orders of magnitude lower than those of the main outburst, respectively, (Z20). These authors showed that the source remained in the hard state during reflares, which were reminiscent of so-called “failed outbursts.” Failed outbursts are usually less bright than regular outbursts at the peak and show no sign of transitions between spectral states (Del Santo et al. 2016; Capitanio et al. 2009; Sturner & Shrader 2005). This phenomenon was also observed in many BH transients (Stiele & Kong 2016; Fürst et al. 2015; Sturner & Shrader 2005; ST09). The study of MAXI J1348–630 with NICER and Swift also revealed different types of low-frequency QPOs at different phases of outburst (Z20; J20). In fact, Z20 and J20 also demonstrated it during the source power spectral evolution of MAXI J1348–630, which was also similar to other known BH transients. In Z20; J20, the results strongly supported a hypothesis that MAXI J1348–630 contained a BH and these authors estimated a BH mass as 8–12 M⊙ (see Table 1). This estimate of a BH mass was made assuming the Shakura-Sunyaev accretion disk (Shakura & Sunyaev 1973, hereafter SS73) and taking into account that the disk temperature, Td. is inversely proportional to the fourth root of a BH mass. Thus, Z20 estimated Td = 0.5 − 0.7 keV during the outburst maximum (see also Tominaga et al. 2020), which is slightly lower than that (Td = 0.8 − 1.2 keV) observed in other BHs during the outburst peak (Dunn et al. 2011). The lower disk temperature of MAXI J1348–630 already indicates that it may harbor a BH with a mass higher than 12 M⊙ (Z20; J20).

Table 1.

Previous BH mass estimates in MAXI J1348–630.

Recently, a X-ray spectroscopic analysis of MAXI J1348–630 was performed by Zhang et al. (2022; hereafter Z22) using Insight-HXMT and Swift data. They found that MAXI J1348–630 demonstrated the peculiar behavior during the ouburst rise in 2019. In Z22, the source spectra were fitted by the power-law plus the disk-blackbody components to find that in the soft intermediate and soft states, the object follows to the canonical relation of between the disk luminosity, L, and the peak color temperature, Td, at a constant inner radius, Rin. However, at other phases of the outburst, the behavior is more unusual and strongly deviates from the canonical evolution of known outbursts in BH transients. In particular, in the outburst rise phase, Rin is smaller than in the soft state and the temperature, Td, decreased to 0.5 keV. This contradicts to the standard model of an optically thick inner disk that moves inward at the start of an outburst, becoming monotonically brighter and hotter and replacing the optically thin Comptonization region. Z22 associated this to a decrease in the hardening factor of disk emission with the outburst evolution at the rise phase. In Z22, it was estimated that Td = 0.5 − 0.75 keV during the outburst maximum. This low disk temperature also indicates that MAXI J1348–630 may contain a BH with a mass above 12 M⊙, which is consistent with the above conclusions on a BH mass by Z20, J20 and Tominaga et al. (2020).

To date, there are other estimates for the BH mass in MAXI J1348–630 based on a large number of model parameters. In particular, J20 (see Sect. 2 and our Table 1) applied five parameters for a BH mass estimates, such as the Keplerian disk accretion rate (ṁ in ṀEd units), sub-Keplerian halo accretion rate (ṁh in ṀEd units), shock location (Xs in units of the Schwarzschild radius rs = 2GMBHc2), and dimensionless shock compression ratio (R = r+/r−, the ratio of post-shock matter density to the pre-shock matter density), which are essentially combined with one instrument parameter, namely, the normalization constant (N). Tominaga et al. (2020) use the Kerrbb model (see our Table 1), which gives relations among the spinning parameter, a, inclination angle, i, and a BH mass under a given source distance, mass accretion rate, and spectral hardening factor. In Z20, the authors assumed the closer distance of 3 kpc (also supported by the large observed flux at the soft-to-hard state transition) and an intermediate inclination of 60°, for the average Rin in the soft state using their model tbnew*(simpl*diskbb). With their parameters, namely, the disk temperature at the inner radius (Tin) in keV, DISKBB normalization (Ndiskbb), photon index, and scattered fraction (FracScatter), these authors obtained Rin = 110 ± 5 km, which is consistent with the ISCO radius for a non-spinning BH of 12 solar masses. Using the MAXI monitoring, Tominaga et al. (2020) utilized the measured evolution of the inner radius of the accretion disk during the soft state to estimate a BH mass (e.g., with an improved distance), however, Lamer et al. (2021) revised their inner disk radius measurements to R = 97 ± 13 km, leading an estimate of a BH mass as 11 ± 2 solar masses using the same model as in Tominaga et al. (2020).

The BH mass estimates using these methods require an accurate knowledge of the distance to the source. However, the distance to MAXI J1348–630 remains highly debated. Depending on the method of measurement, the distance of MAXI J1348–630 is 3–10 kpc (Nowak 1995; Maccarone 2003; Vahdat Motlagh et al. 2019; Russell et al. 2019; Tominaga et al. 2020; J20). In Table 1, we compare all published values of a BH mass and the distance to MAXI J1348–630. Recent observations taken during the first X-ray all-sky survey, using the SGR/eROSITA telescopes installed at the Spektr-RG space observatory, have led to a refinded distance of DJ1348 = 3.4 ± 0.4 kpc (Lamer et al. 2021). This places MAXI J1348–630 in a region of a relatively low stellar density located between the spiral arms of Sagittarius and Centauri of the Milky Way. The new distance estimate has made it possible to now estimate a new BH mass as 11±2 M⊙ (see Table 1) based on the assumption that its companion is a K-type star (Lamer et al. 2021).

The existing estimates for the BH mass in this binary (Table 1) have a large scatter and are often based on a great number of model parameters, therefore these need to be refined. Since there is no dynamical estimate of the BH mass, a re-estimation based on models with a smaller number of parameters, as well as using alternative methods, is desirable. In addition, it is important to prove the presence of a BH in this binary system – not only on the basis of the mass value of the central object (> 3 M⊙) but, for example, using other indicators as well, such as the detection of the constancy (or “saturation”) of the photon index, Γ, vs. the mass accretion rate, Ṁ, during X-ray outburst maximum, which is typical for other reliably established BHs (Stiele et al. 2013; ST09). In fact, the index-saturation effect when Ṁ is increased was already demonstrated in the early work by Titarchuk et al. (1998), offering a semi-analytical solution for the full kinetic equation; it was then was then done using the Monte-Carlo simulations for BH sources (see Laurent & Titarchuk 1999, 2011).

At this point, we can estimate a BH mass in MAXI J1348–630 using the scaling technique. This technique was proposed by Shaposhnikov & Titarchuk (2007; hereafter ST07) and developed by ST09. It was successfully tested in application to a large number of stellar mass BHs (e.g., Seifina et al. 2014; Titarchuk et al. 2010; ST09, see Fig. 1), as well as intermediate-mass BHs (Titarchuk & Seifina 2016, 2017; Seifina et al. 2017), and supermassive BHs (Seifina et al. 2016, 2018a,b; Sobolewska & Papadakis 2009; Giacche et al. 2014; Titarchuk & Seifina 2021).

thumbnail Fig. 1.

BH mass from the scaling method (using saturation of the photon index with the mass accretion rate), Mscal, compared to the corresponding dynamical masses Mdyn for stellar mass BHs. Data are taken from ST09, Shrader & Titarchuk (2003), Shaposhnikov & Titarchuk (2007), Seifina & Titarchuk (2010; for Mscal values), and Greene et al. (2001), Hjellming & Rupen (1995), Herrero (1995), Ninkov et al. (1987), Munoz-Darias et al. (2008), Hynes et al. (2004), Park et al. (2004), Orosz et al. (2002), Sanchez-Fernandez et al. (1999), Sobczak et al. (1999), Petri (2008), Homan et al. (2006), Filippenko & Chornock (2001), Miller-Jones et al. (2021; for Mdyn values). The yellow strip indicates a BH mass spread of 1.3 M⊙. The deviation from the yellow strip for Cyg X–1 reflects new estimates of the BH mass (marked with an pink arrow), taking into account the strong wind in this binary and possibly associated with the refinement of the source distance (from 2.5 to 2.2 kpc) from the radio data – due to which the BH mass estimate increased in Cyg X–1 from 6.8–13.3 M⊙ to 21 M⊙ (Miller-Jones et al. 2021).

We note that according to ST07 and ST09, there are two scaling methods: based on the correlation between Γ and the quasi-periodic oscillation frequency (QPO) νL; and based on the correlation between Γ and normalization of the spectrum proportional to Ṁ (see below Eqs. (1)–(2) for the definition of a mass accretion rate Ṁ). For the first method (Γ − νL), obtaining an estimate of the mass of the BH the distance to the source is not required (ST07); whereas for the second method (Γ − Ṁ), the source distance and the inclination are needed (ST09).

For both methods, it is important for the source to show a change in spectral states during the outburst and a characteristic behavior of Γ; namely, a monotonic increase of Γ with νL or Ṁ in the LHS→IS→HSS transition and reaching a constant level (saturating) at high values of νL or Ṁ. The saturation of Γ (i.e., the so-called “Γ-saturation phase”) during the outburst is a specific signature that supports the notion that this particular object containing a BH (Titarchuk et al. 1998). Indeed, the Γ-saturation phase can be caused only by an accretion flow converging to the event horizon of a BH (see the Monte-Carlo simulation results in Laurent & Titarchuk 1999, 2011).

The scaling method has advantages in determining a BH mass, namely: using X-ray data associated with the innermost regions of the accretion disk carry the direct information about a BH and consequently, an estimate of a BH mass is independent of the distance to the object and its inclination [using (Γ − νL) correlation].

In this paper, based on Swift data analysis, we estimate a BH mass in MAXI J1348–630 and the system’s inclination, by applying the scaling technique. In Sect. 2 we provide details of our data analysis, while in Sect. 3.1 we present a description of the spectral models used to fit these data. In Sects. 3.2.1–3.3 we focus on observational results and their interpretation. In Sect. 4 we discuss the main results of the paper. In Sect. 5 we present our final conclusions.

2. Data Reduction

Using Swift/XRT data in the 0.3–10 keV energy range, we analyzed a total of 53 observations of the X-ray transient MAXI J1348–630 during its outburst from January 26 to September 8, 2019. In Table 2, we report the log of observations for MAXI J1348–630 used in our study.

Table 2.

List of Swift observations of MAXI J1348–30 used in our analysis.

The data were processed using the HEASOFT v6.14, the tool xrtpipeline v0.12.84 and the calibration files (CALDB version 4.1). The ancillary response files were created using xrtmkarf v0.6.0 and exposure maps generated by xrtexpomap v0.2.7. Source events were accumulated within a circular region with radius of 20 pixels (1 pixel = 2.35 arcsec) centered at the position of MAXI J1348–630 (7 and , see Kennea & Negoro 2019) when the X-ray source was faint (see low-count plateau in Fig. 3). In the peak phase of the outburst (MJD 58510–58606), when the source became extremely bright and a pile-up effect occurred, we used an annulus extraction region with variable inner and outer radius (see Col. 11 in Table A.1) to attenuate this problem (Vaughan et al. 2006). We used XRT data both in the Windowed Timing (WT) mode during the bright part of the outburst (MJD 58509–58720) and in the Photon Counting (PC) mode for the remaining observations when the X-ray source became sufficiently faint (≤1 count s−1). The background was estimated in a nearby source-free circular region. Using xselect v2.4 task, the source and background light curves (0.01 s time resolution) and spectra were generated. The spectra were re-binned with 20 counts in each energy bin using the grppha task in order to apply χ2-statistics. We also used the online XRT data product generator1 to obtain the image of the source field of view in order to make a visual inspection and to get rid of a possible contamination from nearby sources (Evans et al. 2007, 2009). In Fig. 2, we show an adaptively smoothed Swift/XRT (0.3–10 keV) image of the MAXI J1348–630 field, obtained from 2019 January 26 to 2020 October 17, with an exposure of 52 ks during MAXI J1348–630, when it was was in outburst and quiescent states.

thumbnail Fig. 2.

Swift/XRT (0.3–10 keV) image of MAXI J1348–30 accumulated from January 26, 2019 to October 17, 2020 with an exposure of 52 ks.

The evolution of Swift/XRT in 0.3–10 keV energy range during 58450–58800 MJD observations is presented in the top panel of Fig. 3. We also obtained 1-day bin MAXI light curves from the 2–20 keV band as well as the 2–4 keV, 4–10 keV and 10–20 keV bands (Fig. 3, bottom panel), through the MAXI ondemand Web interface2.

thumbnail Fig. 3.

Evolution of Swift/XRT (0.3–10 keV, top panel) and MAXI/GSC flux (bottom panel) in 2–20 keV, 2–4 keV, 4–10 keV and 10–20 keV energy ranges during 58450–58800 MJD observations of MAXI J1348–630. Vertical bright blue, hazel, and white strips indicates the LHS, IS and HSS spectral states, correspondingly (for identification of spectral states see Sect. 3.1). Pink arrow (at top of the panel) indicate the time interval under our study (from January to September, 2019) for data sets listed in Table 2.

Only one outburst of this object is known to date (Fig. 3), when it showed a rapid increase in X-ray luminosity (on the order of 10 days, during outburst rise phase) before reaching its peak luminosity, then followed by a slow luminosity decline over about four months (outburst decay phase). During this active phase, we can see transitions between different spectral states (see color strip indications in Fig. 3).

3. Analysis and results

In this section, we present the results of spectral analysis during the 2019 outburst of MAXI J1348–630 observed by Swift/XRT. In particular, we analyze how the X-ray spectrum of the source behaves, especially Γ, during the outburst from MJD 58509 to 58734 MJD.

3.1. Spectral analysis

To fit the energy spectra of this source, we used a XSPEC model consisting of the Comptonization (bulk-motion Comptonization, hereafter BMC) component (see Titarchuk et al. 1998; Laurent & Titarchuk 1999) and the iron line (Gaussian) components. We also used a multiplicative tbabs model (Wilms et al. 2000), which takes into account absorption by neutral material. We assume that accretion onto a BH is described by two main zones (see, for example, Fig. 1 in Titarchuk & Seifina 2021): a geometrically thin accretion disk, such as the standard Shakura–Sunyaev disk, (see SS73), and a transition layer (TL), which is an intermediate link between the accretion disk, and a converging (bulk) region (see Titarchuk & Fiorito 2004). The latter is assumed to exist, at least below 3 Schwarzschild radii, 3RS = 6GMBH/c2. The spectral model parameters are the equivalent hydrogen absorption column density, NH; the photon index, Γ; whereas log(A) is related to the Comptonized factor, f [=A/(1 + A)], and the color temperature and normalization of the seed photon blackbody component, kTs and Nbmc, respectively. The Comptonized component is additively combined with the gaussian line model for which the fit parameters are the line energy, Eline, and normalization, Nline. The centroid of the gaussian (Fe Kα) line can vary from 6.3 to 6.9 keV; the Fe line width was varied from 0.1 to 1 keV and then subsequently fixed at 0.5 keV (as the best-fit value). The parameter log(A) of the BMC component is fixed at 2 when the best-fit log(A)≫1. In fact, for a sufficiently high log(A)≫1 (and, therefore, a high value A), the illumination factor f = A/(1 + A) becomes a constant value close to 1 (that is, the same as in the case of log(A) = 2). NH was fixed at the level of 0.64 × 1022 cm−2 (Z20).

Similarly to the ordinary body XSPEC model, the BMC normalization is a ratio of the source (disk) luminosity L to the square of the distance, d (ST09, see Eq. (1) in that work):

(1)

This encompasses an important property of the BMC model. That is to say that using this model can lead to a correct evaluation of the normalization of the original “seed” component, which is presumably a correct Ṁ indicator (Seifina & Titarchuk 2011). In turn, we have:

(2)

Here R* = r*RS is an effective radius where the main energy release takes place in the disk, RS = 2GM/c2 is the Schwarzschild radius, η = 1/(2r*), ṁ = Ṁ/Ṁcrit is the dimensionless Ṁ in units of the critical mass accretion rate, Ṁcrit = LEd/c2, and LEd is the Eddington luminosity. For the formulation of the Comptonization problem, we can look to Titarchuk et al. (1997), Titarchuk et al. (1998), Laurent & Titarchuk (1999), Borozdin et al. (1999), Shaposhnikov & Titarchuk (2009).

The best-fit model parameters for all states are shown in Table A.1. A systematic uncertainty of 1% is intended to represent the instrumental flux calibration uncertainty and has been applied to all analyzed Swift spectra.

A spectral analysis of the Swift/XRT data fits of MAXI J1348–630, in principle, can provide a general picture of the spectral evolution. We can trace the change in the spectrum shape during the LHS-IS-HSS transition in Fig. 4, which demonstrates three representative E * FE spectral diagrams for different states of MAXI J1348–630.

thumbnail Fig. 4.

Evolution of MAXI J1348–630 spectra, fitted using the tbabs*(bmc+gauss) model for three spectral states. Data are taken from the Swift/XRT observations: 00088843001 (MJD = 58515.75, left), 00011107003 (MJD = 58519, center), and 00011107007 (MJD = 58524, right). Data are shown as black crosses and the spectral model components are displayed as dashed green and blue lines for the BMC and gaussian components, respectively. The resulting spectrum as a sum of these components are presented by red line. In the bottom panels, we show the corresponding Δχ vs. photon energy (in keV).

To identify the spectral states, we relied on the best-fit value of the photon index: LHS (Γ < 1.6), IS (1.6 < Γ < 1.8) and HSS (Γ > 1.8). The emergent spectra (see Fig. 4) can be described as a sum of the low-energy blackbody and its fraction convolved with the Comptonization Green function (CGF; see Eqs. (16) and (B5) in Sunyaev & Titarchuk 1980). The HSS and IS spectra are characterized by a strong soft blackbody component (presumably related to the accretion disk) and a power law (as the hard tail of the CGF). In the LHS, the Comptonization component is dominant and the blackbody component is barely seen because the innermost part of the disk is fully covered by the scattering media which has a Thomson optical depth more than 2.

The general picture of the LHS-IS-HSS transition is illustrated in Fig. 5, where we put together spectra of the LHS, IS, and HSS, to demonstrate the source spectral evolution from the high-soft to low-hard states based on the Swift observations. Here, the data are presented in the left panel for LHS, taken from observations 0008884300 (bright blue), 0088496000 (red) and 0088596000 (pink); at the right panel for IS, we have 00011107003 (black), and 0088826000 (orange) as well as for HSS [00011107007 (blue). We should point out the fact that the HSS and IS spectra are characterized by a strong soft blackbody component and a power law extending up to 10 keV, while in the LHS spectrum, the Comptonization component is dominant and the blackbody component is barely seen.

thumbnail Fig. 5.

Six representative EFE spectral diagrams during different spectral states of MAXI J1348–30. Left panel: data taken from Swift/XRT observations 0008884300 (bright blue, LHS), 0088496000 (red, LHS), and 0088596000 (pink, LHS). Right panel: data taken for 00011107003 (black, IS), 0088826000 (orange, IS), and 00011107007 (blue, HSS).

An analysis of the Swift/XRT data fits (see Fig. 6 and Table A.1) showed that Γ monotonically increases from 1.1 to 3 (red points in Fig. 6), when the normalization of the BMC component (or Ṁ) increases by a factor of 10 (green points, in Fig. 6) at the outburst rise phase (LHS-IS, MJD 58509–58512). At the rise-phase start of the outburst (LHS, MJD 58509–58519), the spectra are gradually softened with a increase in the total flux and Γ slowly increases from 1.1 to 2, together with a slight decrease in the disk seed photon temperature, kTs, from 0.45 to 0.2 keV (black points, in Fig. 6). In this case, the contribution of the Comptonized component, f, to the total flux increased from 0.7 to 0.9 (blue points, in Fig. 6). Furthermore, at the end of the outburst-rise phase (HSS, MJD 58519–58525), the spectra further softened, with an increase in the total flux, and Γ continued to increase from 2 to 3, along with a slight increase in the disk seed photon temperature, kTs, from 0.2 to 0.75 keV. At the same time, the contribution of the Comptonized component, f, to the total flux remained almost constant, increasing from 0.9 to 1 (blue dots, in Fig. 6). This interesting behavior of kTs and f at the beginning of the outburst is further discussed in Sect. 4. In turn, at the decay phase of the outburst (HSS, MJD 58525–58597), the spectra are gradually hardened, with a decrease in the total flux, and Γ slowly decreases from 3. to 1.7, together with a slight decrease in the disk seed photon temperature kTs from 0.7 to 0.5 keV (black points, in Fig. 6). In this case, the contribution of the Comptonized component, f, to the total flux decreased from 1 to 0.5 (blue points, in Fig. 6). When the source passed from the IS to the LHS (MJD 58612), the temperature, kTs, dropped to ∼0.25 keV, and Γ decreased to Γ ∼ 1.4, while the contribution of the Comptonized component to the total flux increased to f = 1. After the source returned to the LHS (MJD 58606), the Comptonized component (f = 1) prevailed in the spectra, while Γ changed in the interval 1.1−1.4 and kTs was about 0.2 keV.

thumbnail Fig. 6.

Temporal evolution of the Swift/XTE count rate (pink) from the LHS to the HSS and back, shown from top to bottom. Comptonized fraction f (blue), seed photon temperature Ts (black), Nbmc (green) and Γ (red) during the MJD = 58509–58734 outburst transition set. We note that the Comptonized fraction f = A/(A + 1) characterizes the fraction of the soft photons illuminating the Compton cloud (CC), and subsequently up-scattered in the CC hot plasma. Vertical bright blue, hazel and white strips indicates the LHS, IS, and HSS spectral states, correspondingly (as in Fig. 3).

3.2. BH mass estimate

The previous BH mass estimates were made based on luminosity determination or were based on the TSAF/Kerrbb spectral model fitting (see Tominaga et al. 2020; Russell et al. 2019; Nowak 1995; Maccarone 2003; Vahdat Motlagh et al. 2019; Lamer et al. 2021; J20). It is worth noting that a BH mass estimate using these methods turns out to be highly dependent on the accuracy of the distance to the source.

Now, we go on to estimate the BH mass (MJ1348) using scaling methods developed by ST09, based on Γ − νL (see our Sect. 3.2.1) and Γ − Nbmc (Sect. 3.2.2) correlations for the target source and the reference source. By using the Γ − νL correlation, we deal with the method that offers the advantage of being independent of the binary inclination and source distance.

3.2.1. Scaling of Γ vs. νL correlation for MAXI J1348–630

We obtained an estimate of a BH mass in MAXI J1348–630 using the results of timing analysis by Z20 (see their Table 1) in comparison with our results of spectral analysis for the close MJD dates (Table A.1). We obtained the Γ dependence on νL and demonstrated that Γ for MAXI J1348–630 is correlated with νL and saturated at Γ = 2.9 ± 0.1 at frequencies above 6 Hz (see Fig. 7)3.

thumbnail Fig. 7.

Photon index, Γ, vs. the QPO frequency, νL, for MAXI J1348–630 (target source) and XTE J1550–564 (reference source). We use a specific function f(ν), detailed in Eq. (3) of Sect. 3.2.1, to fit the data, which gives us the corresponding solid lines. We can see that Γ is correlated with νL and saturated for νL > 6.8 Hz and νL > 10 Hz for MAXI J1348–630 and XTE J1550–564, respectively. Data for XTE J1550–564 were taken from ST09.

In order to estimate MJ1348, we chose Galactic source XTE J1550–564 as the reference source (see a detailed explanation of the scaling method in ST09). It is worth noting that XTE J1550–564 is a source with the well-known parameters of the reference source: the spatial orientation (the inclination ir), BH mass (mr), and distance (dr) were determined by a dynamic method (see Table 3 and Orosz et al. 2002). Figure 7 shows that Γ − νL correlations for MAXI J1348–630 and XTE J1550–564 follow a similar pattern of Γ with νL: it is linear and monotonically increases until it reaches a transition frequency, νtr; whereas around νtr the function Γ − νL smoothly transitions into a horizontal line. It becomes a constant at a value 2.9 ± 0.1, which we assume to be the Γ saturation.

Table 3.

BH masses and distances.

This behavior is well reproduced by the analytical function f(ν), (see ST09):

(3)

Using this function, f(ν), we fit the observed Γ − νL correlations applying the least-squares method. Specifically, we minimized the sum of squared residuals of the function f(ν, A, B, D, νtr) from the observed Γ − νL track by selecting values of the parameters A, B, D, νtr for which this function, f(ν, A, B, D, νtr) is closest to the observable Γ − νL correlation.

The significance of the parameters A and B follows from the asymptotic of the function f(ν). For ν ≪ νtr we see that B is the slope of the correlation. On the other hand, for ν ≫ νtr the function f(ν) equals to A. From this it is immediately clear that the parameter A is a value of the Γ-saturation level. We introduced the parameter D in order to control how fast the transition occurs.

Results after fitting the Γ − νL correlations for these sources using Eq. (3), presented in Table 4, where A = 2.94 ± 0.08, B = 1.27 ± 0.01, νtr = 10.1 ± 0.5 Hz and A = 2.93 ± 0.09, B = 1.25 ± 0.04, νtr = 6.48 ± 0.07 Hz for XTE 1550–564 and MAXI J1348–630, respectively. It is worth noting all these parameters are relatively close to each other. Numerous fit tests have shown that parameter D varies slightly around 1 Hz, so we fixed it at 1.0 Hz for the convenience of the fitting procedure. We fit the correlations in order to get these parameters, A, B, D, and νtr (see Table 4), and thus to obtain the scaling factor, sν (Eqs. (4) and (5)). Finally, we estimated the BH mass in MAXI J1348–630 applying the scaling method (see ST09, Eq. (2) therein):

(4)

Table 4.

Parameterizations of scaling patterns for reference and target sources.

where

(5)

is the scaling factor and subscripts r and t denote the reference and target sources.

For the reference source, we chose the data from the rise of the 1998 XTE J1550–564 outburst, because its Γ-saturation level is approximately that of MAXI J1348–630, Γsat = 2.9 ± 0.1. The best-fit curves are shown by blue and red lines in Fig. 7. The inferred uncertainty (error bar) of MJ1348 is mostly affected by scattering and error bars of the Γ − νL points.

As a result, the BH mass in MAXI J1348–630 is

(6)

using the scaling technique and the reference BH mass, 9.5 ± 1.1 M⊙ (for XTE J1550–564). For details, see Table 3.

3.2.2. Scaling of Γ − Nbmc correlation for MAXI J1348–630

The BH mass scaling method using the Γ − Nbmc correlation is described in detail in ST09. This method is aimed at: (i) searching for such a pair of BHs for which the Γ correlates with increasing Nbmc (which is proportional to Ṁ, see ST09, Eqs. (4) and (7) therein) and the saturation level Γsat are the same and (ii) calculating the scaling coefficient sN, which allows us to determine a BH mass of the target object. It is worthwhile emphasizing that we needs a ratio of distances for the target and reference sources in order to estimate a BH mass using the following equation for the scaling coefficient:

(7)

where Nr, Nt are normalizations of the spectra, mt = Mt/M⊙, mr = Mr/M⊙ are the dimensionless BH masses with respect to solar, dt and dr are distances to the target and reference sources, correspondingly. We have a geometry factor of fG = cos ir/cos it, where ir and ir are the disk inclinations for the reference and target sources, respectively (see ST09, Eq. (7)). We compared the difference of the disk X-ray fluxes for the reference and target sources, in the direction towards the Earth observer. We used XTE J1550–564 as the reference source.

In Fig. 8, we demonstrate the Γ vs. Nbmc, where Nbmc is presented in the units of (L39 is the source luminosity in units of 1039 erg s−1 and d10 is the distance to the source in units of 10 kpc). As we can see, the correlations of both sources are characterized by similar shapes and saturation levels, Γsat ∼ 2.9 ± 0.2. In order to implement the scaling method, we used an analytical approximation F(N) for the Γ − Nbmc correlation, (see ST09):

(8)

thumbnail Fig. 8.

Γ vs. Nbmc correlations those for MAXI J1348–630 (target source) and for a BH XTE J1550–564 (reference source). We use a specific function, F(N), (see Eq. (8)) to fit the data, which gives us the corresponding solid lines.

where N = Nbmc. This function F(N) is widely used for a description of the Γ − Nbmc correlation (Sobolewska & Papadakis 2009; ST09; Seifina & Titarchuk 2010; Giacche et al. 2014; Seifina et al. 2014, 2016, 2017, 2018a,b).

As a result of fitting the observed correlation by this function F(N), we obtained a set of the best-fit parameters 𝒜, ℬ, 𝒟, Ntr, and β (see also Table 4). 𝒜 is the Γ saturation level for Γ − N correlation and ℬ is the slope of this correlation. The parameter 𝒟 controls how fast the transition occurs, Ntr is the normalization at which the Γ − N correlation levels of,f and β is the power-law index of the part of the curve for lower argument values.

We estimated a BH mass for MAXI J1348–630 using Fig. 7. We also fit the correlation Γ − Nbmc by Eq. (8) to get an estimate for taken at the beginning of the Γ-saturation part. We obtain sN = Nr/Nt applying N-values (see Table 4). Finally, Eq. (7) provides us a BH mass value with an accuracy of a factor fG, namely,

(9)

We then obtain

(10)

if we use values of mr = 9.5, dt = 3.39 kpc and dr = 2.5 kpc (Table 3) and cN = (Nr/Nt) = 0.875 (Table 4).

Thus, we estimate mt = mJ1348 with an accuracy of factor fG assuming dJ1348 = 3.39 kpc (Lamer et al. 2021). We used all the parameters of the formulas in Eqs. (3) and (8) to fit the observed correlations Γ vs. νQPO and Γ vs. NBMC (see Table 4, Figs. 7–8).

3.3. Estimate of the orbital inclination for MAXI J1348–630 using the scaling technique

Now, we estimate the inclination using a value of the geometric factor fG. We can evaluate fG more accurately, knowing a value of a BH mass obtained using the Γ − νL scaling (Eqs. (6) and (10)) that for the Γ − N scaling. Thus, equating a BH mass using the Γ − νL correlation (Eq. (6)) to that for the Γ − N one (Eq. (10)), we found that:

(11)

Moreover, we can estimate the inclination in MAXI J1348–630 knowing the inclination i of the XTE J1550–54 (see Table 3). Indeed, since:

(12)

we obtain the following:

(13)

In addition, we can evaluate a range of inclination values depending on the distance to MAXI J1348–630; for example, for a distance range of 3–5 kpc, the inclination range can be estimated using the scaling method as then would be obtained using the Lamer et al. result to be 70–35°. For the distance, kpc, obtained by Chauhan et al. (2021), taking into account the large uncertainties in the source distance, we can only give a limiting range of the inclination as 75° < it < 80°. This clearly contradicts the absence of eclipses in the observed light curve (see Fig. 3) in this binary system.

4. Discussion

The Swift/XRT data of the MAXI J1348–630 outburst are well fitted by the BMC model for all analyzed LHS, IS and HSS spectra (see Figs. 4 and 6). Our results from the spectral analysis are consistent with previous results by other authors using various X-ray observations of MAXI J1348–630 (see Z20; J20; Lamer et al. 2021). In particular, spectral parameter behavior observed by us is also consistent with those recently reported by Carotenuto et al. (2021a), who modeled the Swift/XRT spectra (1–10 keV) of MAXI J1348–630 using the tbabs*powerlaw model. They found that the index Γ changes from 1.5 to 2.4 during the outburst using their simplified model, tbabs*powerlaw. However, these authors could not constrain Γ during the HSS and they fixed it at 2.4 (see their Fig. 2). This outcome was not by chance, as Carotenuto et al. (2021a) used the phenomenological model tbabs*powerlaw instead of the physical (Comptonization) model which we applied to the same data.

Tominaga et al. (2020) modeled the MAXI J1348–630 spectra detected by MAXI/GSC in 2–20 keV energy range using the tbabs*(simple*diskbb) model and found that Γ changes from 1.5 to 2.9 – this result is similar to ours (see our Figs. 7 and 8). Furthermore, Tominaga et al. (2020) estimated the BH mass by applying the XSPEC kerrbb model and found that the values of mBH = MBH/M⊙ were 7.0. It is worth pointing out that the kerrbb model has five main parameters for the BH mass estimate: the spinning parameter, a, inclination angle, i, and a black hole mass, mBH, under a given source distance, mass accretion rate, and a spectral hardening factor. However, in our case, we used observational points of the Γ vs. QPO frequency correlation and only one the best-fit parameter, mBH. Our scaling method allows us to estimate mJ1348 as 14.8 ± 0.9, using the XTE J1550 source as a reference.

We compared our results with those obtained by Z20 based on NICER data. In Z20, the MAXI J1348–630 spectra were fitted during the outburst with the tbnew*(diskbb+nthcomp) model and then compared with the tb-new*(simple*diskbb) model results. In Z20, higher values of Γ were obtained throughout the whole outburst from MJD 58520 to 58635 (Γ = 1.5 − 3.8), as compared to our results (Γ = 1.1 − 3). In particular, at the decay phase of the outburst (MJD 58525–58597), Z20 reported that Γ decreases only from 3.5 to 3, which is very different from that found in this paper (from 3 to 1.4). Moreover, a decrease of Γ in our estimate is from 1.9 to 1.6 while in Z20 it is from 3 to 1.7 during MJD 58580–58610. Z20 found a decrease in the temperature of the inner disk from kTin ∼ 0.7 to 0.5 keV (MJD 58520–58600), which is consistent with our results (from 0.7 to 0.4 keV). The decrease in the contribution of the Comptonized component, f, to the total flux found by Z20 from 0.6 to 0.1 (MJD 58520–58600) is also consistent with the behavior of log(A) [f = A/(1 + A)] (see Table A.1) obtained in our spectral analysis as the X-ray flux decreases. However, here we found a wider range of a decrease of f from 1 to 0.1. Again, the contribution of the Comptonized component, f, to the total flux increases up to 0.7 in Z20, which is somewhat more modest then the result we obtained: (f ∼ 1, MJD 58600–58635). Furthermore, Z20 found a sharp decrease in kTs from 0.5 to 0.2 keV when the source passed from the HSS to the LHS (MJD 58608), which is consistent with our results in general; however, we found a decrease in kTs only from 0.4 to 0.3 keV. In Z20, the behavior of the spectral parameters is similar with those found in our paper. The general picture of the outburst in MAXI J1348–630 is adequately reproduced in both models (compare our Fig. 6 to Fig. 5 in Z20).

It is worth emphasizing that we have found a specific type of behavior with regard to the temperature of seed photons originating in the disk, kTs, at the very beginning of the outburst, just before the transition to the soft state (MJD 58510–58518). The temperature, kTs, initially decreases (from 0.45 keV to 0.2 keV) and the Comptonized fraction, f, increases from 0.75 to 0.9 during the initial rise in the low-hard state (Fig. 6). It is interesting to note that a similar behavior for kTs was found for the same source for these MJD dates by Zhang et al. (2022), although kTs decreased somewhat within different limits: from 0.75 to 0.5 keV. According to our spectral analysis the comptonized fraction f, at the same time, increases from 0.75 to 0.9 during the initial rise in LHS (Fig. 6). We note that f is a parameter associated with the relative size of the corona with a respect to a distance from the soft photon source (disk). As a result, its increase in f immediately before the outburst (see panel 2 at the top of Fig. 6) simultaneously with the decrease in kTs points to an initial increase in the corona size. Furthermore, at the end of the outburst-rise phase (HSS, MJD 58519–58525), the spectra further soften with an increase in the total flux along with a slight increase in the disk seed photon temperature kTs from 0.2 to 0.75 keV. At the same time, the contribution of the Comptonized component, f, to the total flux remained almost constant, increasing from 0.9 to 1 (blue dots, in Fig. 6). This effect has a simple physical interpretation in terms of the BMC model (Titarchuk et al. 1998; Laurent & Titarchuk 1999). At the beginning of the outburst (see Fig. 6), the corona is very extended and, thus, seed photons are injected into the corona from a relatively far-away region of the disk, where the disk temperature is about 0.2–0.4 keV. As the mass accretion rate increases (or the luminosity increases), the corona contracts and consequently kTs increases (see an illustration of this phenomenon in Fig. 2 of Seifina et al. (2014) and an analytical explanation of the evolution of the spectral index from the low hard state to softer states in black holes in Seifina et al. (2018b). In this case, the parameter f increases sharply (from 0.7 to 0.9). It is possible that such a decrease in kTs and a simultaneous increase in f immediately before the outburst can be considered a signature of the transition of a BH object into a flare (or of the readiness of the BH object to go into an outburst). This effect has also been observed in other black holes (e.g., GX 339–4, GRO J1655–40, 4U 1543–47, XTE J1550–564, XTE J1650–500, H 1743–322, and XTE J1859–226 (ST09), GRS 1915+105 (Titarchuk & Seifina 2009), and 4U 1630–47 (Seifina et al. 2014) as well as in other studies of MAXI 1348 (Z22). Future observations of other BH sources that will demonstrate such behavior of kTs and f on the eve of the flare may help verify the validity or even the universality of this signature.

Our results are also consistent, with the results of the spectral analysis by Z22 based on HXMT and Swift data. However, those authors find, on average, a flatter , during outburst decay than our best-fit results (). Perhaps the difference in Γ compared to our results is due to the different energy range, or perhaps caused by a different spectral model. Throughout the outburst, their Γ ranges from 1.3 (ID = 0214002002) to 2.9 (ID = 0214002065, see their Table 1). This is in full agreement with our results (Γ = 1.1 − 2.9). We note that when fitting the Swift data, Z22 simply fixed Γ at the canonical value during the outburst decay, Γ = 2.5, rather than looking for the best-fit solution (see their Table 2).

In Figs. 7 and 8, we show how smoothly Γ evolves from the LHS to the HSS, with a clear indication of the saturation of Γ, that is, at least there is a sharp change in the Γ vs. QPO frequency slope for high values of νL and high mass accretion rates, Ṁ, respectively. This effect was predicted semi-analytically by Titarchuk et al. (1998) and then using Monte-Carlo simulations by Laurent & Titarchuk (1999, 2011). Moreover it was confirmed using the RXTE observations of Cyg X–1 (see ST07 and ST09), XTE J1859–226, XTE J1650–500, H1743–322, GX339–4, XTE J1543–47 (ST09), 4U1630–47 (Seifina et al. 2014), and GRS 1915+105 (Titarchuk & Seifina 2009), as well as observed in our study, which allowed us to confirm the presence of a BH in MAXI J1348–630.

Using the scaling method (Γ − νL), (ST07, ST09) we estimated the BH mass in MAXI J1348–630 (see Fig. 7 and Table 3). The BH mass value 14.8±0.9 M⊙ is relatively far from the previous BH mass estimate in MAXI J1348–630 of 7–12 M⊙ (Lamer et al. 2021; Tominaga et al. 2020), J20; Z20, see also our Tables 1 (compare Tables 1 and 3). A possible reason for the discrepancy between our estimate of a BH mass and that based on luminosity (Z20; Lamer et al. 2021) is an assumption by those authors that the object emits at the Eddington luminosity regime, which, in fact may not be the case. As a result, a BH mass value is naturally under-estimated.

In contrast to Z20 and Lamer et al. (2021), we determined a BH mass using the first scaling Γ − νL method and it was not necessary to know the distance to the source. Thus, the main advantages of the scaling method (Γ − νL) to estimate a BH mass in comparison with other methods we used is that only one of the best-fit parameters is required, namely, a BH mass, MBH, for at least nine observational points of Γ − νL (see Fig. 7). It is worth noting that we also need a similar Γ − νL correlation with a known BH mass, which is that of XTE J1550–564.

We estimated the inclination, i, by combining the two scaling methods (Γ − νL and Γ − Nbmc). This estimate is very different from the radio inclination estimate irad < 46° (Carotenuto et al. 2021a). A possible reason for this discrepancy may be related to the fact that the inclination estimate from radio data is based on the difference in the brightness of the approaching jet and the receding jet based on the assumption that these jets are identical and oppositely directed, which may not necessarily be the case (Chatterjee et al. 2020; Davis & Tchekhovskoy 2020).

Another reason for this discrepancy using radio data and X-ray data is their association with different geometric scales. It is known that the radio data is mostly formed in the outer part of the source, while the X-ray emission originates in the innermost region (TL). Therefore, this estimate (irad < 46°) may turn out to be unreliable for the inner part of the X-ray source. On the other hand, our scaling estimate [i = (65 ± 5)°] can be a useful alternative because we evaluate i using X-ray emission presumably originated in the TL.

5. Conclusions

We studied the spectral evolution of MAXI J1348–630 using fits of the observed X-ray emission by Swift/XRT. We demonstrated that the energy spectra during all spectral states could be fitted by an additive model consisting of the Comptonization (BMC) and Gaussian iron-line components. As a result, we found that Γ monotonically increased with νL and Ṁ during the transition from the LHS to the HSS and then became saturated at Γ ∼ 2.9 for high νL and Ṁ values. We applied these correlations and found that they were similar to those established in a number of other BH candidates and could be considered as an observational evidence for the presence of a BH in MAXI J1348–630.

We estimated a BH mass for MAXI J1348–630 using the above scaling methods (see Sect. 3.2). In particular, the Γ − νL correlation scaling method, which relies on XTE J1550–564 as a reference source, allowed us to estimate the BH mass in MAXI J1348–630 of MBH = 14.8 ± 0.9 M⊙. It is important to emphasize once again that the Γ − νL correlation is independent of the distance and inclination of the object and it is therefore are fairly accurate in the determination of a BH mass.

We also detected a specific decrease in the disk seed photon temperature, kTs, at the beginning of the outburs: kTs initially decreases from 0.4 to 0.2 keV and increases only after the source transits to the outburst rise-maximum phase. Initial decrease in kTs occurred simultaneously with an increase in the illumination fraction, f. We interpreted this effect in terms of the Comptonizaion model. Since the Compton cloud (or corona) is very extended at the outburst beginning and, thus, the seed photons injected to the corona from the relatively cold and peripheral disk region, where kTs is about 0.2–0.4 keV. While Ṁ increases (or luminosity increases), the corona contracts and, thus, the seed photon temperature, kTs, increases. It is possible that such a specific decrease in kTs taking place simultaneously with an increase in the illumination fraction, f, can be considered to be a signature of the readiness of a BH object to go into an outburst.

3

Hereafter, we consider the term of the Γ saturation as a constant of Γ in the Γ − νL correlation track at high values of νL.

Acknowledgments

We acknowledge support from UK Swift Science Data Centre at the University of Leicester for supplied data. We thank the anonymous referee for the careful reading of the manuscript and for providing valuable comments. We are very happy to get a careful reading and editing our manuscript by Chris Shrader. This research has made using the data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. The data used in this paper are public and available through the GSFC public archive at https://heasarc.gsfc.nasa.gov. This work was made use of XRT and BAT data supplied by the UK Swift Science Data Centre at the University of Leicester (https://www.swift.ac.uk/swift_portal), and MAXI data was provided by RIKEN, JAXA (http://maxi.riken.jp/mxondem), and the MAXI team.

References

  1. Bassi, T., Del Santo, M., D’Ai, A., Motta, S., Marino, A., & Segreto, A. 2019, ATel, 12477, 1 [NASA ADS] [Google Scholar]
  2. Borozdin, K., Revnivtsev, M., Trudolyubov, S., et al. 1999, ApJ, 517, 367 [NASA ADS] [CrossRef] [Google Scholar]
  3. Burrows, D. N., Hill, J. E., Nousek, J. A., et al. 2005, Space Sci. Rev., 120, 165 [Google Scholar]
  4. Capitanio, F., Belloni, T., Del Santo, M., & Ubertini, P. 2009, MNRAS, 398, 1194 [NASA ADS] [CrossRef] [Google Scholar]
  5. Carotenuto, F., Corbel, S., Tremou, E., et al. 2021a, MNRAS, 505, L58 [NASA ADS] [CrossRef] [Google Scholar]
  6. Carotenuto, F., Corbel, S., Tremou, E., et al. 2021b, MNRAS, 504, 444 [NASA ADS] [CrossRef] [Google Scholar]
  7. Chatterjee, K., Younsi, Z., Liska, M., et al. 2020, MNRAS, 499, 362 [NASA ADS] [CrossRef] [Google Scholar]
  8. Chauhan, J., Miller-Jones, J., Raja, W., et al. 2021, MNRAS, 501, L60 [NASA ADS] [CrossRef] [Google Scholar]
  9. D’Ai, A., Zycki, P., di Salvo, T., et al. 2007, ApJ, 667, 411 [CrossRef] [Google Scholar]
  10. Davis, S., & Tchekhovskoy, A. 2020, ARA&A, 58, 407 [NASA ADS] [CrossRef] [Google Scholar]
  11. Del Santo, M., Belloni, T. M., Tomsick, J. A., et al. 2016, MNRAS, 456, 3585 [NASA ADS] [CrossRef] [Google Scholar]
  12. Ding, G. Q., Chen, T. T., & Qu, J. L. 2021, MNRAS, 500, 772 [Google Scholar]
  13. Dunn, R. J. H., Fender, R. P., Körding, E. G., Belloni, T., & Merloni, A. 2011, MNRAS, 411, 337 [NASA ADS] [CrossRef] [Google Scholar]
  14. Evans, P. A., Beardmore, A. P., Page, K. L., et al. 2007, A&A, 469, 379 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  15. Evans, P. A., Beardmore, A. P., Page, K. L., et al. 2009, MNRAS, 397, 1177 [Google Scholar]
  16. Filippenko, A. V., & Chornock, R. 2001, IAU Circ., 7644, 2 [NASA ADS] [Google Scholar]
  17. Fürst, F., Nowak, M., Tomsick, J., et al. 2015, ApJ, 808, 122 [CrossRef] [Google Scholar]
  18. Garcia, F. et al. 2021, MNRAS, 501, 3173 [NASA ADS] [CrossRef] [Google Scholar]
  19. Giacche, S., Gili, R., & Titarchuk, L. 2014, A&A, 562, A44 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  20. Greene, J., Bailyn, C. D., & Orosz, J. A. 2001, ApJ, 554, 1290 [NASA ADS] [CrossRef] [Google Scholar]
  21. Herrero, J., et al. 1995, A&A, 297, 556 [NASA ADS] [Google Scholar]
  22. HI4PI Collaboration (Ben Bekhti, N., et al.) 2016, A&A, 594, A116 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Hjellming, R. M., & Rupen, M. P. 1995, Nature, 375, 464 [NASA ADS] [CrossRef] [Google Scholar]
  24. Homan, J., & Belloni, T. 2005, Ap&SS, 300, 107 [Google Scholar]
  25. Homan, J., Wijnands, R., Kong, A., et al. 2006, MNRAS, 366, 235 [NASA ADS] [Google Scholar]
  26. Hynes, R. I., Steeghs, D., Casares, J., Charles, P. A., & O’Brien, K. 2004, ApJ, 609, 317 [Google Scholar]
  27. Jana, A., Debnath, D., Chatterjee, D., et al. 2020, ApJ, 897, 3 [Google Scholar]
  28. Kennea, J. A., & Negoro, H. 2019, ATel, 12434, 1 [NASA ADS] [Google Scholar]
  29. Lamer, G., Schwope, A. D., Predehl, P., et al. 2021, A&A, 647, A7 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  30. Laurent, P., & Titarchuk, L. 1999, ApJ, 511, 289 [NASA ADS] [CrossRef] [Google Scholar]
  31. Laurent, P., & Titarchuk, L. 2011, ApJ, 727, L34 [NASA ADS] [CrossRef] [Google Scholar]
  32. Long, X., Feng, H., Li, H., et al. 2022, ApJ, 924, L13 [NASA ADS] [CrossRef] [Google Scholar]
  33. Maccarone, T. J. 2003, A&A, 409, 697 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  34. McClintock, J., & Remillard, R. 2006, Black Hole Binaries, 157 [Google Scholar]
  35. Miller-Jones, J. C. A., Bahramian, A., Orosz, J. A., et al. 2021, Science, 371, 1045 [Google Scholar]
  36. Munoz-Darias, T., Casares, J., & Martinez-Pais, I. G. 2008, MNRAS, 385, 2205 [NASA ADS] [CrossRef] [Google Scholar]
  37. Ninkov, Z., Walker, G. A. H., & Yang, S. 1987, ApJ, 321, 425 [NASA ADS] [CrossRef] [Google Scholar]
  38. Nowak, M. A. 1995, PASP, 107, 1207 [Google Scholar]
  39. Orosz, J. A., McClintock, J. E., Aufdenberg, J. P., et al. 2002, ApJ, 568, 84 [Google Scholar]
  40. Park, S. Q., Miller, J. M., McClintock, J. E., et al. 2004, ApJ, 610, 378 [NASA ADS] [CrossRef] [Google Scholar]
  41. Petri, J. 2008, Ap&SS, 318, 181 [NASA ADS] [CrossRef] [Google Scholar]
  42. Russell, D. M., Baglio, C. M., & Lewis, F. 2019, ATel, 12439, 1 [NASA ADS] [Google Scholar]
  43. Sanchez-Fernandez, C., Castro-Tirado, A. J., Duerbeck, H. W., et al. 1999, A&A, 348, L9 [NASA ADS] [Google Scholar]
  44. Seifina, E., & Titarchuk, L. 2010, ApJ, 722, 586 [NASA ADS] [CrossRef] [Google Scholar]
  45. Seifina, E., & Titarchuk, L. 2011, ApJ, 737, 128 [NASA ADS] [CrossRef] [Google Scholar]
  46. Seifina, E., Titarchuk, L., & Shaposhnikov, N. 2014, ApJ, 789, 57 [NASA ADS] [CrossRef] [Google Scholar]
  47. Seifina, E., Titarchuk, L., & Shaposhnikov, N. 2016, ApJ, 821, 23 [NASA ADS] [CrossRef] [Google Scholar]
  48. Seifina, E., Titarchuk, L., & Virgilli, E. 2017, A&A, 607, A38 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  49. Seifina, E., Titarchuk, L., & Ugolkova, L. 2018a, A&A, 619, A217 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  50. Seifina, E., Chekhtman, A., & Titarchuk, L. 2018b, A&A, 613, A48 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  51. Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337 [NASA ADS] [Google Scholar]
  52. Shaposhnikov, N., & Titarchuk, L. 2007, ApJ, 663, 449 [Google Scholar]
  53. Shaposhnikov, N., & Titarchuk, L. 2009, ApJ, 699, 453 [NASA ADS] [CrossRef] [Google Scholar]
  54. Shaposhnikov, N., Swank, J., Shrader, C. R., et al. 2007, ApJ, 655, 434 [NASA ADS] [CrossRef] [Google Scholar]
  55. Shrader, C., & Titarchuk, L. G. 1999, ApJ, 521, L121 [NASA ADS] [CrossRef] [Google Scholar]
  56. Shrader, C., & Titarchuk, L. G. 2003, ApJ, 598, 168 [NASA ADS] [CrossRef] [Google Scholar]
  57. Sobczak, G. J., McClintock, J. E., Remillard, R. A., & Bailyn, C. D. 1999, ApJ, 520, 776 [NASA ADS] [CrossRef] [Google Scholar]
  58. Sobolewska, M. A., & Papadakis, I. E. 2009, MNRAS, 399, 1997 [Google Scholar]
  59. Stiele, H., & Kong, A. K. H. 2016, MNRAS, 459, 4038 [NASA ADS] [CrossRef] [Google Scholar]
  60. Stiele, H., Belloni, T. M., Kalemci, E., & Motta, S. 2013, MNRAS, 429, 2655 [NASA ADS] [CrossRef] [Google Scholar]
  61. Sturner, S. J., & Shrader, C. R. 2005, ApJ, 625, 923 [NASA ADS] [CrossRef] [Google Scholar]
  62. Sunyaev, R. A., & Titarchuk, L. G. 1980, A&A, 86, 121 [NASA ADS] [Google Scholar]
  63. Titarchuk, L., & Seifina, E. 2009, ApJ, 701, 1463 [NASA ADS] [CrossRef] [Google Scholar]
  64. Titarchuk, L., & Seifina, E. 2016, A&A, 585, A94 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  65. Titarchuk, L., & Seifina, E. 2017, A&A, 602, 113 [Google Scholar]
  66. Titarchuk, L., & Seifina, E. 2021, MNRAS, 501, 5659 [NASA ADS] [Google Scholar]
  67. Titarchuk, L. G., & Fiorito, R. 2004, ApJ, 612, 988 [NASA ADS] [CrossRef] [Google Scholar]
  68. Titarchuk, L. G., Mastichiadis, A., & Kylafis, N. D. 1997, ApJ, 487, 834 [NASA ADS] [CrossRef] [Google Scholar]
  69. Titarchuk, L. G., Lapidus, I., & Muslimov, A. 1998, ApJ, 499, 315 [NASA ADS] [CrossRef] [Google Scholar]
  70. Titarchuk, L. G., Shaposhnikov, N., & Seifina, E. 2010, AIP Conf. Proc., 1205, 168 [NASA ADS] [CrossRef] [Google Scholar]
  71. Titarchuk, L. G., Seifina, E., & Shrader, Ch. 2014, ApJ, 789, 98 [NASA ADS] [CrossRef] [Google Scholar]
  72. Tominaga, M., Nakahira, S., Shidatsu, M., et al. 2020, ApJ, 899, L20 [Google Scholar]
  73. Vahdat Motlagh, A., Kalemci, E., & Maccarone, T. J. 2019, MNRAS, 485, 2744 [Google Scholar]
  74. Vaughan, S., Goad, M. R., Beardmore, A. P., et al. 2006, ApJ, 638, 920 [NASA ADS] [CrossRef] [Google Scholar]
  75. Wilms, J., Allen, A., & McCray, R. 2000, ApJ, 542, 914 [Google Scholar]
  76. Yatabe, F., Negoro, H., Nakajima, M., et al. 2019, ATel, 12425, 1 [NASA ADS] [Google Scholar]
  77. Zhang, L., Chen, L., Qu, J.-L., Bu, Q.-C., & Zhang, W. 2015, ApJ, 813, 90 [NASA ADS] [CrossRef] [Google Scholar]
  78. Zhang, L., Altamirano, D., Cúneo, V. A., et al. 2020, MNRAS, 499, 851 [NASA ADS] [CrossRef] [Google Scholar]
  79. Zhang, W., Tao, L., Soria, R., et al. 2022, ApJ, 927, 210 [NASA ADS] [CrossRef] [Google Scholar]

Appendix A: Additional table

Table A.1.

Best-fit parameters† of the MAXI J1348–630 spectra during 2019 outburst events observed by Swift.

All Tables

Table 1.

Previous BH mass estimates in MAXI J1348–630.

In the text
Table 2.

List of Swift observations of MAXI J1348–30 used in our analysis.

In the text
Table 3.

BH masses and distances.

In the text
Table 4.

Parameterizations of scaling patterns for reference and target sources.

In the text
Table A.1.

Best-fit parameters† of the MAXI J1348–630 spectra during 2019 outburst events observed by Swift.

In the text

All Figures

thumbnail Fig. 1.

BH mass from the scaling method (using saturation of the photon index with the mass accretion rate), Mscal, compared to the corresponding dynamical masses Mdyn for stellar mass BHs. Data are taken from ST09, Shrader & Titarchuk (2003), Shaposhnikov & Titarchuk (2007), Seifina & Titarchuk (2010; for Mscal values), and Greene et al. (2001), Hjellming & Rupen (1995), Herrero (1995), Ninkov et al. (1987), Munoz-Darias et al. (2008), Hynes et al. (2004), Park et al. (2004), Orosz et al. (2002), Sanchez-Fernandez et al. (1999), Sobczak et al. (1999), Petri (2008), Homan et al. (2006), Filippenko & Chornock (2001), Miller-Jones et al. (2021; for Mdyn values). The yellow strip indicates a BH mass spread of 1.3 M⊙. The deviation from the yellow strip for Cyg X–1 reflects new estimates of the BH mass (marked with an pink arrow), taking into account the strong wind in this binary and possibly associated with the refinement of the source distance (from 2.5 to 2.2 kpc) from the radio data – due to which the BH mass estimate increased in Cyg X–1 from 6.8–13.3 M⊙ to 21 M⊙ (Miller-Jones et al. 2021).
In the text
thumbnail Fig. 2.

Swift/XRT (0.3–10 keV) image of MAXI J1348–30 accumulated from January 26, 2019 to October 17, 2020 with an exposure of 52 ks.
In the text
thumbnail Fig. 3.

Evolution of Swift/XRT (0.3–10 keV, top panel) and MAXI/GSC flux (bottom panel) in 2–20 keV, 2–4 keV, 4–10 keV and 10–20 keV energy ranges during 58450–58800 MJD observations of MAXI J1348–630. Vertical bright blue, hazel, and white strips indicates the LHS, IS and HSS spectral states, correspondingly (for identification of spectral states see Sect. 3.1). Pink arrow (at top of the panel) indicate the time interval under our study (from January to September, 2019) for data sets listed in Table 2.
In the text
thumbnail Fig. 4.

Evolution of MAXI J1348–630 spectra, fitted using the tbabs*(bmc+gauss) model for three spectral states. Data are taken from the Swift/XRT observations: 00088843001 (MJD = 58515.75, left), 00011107003 (MJD = 58519, center), and 00011107007 (MJD = 58524, right). Data are shown as black crosses and the spectral model components are displayed as dashed green and blue lines for the BMC and gaussian components, respectively. The resulting spectrum as a sum of these components are presented by red line. In the bottom panels, we show the corresponding Δχ vs. photon energy (in keV).
In the text
thumbnail Fig. 5.

Six representative EFE spectral diagrams during different spectral states of MAXI J1348–30. Left panel: data taken from Swift/XRT observations 0008884300 (bright blue, LHS), 0088496000 (red, LHS), and 0088596000 (pink, LHS). Right panel: data taken for 00011107003 (black, IS), 0088826000 (orange, IS), and 00011107007 (blue, HSS).
In the text
thumbnail Fig. 6.

Temporal evolution of the Swift/XTE count rate (pink) from the LHS to the HSS and back, shown from top to bottom. Comptonized fraction f (blue), seed photon temperature Ts (black), Nbmc (green) and Γ (red) during the MJD = 58509–58734 outburst transition set. We note that the Comptonized fraction f = A/(A + 1) characterizes the fraction of the soft photons illuminating the Compton cloud (CC), and subsequently up-scattered in the CC hot plasma. Vertical bright blue, hazel and white strips indicates the LHS, IS, and HSS spectral states, correspondingly (as in Fig. 3).
In the text
thumbnail Fig. 7.

Photon index, Γ, vs. the QPO frequency, νL, for MAXI J1348–630 (target source) and XTE J1550–564 (reference source). We use a specific function f(ν), detailed in Eq. (3) of Sect. 3.2.1, to fit the data, which gives us the corresponding solid lines. We can see that Γ is correlated with νL and saturated for νL > 6.8 Hz and νL > 10 Hz for MAXI J1348–630 and XTE J1550–564, respectively. Data for XTE J1550–564 were taken from ST09.
In the text
thumbnail Fig. 8.

Γ vs. Nbmc correlations those for MAXI J1348–630 (target source) and for a BH XTE J1550–564 (reference source). We use a specific function, F(N), (see Eq. (8)) to fit the data, which gives us the corresponding solid lines.
In the text

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