Probing the origin of the extended flaring branch of Z-type X-ray binaries GX 340+0 and GX 5-1 using AstroSat

ABSTRACT

‘Z’ type neutron star low-mass X-ray binaries typically show a ‘Z’-like three-branched track in their hardness intensity diagram. However, a few such ‘Z’ sources show an additional branch known as the extended flaring branch (EFB). EFB has been poorly studied, and its origin is not known. It is thought to be an extension of the flaring branch (FB) or associated with Fe K |$\alpha$| complex or an additional continuum due to the radiative recombination continuum (RRC) process. Using AstroSat observations, we have detected the EFB from two ‘Z’ sources, GX 340+0 and GX 5–1, and performed a broad-band spectral analysis in the 0.5–22 keV energy range. During EFB, both sources show the presence of a significant RRC component with absorption edges at |$7.91^{+0.16}_{-0.15}$| and |$8.10^{+0.16}_{-0.17}$| keV, respectively along with blackbody radiation and thermal Comptonization. No signature of RRC was detected during the FB, which is adjoint to the EFB. No Fe K |$\alpha$| complex is detected. Interestingly, inside EFB dips of GX 5-1, for the first time, we have detected flaring events of 30–60 s, which can be modelled with a single blackbody radiation. During the FB to EFB transition, an increase in the blackbody radius by a factor of 1.5–2 is observed in both sources. Our analysis strongly suggests that EFB is not an extension of FB or caused by the Fe K |$\alpha$| complex. Rather, it is caused by a sudden expansion of the hot, thermalized boundary layer and subsequent rapid cooling.

1 INTRODUCTION

Based on the behaviour in the hardness intensity diagram (HID), an accreting neutron star X-ray binary (NSXB) source can be classified into two classes: ‘Z’-type and atoll source (Hasinger & van der Klis 1989). Such a distinction was primarily attributed to the different mass-accretion rates and spectroscopic evolution in the two different systems. There are mainly three spectral branches that we see in the HID of the Z-type sources: horizontal branch (HB), normal branch (NB), and flaring branch (FB) (Hasinger & van der Klis 1989). The sources are observed to spend an arbitrary duration of time at a particular branch but show a continuity while evolving along the Z-track (without jumping across different branches; Bhargava et al. 2023; Pahari et al. 2024). The transition between the different branches, especially from HB to NB, is widely believed to be due to the radio jets and outflows (Migliari & Fender 2006). There is no clear consensus on which physical model describes the spectral evolution of different branches. But spectral evolution is usually described as a combination of soft thermal emission from the accretion disc, a blackbody emitting component known as the boundary layer and a hard, non-thermal Compton component (Homan et al. 2010; Bhargava et al. 2023).

In ‘Z’ sources, very seldom, a fourth branch, known as the extended flaring branch (EFB) (Church et al. 2010; Gibiec, Balucinska-Church & Church 2011), is observed at the end of the FB. Despite a few efforts, the origin of such a branch is still unclear. Hasinger et al. (1990) conducted a comprehensive study of Cyg X-2 across multiple wavelengths using Ginga. They observed intensity decreases on the FB, which were interpreted as absorption dips. Kuulkers & van der Klis (1995) proposed that in Cyg X-2 and GX 340+0, the FB in colour–colour representations correlates with X-ray dipping, contrasting to the behaviour observed in Sco-like sources where the FB corresponds to significant increases in intensity during flaring episodes. They suggested that Cyg-like sources have higher inclination angles compared to Sco-like sources, proposing a model to explain the differences between the two involving absorption or scattering within the inner disc. However, reliable spectral fitting of the EFB was lacking in establishing its nature definitively. Using RXTE observations, EFB has been reported from GX 340+0 (Penninx et al. 1991) and GX 5-1 (Jonker et al. 2000). Both sources have been chosen here to study the origin of EFB using AstroSat broad-band spectral analysis. GX 340+0, a luminous, low mass neutron star X-ray binary, traces a ‘Z’ shaped track in HID (Hasinger & van der Klis 1989). Previously, Bhargava et al. (2023) have thoroughly performed HB and NB branch-resolved spectral analysis of GX 340+0 using AstroSat in 0.8–25 keV. They have found that HB, NB, and hard apex can be modelled by the emission from the neutron star surface, accretion disc, and compromising corona covering the inner disc/boundary layer. With the launch of the Imaging X-ray Polarimetry Explorer (IXPE), there has been significant improvement achieved in understanding X-ray emission geometry of Z-type NSXBs using spectropolarization measurements (Cocchi et al. 2023; Bhargava et al. 2024a; Fabiani et al. 2024; La Monaca et al. 2024; Soffitta 2024; Yu et al. 2024). Among them, Fabiani et al. (2024) discovered variable polarization in GX 5-1: 3.7|$\pm$|0.4 per cent in HB while 1.8|$\pm$|0.4 per cent during NB/FB using a multiwavelength campaign. Similarly, Bhargava et al. (2024a) has discovered significant X-ray polarization (4.02 |$\pm$| 0.35 per cent) in the HB of GX 340+0 while a weaker polarization of 1.22 |$\pm$| 0.25 per cent is detected during NB in GX 340+0 (Bhargava et al. 2024b).

Discovered in 1968, GX 5-1 is the second brightest LMXB (after Sco X-1) (Fisher et al. 1968). Using Ginga observations, the source is classified as the ‘Z’ source by Hasinger & van der Klis (1989). In the analysis of Exosat and Ginga data, the flaring branch was discovered for the first time by Kuulkers et al. (1994). The first EFB was observed in the source by Church et al. (2010) using the data from RXTE satellite. The branch-resolved timing analysis of GX 5-1 was carried out using AstroSat observations (Bhulla et al. 2019). Using RXTE data Church et al. (2010) found that the EFB is an extension of the flaring branch, which maintains similar characteristics as per EFB. The mass accretion rate continues to fall, and unstable nuclear burning continues. During EFB, Church et al. (2010) detected strong emission lines at energies between 7.8 and 9.4 keV, suggesting radiative recombination continuum (RRC) of Fe xxvi at 9.28 keV and of lower energy states. During RRC, the photon emitted during the recombination of an electron and an ion has the same energy as the kinetic energy of the electron. Therefore, the emitted spectrum is a continuum in nature with a sharp edge at the binding energy level (Tucker & Gould 1966). The detection of RRC in X-ray spectra has been reported few times in other sources, e.g. using Suzaku observations, Ozawa et al. (2009) detected a line-like excess around Fe Ly |$\alpha$| and saw-edge-shaped bump around 8 keV from the Galactic supernova remnant (SNR) W49B while Yamaguchi et al. (2009) observed the same from another SNR IC 443. The detection from both SNRs is highly suggestive of an overionized plasma with a large fraction of H-like ions. By analysing XMM–Newton/EPIC spectra using redge model Sugawara, Tsuboi & Maeda (2008) detected RRC structure around 0.49 keV from the Wolf–Rayet binary |$\theta$| Muscae. Using X-ray spectral analysis of SNR ejecta Greco et al. (2020) observed that the RRC component appeared when the plasma was made of pure metal ejecta. Although X-ray spectral features observed during EFB of Z-type NSXBs are similar to what is predicted by RRC, the origin is unclear. Investigating the nature of EFB in Cygnus X 2, Gibiec et al. (2011) found that the extended flaring branch is not the continuation of the flaring branch; rather, it is due to the absorption of the flaring branch due to the outer layer of the accretion disc. Therefore, the origin of EFB remains unclear. To shed further light on such an unsettled issue, we have thoroughly analysed the extended flaring branch of the two Cyg-like sources, GX 5-1 and GX 340+0, using the simultaneous LAXPC and SXT observations on-board AstroSat using broad-band energy range of 0.3–30.0 keV. We have separately analysed spectra exclusive to FB and EFB and have compared their properties. Interestingly, we have detected flaring events within EFB, which can be described by a single blackbody emission with a blackbody emission significantly higher than that observed during FB. We observed that the EFB is not a continuation of the flaring branch but rather due to the new spectral component known as RRC. Such a component is different than Fe K |$\alpha$| complex and absent in FB.

The observation and data reduction for LAXPC and SXT are provided in Sections 2.1 and 2.2, respectively, while the analysis procedures for GX 5-1 and GX 340+0 are detailed in Sections 3.1 and 3.2, respectively. Results of our analysis during FB, EFB, and flaring within EFB for GX 5-1 are discussed in Section 4.1 while the FB and EFB results for GX 340+0 are provided in Section 4.2. Detection significance testing of the new spectral component over continuum is presented in Section 5. We have discussed the implications of our results in Section 6.

2 OBSERVATION AND DATA REDUCTION

The data has been obtained through India’s broad-band X-ray observatory, AstroSat (Singh et al. 2014), using simultaneous observations from both large area X-ray proportional counter (LAXPC) and soft X-ray telescope (SXT) instruments. LAXPC and SXT observation details of GX 340+0 and GX 5-1 are provided in Table 1.

2.1 LAXPC

LAXPC (Yadav et al. 2016; Antia et al. 2017) consists of three independent but identical detectors, giving a collecting area of |$\sim$|6000 cm² at 15 keV. Its operational energy range is 3–80 keV. The LAXPC data has been reduced using laxpcsoft v21june2023 with suitable response files for corresponding LAXPC units. Cleaned event files and good time intervals (GTIs) for each satellite orbit have been created using LAXPC10 and LAXPC20 units. Due to poor data quality and calibration issues, data from LAXPC30 is excluded from all further analyses. GTIs have been cleaned further to remove segments with poor data quality caused by telemetry losses or other factors like the initial and the final 100s transition in and out to the South Atlantic Anomaly (SAA) region, respectively. Such a screening accounts for nearly 5 per cent of total effective exposure. Light curves in 6–10, 10–20, and 6–20 keV energy bands are extracted using the cleaned GTIs, and hardness intensity diagrams are computed for both sources GX 5-1 and GX 340+0.

2.2 SXT

SXT onboard AstroSat is a focusing X-ray telescope utilizing a charge-coupled device capable of X-ray imaging in the energy range of 0.3–7.0 keV with medium resolution (Singh et al. 2017). For both sources, we have used data from orbits similar to LAXPC. SXT data has been reduced using SXTPIPELINE v1.5b,¹ and xselect v2.4g. We have used an annular region in the image for spectral extraction to avoid the pileup issue. The annular region consists of two concentric circles with radii of 5 and 15 arcmin, respectively. Using LAXPC GTI files, which correspond to FB and EFB, spectra and light curves have been extracted for both sources during FB and EFB. Orbit-specific arf files are generated using sxt_ARFModule_v02 tool for spectral fitting.

3 DATA ANALYSIS

3.1 GX 5-1

To identify the FB and EFB, we have used data from all orbits (2318–2344) for the observation ID T01_056T01_9000000356. Using the standard LAXPC analysis procedure, we have extracted the background-subtracted light curve in 6–20 keV, combining LAXPC10 and LAXPC20. HID is computed using all orbit data where hardness is defined as the ratio of the count rate in the energy range 10–20 to 6–10 keV, and intensity is defined as the count rate in 6–20 keV. HID and light curves are shown in Fig. 1. Different branches like NB, FB, and EFB are visible. Since this study focuses on FB and EFB, they are marked by pluses and circles in both HID and light curves. The EFB branch is similar and parallel to the NB, but it has a lower hardness.

For further studies, we have extracted the spectra of FB and EFB from GX 5-1 using LAXPC20 for the energy range 3–22 keV. Due to instrument gain instability and poor channel-to-energy calibration, LAXPC10 spectrum is excluded from further analysis. To match the energy resolution of LAXPC20 (approximately 15 per cent), we used optimal settings to have three energy bins per resolution or at a 5 per cent level. Background spectra are extracted using the GTI, the same as the source spectrum. Suitable response files are used for spectral fitting. SXT spectra simultaneous to LAXPC20 were extracted in the energy range 0.3–7 keV. SXT spectra are binned such that each bin has a minimum of 30 counts. SXT and LAXPC20 spectra of FB and EFB are jointly fitted with a suitable model using XSpec version 12.14.0h (Arnaud 1996).

3.2 GX 340+0

To identify different branches from GX 340+0, we have used data on 2016 March 4 from all AstroSat orbits (9939–9959) of the observation ID G07_016T01_9000001420. We have extracted the spectrum of the FB and EFB using appropriate GTI for the LAXPC20 unit in the energy range of 3–22 keV. Similar to GX 5-1 analysis, spectra are grouped into three energy bins per resolution. Similar to GX 5-1, SXT spectra are extracted and fitted jointly with LAXPC20 using similar models in XSpec v 12.14.0h (Arnaud 1996).

4 RESULTS

4.1 GX 5-1

We have considered AstroSat/LAXPC and AstroSat/SXT data from the observation epoch between 2016 March 3–4. In the left panel of Fig. 1, we have shown the 6–20 keV light curve of GX 5-1 using LAXPC observations spanning over |$\sim$|46 ks, while in the right panel, we have shown the HID of the same span of the light curve. NB, FB, and EFB are clearly detected in the HID. In both panels, the positions of FB and EFB are shown in black crosses and red circles, respectively. As we wish to understand the origin of EFB and its connection to FB, we have shown the zoomed-in portion of the light curve and HID, which is part of FB and EFB in the top left and top right panels of Fig. 2. The hardness as a function of time is shown in the bottom left panel of Fig. 2. A symbol convention similar to Fig. 1 is used. During EFB, the hardness ratio drops significantly by a factor of |$\sim$|1.5. The bottom right panel of Fig. 2 shows the simultaneous SXT light curve in 0.3–7 keV with the bin size of 7s. Due to the lower observational efficiency compared to LAXPC, only one dip is observed. Following the colour and symbol convention similar to LAXPC, the FB and EFB sections are shown in the SXT light curve.

4.1.1 FB spectral analysis

We have carried out the spectral analysis of FB using joint and simultaneous observations of SXT and LAXPC in the energy range 0.5–7.0 and 3.0–22.0 keV, respectively. Motivated by earlier works, we have fitted joint spectra using a combination of blackbody radiation (bbodyrad in XSpec), thermal Comptonized emission from the boundary layer (nthcomp in XSpec) modified by the absorption (TBabs) (ModelA). Such a choice of model components is similar to that used by Church et al. (2010) while analysing rXTE spectra of GX 5-1 during FB and EFB branches. We have obtained the |$\chi ^2/$|dof|$=135/123$| (1.09). However, the photon index of the (nthcomp in XSpec) is unusually high (⁠|$\sim$|5.3), which cannot be explained. A very high photon index may indicate the presence of another missing blackbody-like component. For further justification, we replaced the bbodyrad model with diskbb and kept other model components the same. With the combination of TBabs*(diskbb+nthcomp), we obtained the |$\chi ^2/$|dof |$=137/123$| (1.11) with the disc blackbody normalization of 52|$^{+4}_{-6}$|⁠. Such a normalization implies an unusually low inner disc radius of 7.7|$\pm$|0.7 km, which is less than the typical neutron star radius of 10 km, assuming the disc inclination angle of 45|$^{\circ }$| and the upper limit of the distance to the source of 9 kpc (Christian & Swank 1997). To address the issue further, we replaced the earlier model with another model combining bbodyrad and diskbb models together with nthcomp. Using a combination of TBabs*(bbodyrad+diskbb+nthcomp) (ModelB), we have obtained an acceptable fit with |$\chi ^2$|/dof = 118/121 (0.97). From the best-fitting spectral parameters, the 1|$\sigma$| upper limit of the power-law index is found to be 2.36, while the disc blackbody normalization is 464|$^{+187}_{-141}$|⁠. Therefore, TBabs*(bbodyrad+diskbb+nthcomp) (ModelB) is considered the best-fitting model for broad-band FB spectral analysis in GX 5-1. Best-fitting parameters for Models A and B for FB spectral analysis are provided in Table 2 along with fluxes and reduced |$\chi ^2$| values. Best-fitting spectra for ModelA and ModelB are shown in the left and right panels of Fig. 3 respectively.

4.1.2 EFB spectral analysis

We have adopted a similar strategy for fitting the EFB spectra in GX 5-1. First, we used ModelA for the EFB spectral analysis. With a combination of TBabs*(bbodyrad + nthcomp), we see a strong residual around 8–11 keV. We have replaced the bbodyrad of ModelA with diskbb and also independently used ModelB to fit the spectra. In all three cases, the residual near 8–11 keV persists. The |$\ chi^2$|/dof values for ModelA and ModelB are 115/86 (1.33) and 112/84 (1.32), respectively. Therefore, Models A and B fail to describe the feature near 8–11 keV. For example, EFB spectra fitted with ModelB are shown in the left panel of Fig. 4 along with the residuals. Hence, the best-fitting model which can adequately describe the FB spectra cannot be used for modelling EFB spectra.

The fitting statistics can be improved significantly by adding a model that describes emission and absorption features near 8–11 keV caused by radiative recombination continuum (redge model in XSpec). When combined with ModelA, the best-fitting model for EFB is TBabs*(bbodyrad + nthcomp + redge) (ModelC). Without (ModelA) and with (ModelC), the RRC model component, the best-fitting |$\chi ^2$|/dof are found to be 115/86 (1.34) and 86/83 (1.04), respectively. An F-test between these two models yields an F statistic value = 9.32 and an F-test probability of 2.21|$\times 10^{-5}$|⁠. Therefore, our spectral analysis strongly suggests the presence of RRC during the EFB in GX 5-1. In Table 3, we have provided the best-fitting spectral parameters using models B, A, and C, respectively.

By comparing the best-fitting parameters for FB (ModelB in Table 2) and EFB (ModelC in Table 3) spectral fitting, we can see an important change: a significant increase (⁠|$\sim$|4 times) in the blackbody normalization from 111|$^{+18}_{-13}$| to 452|$^{+10}_{-13}$| is noted during the transition from FB to EFB. Assuming the distance to the source 9 kpc (Christian & Swank 1997), the blackbody emitting area is observed to increase from 90.3|$^{+1.9}_{-1.7}$| to 361|$^{+14}_{-11}$| km|$^2$| during the transition from FB to EFB in GX 5-1.

4.1.3 Flaring within EFB

A close look at the EFB dips in the top left panel of Fig. 2 reveals that nearly all dips consist of a sharp flaring activity which lasts from a few seconds to a few tens of seconds. The left panel of Fig. 5 shows the zoomed-in EFB where flares within EFB dips are clearly visible. We have created a GTI file with all flare intervals shown by stars in the top left panel of Fig. 5. Flare interval is defined in the time range of |$\pm$|10 s around flare peak time. These criteria ensure the exclusive selection of active flaring regions with good data statistics. The position of flares is shown in the HID of FB and EFB in the top right panel of Fig. 5. Using the selected GTI, we have extracted LAXPC20 source and background spectra in 3–15 keV and have used them for further analyses. We found that background-subtracted spectrum can be fitted by a single blackbody radiation model bbodyrad modified by absorption with the best-fitting |$\chi ^2$|/dof = 15/16. The absorption is kept fixed at 1.96 × 10²² cm⁻², which is the best-fitting value obtained from joint SXT and LAXPC spectral modelling provided in Table 3. The best-fitting blackbody temperature and normalization are found to be 1.31|$^{+0.03}_{-0.02}$| keV and 538|$^{+13}_{-12}$| respectively. Interestingly, the blackbody emitting area is larger by a factor of |$\sim$|2.5 compared to that observed during FB. Therefore, such a rapid expansion of the blackbody emitting region occurs in a time-scale of a few tens of seconds, which is interesting. A similar rapid expansion of blackbody radius has been observed from the time-resolved spectral analysis of type-I X-ray bursts from neutron star surfaces of different NSXBs (Kuulkers et al. 2003; Galloway et al. 2008; Beri et al. 2019). Short bursts, of the order of 30–50 s, are explained in terms of either a pause in nuclear chain reaction (Fisker, Thielemann & Wiescher 2004) or by convective transportation of leftover material to the ignition depth from the previous burst (Keek & Heger 2017). However, we may observe that the profile of type-I burst and the EFB flare are different: type-I bursts have a sharp rise (⁠|$\le$| 2 s) and exponential fall (10 s or more) (Galloway et al. 2008) while EFB flares are more symmetric with the rise and fall time around 20–30 s. Therefore, it is unclear whether type-I X-ray bursts and observed EFB flares have the same origin, which is subject to further investigation and out of the scope of this work. We have extracted 0.1–1000 Hz power density spectra during burst intervals in the energy range of 3–80.0 keV. No high-frequency burst oscillations have been detected with the 0.1–1000.0 Hz integrated fractional rms upper limit of 4.47 per cent. For comparison, the best-fitting model parameter values for the FB, EFB, and flares are provided in Table 4, and best-fitting unfolded models are shown in the bottom right panel of Fig. 5. As the table suggests, the FB has a higher total flux than the EFB, while the flare within the EFB has the highest Bolometric flux. Moreover, a Comptonization tail is evident during EFB, which is absent from FB. Therefore, our spectral modelling of FB, EFB, and flare suggests that EFB is not an extension of FB. For FB, EFB, and flare, we have calculated |$L/L_{\rm Edd}$| using best-fitting flux in 0.01–100 keV (calculated using cflux model in XSpec) and assuming the neutron star mass of 1.7 |$\mbox{M}_\odot$| and a distance of 9 kpc (Christian & Swank 1997). The |$L/L_{\rm Edd}$| values are found to be 80|$^{+4}_{-5}$| per cent, 74|$^{+3}_{-3}$| per cent, and 96|$^{+6}_{-5}$| per cent during the FB, EFB, and flare, respectively. Assuming an upper and lower limit of the neutron star mass of 2.0|$\mbox{M}_\odot$| and 1.5|$\mbox{M}_\odot$| respectively, we have determined |$L/L_{\rm Edd}$| within the range of 66–98 per cent, 58–83 per cent, and 78–123 per cent for the EFB and flare, respectively.

4.2 GX 340+0

The spectral properties of HB and NB were studied in detail by Bhargava et al. (2023) using AstroSat/LAXPC and AstroSat/SXT, while the timing analysis was performed by Pahari et al. (2024). Here, we have used the AstroSat data from the epoch, the same as Pahari et al. (2024), since it shows the presence of EFB. The left panel of Fig. 6 shows the 6–20 keV light curve of the source using LAXPC observations, while the right panel shows the HID. In both panels, the positions of FB and EFB are shown in pluses and circles. The zoomed-in portion of the light curve and HID that belongs to FB and EFB are shown in the top left and top right panels of Fig. 7. The hardness as a function of time is shown in the bottom left panel of Fig. 7. During EFB, the hardness drops significantly. The bottom right panel of Fig. 7 shows the simultaneous SXT light curve in 0.3–8 keV with a bin size of 7 s. Following the colour and symbol convention similar to LAXPC analysis, the FB and EFB are shown in the SXT light curve.

4.2.1 FB and EFB spectral analysis

Following the strategy similar to GX 5-1, we have carried out the spectral analysis of FB and EFB in GX 340+0 separately using joint observation of SXT and LAXPC in the energy range (0.5–22 keV). The left panel of Fig. 8 shows the best-fitting spectra of FB along with the residual when the spectrum was fitted with ModelA: a combination of blackbody radiation (bbodyrad in XSpec), thermal Comptonized emission from the boundary layer (nthcomp in XSpec) modified by the absorption (TBabs). The fit returned an acceptable |$\chi ^2$|/dof = 217/170 (1.28). However, the fit returned an unusually high photon index of the thermal Comptonization model: 4.55|$^{+0.20}_{-0.18}$|⁠. The issue is similar to that observed during the FB spectral analysis of GX 5-1 and has not been resolved even with replacing bbodyrad with diskbb.

Therefore, we use ModelB: TBabs*(diskbb+bbodyrad+nthcomp) to fit the SXT+LAXPC joint spectra. There is a marginal improvement in model fitting with |$\chi ^2$|/dof = 199/168(1.18); moreover, the 1|$\sigma$| upper limit of the photon index is found to be 2.19. The electron temperature and disc blackbody model parameters are also constrained and within an acceptable range. Therefore, similar to GX 5-1, ModelB is found to be the best-fitting model for the broad-band spectral analysis of FB in GX 340+0. The best-fitting parameters of ModelA and ModelB are provided in Table 5.

We may note that using a combination of blackbody radiation bbodyrad and thermal Comptonization thcomp, Chattopadhyay et al. (2024) carried out the ‘Z’ track-resolved spectral analysis of GX 340+0 using SXT and LAXPC observations of GX 340+0. Spectral parameters corresponding to the FB branch are similar to what we obtained in this work.

A strategy similar to EFB spectral modelling of GX 5-1 has been adopted to fit the EFB spectra in GX 340+0. First, we have used ModelA and ModelB to fit EFB spectra from GX 340+0. Best-fitting spectral parameters are shown in Table 6. Fitting with ModelA and ModelB returned similar goodness of fit with |$\chi ^2$|/dof = 153/122 (1.25) and 149/120 (1.24), respectively. For either case, strong residuals have been observed around 8–11 keV in the left panel of Fig. 9. A significant improvement in the fit statistics has been observed when the RRC model component redge is added with ModelA and the spectra are fitted with ModelC: TBabs*(bbodyrad+nthcomp+redge). Due to the addition of redge to ModelA, |$\chi ^2$|/dof changes from 153/122 (1.25) to 123/119 (1.03). The RRC energy and electron temperature are kept free to vary. An F-test between these two models yields an F statistic value = 9.68 and an F-test probability of 9.18 |$\times$| 10|$^{-6}$|⁠. The best-fitting RRC energy and temperature are found to be 7.91|$^{+0.25}_{-0.22}$| and 1.25|$^{+0.45}_{-0.43}$| keV, respectively. Therefore, energy spectral analysis supports the presence of RRC during the EFB in GX 340+0. Table 6 provides the best-fitting spectral parameters with the RRC model component (ModelC). Two important changes have been noted when best-fitting FB and EFB parameters are compared from Tables 5 and 6: A significant increase in the blackbody normalization (indicating blackbody emitting area) from 173|$^{+36}_{-57}$| to 411|$^{+12}_{-11}$| during the transition from FB to EFB.

5 SIGNIFICANCE TESTING OF THE RRC COMPONENT

To assess the statistical significance of the presence of the RRC component during EFB in GX 5-1 and GX 340+0, we have used a statistical test based on Bayesian posterior predictive probability values following the prescription of Protassov et al. (2002). For this purpose, we have used ModelC, i.e. model with redge component and model without redge component, i.e. ModelA. Choices of ModelC and ModelA are appropriate because ModelC = ModelA + redge. For significance testing purposes, we have considered ModelA rather than ModelB since ModelB is the best-fitting model for FB spectral analysis only and not for EFB. Secondly, ModelB + redge (ModelD) significantly over-fit the EFB spectra, e.g. in the case of GX 340+0, best-fitting with ModelD yields a |$\chi ^2/\rm dof$| = 96/117 (0.82).

• For each source, 100 000 fake spectra (N) have been generated for each of the null models without the redge component [ModelA: tbabs*(bbodyrad + nthcomp)] and the alternative model that includes the redge component [ModelC: tbabs*(bbodyrad + nthcomp + redge)]. 100 000 fake spectra (using fakeit in XSpec) are generated using the best-fitting parameter values for the best-fitting ModelA and ModelC, considering their errors when applying counting statistics. Suitable background spectra and response files are used.

• For each of the two models, the F-test was carried out for all the 100 000 spectra, and the corresponding F-statistic was obtained.

• The posterior predictive p value has been obtained by setting the Boolean values in correspondence to the F-statistic value where the F-statistic values greater than the F-statistic computed from the original data set was assigned a value of 1 and the rest were 0. The mean of this Boolean array has been calculated to find the posterior predictive p-value. This is done for both models. The p-value is then converted to |$\sigma$| significance using the following method suggested by James (2006)

  $$\begin{eqnarray} \sigma =\Phi ^{-1}(1-p/2), \end{eqnarray}$$

  (1)

  where p denotes the p-value and |$\Phi ^{-1}$| is the inverse of the cumulative distribution function.

• If the posterior predictive p-value is very small (near 0), it indicates that the ModelA should be rejected in favour of the ModelC. Conversely, if the p-value is sufficiently high (close to 1), it suggests that the ModelC should be rejected and the ModelA can be valid.

In the case of GX 5-1, for ModelA, a p-value of 0.0039 is obtained. Similarly, for GX 340+0, for the ModelA, a p-value of 0.00088 clearly shows that the model without redge, i.e. ModelA, can be rejected for the EFB spectral analysis. Following equation (1), such p-values correspond to 2.7|$\sigma$| and 3.1|$\sigma$|⁠, respectively. Hence, statistical analysis shows that the modelling requires an additional redge component, and the residual around 8–9 keV is not due to a statistical fluctuation. Both panels of Fig. 10 show the probability density function for the F-statistic distribution of ModelC, i.e. the model with the redge component in GX 5-1 (left panel) and GX 340+0 (right panel) and the corresponding significances.

6 DISCUSSION AND CONCLUSION

In this work, we have revisited the origin of the extended flaring branch or EFB, an additional branch observed in the HID of a few ‘Z’ type NSXBs at the end of their flaring branch (FB). During the monitoring campaign with AstroSat, EFB has been observed from two ‘Z’ type NSXBs: GX 340+0 and GX 5-1. Here, we present the 0.5–22 keV broad-band spectral analysis of FB and EFB using joint observations from SXT and LAXPC onboard AstroSat. Broad-band spectra during FB can be well described by combining blackbody radiation from the NS surface and thermal Comptonization from the boundary layer. However, during EFB, a strong residual is observed between 8 and 11 keV, which requires an additional spectral component to describe satisfactorily: radiative recombination. The radiative recombination continuum consists of continuum emission caused by the expansion of boundary layers or unstable nuclear burning on the NS surface, along with strong absorption edges caused by adiabatic cooling. In a thermally hot plasma with low optical density and temperature (⁠|$\sim$|0.1 keV) and which is not in ionization equilibrium, the prominence or absence of RRC features depends on the plasmaś conditions. A plasma undergoing ionization (e.g. due to recent shock heating) will exhibit faint RRC emission because few highly ionized ions are available for recombination. Conversely, a hot plasma (⁠|$\sim$|2–3 keV) undergoing recombination (such as when rapidly cooled by expansion) will display robust RRC characteristics as most ions are in the process of recombining. Our results from the spectral analysis support the latter case.

Our light-curve analysis from both sources shows that within FB, EFB has originated, and it is similar to the absorption features/dips occurring within a time-scale of a few seconds to tens of seconds (see Figs 2, 5, and 7). Two possible origins of such dip-like features in the light curve could be (1) clumpy outflowing disc wind from the system causing ionized absorption-induced variability; similar absorption dips have been observed from XV 1323-619 (Bałucińska-Church et al. 1999), H 1743-322 (Miller et al. 2006), Cyg X-2 (Bałucińska-Church et al. 2011) or (2) sudden radiation pressure-driven expansion and rapid cooling of an emitting region close to the NS surface (Pike et al. 2021) or rapid collapse of corona/boundary layer due to cooling and bloated inner-disc due to enhanced accretion rate (Ballantyne 2023). Individual spectral analysis of FB and EFB suggests that there are no significant differences in the broad-band absorption properties of FB and EFB. The moderate absorption column density of |$\sim$|4-5 |$\times$| 10|$^{22}$| cm|$^{-2}$| is observed during both branches in GX 340+0 while the same in the range of |$\sim$|1.7–3 |$\times$| 10|$^{22}$| cm|$^{-2}$| is observed in both branches of GX 5-1. Such an analysis was not possible with earlier studies due to the absence of spectral information below 3 keV. Therefore, the hypothesis that sudden and significant changes in the local absorption cause the EFB dip can be ruled out. Moreover, comparing FB and EFB spectral fitting of Cyg X-2 observations using XMM–Newton grating spectra (Bałucińska-Church, Church & Gibiec 2012) shows that the occurrence of EFB neither explicitly depends on inclination-dependent absorption nor on the monotonous increase in mass accretion rate across all branches. Therefore, it is likely that the spectral components present during FB will be different than the spectral components present in the EFB.

Hence, our second hypothesis is that the presence of an additional physical process causing radiation-driven rapid expansion (since the L/L|$_{\rm Edd}$| can be 100 per cent or higher) and subsequent cooling may play an important role in explaining the occurrence of EFB. We found that the model describing the radiation recombination continuum (redge in XSpec) best describes the process causing residual in 8–11 keV in both sources. From the best-fitting spectral parameters shown in Tables 3 and 6, edge energies observed from both sources during EFB are 7.91|$^{+0.21}_{-0.15}$| and 8.11|$^{+0.17}_{-0.16}$| keV, respectively. Therefore, such line energies are consistent with the absorption edges due to Fe xvii, Fe xviii, Fe xix, and Fe xx. Using our spectral analysis, we have computed the blackbody radius (⁠|$R_{\rm bb}$|⁠), which is related to the bbodyrad model normalization (⁠|$N_{\rm bbodyrad}$|⁠) by: |$N_{\rm bbodyrad}$| = |$R_{\rm bb}^2$|/|$D_{10}^2$|⁠, where |$R_{\rm bb}$| is the blackbody radius in km, and |$D_{10}$| is the distance to the source in the unit of 10 kpc. Assuming the distance to GX 5-1 as 9 kpc (Christian & Swank 1997) and using best-fitting normalization from Tables 2 and 3, we have found that the blackbody radius increases from 9.5|$^{+0.8}_{-0.7}$| to 19|$^{+2}_{-1}$| km while transiting from FB to EFB in GX 5-1. Additionally, we have observed short time-scale flares within EFB of GX 5-1. Spectral analysis shows that the flare spectrum within the EFB can be fit with only blackbody emission (with the blackbody radius of 21|$^{+2}_{-1}$| km). On the other hand, EFB spectral fitting needs two more components than EFB flares. This shows that EFB-flare may be a separate Z-source spectral state, which was not reported earlier. During the flare and EFB, the radius of the blackbody emission increases nearly by a factor of 2 when compared to that of FB.

A similar change in the radius of the blackbody-emitting component is observed in GX 340+0. Assuming a distance of 11|$\pm$|3 kpc (Fender & Hendry 2000) and using best-fitting blackbody normalizations from ModelB in Table 5 and ModelC in Table 6, we found that the blackbody radius increases from 14|$^{+5}_{-6}$| to 23|$^{+6}_{-7}$| km while transiting from FB to EFB.

There could be one of the following two origins of the blackbody-emitting flare: (I) Thermonuclear burning on the neutron star, where the source of energy is nuclear fusion (Bildsten 2000; Bhattacharyya 2022), (II) The emission from the boundary layer (accreted material between the accretion disc and the neutron star), where the source of energy is the gravitational potential energy (Gilfanov & Sunyaev 2014). The first scenario is clearly not possible because, given that there is no burst observed in the FB and most of EFB, a nuclear burning would be a stable nuclear burning. In that case, there is no reason that the blackbody normalization (proportional to the blackbody emission area) would significantly increase during EFB when the luminosity decreases. Therefore, an increase in the boundary layer volume (and hence the emission area) may explain the observed EFB flare. During the flare, both the boundary layer volume and temperature increase compared to EFB (which explains the observed higher luminosity). This perhaps affects the Comptonization and RRC model components, making them undetectable in the spectrum. More high-resolution X-ray grating spectroscopic observations during EFB can provide more details of the geometry associated with the occurrence of the radiative recombination phenomenon and associated EFB. However, such an analysis is currently out of the scope of this work.

ACKNOWLEDGEMENTS

This work makes use of data from the AstroSat mission of the Indian Space Research Organisation (ISRO), archived at the Indian Space Science Data Centre (ISSDC). This work has been performed utilizing the calibration data bases and auxiliary analysis tools developed, maintained, and distributed by AstroSat/LAXPC teams with members from various institutions in India and abroad. This work has used data from the Soft X-ray Telescope (SXT), developed at TIFR, Mumbai, and the SXT POC at TIFR is thanked for verifying and releasing the data via the ISSDC data archive and providing the necessary software tools.

DATA AVAILABILITY

The AstroSat data used in this research are publicly available can be downloaded from https://astrobrowse.issdc.gov.in/astro archive using the observation IDs mentioned in Table 1.

Footnotes

REFERENCES