GX 3+1: THE STABILITY OF SPECTRAL INDEX AS A FUNCTION OF MASS ACCRETION RATE

Low-mass X-ray binaries (LMXBs) hosting a neutron star (NS) show a variety of spectral states and transitions between them. In this regard, the so-called atoll sources (see, e.g., Hasinger & van der Klis 1989; van der Klis 2005) are particularly interesting because they demonstrate a wide range of luminosities (most of them show from 0.01 to 0.5 of the Eddington limit L_Edd). It is worth noting that the name of atoll sources is associated with the shape traced in the color–color diagram (CD). This shape can be divided into two main regions, corresponding to two X-ray states of the source: the harder one is related to the island state (IS), and the softer one is related to the banana (B) state.

These spectra of NS sources can be described by blackbody (BB) components, with color temperatures kT_BB < 1 keV and kT_s > 1 keV that are presumably related to the accretion disk and NS surface, respectively. In addition, there is a thermal Comptonization component with electron temperature kT_e = 2.3–15 keV that is probably related to the transition layer (TL) located between the disk and NS (see Paizis et al. 2006; Farinelli & Titarchuk 2011; Seifina & Titarchuk 2011, hereafter FT11 and ST11, respectively). An analysis of X-ray power spectra of atoll sources indicates a tight relation between timing properties and the position on the CD, suggesting that the source timing and spectral properties are well determined by basic parameters such as mass accretion rate (see, e.g., Di Salvo et al. 2001).

GX 3+1 is one of the brightest atoll sources associated with a bulge component of our Galaxy. GX 3+1 along with GX 9+9, GX 9+1, and GX 13+1 form the subclass of persistently bright atoll sources, which are always in the banana state (see Hasinger & van der Klis 1989). In particular, two-branch structures have been observed in the CD and hardness-intensity diagram (HID) of GX 3+1 (Stella et al. 1985; Lewin et al. 1987; Schultz et al. 1989; Homan et al. 1998; Muno et al. 2002; Schnerr et al. 2003). Specifically, their tracks in the X-ray CD are long, diagonal, and slightly curved, while their fast timing properties are dominated only by a relatively weak (1%–4% rms) power-law-shaped noise component. These aforementioned atoll sources are intermediate in terms of luminosity that changes in the range 0.1–0.5 of L_Edd (see Christian & Swank 1997; Ford & van der Klis 2000).

In contrast to other atoll sources and Z sources, these bright atoll sources have so far not shown kHz quasi-periodic oscillations (QPOs) (see Wijnands et al. 1998; Strohmayer 1998; Homan et al. 1998; Oosterbroek et al. 2001; Schnerr et al. 2003), which can be attributed to the fact that these objects do not reach the left lower banana (LLB), where other atoll sources exhibit kHz QPOs (van der Klis 2000). For example, the weaker atoll sources, such as, e.g., 4U 1608-52, 4U 0614+09, or 4U 1728-34, show kHz QPOs in LLB.

X-ray data of GX 3+1 (4U 1744-26) obtained in broad energy ranges using BeppoSAX (0.1–200 keV) and Rossi X-Ray Timing Explorer (RXTE) (3–200 keV) offer a unique possibility to further investigate, in detail, the evolution of X-ray spectral properties during transition events. This bright atoll source shows long-term transitions from the fainter phase to its brighter phase in X-rays and vice versa when the corresponding luminosity changes, at least, by a factor of four, while on timescales of hours GX 3+1 demonstrates low flux variabilities as transitions between LB and upper banana (UB) states. Naturally one can pose a fair question: what is the physical mechanism responsible for the source emission during these luminosity changes and particularly how the spectral index changes during these transitions?

GX 3+1 was discovered during an Aerobee-rocket flight on 1964 June 16 (Bowyer et al. 1965). Subsequently, this source was observed many times during various observational campaigns. Detailed long-term monitoring observations of GX 3+1 were performed by the all-sky monitor (ASM) on GINGA (see Asai et al. 1993), EXOSAT (see Schultz et al. 1989), RXTE (see Bradt et al. 1993; Kuulkers & van der Klis 2000), Wide-Field Camera (WFC) of BeppoSAX (see den Hartog et al. 2003), and INTEGRAL (see Paizis et al. 2006). In particular, den Hartog et al. (2003) found three types of variability: short-term variation (of order of seconds), mild variability on a daily (hourly) timescale, and slow sinusoidal-like variation on a timescale of years. However, it is surprising that the hardness ratio, which can be a measure of the spectral shape, stays almost constant during these observations.

Although an optical counterpart has not yet been identified (e.g., Naylor et al. 1991), GX 3+1 is presumably a low-mass X-ray binary in which a NS is accompanied by a low-mass star of spectral type A or a later. During an active stage, the companion overflows its Roche lobe and transfers matter onto the NS via an accretion disk. This process is possibly accompanied by nuclear burning of a helium or hydrogen layer of the NS surface as a result of the matter accumulation on the NS surface (Hanson & van Horn 1975). Unstable fusion occurs, leading to thermonuclear flashes that can be observable in the form of so-called type-I X-ray bursts (Woosley & Taam 1976). GX 3+1 does exhibit fast variability in the form of type-I X-ray bursts, which were extensively studied by a number of X-ray missions: GINGA (Asai et al. 1993), Granat (Pavlinsky et al. 1994; Molkov et al. 1999), RXTE (Kuulkers & van der Klis 2000; Kuulkers 2002), and INTEGRAL (Chenevez et al. 2006).

A unique superburst with a decay time of 1.6 hr was detected with the ASM on RXTE (Kuulkers 2002). One of the shortest bursts ever seen exhibits a quick (i.e., less than 2 s) radius expansion phase, indicating that the burst luminosity was at the Eddington luminosity, causing the NS atmosphere to expand owing to radiation pressure. This implies that a distance to the source is about 4.5 kpc, assuming that the NS atmosphere is hydrogen-rich (see more details in Kuulkers & van der Klis 2000).

In this paper, we concentrate our efforts on the spectral and timing properties of GX 3+1 related to changes in mass accretion rate, which are seen as the mild and slow variabilities. Previously, an analysis of the burst properties of GX 3+1 as a function of mass accretion rate on timescales larger than 1 minute was presented by Asai et al. (1993) and den Hartog et al. (2003). In particular, the slow variability has been revealed during transitions from the faint phase to the bright phase of luminosity and is generally caused by significant increase of mass accretion rate. The mild variability is presumably related to moderate local variability of mass accretion rate and revealed as local transitions between LB and UB states. The slow variability has been investigated with the RXTE/ASM light curve, WFC of BeppoSAX (den Hartog et al. 2003), and the ASM on GINGA (Asai et al. 1993), and these observations indicate that the flux oscillates semi-sinusoidally with a period of 6–7 years (see Figure 1).

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Moreover, the GINGA measurements with its Large Area Detector (Asai et al. 1993) show a constant 1–20 keV spectral shape over the fainter phases and also during brighter phases on luminosity, suggesting a constancy of the spectral index.

This stability of the X-ray spectral shape over the bright and faint phases has also been confirmed by the WFC BeppoSAX measurements in the 2–28 keV band, which showed minimal spectral changes (den Hartog et al. 2003).

The stability of the index was noted previously by FT11, for a number of NS LMXBs at different luminosities. They collected X-ray spectra obtained by BeppoSAX and demonstrated the relative stability of spectral index α of approximately 1 (Γ = α + 1) for quite a few NS sources: X1658-298, GX 354-0, GS 1826-238, 1E 1724-3045, Cyg X-1, Sco X-1, GX 17+2, and GX 349+2 at different spectral states. Recently ST11 presented results of analysis of X-ray spectra for "atoll" source 4U 1728-34, detected with BeppoSAX and RTXE at different luminosities and values of the best-fit electron temperatures. These results indicate that the value of the index varies slightly about a value of 1 (or the photon index varies around 2) independently of the electron temperature of the Compton cloud (CC) kT_e and luminosity. This unique stability of the photon index may be an intrinsic property of NSs at least for the atoll sources. It is probably determined by common physical conditions for this class of sources. FT11 and ST11 interpreted this quasi-stability of the index Γ in the framework of a model in which the spectrum is dominated by a strong thermal Comptonized component formed in the TL located between the accretion disk and NS surface. Indeed, the index quasi-stability takes place when the energy release in the TL is much higher than the photon energy flux coming from the accretion disk and illuminating the TL.

The evolution of spectral parameters of compact objects in X-ray binaries is of great interest for understanding their nature. It is well known that many black hole (BH) candidate binaries exhibit correlations between mass accretion rate $\dot{M}$ and photon power-law index Γ (see Shaposhnikov & Titarchuk 2009 and Titarchuk & Seifina 2009, hereafter ST09 and TS09, respectively). In the soft states of BHs these index-$\dot{M}$ correlations almost always show a saturation of Γ at high values of the $\dot{M}$. This saturation effect can be considered as a BH signature or equivalently as a signature of a converging flow into a BH (ST09 and TS09).

In this paper, we present the analysis of the BeppoSAX available observations and RXTE/PCA observations during 1996–2010 for GX 3+1. In Section 2, we present the list of observations used in our data analysis, while in Section 3, we provide the details of X-ray spectral analysis. We analyze the evolution of X-ray spectral and timing properties during the state transition in Section 4. We make our conclusions in Section 5.

Broadband energy spectra of the source were obtained combining data from three BeppoSAX Narrow Field Instruments (NFIs): the Low Energy Concentrator Spectrometer (LECS) for 0.3–4 keV (Parmar et al. 1997), the Medium Energy Concentrator Spectrometer (MECS) for 1.8–10 keV (Boella et al. 1997), and the Phoswich Detection System (PhDS) for 15–60 keV (Frontera et al. 1997). The SAXDAS data analysis package is used for processing data. For each of the instruments we performed the spectral analysis in the energy range for which the response matrix is well determined. The LECS data have been re-normalized based on MECS. Relative normalization of the NFIs was treated as free parameters in model fitting, except for the MECS normalization that was fixed at a value of 1. We then checked this fitting procedure if these normalizations were in a standard range for each instrument.⁵ In addition, spectra are rebinned accordingly to energy resolution of the instruments in order to obtain significant data points. We rebinned the LECS spectra with a binning factor that is not constant over energy (Section 3.1.6 of Cookbook for the BeppoSAX NFI spectral analysis) using template files in GRPPHA of XSPEC.⁶ Also we rebinned the PhDS spectra with a linear binning factor of two, grouping two bins together (resulting bin width is 1 keV). Systematic error of 1% has been applied to these analyzed spectra. In Table 1, we listed the BeppoSAX observations used in our analysis.

We have analyzed the available data obtained with RXTE (Bradt et al. 1993), which have been found in the time period from 1996 October to 2010 September (see also a review by Galloway et al. 2008). In our investigation we selected 101 observations made at different count rates (luminosity states) with a good coverage of rise–decay transition tracks. We have made an analysis of RXTE observations of GX 3+1 during 14 years for seven intervals indicated by blue rectangles in Figure 1 (top).

RXTE/PCA spectra have been extracted and analyzed, wherein PCA Standard 2 mode data, collected in the 3–50 keV energy range, use the most recent release of PCA response calibration (ftool pcarmf v11.1). The relevant dead-time corrections to energy spectra have been applied. We used the data that are available through the GSFC public archive (http://heasarc.gsfc.nasa.gov). In Table 2, we presented the groups of RXTE observations that cover the source evolution from faint to bright (phase) events. Note that available RXTE data contain one "bright phase" set (R4) and six "faint phase" sets (R1–R3, R5–R7). The PCA energy spectra were modeled using XSPEC astrophysical fitting software. A systematic error of 0.5% has been applied to the analyzed spectra.

We have also used public GX 3+1 data from the ASM on board RXTE, which show long-term quasi-periodic variability of the mean soft flux during a ∼6 year cycle (Figure 1). We use definitions of the fainter and brighter luminosity phases to relate these phases to the source luminosity, and we demonstrate that during the bright/faint phase transition of GX 3+1 COMPTB normalization changes from 0.04 to 0.14 L^soft₃₉/D²₁₀, where L^soft₃₉ is the soft photon luminosity in units of 10³⁹ erg s⁻¹ and D₁₀ is distance to the source in units of 10 kpc.

In our spectral data analysis, we use a model that consists of a sum of a Comptonization component (COMPTB) (COMPTB is an XSPEC contributed model,⁷ see Farinelli et al. 2008, hereafter F08), soft BB component of temperature T_BB, and Gaussian line component. The COMPTB spectral component has the following parameters: temperature of the seed photons T_s, energy index of the Comptonization spectrum α (=Γ − 1), electron temperature T_e, illumination (Comptonization) fraction f of the CC by the soft (NS) photons, f = A/(1 + A), and the normalization of the seed (NS) photon spectrum N_COM.

We include a simple Gaussian component in the model, whose parameters are a centroid line energy E_line, the width of the line σ_line, and the normalization N_line to fit the data in the 6–8 keV energy range. We also use the interstellar absorption with a column density N_H. It should be noted that we fixed certain parameters of the COMPTB component: γ = 3 (low-energy index of the seed photon spectrum) and δ = 0 because we neglect an efficiency of the bulk inflow effect versus the thermal Comptonization for NS GX 3+1. We apply a value of hydrogen column N_H = 1.6 × 10²² cm⁻², which was found by Oosterbroek et al. (2001).

Initially, we have tried a model consisting of an absorbed thermal component (bbody) and a thermal Comptonization component (COMPTB), but this model gave a poor description of data. Significant positive residuals around ∼6.5 keV suggest the presence of fluorescent iron emission line. The addition of a Gaussian line component at 6.4 keV considerably improves fit quality and provides a statistically acceptable χ²_red.

The fluorescent iron emission line in GX 3+1 was detected for the first time by Oosterbroek et al. (2001) using BeppoSAX on 1999 August 30 (id=20835001). Oosterbroek et al. (2001) successfully described this emission feature with the Gaussian line model and used a model consisting of a thermal component (dominating energy release around 1 keV) and a thermal Comptonization tail to describe the 0.1–50 keV continuum. However, they needed to add a 2% systematical uncertainty to LECS and MECS data to obtain acceptable χ²_red. We investigate a possibility to further improve the quality of the fit.

In Figure 2, we illustrate our spectral model as a basic model for fitting the BeppoSAX and RXTE spectral data for GX 3+1. We assume that accretion onto a NS takes place when the material passes through the two main regions: a geometrically thin accretion disk (the standard Shakura–Sunyaev disk, see Shakura & Sunyaev 1973) and the TL, where NS and disk soft photons are upscattered off hot electrons. In other words, in our picture, the emergent thermal Comptonization spectrum is formed in the TL, where thermal disk seed photons and soft photons from the NS are upscattered off the relatively hot plasma (electrons). Some fraction of these seed soft photons can also be seen directly. Red and blue photon trajectories shown in Figure 2 correspond to soft (seed) and hard (upscattered) photons, respectively.

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We show examples of X-ray spectra in Figures 3 and 4 for BeppoSAX and RXTE data, respectively. Spectral analysis of BeppoSAX and RXTE observations indicates that X-ray spectra of GX 3+1 can be described by a model with a Comptonization component represented by the COMPTB model. Moreover, for broadband BeppoSAX observations this spectral model component is modified by photoelectric absorption at low energies.

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On the top of Figure 3 we demonstrate the best-fit BeppoSAX spectrum of GX 3+1 in units of E*F(E) (top) (where F(E) is energy flux in erg, per keV and per second) using our model for the BeppoSAX observation (id=20603001) carried out on 1999 February 28–March 1. The data are presented by crosses and the best-fit spectral model wabs*(blackbody + COMPTB + Gaussian) by a green line. The model components are shown by blue, red, and crimson lines for blackbdody, COMPTB, and Gaussian components, respectively. On the bottom we show Δχ versus photon energy in keV. The best-fit model parameters are Γ = 1.99 ± 0.07, kT_e = 3.68 ± 0.05 keV, and E_line = 7.4 ± 0.1 keV (reduced χ² = 1.08 for 457 dof; see more details in Table 3). In particular, we find that an addition of the soft thermal component with temperature kT_BB = 0.5–0.7 keV to the model significantly improves the fit quality of the BeppoSAX spectra. For the BeppoSAX data (see Tables 1 and 3) we find that the spectral index α is 1.03 ± 0.04 (or the corresponding photon index Γ = α + 1 is 2.03 ± 0.04).

Unfortunately, RXTE detectors do not provide well-calibrated spectra below 3 keV, while the broad energy band of BeppoSAX telescopes allows us to determine the parameters of BB components at low energies. Thus, in order to fit the RXTE data, we have to fix the temperature of the BB component at a value of kT_BB = 0.6 keV, obtained as an upper limit in our analysis of the BeppoSAX data. The best-fit spectral parameters using RXTE observations are presented in Table 4. In particular, we find that electron temperature kT_e of the COMPTB component varies from 2.3 to 4.5 keV, while the photon index Γ is almost constant (Γ = 1.99 ± 0.02) for all observations. It is worth noting that the width σ_line of the Gaussian component does not vary significantly and is in the range of 0.5–0.8 keV.

Color temperature kT_s of the COMPTB component changes from 1.2 keV to 1.7 keV, which is consistent with that using the BeppoSAX data set of our analysis (see Table 3) and previous studies by Oosterbroek et al. (2001), den Hartog et al. (2003), and Chenevez et al. (2006). We should also emphasize that the temperature of the seed photons kT_s of the COMPTB component usually increases up to 1.7 keV in the fainter phases and generally decreases to 1.2 keV in the bright phases.

In Figure 4, we show an example of the best-fit RXTE spectrum of GX 3+1 for the fainter luminosity phases and the residuals (bottom panel) with Δχ for the 94307-05-01-000 observation. Blue, red, and purple lines stand for BB, COMPTB, and Gaussian components, respectively.

In Figure 5, we also show examples of typical photon spectra E*F(E) spectral diagrams of GX 3+1 during the fainter phase (94307-05-01-00, blue) and the brighter phases (60022-01-13-01, red) detected with RXTE on MJD 55440.62 and 52544.48, respectively. The adopted spectral model shows a very good fidelity throughout all data sets used in our analysis. Namely, a value of reduced χ²_red = χ²/N_dof, where N_dof is the number of degrees of freedom, is less than or about 1.0 for most observations. For a small fraction (less than 2%) of spectra with high counting statistics χ²_red reaches 1.5. However, it never exceeds our rejection limit of 1.7. Note that the energy range for the cases in which we obtain the poor fit statistic (two among 101 spectra with χ² = 1.7 for 67 dof) is related to the iron line region. It is possible that the shape of the iron line is more complex than a simple Gaussian (i.e., a blend of different energies, presence of the edge, or broadening by Comptonization). The fits tend to favor a broad line (see Table 4), which might be caused by Comptonization. However, this possible complexity is not well constrained by our data.

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It is worth noting that we find some differences between our values of the best-fit model parameters and those in the literature. In particular, the photon index Γ, estimated by Oosterbroek et al. (2001) for observation id=20835001, is 1.60 ± 0.25. This discrepancy in index values can be a result of using slightly different spectral models than Oosterbroek et al. (2001).

Thus, using the broadband BeppoSAX observations, we can accurately determine all of the parameters of our spectral model while using the extensive observations of GX 3+1 by RXTE. We are able to investigate the overall pattern of the source behavior during the spectral transitions in the 3–50 keV energy range.

4.1. Evolution of X-Ray Spectral Properties during Transitions

As was mentioned above, at timescales larger that 1 minute, GX 3+1 exhibits two kinds of variability, slow and mild. The former one (slow) has a timescale of order years. This slow variability is seen in the faint phases and bright phases, which are related to low and high luminosities, respectively. On the other hand, the mild variability has a timescale of order of days, and modulation depth in the 3–10 keV band is typically 20%. The ASM (2–12 keV) mean flux correlates with COMPTB normalization (N_COM) and tends to anticorrelate with the electron plasma temperature of CC T_e (see Figure 6). Such mild variability is detected for both the fainter and brighter phases for GX 3+1. It should be noted that the COMPTB normalization changes are larger in the bright phase than those during the faint phase, while the electron temperature T_e variations are almost the same for both phases.

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One can relate slow and mild variabilities of GX 3+1 to slow and mild changes of mass accretion rate, respectively. The slow variability by a factor of four has been seen in the 1996–2010 observations by ASM/RXTE. The same kind of changes of the flux were also observed in the earlier observations by Makishima et al. (1983). In turn, in the next section it will be shown that the slow variability can be related to transitions between the brighter and fainter phases along with small variations of the electron temperature kT_e.

We found that the X-ray spectra of GX 3+1 over the bright and faint phases are quite stable. Moreover, we detected a constant 3–50 keV spectral shape over the slow and mild variability stages. The best-fit parameters are listed in Table 4. The faint/bright phase transitions are characterized by the spectra with an almost constant spectral index α of 1 or photon index Γ of 2 (see Figure 7). We have also established common characteristics of the rise–decay spectral transition of GX 3+1 based on their spectral parameter evolution of X-ray emission in the energy range from 3 to 50 keV using PCA/RXTE data. In Figures 4 and 5 we present typical examples of the RXTE bright and faint phase spectra for GX 3+1. In fact, one can clearly see from these figures that the normalization of the thermal component is a factor of two higher in the bright phase than that in the faint phase, although the photon indices Γ for each of these spectra are concentrated around 2 (see Figures 6 and 7).

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In fact, we test the hypothesis of Γ_appr ≈ 2 using the χ²-statistic criterion. We calculate the distribution of $\chi ^2_{{\rm red}}(\Gamma _{{\rm appr}})=\frac{1}{N}\sum _{i=1}^N({\Gamma _i-\Gamma _{{\rm appr}}}/{\Delta \Gamma _i} )^2$ versus Γ_appr and find a sharp minimum of function χ²_red(Γ_appr) around 1, which takes place in the range of Γ_appr = 1.99 ± 0.01 with a confidence level of 67% and Γ_appr = 1.99 ± 0.02 with a confidence level of 99% for 101 dof (see the similar figure of χ²_red(Γ_appr) for 4U 1728-34 in ST11). Using BeppoSAX data, FT11 suggested that the photon index Γ is approximately 2 for many NS binaries that are observed in different spectral states. FT11 characterize the spectral state by a value of electron temperature T_e and show that Γ = 2 ± 0.2 (or α = 1 ± 0.2) when kT_e changes from 2.5 to 25 keV.

A number of X-ray flaring episodes of GX 3+1 have been detected with RXTE during 2001–2002 (R4 set) with a good rise–decay coverage. We have searched for common spectral and timing features that can be revealed during these spectral transition episodes. We present the combined results of the spectral analysis of these observations using our spectral model wabs*(blackbody + COMPTB + Gaussian) in Figures 6 and 7. ASM/RXTE count rate is shown in the top panel of these figures. Further, from the top to the bottom, we show the model flux in two energy bands 3–10 keV (blue points) and 10–50 keV (crimson points). In the next panel we show a change of the TL electron temperature kT_e. One can clearly see the low-amplitude spectral transition on timescales of ∼1–2 days from the brighter phase to the fainter phase during the time period from MJD 52000 to MJD 52200, while kT_e only varies from 2.3 keV to 4.5 keV during this transition.

Normalizations of the COMPTB and BB component (crimson and blue points, respectively) are shown in the next panel of Figures 6 and 7. In particular, one can see from Figures 6 and 7 how the COMPTB normalization N_COM correlates with the variations of ASM count rate and the model flux in the 3–10 keV energy band. On the other hand, the normalization of the BB component N_BB is almost constant except at the mild variability episode peak, when N_BB increases from 0.02 to 0.14 (see blue points in Figure 6 at MJD = 52130 and 52170). Moreover, these spectral variability transitions are related to a noticeable increase of flux in the 3–10 keV energy range and corresponding decrease of flux that takes place in the 10–50 keV energy range (see the second panels from above in Figures 6 and 7).

The illumination fraction f varies from 0.1 to 0.9 as seen from Figure 8, while the index α only slightly varies with time around 1 (or Γ ∼ 2) (see Figures 6 and7). However, in most cases the soft disk radiation of GX 3+1 is subjected to reprocessing in a CC and only some fraction of the soft photon emission component (1 − f) is directly seen by the Earth observer. Note that f changes with COMPTB normalization (see Figure 8, the inner panel in the left-hand upper corner). The energy spectrum of GX 3+1 during almost all states is dominated by a Comptonized component, while the direct soft photon emission is always weaker and detectable in the flaring episodes only (see also Figures 6 and 7).

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Note that for BHs a definition of spectral transition involves a change of photon index Γ (see, e.g., ST09). However, there is no one-to-one correspondence between Γ and cutoff (or e-fold) energy E_fold. Titarchuk & Shaposhnikov (2010) demonstrate, using RXTE data for BH binary XTE J1550-564, that E_fold decreases when Γ increases from 1.4 to 2.1–2.2 until Γ reaches 2.2 and then E_fold increases. Thus, for a BH the main parameter used for the spectral transition definition is a variable photon index Γ, which monotonically increases when the source goes into the bright phase.

It is important to emphasize once again that in the NS binary GX 3+1 the transition from the faint phase to the bright phase takes place when COMPTB normalization N_COM = L^soft₃₉/D²₁₀ changes from 0.04 to 0.15. Thus, we define the NS spectral transition in terms of the COMPTB normalization. In this case the faint phase is characterized by the low normalization value while the bright phase is related to the high normalization value. In Figure 9, we demonstrate the dependence of COMPTB normalization L^soft₃₉/D²₁₀ on kT_e using these best-fit parameters for GX 3+1 and 4U 1728-34 for the BeppoSAX and RXTE data. From this figure one can clearly see a monotonic behavior N_COM versus kT_e, namely, kT_e decreases when the soft flux increases. It is worth noting that the kT_e values obtained using GX 3+1 data for BeppoSAX and RXTE reach the asymptotic value of about 2.5 keV at high values of the soft flux (N_COM > 0.05).

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To demonstrate transition properties of GX 3+1 in terms of flux (or luminosity), we define the hard color (HC) as a ratio of the flux in the 10–50 keV to that in the 3–50 keV energy band, and the soft color (SC) as a ratio of the flux in the 3–10 keV to that in the 10–50 keV energy band. Plotting HC versus SC, we created our CD (see the left panel of Figure 10) for two atoll sources GX 3+1 (pink) and 4U 1728-34 (blue). As it appears from this figure, the tracks of these two sources display a smooth and continuous (monotonic) function, pointing out the similar physical mechanism of hard/soft flux transition during a long-term source evolution for these two objects. In Figure 10 (right panel), we demonstrate a fragment of the ASM light curve of GX 3+1, which illustrates two types of flux variability. The long-term time trend (from bright to faint) is related to COMPTB normalization changes, while the second one shows short-term time variations (UB–LB) related to the CC electron temperature variations. The blue line displays a mean count rate and indicates long-term variability of GX 3+1 flux. Note that the track of Figure 10 (left panel) reflects a long-term evolution of GX 3+1.

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It is worth noting that among all NSs only a few atoll and Z-sources demonstrate a full track on the CD in a wide range of luminosity. For example, atoll sources, such as 4U 1728-34, usually show a wide range of spectral states during transitions that are related to changes of the total luminosity and mass accretion rate. One can establish a substantial difference between a NS and a BH owing to these flare episodes when a source evolves from the faint phase to the bright phase and when the plasma temperature of a Comptonized region changes remarkably (like in 4U 1728-34 from 2.5 keV to 15 keV during IS–B states). On the other hand, GX 3+1 shows significant changes in the total luminosity but with only a slight variation of electron temperature kT_e in its banana state. However, the photon index Γ stays around a value of two and is independent of the soft photon luminosity in both the faint phase and the bright phase.

4.2. Timing Properties during LB–UB Transitions

The RXTE light curves have been analyzed using the powspec task from FTOOLS 5.1. The timing analysis PCA/RXTE data were performed in the 13–30 keV energy range using the event mode. The time resolution for this mode is 1.2× 10⁻⁴ s. We generated power density spectra (PDS) in the 0.1–500 Hz frequency range using light curves with 10⁻³ s time resolution. We subtracted the contribution due to Poissonian noise and Very Large Event Window for all PDS. We used the QDP/PLT plotting package to model PDS.

Previously, timing analysis of PCA/RXTE data for GX 3+1 observed on 1999 August (our R3 set), when the source was in LB phase, was made by Oosterbroek et al. (2001). We investigated a timing behavior of GX 3+1 for our data set during all transitions between LB and UB phases (see Figure 11). In particular, the power spectrum of GX 3+1 consists of very low frequency noise (VLFN, described by a power law) and high-frequency noise (HFN, described by a cutoff power law; see van der Klis 2005).

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In the LB phases (A red, 60022-01-13-01, MJD = 52554; A blue, 60022-01-01-00, MJD = 51998) the best fit to the average power spectrum results in an rms VLFN component of 2% (in the 0.1–1 Hz range) described by power law $\nu ^{-\alpha _{{\rm LF}}}$ with the index of α_LF ∼ 1.7, whereas HFN rms (in the 1–100 Hz range) has 4.7% with α_HF ∼ 1.0 and ν_cutoff ∼ 30 Hz. Generally the index of VLFN α_LF gradually decreases from 1.7 to 1.4 toward UB. However, in the vicinity of a transition point between LB and UB (red histogram of panel (B) of Figure 11) α_LF jumps to 1.8 (B red, 94307-05-01-00, MJD = 55129) and decreases again to 1.4 (B blue, 60022-01-11-03, MJD = 52357). In general, the UB power spectra of GX 3+1 are dominated by the VLFN with the brake at around 20 Hz at the lowest kT_e = 2.4 keV (see blue B point in the right-hand panel of Figure 11). Specifically, during UB (blue histogram of panel (B) of Figure 11) one can see strong VLFN (rms = 5.1% ± 0.4%, α_LF = 1.4 ± 0.3, χ² = 139 for 102 dof; all parameter errors correspond to 1σ confidence level) and HFN with rms = 1.7% ± 0.3% and break frequency shifted from 30 Hz to 6 Hz. After UB GX 3+1 again returns to the LB, showing properties of PDS similar to panel (A) (see panel (C) of Figure 11).

Note that these components and their CD evolution are typical for atoll sources in the banana state (Hasinger & van der Klis 1989) and caused by mass accretion rate change (van der Klis 2005). This phase identification is supported by a combination of spectral (see Section 4.1) and timing properties in agreement with the atoll–Z scheme.

While the aforementioned CD evolution of power spectra of GX 3+1 occurs on timescales from hours to days, we detected similar patterns for power spectrum evolution during LB–UB transitions for both faint phase and bright phase on luminosity during long-term variability within 14 years with a quasi-periodic trend during 6 years. The similarity of LB–UB transitions, which are independent of bright/faint phases on luminosity, indicates similar accretion configurations in all phases.

In a previous analysis of other RXTE data of GX 3+1 Oosterbroek et al. (2001) report VLFN and HFN values, in LB state, which are similar to our values in interval R3, with the exception of VLFN strength, for which they report 7.5% rms while we find 1.7% rms. All of the VLFN and HFN values of the analysis of EXOSAT data reported by Hasinger & van der Klis (1989) for GX 3+1 agree with our results.

4.3. Comparison of Spectral and Timing Characteristics of Atoll Sources GX 3+1 and 4U 1728-34

We present our analysis of the spectral properties observed in X-rays from the NS X-ray binary GX 3+1 during long-term transitions between the faint phase and the bright phase superimposed by short-term transitions between LB and UB states. We analyze all transition episodes for this source observed with BeppoSAX and RXTE. For our analysis we apply the good spectral coverage and resolution of BeppoSAX detectors from 0.1 to 200 keV along with extensive RXTE coverage in the energy range from 3 to 50 keV.

We show that the X-ray broadband energy spectra during all spectral states can be adequately fitted by the combination of a BB, a Comptonized, and a Gaussian component. We also show that photon index Γ of the best-fit Comptonized component in GX 3+1 is almost constant, with a value of two, and consequently is almost independent of COMPTB normalization L^soft₃₉/D²₁₀, which is presumably proportional to mass accretion rate $\dot{m}$ (see Figures 6, 7, and 11). We should remind the reader that this index stability has recently been suggested using X-ray observations of quite a few other NS sources, namely, atoll sources X1658-298, GS 1826-238, and 1E 1724-3045 and also Z-sources Cyg X-2, Sco X-1, GX 17+2, GX 340+0, and GX 349+2 were observed by BeppoSAX at different spectral states, as well as atoll source 4U 1728-34 observed by BeppoSAX and RXTE (see details in FT11 and ST11, respectively).

A wide variation of parameter f = 0.1–0.9, obtained in the framework of our spectral model, points out a significant variation of the illumination of the Comptonization region (TL) by X-ray soft photons in GX 3+1.

Using BeppoSAX observations, we find that there are two sources of blackbody emission: one is presumably related to the accretion disk, and another one is related to the NS surface, for which temperatures of soft photons are about 0.7 keV and 1.3 keV, respectively.

We demonstrate that our analysis of X-ray spectral and timing properties in atoll source GX 3+1 allows us to distinguish between mild and long-term variabilities, and we link them with LB–UB state transitions and transitions between bright and faint phases in luminosity, respectively. In this way we described mild flux variability between LB and UB states on a timescale of hours to days in terms of two basic spectral parameters, the electron temperature kT_e and illumination fraction f. We argue that kT_e monotonically increases from 2.3 keV to 4.5 keV when GX 3+1 makes a transition from UB state to LB state. We also find two noise components (VLFN and HFN) and their evolution during LB–UB transitions: the X-ray power spectra (PDS) in UB are dominated by VLFN with the break around 20 Hz, whereas in LB the PDS are dominated by an HFN in the 1–100 Hz range and accompanied by reduced VLFN below ∼1 Hz.

We demonstrate that the photon index Γ ∼ 2 is approximately constant when the source moves from the faint phase to the bright phase, as well as during local transitions from LB to UB. In ST11 we presented strong theoretical arguments that the dominance of the energy release in the TL with respect to the soft flux coming from the accretion disk, Q_disk/Q_cor ≪ 1, leads to almost constant photon index Γ ≈ 2.

Thus, we argue that the stability of this index is an intrinsic signature of atoll sources, while in BHs the index monotonically changes with mass accretion rate and ultimately saturates (see ST09 and ST11). Photon indices of BH candidates (GRS 1915+105, GX 339-4, SS 433, H1743-322, 4U 1543-47, Cyg X-1, XTE J1550-564, and GRO J1655-40) show clear correlation with mass accretion rate $\dot{m}$ (ST09, TS09, and Seifina & Titarchuk 2010). This correlation is accompanied by an index saturation when $\dot{m}$ exceeds a certain level. The behaviors of the index for GX 3+1 and 4U 1728-34 are clearly different from that for the sample of black hole candidate sources. The photon index Γ ≈ 2, while mass accretion rate changes by a factor of four.

We acknowledge discussion and editing of the paper content with Chris Shrader. We are very grateful to the referee, whose constructive suggestions helped us improve the paper quality.