X-RAY SPECTRAL AND TIMING BEHAVIOR OF SCORPIUS X-1. SPECTRAL HARDENING DURING THE FLARING BRANCH

Lev Titarchuk; Elena Seifina; Chris Shrader

doi:10.1088/0004-637X/789/2/98

1. INTRODUCTION

The neutron stars (NSs) in X-ray binaries offer a unique opportunity to study the properties of matter under the most extreme conditions. These sources show a variety of observational manifestations which can be used to verify different theoretical models. The Z sources, being related to NSs in X-ray binaries radiating close to the Eddington limit (L_Edd), sometimes show properties similar to black holes (BHs). For example, the Z-source Scorpius X-1, hereafter Sco X-1, exhibits a strong hard tail in its X-ray spectrum, which for a long time was considered to be a unique BH signature (Rothschild et al. 1980).

Sco X-1 and other Z sources, GX 349+2, GX 340+0, GX 17+2, GX 5-1, and Cyg X-2, which have similar behavior in three spectral branches, form a group (Hasinger & van der Klis 1989). However, there are differences in the detailed observational behavior of these Z sources. Sco X-1 and GX 17+2 and GX 349+2 show strong flares in the intensity during the flaring branches (FB), while GX 340+0, Cyg X-2 and GX 5-1 undergo dips in the FB (Hasinger & van der Klis 1989; Penninx et al. 1991; Kuulkers et al. 1994). It is worth noting that the normal branch (NB) properties are similar for these two groups of Z sources, but the horizontal branch (HB) and FB properties are fundamentally different.

The distinct observational appearances between these two groups are not fully understood. An interesting suggestion was made by Lin et al. (2009), hereafter LRH09, and Homan et al. (2010) based on observations of the transient NS source XTE J1701-462. They found that this source showed characteristic features of a Z source, and then an atoll source when the luminosity decreased. They claimed that the initial Cyg-like behavior was followed by a Sco-like one when the luminosity decreased and then they concluded that Cyg and Sco types depended on the luminosity.

Sco X-1 is the brightest persistent X-ray source in the sky and the first identified X-ray extrasolar source (Giacconi et al. 1962). It is located at a distance of 2.8 ± 0.3 kpc (Bradshaw et al. 1999) and its binary orbit has a low inclination angle to the Earth observer and thus is suitable for a study of the flaring events in Z sources. This binary system consists of an old, weakly magnetized NS with a mass ∼1.4 M_☉ in which accreting matter is transferred through Roche lobe overflow from a low-mass companion (recently identified as an M-class star of ∼0.4 M_☉; see details in Steeghs & Casares 2002). Sco X-1 is a prototype of the class of low-mass X-ray binaries (LMXBs), which emit close to the Eddington limit for a 1.4 M_☉ NS (L_Edd = 2 × 10³⁸ erg s⁻¹).

Sco X-1, similar to other Z sources, shows quasi-periodic oscillations (QPOs) along all the branches of its color–color diagram (CCD). Extensive timing analysis of Sco X-1 with EXOSAT indicates that the QPO phenomenon is closely related to the transition of Sco X-1 between different spectral states (e.g., van der Klis et al. 1987a, 1987b; Middleditch & Priedhorsky 1986; Priedhorsky et al. 1986; Hasinger et al. 1989, hereafter HPM89, and Hertz et al. 1992). In particular, the transition between the HB − NB and the FB states is characterized by variations in the QPO frequency between 6 Hz and 16 Hz (with no intensity correlation). When Sco X-1 enters into the prolonged NB state the QPO frequency settles in the 6–8 Hz range (anti-correlated with intensity). The low-frequency noise (LFN) component of the power spectrum becomes stronger when the source intensity increases at the FB and at the same time the QPOs disappear. In turn, Dieters & van der Klis (2000), using EXOSAT, detected an abrupt increase of the QPO frequency from 6 Hz to 10 Hz, so-called rapid excursions near the soft apex in the hardness–intensitydiagram (HID) along with grand transitions from 8 Hz to 21 Hz when the object went from the lower FB to the upper FB.

Based on the Rossi X-ray Timing Explorer (RXTE) observations, van der Klis et al. (1996) reported the discovery of 45 Hz QPOs, mostly prominent in the middle of the NB. Casella et al. (2006) detected a monotonic (smooth) increase of the QPO centroid frequency from 4.5–7 Hz (at the NB) to 6–25 Hz (at the FB), which can indicate the same nature as these low frequency QPOs. The power spectrum of Sco X-1 also includes a pair of QPOs, whose frequencies are in the range 800–1100 Hz, the so-called kHz QPOs. The peak frequency separation is weakly frequency-dependent (Zhang et al. 2006).

The physical interpretation of these timing features is not unique, and the related scientific debate is still open. Apart from detailed knowledge of the timing properties of Sco X-1, the spectral studies have not been that extensive. This is mostly caused by the brightness of Sco X-1 that prevents this source from direct observation with high resolution X-ray satellites, e.g., Chandra and XMM-Newton. However, significant progress was achieved in this regard due to the detailed investigations of the broadband spectra of Sco X-1 based on RXTE observations by D'Amico et al. (2001), Barnard et al. (2003), Bradshaw et al. (2003), D'Ai et al. (2007), and Church et al. (2012). These authors demonstrated that the X-ray spectrum of Sco X-1 is well fit by a two-component model consisting of a thermal component, related to the NS, and a Comptonized component, associated with an extended accretion disk corona. In addition, a broad emission line with a Gaussian profile is applied to this model in all spectral states. However, the results of this analysis and their interpretation depend on the energy band considered and the adopted spectral model for the thermal and Comptonized components.

In particular, D'Amico et al. (2001) studied only the high-energy band above 20 keV using High Energy X-Ray Timing Experiment (HEXTE) data and tried to find a correlation between the X-ray hard tail emission in the spectra of Sco X-1 with the position of the source along the Z-track. However, they did not find any apparent correlation using a bremsstrahlung component and a simple power-law component in their spectral model. Furthermore, D'Amico et al. (2001) claimed a non-thermal origin of the hard tail. Bradshaw et al. (2003) used only Proportional Counter Array (PCA) data in the moderate energy range 3–18 keV, applying a model that consisted of a blackbody emission and a Comptonization component (Shrader & Titarchuk 1998). They studied the evolution of an X-ray spectrum of Sco X-1 as a function of accretion rate and, in particular, detected an increase of the absorption at low energies of a factor of two when the object moved from the HB to NB/FB vertex. Barnard et al. (2003) used data from the PCA and HEXTE, applying a blackbody component and a cutoff power law to the data in the energy range 2.5–50 keV. In the framework of this model, the so-called Birmingham model (Church & Balucin`ska-Church 2001), they studied the evolution of blackbody emission (from the NS) and Comptonized emission (from an extended accretion disk corona) between different spectral states. Church et al. (2012) also used data from PCA and HEXTE, showing that the spectrum, in the energy range 2–50 keV, can be approximated by a soft blackbody component plus a cutoff power law and a broad Gaussian line. As a result, they revealed the apparent non-monotonic behavior of the mass accretion rate in Sco X-1 along the Z-track. They also argued that the mass accretion rate increase is a function of the NS temperature. D'Ai et al. (2007) also analyzed the mass accretion rate variations, studying energy spectra from selected regions in the Z-track of the CD. They demonstrated that X-ray spectra of Sco X-1 based on PCA and HEXTE observations can be adequately fitted by a three-component model, consisting of a soft thermal component (diskbb), a thermal Comptonization component (compps/comptt/thcomp), and a power-law component (pegpwrlw).

Revnivtsev & Gilfanov (2006) also studied the contribution of the boundary layer in the emergent X-ray spectrum of NS LMXBs as a function of the Z-track position. They fitted the spectra of various NS sources using two Comptonization (CompTT) components, one related to the NS emission and another to the transition layer (TL). Gilfanov & Revnvitsev (2005) also argued that the boundary layer is the source of rapid variability based on Fourier-resolved spectral component analysis.

In this paper we present the analysis of the RXTE observations during 1996–2002 for Sco X-1. In Section 2 we present the list of observations used in our data analysis. In Section 3 we provide results of our X-ray spectral analysis and in Section 4 we interpret the observed X-ray spectral properties using the TL model. We make our final conclusions in Section 5.

2. DATA REDUCTION AND ANALYSIS

We used publicly available RXTE data for Sco X-1 obtained from 1996 May to 2002 May. In total, these data are derived from 60 observations taken at distinct spectral states of the source. Standard tasks of the LHEASOFT/FTOOLS 5.3 software package were utilized for data processing. For spectral analysis we used PCA Standard 2 mode data, collected in the 3–23 keV energy range, using the most recent release of PCA response calibration (ftool pcarmf v11.7). The standard dead time correction procedure has been applied to the data. We also used data from the HEXTE detectors to construct the background-subtracted broadband spectra. Only data in the 19–250 keV energy range were used for spectral analysis in order to account for the uncertainties of the HEXTE response and background determination. The data are available through the GSFC public archive (http://heasarc.gsfc.nasa.gov). In Table 1 we list the groups of observations covering the complete range of the source evolution during different spectral state events.

Table 1. List of Groups of RXTE Observations of Sco X-1

Number of Set	Dates, MJD	RXTE Proposal ID	Dates UT
R1	50227–50228; 50522, 50815	10061¹	1996 May 24–25, 1997 Mar 15; 1998 Jan 2
R2	50556–50562; 50816-50821	20053^{1, 2, 3}	1997 Apr 18–24; 1998 Jan 3–8
R3	50820–50821; 50963-50999	30036^{1, 2, 3, 4}; 30035^{1, 2}	1998 Jan 7–8; May 30–Jul 5
R4	51186–51194	40020²	1999 Jan 1–16
R5	51339–51342	40706^{1, 3, 5}	1999 Jun 10–13†
R6	52413.9–52414	70015²	2002 May 19 21:55:44–23:45:28†

References. (1) D'Amico et al. 2001; (2) D'Ai et al. 2007; (3) Church et al. 2006, 2012; (4) Barnard et al. 2003; (5) Bradshaw et al. 2003.

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We analyzed RXTE observations of Sco X-1 spanning seven years for the six intervals indicated in Table 1. To model the spectral evolution of the source we made spectra on an appropriate timescale. This timescale should be short enough to describe a spectral evolution, but long enough to provide reliable statistics. We selected regions in the CCDs; see Figures 1 and 2) for each observational data set and created the CCD-selected spectra. For our analysis we use version 6.0 of the FTOOLS package and version 12.1 of XSPEC. A systematic error of 0.5% was applied to all analyzed spectra to account for the absolute calibration uncertainties. We also used data from the All-Sky Monitor (ASM) on board RXTE to construct a long baseline 3–10 keV light curve bracketing the PCA and HEXTE observations.

**Figure 1.** CCDs (left panel) and HIDs (right panel) for all observations of Sco X-1 used in our analysis, with bin size 16 s. The typical error bars for the colors are shown in the bottom right corner of the left panel; errors in the intensity are negligible. The sets with strong flaring activity are marked by black points, while the sets with reduced flaring activity are highlighted by red points. Three typical tracks with transitions in the direction HB→NB→FB for strong flaring activity sets are indicated by corresponding arrows. Here the spectral branches have been indicated: the flaring branch (FB), normal branch (NB), and horizontal branch (HB) for the blue line track. Different positions of the transitional tracks in these diagrams demonstrate a secular shifting of Sco X-1.
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**Figure 2.** CCDs extracted using *RXTE* data sets. Different colors point to different selected regions from which the CCD-resolved spectra were produced. We label the spectra in accordance with Table 2.
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The ASM (2–12 keV) light curve of Sco X-1 demonstrates irregular flaring activity with intervals of more frequent flares as well as intervals of reduced flaring. Thorough analysis of the flares detected in such a manner shows that the spacing of adjacent flares varies between 0.3 and 2.5 days in most cases. Less frequently, flares have much larger gaps of about 10 days. Because of this, we have chosen the observational sets consisting of flaring patterns for our detailed analysis of Sco X-1.

3. RESULTS

3.1. Color–color and Hardness–Intensity Diagrams of Sco X-1

We investigate the light curves with 16 s time binning for four energy channel ranges 5–10, 11–24, 25–54, and 55–107. These energy ranges correspond to energies 1.94–4.05 keV, 4.05–9.03 keV, 9.03–20.3 keV, and 20.3–39.99 keV, respectively. We constructed CCDs of the source using the energy-dependent light curves and defined the soft color (SC) as the ratio of the count rates in the 4.05–9.03 keV and 1.94–4.05 keV energy bands, while the hard color (HC) is defined as a ratio of the count rates in the 20.3–39.99 keV and 9.03–20.3 keV energy ranges. Note that the above channel-to-energy conversion is given for epoch 3, which is presented for most of our data (R1–R5; see Table 1). For the data set R6, the energy ranges are slightly shifted, taking into account the change of the instrumental epoch of the satellite (epoch 5), which led to a small shift on the HC and on the SC axes.

The obtained CCDs and HIDs are shown in Figure 1 for available RXTE data of Sco X-1 using a bin size of 16 s. They present a family of tracks, which are characterized by a clear ν-like shape. The left part of ν-like track is related to the HB and NB branches, while the right part of this ν-like track corresponds to the FB. The sharp minimum of such a ν-like track is the so-called soft apex (or NB/FB vertex), where the luminosity of Sco X-1 notably decreases. The typical error bars for the colors are shown in the bottom right corner of the left panel; errors in the intensity are negligible.

As one can see from this figure, the CCDs and HIDs provide a family of Z-cycles for all data sets (see Table 1). It is worth noting that these particular sets partly overlap each other. The sets with strong flaring activity are pointed out by black points, while the sets with reduced flaring activity are highlighted by red points. The "reduced flaring activity" set shows an underdeveloped Z-cycle. Three typical tracks with HB→NB→FB transitions for strong flaring activity sets are indicated by the corresponding bent arrows. The shifted Z-tracks in the CCD and HID can be seen as an NB/FB vertex shift. The evolution of the NB/FB vertex position in Sco X-1 cannot be described as a one-to-one correspondence with X-ray luminosity as in the case of XTE J1701-462, when the position of the NB/FB vertex (at Sco-like stage) moves with the X-ray luminosity with a decrease of SC and HC (see Figure 5 of LRH09). In order to understand the X-ray evolution of Sco X-1 one needs to investigate the Z-track behavior using spectral (Section 3.3) and timing analysis (Section 3.6) together.

3.2. Evolution of Spectral Hardness throughout all Z Branches of Sco X-1

Evolution sequences along the CCD and HID tracks of Sco X-1 are presented in Figures 2 and 3 in ten panels for corresponding subgroups of successive observational intervals. In particular, in Figure 2 we indicate selected regions, which are related to the CCD-resolved spectra, using different colors.

**Figure 3.** Evolution of the HID tracks of Sco X-1 as a function of the count rate in the (9–20 keV) energy band. Data groups (I–X) correspond to the same data groups shown in Figure 2.
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We label the spectra through progressive numbering (according to Table 2, first column).

Table 2. Best-fit Parameters of the Spectral Analysis of PCA+HEXTE/RXTE Observations of Sco X-1 in the 3–250 keV Energy Range^a

No.	Observational	MJD,	α₁ =	$kT^{(1)}_e,$	log (A₁)	N_Com1^b	kT_s2,	α₂ =	$kT^{(2)}_e,$	log (A₂)	N_Com2^b	E_line,	N_line^b	$\chi ^2_{{\rm red}}$ (d.o.f.)
No.	ID	day	Γ₁ − 1	(keV)	log (A₁)	N_Com1^b	(keV)	Γ₂ − 1	(keV)	log (A₂)	(keV)	E_line,	N_line^b	$\chi ^2_{{\rm red}}$ (d.o.f.)
01	10061-01-01-00	50227.865	1.03(2)	16(4)	−2.0(5)	2.47(3)	1.42(6)	1.01(3)	2.94(1)	2.00^c	2.09(1)	5.99(4)	1.18(5)	1.21(87)
02	10061-01-01-01	50228.003	1.00(3)	7(2)	−1.6(2)	1.97(8)	1.27(4)	1.00(1)	2.97(4)	2.00^c	1.89(2)	6.02(6)	0.76(7)	0.93(87)
03	10061-01-02-00	50522.766	0.98(4)	80(3)	−1.40(1)	0.21(7)	1.17(2)	1.00(2)	3.05(1)	2.00^c	2.26(1)	6.12(6)	0.80(9)	1.14(87)
04	20053-01-02-05	50556.570	0.99(3)	40(1)	−1.36(7)	0.004(2)	0.72(8)	1.03(6)	2.89(5)	0.84(5)	2.65(9)	6.79(7)	0.22(7)	1.02(85)
05	20053-01-01-00	50556.639	1.06(1)	30(5)	−1.69(8)	0.61(8)	0.95(9)	0.98(1)	2.99(2)	2.00^c	2.19(4)	6.3(2)	0.51(9)	1.16(87)
06	20053-01-01-01	50557.183	0.71(4)	90(10)	−2.01(4)	0.004(1)	0.45(7)	0.95(1)	3.01(1)	0.9(1)	2.7(1)	6.46(9)	0.30(5)	1.32(87)
07^a	20053-01-01-02^a	50558.774	1.01(2)	15(4)	−2.0(1)	0.8(2)	0.55(6)	1.00(3)	2.79(2)	1.27(5)	2.05(4)	6.39(8)	0.72(7)	1.02(87)
07^b	20053-01-01-02^b	⋅⋅⋅	1.00(3)	14(3)	−2.1(2)	0.8(1)	0.58(8)	1.01(2)	2.82(2)	1.63(8)	2.06(7)	6.54(7)	0.83(7)	1.04(87)
07^c	20053-01-01-02^c	⋅⋅⋅	1.03(2)	18(6)	−1.9(1)	0.7(2)	0.52(4)	1.03(3)	2.93(3)	1.82(9)	2.05(6)	6.29(9)	0.91(7)	1.01(87)
08	20053-01-01-03	50559.841	1.00(3)	61(2)	−2.34(8)	0.2(1)	1.1(1)	0.99(2)	2.86(1)	0.23(8)	2.2(1)	6.4(1)	0.59(6)	1.19(87)
09	20053-01-01-04	50560.641	0.41(3)	120(10)	−1.68(7)	0.001(1)	0.66(7)	1.01(1)	3.03(3)	0.72(7)	2.75(2)	6.46(9)	0.10(2)	1.03(87)
10	20053-01-01-05	50561.576	0.99(4)	46(3)	−1.29(3)	0.003(1)	0.56(4)	1.05(2)	2.86(1)	1.10(5)	2.50(3)	6.70(5)	0.44(5)	1.16(85)
11	20053-01-01-06	50562.509	0.98(3)	50(2)	−1.90(4)	0.007(2)	0.47(6)	1.00(1)	2.93(1)	1.11(6)	2.47(2)	6.93(9)	0.37(6)	0.97(85)
12	10061-01-03-00	50815.621	1.01(2)	70(5)	−1.05(8)	0.05(1)	0.72(6)	1.08(3)	2.92(3)	0.78(6)	2.59(4)	6.78(8)	0.33(7)	1.23(87)
13^a	20053-01-02-00^a	50816.887	0.44(6)	120(10)	−2.0(9)	0.002(1)	0.44(9)	0.95(1)	2.76(1)	0.73(4)	2.9(1)	6.72(7)	0.75(6)	1.25(85)
13^b	20053-01-02-00^b	⋅⋅⋅	0.45(5)	120(10)	−2.0(9)	0.001(2)	0.45(8)	0.94(2)	2.77(1)	0.65(3)	2.7(2)	6.67(4)	0.73(4)	1.26(85)
13^c	20053-01-02-00^c	⋅⋅⋅	0.44(4)	110(10)	−2.0(9)	0.001(1)	0.46(9)	0.95(1)	2.65(2)	0.78(4)	2.8(1)	6.52(8)	0.74(6)	1.23(85)
13^d	20053-01-02-00^d	⋅⋅⋅	0.46(6)	120(10)	−2.0(9)	0.001(1)	0.45(7)	0.96(1)	2.93(1)	0.92(1)	2.6(3)	6.87(9)	0.72(3)	1.26(85)
14^a	20053-01-02-01^a	50817.931	0.39(7)	156(8)	−2.3(4)	0.19(9)	0.71(8)	0.91(2)	2.85(6)	0.35(7)	3.10(2)	6.96(8)	0.45(5)	1.16(85)
14^b	20053-01-02-01^b	⋅⋅⋅	0.39(7)	149(7)	−2.0(4)	0.17(8)	0.75(8)	0.93(2)	2.93(5)	0.34(6)	3.02(4)	7.10(9)	0.44(6)	1.14(85)
15	20053-01-02-020	50818.773	0.90(4)	50(5)	−1.39(6)	0.003(1)	0.7(1)	1.00(4)	2.93(4)	0.82(5)	2.67(8)	6.90(8)	0.2(1)	1.00(85)
16^a	20053-01-02-030^a	50819.623	0.71(2)	85(5)	−1.01(5)	0.001(1)	0.60(3)	0.95(2)	2.85(1)	−0.17(5)	3.0(2)	7.02(9)	0.13(3)	1.06(85)
16^b	20053-01-02-030^b	⋅⋅⋅	0.72(1)	76(4)	−1.00(6)	0.001(1)	0.64(3)	0.97(1)	2.81(2)	−0.18(7)	3.0(1)	6.93(4)	0.14(2)	0.08(85)
16^c	20053-01-02-030^c	⋅⋅⋅	0.71(2)	82(9)	−1.06(5)	0.002(1)	0.60(4)	1.01(3)	3.17(1)	−0.26(5)	2.8(2)	7.01(7)	0.15(2)	1.01(85)
16^d	20053-01-02-030^d	⋅⋅⋅	0.70(1)	86(5)	−1.03(4)	0.001(1)	0.61(2)	0.98(2)	2.80(1)	−0.15(6)	2.9(3)	7.02(9)	0.14(3)	1.06(85)
16^e	20053-01-02-030^e	⋅⋅⋅	0.71(2)	80(7)	−1.10(5)	0.001(1)	0.60(3)	1.00(1)	2.87(3)	−0.09(7)	2.9(2)	6.95(8)	0.14(2)	1.11(85)
17^a	30036-01-01-000^a	50820.562	0.26(2)	120(10)	−4.05(4)	0.15(9)	0.71(4)	1.00(1)	3.04(2)	0.49(2)	3.12(2)	6.29(6)	0.84(7)	1.05(87)
17^b	30036-01-01-000^b	⋅⋅⋅	0.26(3)	120(10)	−4.03(5)	0.16(8)	0.72(3)	1.04(1)	3.15(3)	0.47(3)	3.11(3)	6.35(7)	0.74(8)	1.16(87)
17^c	30036-01-01-000^c	⋅⋅⋅	0.27(3)	110(10)	−4.16(4)	0.15(7)	0.76(4)	1.03(1)	3.07(2)	0.58(2)	2.93(3)	6.76(5)	0.54(9)	1.12(87)
17^d	30036-01-01-000^d	⋅⋅⋅	0.28(2)	100(10)	−4.07(3)	0.17(9)	0.70(5)	0.99(2)	3.06(1)	0.39(4)	2.91(4)	6.21(8)	0.86(8)	0.99(87)
17^e	30036-01-01-000^e	⋅⋅⋅	0.27(3)	110(9)	−4.03(4)	0.14(8)	0.72(4)	1.02(1)	3.02(2)	0.46(3)	2.98(3)	6.19(7)	0.93(9)	1.08(87)
18^a	20053-01-02-04^a	50820.955	0.23(3)	190(10)	−2.2(3)	0.12(8)	0.71(6)	1.01(2)	2.86(1)	0.39(5)	3.23(8)	7.00(9)	0.39(7)	1.18(85)
18^b	20053-01-02-04^b	⋅⋅⋅	0.25(2)	195(9)	−2.1(1)	0.11(9)	0.69(5)	0.99(1)	2.81(2)	0.42(4)	3.22(7)	6.95(8)	0.40(6)	1.17(85)
18^c	20053-01-02-04^c	⋅⋅⋅	0.26(3)	200(10)	−2.2(2)	0.10(7)	0.63(4)	1.04(1)	2.87(1)	0.37(5)	3.21(9)	6.99(9)	0.41(9)	1.09(85)
19	30036-01-02-000	50821.555	1.01(2)	60(10)	−2.78(5)	0.07(2)	1.47(3)	1.00(1)	2.94(2)	0.11(4)	2.09(2)	6.00(5)	0.91(8)	1.17(87)
20	30035-01-01-00	50963.019	1.01(3)	40(2)	−2.25(6)	1.58(9)	1.18(6)	0.99(2)	3.08(1)	0.75(6)	2.17(4)	6.4(1)	0.35(2)	1.26(87)
21	30035-01-02-000	50964.018	1.08(2)	45(5)	−1.69(3)	0.24(1)	0.96(2)	1.00(1)	2.81(1)	0.13(2)	2.45(2)	6.7(1)	0.30(1)	1.19(87)
22	30035-01-05-00	50965.018	1.02(3)	60(5)	−1.7(1)	0.33(4)	0.81(3)	1.01(2)	2.81(2)	0.41(5)	2.33(4)	6.7(1)	0.30(2)	1.15(87)
23	30035-01-03-00	50965.085	1.03(4)	50(2)	−1.7(2)	0.19(1)	0.93(1)	1.03(1)	2.81(1)	0.16(2)	2.46(2)	6.7(1)	0.31(3)	1.25(87)
24^a	30035-01-06-00^a	50966.019	0.98(3)	53(5)	−1.7(4)	0.20(4)	0.88(4)	1.02(3)	2.73(9)	0.60(8)	2.46(5)	6.71(4)	0.30(2)	1.04(87)
24^b	30035-01-06-00^b	⋅⋅⋅	0.90(2)	53(5)	−1.7(4)	0.21(3)	0.89(3)	1.04(2)	2.75(8)	0.59(6)	2.89(6)	6.68(3)	0.35(3)	0.98(87)
24^c	30035-01-06-00^c	⋅⋅⋅	0.95(3)	53(5)	−1.7(4)	0.19(4)	0.91(4)	1.03(3)	2.76(9)	0.61(8)	2.61(5)	6.69(4)	0.32(2)	1.01(87)
25	30035-01-04-00	50966.083	0.99(4)	3.9(1)	−3.0(9)	0.26(3)	0.68(3)	1.00(1)	2.67(5)	1.05(5)	2.40(9)	6.73(8)	0.39(8)	1.17(87)
26^a	30035-01-07-00^a	50996.268	1.00(1)	3(1)	3.0(8)	1.7(2)	0.58(5)	0.98(2)	2.7(2)	−0.03(1)	2.63(8)	6.71(4)	0.36(7)	1.31(87)
26^b	30035-01-07-00^b	⋅⋅⋅	0.95(2)	2.5(2)	3.0(8)	1.9(1)	0.57(3)	0.99(1)	2.8(1)	−0.06(2)	2.97(8)	6.75(4)	0.38(3)	1.30(87)
26^c	30035-01-07-00^c	⋅⋅⋅	0.99(2)	3(1)	3.0(8)	1.8(2)	0.59(4)	0.97(2)	2.7(2)	−0.04(1)	2.83(8)	6.69(4)	0.37(5)	1.28(87)
27	30035-01-08-00	50997.268	1.01(3)	40(5)	−2.42(2)	1.88(6)	1.34(3)	1.00(1)	3.01(2)	0.45(6)	2.03(2)	6.10(8)	0.46(2)	1.23(87)
28	30035-01-09-00	50998.268	0.90(4)	45(3)	−3.0(8)	0.004(1)	0.69(4)	1.01(1)	3.08(1)	0.89(8)	2.56(6)	6.72(4)	0.29(1)	1.05(87)
29	30035-01-10-00	50999.268	0.98(3)	50(6)	−3.0(9)	0.001(1)	0.60(7)	1.03(2)	2.89(7)	0.27(6)	2.39(2)	6.72(4)	0.73(2)	1.19(87)
30	30035-01-11-00	50997.402	1.02(2)	47(8)	−2.26(2)	1.63(6)	1.34(3)	1.00(1)	3.09(1)	0.59(8)	2.12(3)	6.2(1)	0.34(5)	1.15(87)
31	40020-01-01-00	51186.402	0.45(4)	110(10)	−1.19(7)	0.005(1)	0.60(7)	1.02(3)	2.83(1)	0.4(2)	2.89(9)	6.4(1)	0.65(7)	1.23(87)
32	40020-01-01-01	51186.920	1.03(2)	43(6)	−1.5(1)	0.01(1)	0.73(3)	0.98(2)	2.82(2)	0.38(4)	2.49(3)	7.24(6)	0.34(5)	1.28(87)
33^a	40020-01-01-020^a	51187.469	0.95(3)	26(3)	−2.0(2)	0.011(3)	0.60(4)	1.03(1)	2.78(3)	0.44(5)	2.58(4)	6.67(8)	0.78(6)	1.21(87)
33^b	40020-01-01-020^b	⋅⋅⋅	0.56(2)	78(9)	−2.1(2)	0.008(2)	0.61(2)	1.01(1)	2.79(3)	0.43(6)	2.59(2)	6.71(2)	0.81(7)	0.98(87)
33^c	40020-01-01-020^c	⋅⋅⋅	0.42(3)	91(8)	−2.0(3)	0.009(1)	0.61(4)	1.03(2)	2.78(3)	0.44(5)	2.57(4)	6.72(4)	0.80(9)	1.15(87)
33^d	40020-01-01-020^d	⋅⋅⋅	0.40(4)	80(9)	−2.3(2)	0.009(1)	0.63(4)	1.02(1)	2.78(3)	0.41(2)	2.56(3)	6.69(9)	0.75(7)	1.20(87)
33^e	40020-01-01-020^e	⋅⋅⋅	0.40(3)	94(9)	−2.1(3)	0.009(1)	0.59(3)	1.03(2)	2.79(3)	0.40(5)	2.62(4)	6.77(7)	0.81(8)	1.19(87)
34^a	40020-01-01-030^a	51188.260	0.44(4)	100(10)	−2.1(2)	0.010(1)	0.7(1)	1.01(1)	2.55(1)	0.40(2)	2.61(2)	6.97(7)	0.50(6)	1.18(87)
34^b	40020-01-01-030^b	⋅⋅⋅	0.43(5)	100(10)	−2.0(3)	0.009(1)	0.7(1)	1.01(2)	2.56(1)	0.42(5)	2.60(4)	6.94(6)	0.49(8)	1.20(87)
34^c	40020-01-01-030^c	⋅⋅⋅	0.44(4)	110(10)	−2.0(2)	0.008(2)	0.7(2)	1.03(1)	2.54(2)	0.41(4)	2.63(3)	6.96(9)	0.50(7)	1.16(87)
34^d	40020-01-01-030^d	⋅⋅⋅	0.43(2)	110(10)	−2.1(3)	0.008(1)	0.6(2)	1.02(1)	2.56(1)	0.40(5)	2.64(2)	6.78(8)	0.49(7)	1.18(87)
34^e	40020-01-01-030^e	⋅⋅⋅	0.43(4)	110(10)	−2.2(3)	0.009(3)	0.7(1)	1.01(2)	2.55(2)	0.40(6)	2.65(3)	6.62(9)	0.50(8)	1.17(87)
34^f	40020-01-01-030^f	⋅⋅⋅	0.43(4)	100(10)	−2.1(2)	0.009(2)	0.6(1)	1.01(1)	2.56(3)	0.39(5)	2.65(2)	6.56(9)	0.47(6)	1.18(87)
35^a	40020-01-01-04^a	51188.804	0.39(3)	110(12)	−1.7(2)	0.04(1)	0.60(3)	0.97(2)	2.75(1)	0.33(1)	2.69(2)	6.49(9)	0.92(5)	1.08(87)
35^b	40020-01-01-04^b	⋅⋅⋅	0.38(2)	110(15)	−1.7(1)	0.03(3)	0.61(2)	0.98(3)	2.76(2)	0.35(2)	2.67(3)	6.47(8)	0.94(6)	1.09(87)
35^c	40020-01-01-04^c	⋅⋅⋅	0.38(3)	120(12)	−1.8(2)	0.02(1)	0.60(1)	0.96(1)	2.75(1)	0.34(1)	2.66(4)	6.48(5)	0.93(7)	1.09(87)
35^d	40020-01-01-04^d	⋅⋅⋅	0.37(4)	120(15)	−1.9(3)	0.03(2)	0.63(2)	0.98(3)	2.73(1)	0.35(2)	2.68(3)	6.47(8)	0.92(6)	1.08(87)
36^a	40020-01-01-05^a	51189.152	0.41(2)	120(10)	−2.1(2)	0.04(1)	0.63(2)	1.01(2)	2.77(2)	0.32(3)	2.69(4)	6.46(7)	0.93(7)	1.15(87)
36^b	40020-01-01-05^b	⋅⋅⋅	0.38(4)	100(15)	−2.0(3)	0.03(2)	0.62(1)	1.02(1)	2.79(3)	0.30(3)	2.66(3)	6.47(8)	0.90(5)	1.25(87)
36^c	40020-01-01-05^c	⋅⋅⋅	0.39(4)	110(10)	−1.9(4)	0.03(1)	0.63(2)	1.00(1)	2.78(1)	0.31(2)	2.66(4)	6.46(7)	0.92(8)	1.28(87)
37^a	40020-01-01-060^a	51191.785	0.98(4)	10(3)	−0.09(3)	0.93(1)	1.17(7)	1.01(1)	3.04(6)	1.89(2)	2.6(1)	6.47(7)	0.42(5)	1.02(87)
37^b	40020-01-01-060^b	⋅⋅⋅	0.38(6)	90(9)	−2.1(2)	1.02(1)	0.52(4)	1.03(2)	2.68(1)	0.57(3)	2.68(4)	6.59(3)	0.89(7)	1.23(87)
37^c	40020-01-01-060^c	⋅⋅⋅	0.37(4)	110(10)	−2.1(2)	0.06(1)	0.54(3)	1.01(3)	2.65(2)	0.56(2)	1.64(3)	6.49(4)	0.68(4)	1.26(87)
37^d	40020-01-01-060^d	⋅⋅⋅	0.98(3)	23(5)	−2.1(2)	0.02(1)	1.14(2)	1.03(2)	2.60(1)	1.45(4)	1.57(2)	6.52(3)	0.83(9)	1.16(87)
37^e	40020-01-01-060^e	⋅⋅⋅	0.99(6)	15(5)	−0.06(2)	0.04(1)	1.15(3)	1.02(2)	2.08(5)	1.74(2)	0.7(1)	6.45(5)	0.76(7)	1.19(87)
38	40020-01-01-07	51192.852	0.41(5)	120(10)	−2.2(4)	0.06(4)	0.59(5)	1.01(2)	2.94(1)	0.60(3)	2.69(4)	6.5(2)	0.43(6)	1.08(87)
39	40020-01-03-00	51193.787	0.80(3)	80(10)	−2.0(2)	0.05(3)	0.51(3)	1.02(3)	3.01(2)	0.82(9)	2.68(3)	6.9(1)	0.32(8)	1.12(87)
40	40020-01-03-01	51194.860	0.82(2)	69(7)	−2.1(3)	0.06(4)	0.45(4)	0.99(1)	2.95(1)	0.69(5)	2.68(3)	6.5(1)	0.39(7)	0.93(87)
41	40706-02-01-00	51339.384	0.98(4)	2.0(3)	−0.08(3)	1.4(1)	1.17(8)	1.01(1)	3.04(9)	2.00^c	0.6(1)	6.27(9)	0.42(5)	1.00(87)
42	40706-02-03-00	51339.642	1.02(1)	3(1)	−0.14(9)	1.4(1)	1.22(9)	0.98(2)	3.01(8)	2.00^c	0.8(1)	6.23(8)	0.42(6)	1.06(87)
43	40706-02-06-00	51339.976	1.05(2)	7.6(5)	−1.83(6)	0.96(9)	0.84(7)	1.03(1)	2.59(1)	2.00^c	1.14(2)	6.39(5)	0.65(4)	1.29(87)
44	40706-01-01-000	51340.092	1.02(1)	2.3(2)	0.26(9)	1.58(5)	1.6(1)	1.01(1)	3.4(1)	2.00^c	0.3(1)	6.3(1)	0.42(5)	1.33(87)
45	40706-02-08-00	51340.908	0.99(3)	8.2(7)	−1.83(7)	1.15(8)	1.09(4)	0.99(2)	2.88(1)	2.00^c	1.38(1)	6.18(8)	0.46(5)	0.76(87)
46	40706-02-09-00	51340.939	1.00(1)	6.4(6)	−1.6(1)	1.11(9)	1.05(3)	1.02(3)	2.85(2)	2.00^c	1.35(2)	6.22(7)	0.44(6)	1.08(87)
47	40706-02-10-00	51340.974	1.03(2)	6.5(4)	−1.58(5)	1.16(8)	1.08(4)	1.03(2)	2.84(2)	2.00^c	1.36(1)	6.18(9)	0.45(5)	1.12(87)
48	40706-02-12-00	51341.155	1.07(4)	5.7(3)	−0.45(9)	1.17(9)	1.07(3)	1.01(1)	2.82(3)	2.00^c	1.34(2)	6.19(7)	0.46(6)	0.92(87)
49	40706-02-13-00	51341.222	0.99(2)	5.2(2)	−0.4(2)	1.09(8)	1.02(5)	0.98(2)	2.78(4)	2.00^c	1.32(3)	6.23(8)	0.44(7)	0.93(87)
50	40706-02-14-00	51341.288	0.97(3)	4.53(9)	−0.07(9)	1.2(1)	1.10(6)	0.99(1)	2.79(7)	2.00^c	1.31(9)	6.18(8)	0.46(6)	0.78(87)
51	40706-01-02-00	51341.355	1.00(2)	2.3(2)	0.2(1)	1.62(7)	1.5(1)	1.01(1)	3.4(1)	2.00^c	0.4(1)	6.32(7)	0.43(5)	1.34(87)
52	40706-02-16-00	51341.576	1.03(1)	3.3(2)	−0.27(8)	1.28(9)	1.02(8)	0.98(3)	2.17(9)	2.00^c	1.0(1)	6.32(6)	0.54(5)	1.04(87)
53	40706-02-17-00	51341.699	1.00(4)	3.7(3)	−0.58(9)	0.97(8)	0.82(9)	1.03(4)	2.36(7)	2.00^c	0.98(9)	6.32(7)	0.49(4)	1.03(87)
54	40706-02-18-00	51341.905	0.93(3)	5.9(8)	−1.50(8)	0.94(9)	0.90(6)	1.02(1)	2.71(2)	2.00^c	1.26(2)	6.32(7)	0.45(5)	0.94(87)
55	40706-02-19-00	51341.972	1.02(4)	6.6(5)	−1.5(3)	0.58(7)	0.67(8)	0.99(2)	2.67(1)	2.00^c	1.22(9)	6.38(8)	0.43(5)	1.23(87)
56	40706-02-21-00	51342.155	1.07(2)	7.8(6)	−1.6(1)	0.5(1)	0.80(6)	1.01(1)	2.65(3)	2.00^c	1.76(3)	6.69(7)	0.54(4)	1.18(87)
57	40706-02-23-00	51342.287	0.99(2)	2.2(1)	0.03(1)	1.4(2)	1.2(1)	0.98(2)	2.89(9)	2.00^c	0.68(9)	6.32(6)	0.50(7)	0.83(87)
58	40706-01-03-00	51342.354	1.01(3)	2.0(1)	0.26(9)	1.49(8)	1.25(9)	1.01(1)	3.03(8)	2.00^c	0.6(1)	6.39(7)	0.50(5)	1.18(87)
59	70015-01-01-00	52413.913	1.01(4)	4.9(3)	−1.9(2)	2.0(1)	0.59(8)	1.02(3)	2.78(2)	0.63(9)	2.23(5)	6.41(9)	0.4(1)	0.86(87)
60	70015-01-01-01	52413.982	1.08(3)	6.5(4)	−1.9(1)	2.01(9)	0.68(7)	0.99(1)	2.68(2)	0.6(1)3	2.09(4)	6.3(1)	0.7(1)	1.17(87)

Notes. Adopted model: wabs*(Comptb1 + Comptb2 + Gaussian). Parameter errors are given at the 90% confidence level. ^aThe spectral model is wabs*(Comptb1 + Comptb2 + Gaussian). ^bNormalization parameters of COMPTB components are in units of $L_{39}/d^2_{10}$ , where L₃₉ is the source luminosity in units of 10³⁹ erg s⁻¹, d₁₀ is the distance to the source in units of 10 kpc, and the Gaussian component is in units of 10⁻² × total photons cm⁻² s⁻¹ in line, σ_line of Gaussian component is fixed to a value of 0.8 keV (see comments in the text), and N_H was fixed at the value of 3 × 10²¹ cm⁻² (Christian & Swank 1997). Some data sets, although having the same proposal number, contain observations separated by time intervals. In these cases we collected all the observations close in time in just one CCD interval (see Figure 1), and distinguish the relative CCDs by superscripts (e.g., "a," "b," etc.), following the proposal number. ^cWhen parameter log (A₂) ≫ 1, this parameter is fixed at 2.0 (see comments in the text).

Download table as: ASCIITypeset images: 1 2

As seen from Figure 2, the CCD tracks are extended, in particular, relative to the FB (see II–VII panels). It is worth noting that the source moves back and forth along the Z-track for these particular observations. We select regions in the CCDs for each observational data set, marked with superscripts, e.g., "a," "b," etc. In contrast, relatively compact areas are seen in panels I, VIII, IX, and X. During these observations the source evolves around a short Z-track segment and thus one can conclude that the spectral variability is small for these observational segments. Using these selection criteria we elaborated the time intervals, which we applied to extract the relevant spectra for the PCA and HEXTE data sets.

The Z-shape evolution and its shift can be clearly seen in Figure 3. The evolution of the HID tracks as a function of the count rate in the (9–20 keV) energy band is characterized by significant HC variability (0.01 < HC < 0.03). One can see a well-developed FB for high intensities (groups I–VII), while a moderate HC variability (0.01 < HC < 0.016) is observed for relatively lower intensities (groups VIII–X).

Note that the FB in Sco X-1 is associated with a monotonic increase of the HC with respect to the total intensity from the bottom of the flaring branch to the top (bot FB and top FB respectively). This behavior in the HID is in contrast to that in the dipping Z-source GX 340+0, which shows only a slight increase and sometimes even a decrease of the HC with the total flux during the entire FB (see Hasinger & van der Klis 1989; Kuulkers & van der Klis 1996, and Seifina et al. 2013, hereafter STF13).

It is also very interesting to compare our study of the CCD and HID for Sco X-1 with those obtained by LRH09 for XTE J1701-462. Whereas the energy bands used for the CCD and HID are different between LRH09 and in our investigations of Sco-like Z-tracks, their evolutions demonstrate changes of the track shape and their positions are similar. In particular, LRH09 found that the position of the NB/FB vertex of the Z-track for XTE J1701-462 is shifted approximately along an inclined line with positive and negative inclinations for CCD and HID, respectively. (e.g., see panels II and III of Figure 5 in LRH09). The shapes of the Z-track for XTE J1701-462 evolve (in CCD and HID) while its ν-shape morphology remains, having clear elements of the HB, NB, and FB and a well-determined NB/FB vertex. In contrast, the HC of the NB/FB vertex in Sco X-1 changes with X-ray intensity (compare the pink and green line tracks in Figure 1) as that in XTE J1701-462, but then the HC increases with intensity.

3.3. Spectral Analysis

Z sources vary on timescales of minutes to hours. This is a subject of many previous investigations of Sco X-1 (see, for example, van der Klis et al. 1996; Bradshaw et al. 2003; Barnard et al. 2003; Belloni et al. 2004). Here we concentrate on specific properties of Sco X-1 related to the hard X-ray emission. The source + background spectra have been compared with the background spectra for both PCA and HEXTE in order to estimate the significance of the hard tail detection and to obtain the high-energy component of the spectrum as best as possible. In addition, we excluded the intervals that did not provide significant signal for the high-energy range (>30 keV).

As the first trial, we tested a model that consisted of an absorbed thermal component Bbody, a thermal Comptonization component Comptb (Farinelli et al. 2008), and a Gaussian line component. However, this model (wabs*(Bbody + Comptb + Gauss)) gave a poor description of about 60% of the data, in particular, of the FB spectra. Significant negative residuals at low energies (less than 4 keV) and greater than 30 keV suggest the presence of additional emission components. Because of this and the following suggestions by Farinelli et al., we also attempted a two-Comptb model wabs*(Comptb + Comptb + Gauss). As a result of these efforts, we found satisfactory fits for all available sets of the data (during all spectral states).

The Comptb model describes an emergent spectrum as a convolution of an input or seed blackbody spectrum having the normalization N_com and the seed photon temperature kT_s with a Comptonization Green function. Similar to the ordinary Bbody XSPEC model, the normalization N_com is a ratio of the source luminosity to square of the distance d

$\begin{equation} N_{{\rm com}}=\left (\frac{L}{10^{39}\ \mathrm{erg\ s^{-1}}}\right)\left (\frac{10\,\mathrm{kpc}}{d}\right)^2. \end{equation} \tag{ 1 }$

It is worthwhile to emphasize that the Comptb model is an updated version of the COMPTT model of XPEC (see Titarchuk 1994), with the only difference that the main parameters in the former model are the seed photon temperature kT_s, the electron temperature kT_e, the spectral index α, and parameter a, which is related to the illumination fraction of the Compton cloud by soft (seed) photons f = A/(1 + A).

This model describes a scenario in which a Keplerian disk is connected to the NS through the TL (see the description of this scenario in Titarchuk et al. 1998). In Figure 4, we illustrate our spectral model as applied to Sco X-1. We assume that accretion onto the NS takes place when the material passes through the two main regions: a geometrically thin accretion disk (for example, a standard Shakura–Sunyaev disk; see Shakura & Sunyaev 1973) and the TL, where the NS surface and soft disk photons are upscattered off hot electrons. In our picture the emergent thermal Comptonization spectrum is formed in the TL, where disk photons of temperature kT_s1 and soft photons from the NS photosphere of temperature kT_s2 are scattered off the TL hot electrons, giving rise to two Comptonized components, herein Comptb1 and Comptb2, respectively. The red and blue photon trajectories, shown in Figure 4, correspond to the soft (seed) and hard (upscattered) photons, respectively.

**Figure 4.** Suggested geometry of Sco X-1. Disk and neutron star soft photons are upscattered off the hotter plasma of the transition layer (TL) located between the accretion disk and NS surface. Red and blue photon trajectories correspond to soft and hard photons, respectively. Two Comptonized components are considered. The first one (*Comptb*1) is related to the *seed* (disk) photon temperature T_s1 ≲ 1 keV and the TL electron temperature $kT^{(1)}_ e$ varies from 3 keV to 180 keV. In the second Comptonized component (Comptb2), the temperatures T_s2 ∼1.5 keV and $kT^{(2)}_ e$ are presumably related to the NS surface and the inner part of its TL, respectively. During the FB (bottom panel) radiation pressure near the Eddington accretion rate disrupts the inner part of the accretion disk.
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**Figure 4.** Suggested geometry of Sco X-1. Disk and neutron star soft photons are upscattered off the hotter plasma of the transition layer (TL) located between the accretion disk and NS surface. Red and blue photon trajectories correspond to soft and hard photons, respectively. Two Comptonized components are considered. The first one (*Comptb*1) is related to the *seed* (disk) photon temperature T_s1 ≲ 1 keV and the TL electron temperature $kT^{(1)}_ e$ varies from 3 keV to 180 keV. In the second Comptonized component (Comptb2), the temperatures T_s2 ∼1.5 keV and $kT^{(2)}_ e$ are presumably related to the NS surface and the inner part of its TL, respectively. During the FB (bottom panel) radiation pressure near the Eddington accretion rate disrupts the inner part of the accretion disk.
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In the framework of the applied model wabs*(Comptb1 +Comptb2 + Gauss), the free parameters of the model are α₁, α₂; kT_s1, kT_s2; log (A₁), log (A₂), which are related to the Comptonized fractions f₁, f₂; $kT^{(1)}_e$ and $kT^{(2)}_e$ ; the normalizations of the BB components N_Com1 and N_Com2 of the Comptb1 and Comptb2 respectively. We also add to our model a Gaussian component, whose parameters are a centroid energy E_line, the width of the emission line σ_line, and normalization N_line.

It should be noted that we fixed certain parameters of the Comptb models: γ_1/2 = 3, which are related to the index of the low-energy part of the spectrum, namely α_1/2 = γ_1/2 − 1 = 2, and δ_1/2 = 0 because we neglect the efficiency of the bulk inflow effect versus the thermal Comptonization for NS accretion. The bulk inflow Comptonization should take place very close to the NS surface. However, if the radiation pressure in that vicinity is sufficiently high, then the bulk motion is suppressed. On the other hand, if mass accretion is quite low then the effect of the bulk motion is negligible. Generally, the bulk effect in NSs is a rare event. We also use a fixed value of the hydrogen column N_H = 3 × 10²¹ cm⁻², which was found by Christian & Swank (1997). We also fixed the value of the Comptb parameter log (A₂) to 2 when the best-fit values of log (A₂) ≫ 1 because in any case when log (A₂) ≫ 1 the Comptonization fraction f = A/(1 + A) approaches unity and further variations of A ≫ 1 no longer improve the fit quality.

Note that in the case of the two-Comptb model, we deal with two seed-photon temperatures, in which a low value of the temperature cannot be determined, because the PCA low-energy threshold (∼3 keV) is above the peak of the disk seed-photon blackbody temperature, which is typically ≲0.7 keV in LMXBs (see Barret 2001; Seifina & Titarchuk 2011, 2012, hereafter ST11 and ST12, respectively; Seifina et al. 2013). The results of these fits to the two-Comptb model are reported in Table 2.

Generally, the adopted spectral model for Sco X-1 exhibits fidelity throughout all the data sets used in our analysis. Namely, the value of the reduced $\chi ^2_{{\rm red}}=\chi ^2/N_{{\rm dof}}$ , 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, $\chi ^2_{{\rm red}}$ reaches 1.4. However, it never exceeds a rejection limit of 1.5 (for 90% confidence level). Note that the energy range for the cases in which we obtain the poor fit statistics (one among 98 CCD-resolved spectra with χ² = 1.46 for 87 d.o.f) is related to the iron line region. The line width σ_line does not vary much and previous measurements suggest that it is in the range of 0.7–0.8 keV. Therefore, we fixed the σ_line of the Gaussian component at a value of 0.8 keV. In this approach we detected only a moderate contribution of the Gaussian component to the spectrum throughout all Z spectral states except for some at the NB/FB vertex region. It is worth noting that LRH09 also detected a weak iron emission line in the spectrum of XTE J1701-462 during all Z-states with some increase at the lower part of the NB.

3.4. Spectral Properties as a Function of the Z-track Stage

In Figure 5, on the left panel we present the HID where the branches are traced out by arrows from HB→NB→bottom FB (on the left part) and then from the bottom FB to the top FB (on the right part). Here we also point out the different regions of the Z-track in HID using different colors. In the middle and right panels we show six representative EF_E spectral diagrams for the left and right parts of ν-shaped Z track, respectively. In the middle panel the spectra correspond to RXTE observations 20053-01-01-03 (green, bot NB), 20053-01-01-06^b (pink, NB; see Table 2), and 20053-01-01-00 (violet, HB). In the right panel we present three other spectral diagrams for the right part of the Z-track from bot FB→top FB. The corresponding data are taken from RXTE observations 20053-01-01-02^e (bright blue, Table 2, bot FB), 20053-01-02-01^a (red, mid FB; Table 2), and 20053-01-02-04 (black, top FB). The corresponding data are taken from RXTE observations 20053-01-01-02^e (bright blue, bot FB; Table 2), 20053-01-02-01^a (red, mid FB; Table 2), and 20053-01-02-04^{a − b} (black, top FB; Table 2). Using this figure, one can see changes of the spectral shape for the HB, NB, and FB spectral branches. In particular, the hard tail gradually decreases when the source moves from the HB through the NB to the bot NB. However, the hard emission becomes stronger when the source evolves from the bot NB to the top FB (see the left and right panels of Figure 5).

In Figure 6 we also show three representative EF_E spectral diagrams for different states along the Z-track. For these spectra, data are taken from RXTE observations 20053-01-01-00 (HB), 20053-01-01-06^b (NB, Table 2), and 20053-01-01-02^e (FB, Table 2). The data are shown by black points and the spectral model components are displayed by blue, red, and purple lines for Comptb1, Comptb2, and Gaussian, respectively. Yellow shaded areas demonstrate the evolution of Comptb1 from the HB, NB, to the FB branches when $kT^{(1)}_e$ monotonically increases from 3 keV to 180 keV. In this figure, one can clearly see changes of the spectral shape in the energy range greater than 30 keV and the relative contribution of Comptonized components for different Zbranches. In particular, the NB panel demonstrates the relative softening of the Comptb1 component in comparison to that presented in the HB panel. While the FB panel shows the hardening of the Comptb1 component in comparison to that seen in the HB–NB panels. We also detect a relative growth of the Gaussian iron line emission at the bottom of the NB (as one can see from panel Z2 of Figure 6).

Spectral changes are also seen in Figures 7 and 8, which show strong and reduced flaring activity sets as a function of time. In particular, the electron temperature $kT^{(1)}_e$ (blue points) ranges between 20 keV and 50 keV during the HB and NB states (see MJD 50556, 50561–50562) and then it decreases to 5 keV at the soft apex (see MJD 50559 in Figure 7 and MJD 51341 in Figure 8). $kT^{(1)}_e$ reaches its maximum at 200 keV during the FB (see MJD 50557, 50560 marked with blue vertical strips in Figure 7). On the other hand, the Comptb normalizations N_Com1 and N_Com2 are only weakly correlated with the variations of the flux ratio coefficient FR and count rate in the 2–9 keV energy band (black points), which is presumably related to the NS emission that dominates during all spectral states (see Figure 7). The normalization N_Com2 exhibits low variability from 0.4 to 3 in units of L₃₉/D²₁₀ (where L₃₉ is the luminosity of the seed blackbody component in units of 10³⁹ erg s⁻¹ and D₁₀ is the distance in units of 10 kpc). The X-ray contribution from the Comptonizaton of the seed photons coming from the disk is weaker by a factor of two than that related to the seed photons coming from the NS surface during all spectral states (Figure 7). It is worth noting that the energy spectral indices α shown in the bottom panels of Figures 7 and 8 only slightly vary with time about a mean value of one except for index α₁ at the FB intervals (marked by the blue vertical strips in Figure 7). At that time the index α₁ significantly decreases down to 0.3 (see MJD 50557, 50560 in Figure 7). These changes are also seen in Figure 9 along the total Z-cycle of Sco X-1.

**Figure 7.** From top to bottom: evolution of the count rate (2–9 keV) in counts s⁻¹ with 16 s time resolution (black points; see left scale axis) and ASM count rate (red points; see right scale axis), the flux ratio coefficient FR [10–50 keV]/[3–10 keV], the electron temperatures $kT^{(1)}_e$ (blue) and $kT^{(2)}_e$ (red) in keV, blackbody normalizations of the Comptb1 and Comptb2 components (blue and red, respectively), and the spectral indices α₁ and α₂ (α = Γ − 1) (blue and red) for the Comptb1 and Comptb2 components, respectively, during MJD 50555–50565(R1 set). The flaring phases of the light curve with the high TL electron temperature ( $kT^{(2)}_e>60$ keV) and the low spectral index (Γ₁ = α + 1 < 2) are marked with blue vertical strips.
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**Figure 8.** Same as that presented in Figure 7 but for MJD 51336–51345 (R5 set) with reduced flaring activity (marked by the yellow vertical strip).
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**Figure 9.** Evolution of spectral parameters vs. $T_e^{(1)}$ . Left column: the photon index (panel (a)), COMPTB normalization (b), and illumination fraction f (c) for the hard Comptonized component (Com 1; blue points) and soft Comptonized component (Com2; red points), vs. $T_e^{(1)}$ . Right column: (d) Hardness [50–250 keV]/[3–50 keV] (green points), (e) the (3–250 keV) flux (yellow points), and the (3–10 keV), (10–20 keV), (20–50 keV), and (50–250 keV) fluxes (panel (f)) vs. $T_e^{(1)}$ (in keV) from top to bottom, respectively.
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**Figure 9.** Evolution of spectral parameters vs. $T_e^{(1)}$ . Left column: the photon index (panel (a)), COMPTB normalization (b), and illumination fraction f (c) for the hard Comptonized component (Com 1; blue points) and soft Comptonized component (Com2; red points), vs. $T_e^{(1)}$ . Right column: (d) Hardness [50–250 keV]/[3–50 keV] (green points), (e) the (3–250 keV) flux (yellow points), and the (3–10 keV), (10–20 keV), (20–50 keV), and (50–250 keV) fluxes (panel (f)) vs. $T_e^{(1)}$ (in keV) from top to bottom, respectively.
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We can compare our spectral results on Sco X-1 with the spectral evolution of XTE J1701-462. In particular, LRH09 used a spectral model which consisted of BB, MCD (multicolor disk), Gaussian, and CBPL (Comptonized broken power law) components to fit the spectrum of XTE J1701-462. In this model they found that the spectrum of XTE J1701-462 on the HB of the Z-stage shows a hard tail (see Figure 13 in LRH09) which can be explained by Comptonization of the soft photons that originated in the innermost disk region. We obtain a similar result for the Sco X-1 case. Namely, using our Comptonization component (Comptb1), indicated by the yellow shaded area in Figure 6 (left panel), we reveal a hard emission in the HB stage. Furthermore, LRH09 found that the spectra of XTE J1701-462 corresponding to the HB/NB vertex, NB, and NB/FB vertex did not have the Comptonized component (in their terms, the CBPL component). In Sco X-1 we detect the Comptonized component (Comptb1) at the NB but it is rather weak (see the central panel of Figure 6). In the FB, the spectrum of XTE J1701-462 was mainly characterized by the BB+MCD components and with some indication for a weak hard emission (see Figure 13 in LRH09). In contrast to LRH09, we detect the strong Comptonized component (Comptb1) at the FB of the Sco X-1 spectrum up to 250 keV (see the right panel of Figure 6). Furthermore, the photon index of Comptb1 is surprisingly decreased during the FB, which is an indication of the hardening of X-ray emission in Sco X-1. It is interesting to note that another Z-source, GX 340+0,does not show a significant Comptonized component at the FB state (see STF13). Such a difference can be related to different distances to these sources (D_ScoX-1 = 2.8 kpc, D₁₇₀₁ = 8.8 kpc, D_{GX340 + 0} = 11 kpc). Thus, the proximity of Sco X-1 to Earth provides us with a unique opportunity to study the FB stage for Z sources.

3.5. Z-state Evolution of X-Ray Spectral Parameters in Sco X-1 as a Function of the Electron Temperature $kT_e^{(1)}$

In Figure 9, we present the dependencies of the photon index Γ, the Comptb normalization N_com, the illumination fraction f, the flux ratio, and the X-ray flux on the electron temperature $kT_e^{(1)}$ . Here we mark the HB and NB states by violet and blue vertical strips, respectively. In addition, the hard and soft apexes are indicated by arrows and a pink vertical strip highlights the interval of the mid-top FB stage where the photon index of the hard component Γ₁ significantly decreases (from 2.0 to 1.3). As it is clearly seen from this figure, the FB, NB, and HB stages of the Z-cycle can be related to a change of $kT_e^{(1)}$ (in the framework of our model).

3.5.1. The FB

The FB of the Sco X-1 spectrum is characterized by a wide range of electron temperature $kT_e^{(1)}$ (from 5 to 200 keV). High and low values of the $kT_e^{(1)}$ occur at the top FB and near the soft apex, respectively (see the HID on the left part of Figure 5). The photon index Γ₁ shows a specific behavior during the FB. In Figure 9 (see panel (a), blue points) one can see that Γ₁ decreases from 2 to 1.3 when the total X-ray flux increases (see panel (e)). In contrast, the soft Comptonized component of the X-ray spectrum (Com 2) shows that Γ₂ only slightly varies around 2 (see the red points in panel (a)). When the object goes into the mid FB (see the pink vertical strip in panel (b) of Figure 9) the COMPTB normalization N_com1 drops by a factor of 4–5, reaching the lowest level ( $N_{{\rm com1}}<0.25 L_{39}/D^2_{10}$ , panel (b), blue points). On the other hand, N_com2 monotonically increases and exceeds $3 L_{39}/D^2_{10}$ (see panel (b), red points). At this stage we find that the Γ₁ and N_com1 of the hard Comptonized component drop. In the FB, the illumination fractions of both components f₁ and f₂ are quite different. While values of f₁ are low (f₁ < 0.1, blue points), those of f₂ is high (f₂ > 0.6, red points of panel (c)). The mid-top FB spectra are characterized by a high hardness ratio (see panel (d)) and high level of the 3–250 keV flux (>3 × 10⁻⁷ erg s⁻¹ cm⁻²; see panel (e)). Note also that the source behavior during the FB was evaluated using CCD-resolved and HID intervals, shown in Figures 2 and 3. Different Z cycles belong to different areas of the CCD and HID although their FB spectral properties are similar and almost independent of the Z-cycle change.

3.5.2. The NB/FB Vertex

The NB/FB vertex of the Z-track for Sco X-1 (indicated as a "soft apex" in Figure 5) is associated with the lowest value of the electron temperature $kT_e^{(1)}$ ( $kT^{(1)}_e\sim 3$ keV). This apex is a boundary between two phases of the photon index behavior, Γ₁ = 2 (at the NB-HB) and Γ₁ < 2 (at the FB). Panel (a) of Figure 9 demonstrates that at this apex Γ₁ (blue points) and Γ₂ (red points) are both equal to 2. Moreover, the soft apex (NB/FB vertex) is characterized by sharp changes of the Comptb normalizations and the illumination factors for both Comptonized components f₁ and f₂ as variations of $kT_e^{(1)}$ are small (see panels (b) and (c) of Figure 9). As one can see from this figure, f₁ and f₂ anticorrelate with each other when $kT_e^{1}$ increases. For the hard Comptonized component Com 1, the normalization N_com1 decreases from $2\times L_{39}/D^2_{10}$ to $0.2\times L_{39}/D^2_{10}$ and f₁ decreases from 0.6 to 0.05 when $kT_e^{(1)}$ increases from 3 to 40 keV (see panels (b) and (c), respectively). While the normalization of the soft Comptonized component N_com2 increases from $0.5\times L_{39}/D^2_{10}$ to $2.5\times L_{39}/D^2_{10}$ , the fraction f₂ increases and saturates at unity (see panels (b) and (c), respectively). In the NB/FB vertex (soft apex) the spectra of Sco X-1 are characterized by lower values of the flux ratio and the 3–200 keV flux (see panels (d) and (e), respectively).

3.5.3. The NB

The NB of the Z-track for Sco X-1 (indicated by the bright blue vertical strip in Figure 9) is associated with a specific range of the electron temperature $kT_e^{(1)}$ . When the source transits from the HB/NB vertex (hard apex) to the NB/FB vertex (soft apex; see left panel of Figure 5) $kT_e^{(1)}$ monotonically decreases from 40 keV to 5 keV. The photon indices Γ₁, Γ₂ throughout the NB state are around 2 (see the blue and red points in panel (a) in Figure 9). The COMPTB normalization parameters (N_{com1, 2}) monotonically increase by a factor of five during the NB (see panel (b) of Figure 9). The hard Comptonized component (Com 1) is characterized by a significant illumination fraction f₁ only in the vicinity of the soft apex, but then throughout the rest of the NB f₁ is extremely low, whilethe illumination fraction f₂ related to the second Comptonization component (Com 2) is high (f₂ → 1) over the NB (see the left bottom panel of Figure 9). The NB spectra of Sco X-1 are characterized by a variable flux ratio (see panel (d)) and a wide range of 3–200 keV flux ((1.5–3.6) × 10⁻⁷ erg s⁻¹ cm⁻²; panel (e)). Note also that in the NB the spectrum is relatively soft (see the middle panel of Figure 6).

3.5.4. The HB

The HB of the Z-track, indicated by the violet vertical strip in Figure 9, is associated with a small range of the electron temperature $kT_e^{(1)}$ ( $40<kT^{(1)}_e<50$ keV). The photon indices Γ₁, Γ₂ throughout the HB are around 2 (the blue and red points in panel (a) in Figure 9). The COMPTB normalization of the hard component N_com1 remains at the level of $1.5\times L_{39}/D^2_{10}$ (blue points in panel (b)), while the soft component is dominant (see red points; $2<N_{com2}<2.7 L_{39}/D^2_{10}$ ). In the HB, the fraction f₂ is variable over a wide range (from 0.6 to 1), while the fraction f₁ is extremely low (f₁ < 0.1; see panel (c)). In the HB the spectra are characterized by a high flux ratio (see panel (d)) and a relatively high 3–200 keV flux ((1.5÷3.6) × 10⁻⁷ erg s⁻¹ cm⁻²; see panel (e)). Note also that in this state the spectrum has a hard tail characterized by Γ₁ ≈ 2, in contrast to the FB hard tail, for which Γ₁ is in the range from 1.4 to 2.

Thus, our analysis allows us to separate the contributions of the two zones related to the hard and soft Comptonized components: one is related to the TL and another to the NS emission. Furthermore, we detect a significant increase of the $kT^{(1)}_e$ in the FB, in contrast to other atoll and Z sources in which the electron temperature kT_e usually reduces during flaring events (see, e.g., Seifina & Titarchuk 2012; Church et al. 2014).

3.6. Timing Properties of Sco X-1 during the NB–HB–FB Evolution

The timing properties of Sco X-1 have been extensively studied previously and well documented by many authors (e.g., van der Klis 1994). However, given our new and unique approach to model the spectral evolution of Sco X-1, we have chosen to perform a joint spectral–temporal analysis for CCD-selected intervals to search for deeper physical insight. The RXTE light curves were analyzed using the powspec task from FTOOLS 5.1. The timing analysis of RXTE/PCA data was performed in the 2–13 keV energy range using the binned mode. The time resolution for this mode is 1/128 s. We found that the shape of the power density spectrum (PDS) at high frequencies is dominated by dead-time effects (see also Zhang et al. 1995) which, in the case of Sco X-1 at a count rate >25,000 counts s⁻¹ PCU⁻¹, are large, uncertain, and not well understood to predict the real shape of the PDS' high-frequency part. Because of this we use PDSs only up to about 100 Hz (see Figure 10). The normalization parameter of Powspec was set to −2, such that Poisson (white) noise is subtracted and the remaining power integrates to give the excess variance in the light curve. To investigate the evolution of the source timing properties and use it for Z-branch identification, we modeled the PDSs using analytic models and the χ² minimization technique in the framework of the QDP/PLT plotting package.⁷

**Figure 10.** Top: HID (left), total luminosity vs. $kT_e^{(1)}$ (middle), and Γ₁ vs. L_com2 in Eddington units (right). Red/blue/black points A, B, and C mark moments at MJD = 50557.2/50556.6/50819.6^a, 50818.7^a/50817.8/50558.7^a, and 50816.9^c/50817.8^b/50820.9^e related to different phases of the Z-track (see Table 2). Bottom: PDSs for the 3–13 keV band (left column) are plotted along with the spectra (right column) for points A (red), B (blue), and C of the X-ray flux ratio vs. flux diagram (see upper left panel). The data are shown by black points and the spectral model components are displayed by the dashed red, blue, and purple lines for the Comptb1, Comptb2 and Gaussian components, respectively. Yellow shaded areas demonstrate the evolution of the Comptb1 component between the HB and FB. The normalization factors of two and 0.5 were applied for the 20053-01-02-01^b (blue) and 20053-01-02-00^c (red) spectra, respectively (see panel C2).
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**Figure 10.** Top: HID (left), total luminosity vs. $kT_e^{(1)}$ (middle), and Γ₁ vs. L_com2 in Eddington units (right). Red/blue/black points A, B, and C mark moments at MJD = 50557.2/50556.6/50819.6^a, 50818.7^a/50817.8/50558.7^a, and 50816.9^c/50817.8^b/50820.9^e related to different phases of the Z-track (see Table 2). Bottom: PDSs for the 3–13 keV band (left column) are plotted along with the spectra (right column) for points A (red), B (blue), and C of the X-ray flux ratio vs. flux diagram (see upper left panel). The data are shown by black points and the spectral model components are displayed by the dashed red, blue, and purple lines for the Comptb1, Comptb2 and Gaussian components, respectively. Yellow shaded areas demonstrate the evolution of the Comptb1 component between the HB and FB. The normalization factors of two and 0.5 were applied for the 20053-01-02-01^b (blue) and 20053-01-02-00^c (red) spectra, respectively (see panel C2).
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From the lower NB to the FB, Sco X-1 shows a monotonic increase of the very low frequency noise (VLFN) below 1 Hz. The shape of the high frequency noise (HFN) component can be fit by an exponentially cutoff power law ( $\nu ^{-\alpha _{{\rm HFN}}} e^{-\nu /\nu _{{\rm cut}}}$ ). The HFN rms amplitude, in contrast to the VLFN, decreases along the Z-track (from ∼7% to 3%).

In addition to the noise continuum in the PDSs, we found QPOs between 5 Hz and 20 Hz that can be modeled by Lorentzians. In particular, we detected reliable QPOs with centroid frequency near 6 Hz when the source moves along the NB. We also found a continuous increase of QPO frequency from 6 Hz to 15 Hz when the source moves from the NB to the FB. Then, during the FB, the QPO frequency steeply increases from 10 Hz to 20 Hz and finally disappears at the highest count rates. Note that almost the same timing behavior was detected in another observation with EXOSAT (Priedhorsky et al. 1986; Dieters & van der Klis 2000) and with RXTE (van der Klis et al. 1996; Casella et al. 2006). One can relate these QPO frequency changes over the FB and its absence at the top of the FB with significant changes of the energy spectra of Sco X-1 (see Section 3.7). Hereafter we use these timing signatures along with spectral signatures (Section 3.4) for additional identification of the Zbranch of Sco X-1.

3.7. Correlation between Timing and Spectral Properties during Spectral State Transitions

We consider the main properties of the power spectra along with those of the energy spectra. We find a specific behavior of Γ₁ and the low QPO changes during the FB. Namely, we detect a significant change in Γ₁ at the FB from quasi-constancy around Γ₁ = 2, which is established for the HB–NB phases. To investigate the timing changes during this index change (1.3 < Γ₁ < 2) we present the results of the FB state analysis for the time interval MJD = 50556−50821 (R2 set). On the top of Figure 10, (top left panel) we show the HID corresponding to this time interval, where the red/blue/black points A, B, and C mark moments at MJD = 50557.2/50556.6/50819.6^a, 50818.7^a/50817.8/50558.7^a, and 50816.9^c/50817.8^b/50820.9^e related to different phases of the Z branches. Here, the superscripts indicate the corresponding CCD-resolved intervals (in accordance with Table 2).

As already mentioned above, the HIDof Sco X-1 consists of two branches of a ν-shaped Z-track. The power and energy spectra of the left branch (HB–NB–soft apex) are presented at the bottom panels (A) in Figure 10, while that of the right branch (soft apex–bot FB–mid FB–top FB) are shown at the two bottom panels (B) and (C). The FB can be divided into three segments: lower (B blue, B red), middle (B black, C red), and upper (C blue, C black). The FB (lower part) stage is associated with the canonical soft apex along the Z-track. As we argue above (see Section 3.4), we do not find significant differences of the energy spectra between the bottom NB point (A black) and the bottom FB points (B red/blue). While the time variability properties for these points in the HID are very different (for comparison, see the bottom left and right panels of Figure 10).

The NS seed photon temperature T_s2 is about 1.5 keV when Sco X-1 is around the bot NB and the bot FB (see Figure 11 for T_s2 values). On the other hand a significant decrease of T_s2 from 1.5 to 0.7 keV was detected when the source transits from the soft to hard apex and from the mid FB to the top FB states. This significant change of T_s2 in the FB is a clear indication of the NS photospheric expansion due to high radiation pressure from the NS during this phase.

**Figure 11.** Seed photon temperature kT_s2 (in keV), using our spectral model wabs*(Comptb1 + Comptb2 + Gaussian), plotted as a function of the COMPTB normalization of the soft Comptonized component N_com2 (in units of $L_{39}/D^2_{10}$ ). The colors of the vertical strips correspond to that of Figure 9.
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In the bottom panels of Figure 10 we show PDS for the 3–13 keV band (left column), which are presented along with the spectra (plotted as E*F(E)) fitted to our model (right column) for A (red), B (blue), and all C points of the HID shown on the upper left panel. The strong and broad Normal Branch Oscillations are seen at 2–10 Hz (peaked at ∼6 Hz, FWHM = 11.2 ± 4.1 Hz, rms = 5.3 ± 1.0% (A red) and FWHM = 9.7 ± 3.5 Hz, rms = 4.8 ± 1.2% (A blue), respectively) during the NB state. For the bottom of the FB (B blue, B red; see left upper panel) the related PDS (see left bottom panel B1) shows two QPO peaks at 10 Hz and 7 Hz, respectively, when the source moves from the bottom FB to the middle FB. On the other hand, PDSs of the middle FB (B black, C red points in the upper left panel) show broad flaring branch oscillations around ∼7 Hz (FWHM = 12.2 ± 3.4 Hz, rms = 7.5 ± 1.4%) along with VLFN (∼5 % rms). As Sco X-1 moves from the middle to the top of the FB we can clearly see an increase in the QPO frequency from 6 Hz to at most ∼20 Hz (FWHM = 10.2 ± 2.5 Hz, rms = 5.3% ± 1.2% for point C blue). The highest QPO frequency measured (∼21 Hz) was found during a flare in 1998 January data (C blue point). Finally, at the top of the FB (C black) we do not find any QPO features, only the strengthened VLFN component (∼3% rms).

Note that a similar QPO frequency evolution between 8 Hz to 5 Hz when the source goes from the bot FB to the mid FB was previously detected with EXOSAT by Dieters & van der Klis (2000); however, they did not detect any energy spectral changes. In contrast, due to the broadband RXTE coverage we discover significant changes of the energy spectra at high-energy range (E > 30 keV) along with ν_QPO excursions.

On the bottom right panels of Figure 10 we present spectra for the 3−250 keV energy range (panels A2, B2, C2), related to the corresponding PDSs (see panels A1, B1, C1). The data are shown by black points and the spectral model components are displayed by the dashed red, blue, and purple lines for the Comptb1, Comptb2, and Gaussian components, respectively. Yellow shaded areas demonstrate an evolution of the Comptb1 component during the state transition. In particular, the energy spectra for groups A and B are very similar, while for group C they show significant changes at the high-energy band (E > 30 keV). For the red/blue/black C points on the upper left panel, we present all corresponding energy spectra on the bottom right panel to demonstrate the spectral evolution of the hard and soft Comptonized components. Comparison of the energy spectra in the B2 and C2 panels reveals a noticeable decrease of the Γ₁ photon index for group C. Furthermore, one can see that the PDS in the C case is completely different from that seen in the B case.

4. INTERPRETATION OF THE OBSERVED SPECTRAL PROPERTIES

Before we proceed with the interpretation of the observations, let us briefly summarize them as follows. (1) The spectral data of Sco X-1 are well fit by two soft and hard Comptonized (Comptb) components for all analyzed HB, NB, and FB spectra. (2) The soft Comptonized component is dominant throughout all spectral states (see Table 2 and the two normalization panels in Figures 7 and 8). (3) The high-energy tail of the X-ray spectra can be fit by the hard Comptonized component.

We find a very unique drop in Γ₁ when Sco X-1 is in the FB and the luminosity of Sco X-1 is close to the critical value L_Edd. This fact is very surprising with respect to other NS LMXBs (e.g., 4U 1728-34 (ST11), 4U 1820-30 (TSF13), GX 3+1 (ST12), GX 340+0 (STF13)), which all demonstrate the constancy of the index (Γ₁ ∼ 2). However, it is important to note that all these sources, besides Sco X-1, were observed at a sub-critical regime throughout all spectral states, while in Sco X-1 we find the source is in the Eddington regime. To take into account this peculiarity, we explore the situation when the luminosity reaches its critical value, which is applicable to the FB of the Sco X-1 case.

4.1. Energy Release in the NS Transition Layer and the Spectral Index of the Emergent Spectrum

As Farinelli & Titarchuk (2011), hereafter FT11, pointed out, the energy release in the TL determines the spectral index of the emergent spectrum. Namely, FT11 (see also Zel'dovich & Shakura 1969) demonstrated that the energy flux per unit surface area of the TL (corona) can be found as

$\begin{equation} Q_{{\rm cor}}=20.2\int _0^{\tau _0}\varepsilon (\tau)T_e(\tau)d\tau, \end{equation} \tag{ 2 }$

where T_e(τ), ε(τ), and τ₀ are the plasma (electron) temperature, the radiation density distributions in the TL, and its Thomson optical depth, respectively.

We obtain the energy distribution ε(τ) as a solution of the diffusion equation

$\begin{equation} \frac{d^2\varepsilon }{d\tau ^2}=-\frac{Q_{{\rm cor}}}{c}q(\tau), \end{equation} \tag{ 3 }$

where c is the speed of light, q(τ) = 1/τ_⋆ for τ ⩽ τ_⋆, and q(τ) = 0 for τ_⋆ ⩽ τ ⩽ τ₀. If one compares this equation with the similar equation in FT11, he/she finds that here we assume that the gravitational energy release takes place only in the part of the TL where 0 ⩽ τ ⩽ τ_⋆ because the high radiation (plus magnetic) pressure from the NS finally stops the accretion flow. We should also add the two boundary conditions at the inner TL boundary (which can be a surface of the NS) and the outer boundary τ = 0. They are correspondingly:

$\begin{equation} \frac{d\varepsilon }{d\tau }|_{\tau =\tau _0}=0, \end{equation} \tag{ 4 }$

$\begin{equation} \frac{d\varepsilon }{d\tau }-\frac{3}{2}\varepsilon |_{\tau =0}=0. \end{equation} \tag{ 5 }$

Using the expression for q(τ) (see Equation (3) and below) we find the solution ε(τ) to Equations (3)–(5)

$\begin{equation} \varepsilon (\tau)= \frac{3Q_{{\rm cor}}}{c}[(\tau +2/3) - \tau ^2/2\tau _{\star }]\quad {\rm for}\ 0\le \tau \le \tau _{\star } \end{equation} \tag{ 6 }$

and

$\begin{equation} \varepsilon (\tau)= \frac{3Q_{{\rm cor}}}{c}(\tau _{\star }/2+2/3)\quad {\rm for}\ \tau _{\star }\le \tau \le \tau _0. \end{equation} \tag{ 7 }$

Thus, integration of ε(τ) gives us

$\begin{equation} \int _0^{\tau _0}\varepsilon (\tau)d\tau = \frac{Q_{{\rm cor}}}{c}\left(\tau ^2_{\star }+2\tau _0\right). \end{equation} \tag{ 8 }$

It is easy to see that the result we obtain is identical to that in FT11 for τ_⋆ = τ₀. Now we can estimate the Comptonization Y-parameter in the TL using Equations (2) and (8). We rewrite Equation (2) using the mean value theorem as

$\begin{equation} Q_{{\rm cor}}=20.2\hat{T}_e \int _0^{\tau _0}\varepsilon (\tau)d\tau, \end{equation} \tag{ 9 }$

where $\hat{T}_e$ is the mean temperature in the TL. Substitution of formula (8) in Equation (9)

$\begin{equation} \frac{k\hat{T}_e\left(\tau _{\star }^2+2\tau _0\right)}{m_ec^2}=0.25 \end{equation} \tag{ 10 }$

leads to the estimate of the Y-parameter in the TL (for a definition of the Y-parameter, see Rybicki & Lightman 1979)

$\begin{equation} Y=\frac{4k\hat{T}_e\tau _0(\tau _{0}+2)}{m_ec^2}=\frac{4\tau _{0}(\tau _{0}+2)}{\tau _{\star }^2+2\tau _0}. \end{equation} \tag{ 11 }$

Now we use this formula for the Y-parameter to determine the spectral index α_diff. Namely, we can write (see FT11)

$\begin{equation} \alpha =-\frac{3}{2}+\sqrt{\frac{9}{4}+Y^{-1}}. \end{equation} \tag{ 12 }$

We rewrite the asymptotic form of this equation when Y⁻¹ ⩽ 1 as

$\begin{equation} \alpha \approx \frac{Y^{-1}}{3}=\frac{4}{3}\frac{(\tau _\star /\tau _0)^2+2/\tau _0}{1+2/\tau _0}. \end{equation} \tag{ 13 }$

Thus, one can see that the spectral index α < 1 when τ_⋆ < τ₀ and τ₀ ≫ 1. In Figure 10 (the upper right panel), we present the observed dependencies of the photon spectral index of the Comptonized component Γ₁ (α₁ = Γ₁ − 1) and thus one can see that Γ₁ is indeed significantly less than 2 (or α₁ < 1) when the observed luminosity L_com2 coming from the TL's inner part is around 1 and higher. This leads us to suggest that in this case the gravitational energy release takes place only in the TL's outer region where L < L_crit.

Now we show that the critical luminosity L_crit, at which the radiation force equals the gravitational force, is higher than the Eddington one for the electron temperature kT_e ≳ 50 keV.

4.2. Temperature Correction of Scattering Cross-section for Critical Luminosity Calculation

In order to explain the observed dependencies of Γ versus L and L versus kT_e (see Figure 10, middle and upper right panels), we have to estimate the critical luminosity for a given plasma characteristic kT_e and its presumed spectrum J_ν(E). To do this, we should calculate the weighted electron cross-section 〈σ〉 using the relativistic photon-Maxwellian electron cross-sectionWienke (1985) for normal chemical abundance

$\begin{equation} \langle \sigma \rangle =\frac{\int J_\nu (E) \sigma (E, kT_e)dE}{\int J_\nu (E)dE}. \end{equation} \tag{ 14 }$

Then, the critical luminosity (which is the Eddington luminosity when 〈σ〉 = σ_T) for a given electron temperature can be found by equating the gravitational force and the radiation force

$\begin{equation} L_{{\rm crit}}=\int J_{\nu } (E)dE= \frac{4\pi c GM_{{\rm NS}}}{\langle \sigma \rangle }. \end{equation} \tag{ 15 }$

We calculate L_crit for M_NS = 1.4 M_☉ and then we make a plot L_crit versus kT_e (see the solid blue line in the upper middle panel) and we see that this theoretical dependence passes through all observed data points (L, kT_e).

We also show here the level of the Eddington luminosity, assuming that σ = σ_T (see the dashed green horizontal line in the upper middle panel of Figure 10). It is clear to see from this plot that the critical luminosity L_crit(T_e) is higher than L_Edd for higher temperature kT_e and the electron temperature correction of the scattering cross-section explains an increase of L_crit versus T_e.

4.3. Comparison between Spectral Characteristics of Z Sources and Atoll Sources

Now we know the correlations between the spectral and timing properties for a variable mass accretion rate observed in X-rays in Sco X-1 during the evolution across the HB–NB–FB track. We identify a new kind of the spectral index behavior in this source in relation to other known NS LMXBs. For this reason, it is interesting to compare Sco X-1 with other NSs and find similarities and differences between them. Therefore, we present a comparative analysis for five sources: Z-sources Sco X-1 and GX 340+0 (STF13) and atoll sources GX 3+1 (ST12), 4U 1820-30 (TSF13), and 4U 1728-34 (ST11) using the same spectral model which consists of the Comptonized continuum and the Gaussian line components (see Table 3). It is also interesting to compare our findings on Sco X-1 with the spectral behavior of the unique NS source XTE J1701-462 since both objects show spectral transitions in the super Eddington luminosity regime.

Table 3. Comparisons of the Best-fit Parameters of Z-sources Sco X-1 and GX 340+0¹ and atoll Sources GX 3+1², 4U 1728-34³, and 4U1820-30⁴, and "atoll+Z" Source XTE J1701-462⁵

Source	Alternative	Class⁴	Distance,	Presence of	kT_e,	N_comptb	kT_s	f
Name	Name	Class⁴	(kpc)	kHz QPO	(keV)	$L_{39}^{{\rm soft}}/{D^2_{10}}$	(keV)	f
4U 1617-15	Sco X-1	Z, Sp, B	2.8⁷	+⁸	3–180	0.3–3.4	0.4–1.8	0.08–1
4U 1642-45	GX 340+0	Z, Sp, B	10.5⁹	+¹²	3–21	0.08–0.2	1.1–1.5	0.01–0.5
4U 1744-26	GX 3+1	Atoll, Sp, B	4.5¹⁰	none¹³	2.3–4.5	0.04–0.15	1.16–1.7	0.2–0.9
4U 1728-34	GX 354-0	Atoll, Su, D	4.2–6.4¹¹	+¹⁴	2.5–15	0.02–0.09	1.3	0.5–1
4U 1820-30	⋅⋅⋅	Atoll, Su, -	5.8–8¹⁵	+¹⁶	2.9–21	0.02–0.14	1.1–1.7	0.2–1
XTE J1701-462	⋅⋅⋅	Atoll+Z, Su, -	8.8¹⁷	+¹⁸	⋅⋅⋅	⋅⋅⋅	1–2.7	⋅⋅⋅

References. (1) STF13; (2) ST12; (3) ST11; (4) TSF13; (5) LRH09; (6) Classification of the system in the various schemes (see the text): Sp = supercritical, Su = subcritical, B = bulge, D = disk; (7) Bradshaw et al. (1999); (8) Zhang et al. (2006); (9) Fender & Hendry (2000), Christian & Swank (1997); (10) Kuulkers & van der Klis 2000; (11) van Paradijs 1978; (12) Jonker et al. 1998; (13) Strohmayer 1998; (14) Titarchuk & Osherovich 1999; (15) Shaposhnikov & Titarchuk 2004; (16) Smale et al. 1997; (17) Lin et al. 2007, 2009; (18) Sanna et al. 2010.

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4.3.1. Quasi-constancy of the Photon Index at the sub-Eddington Regime and a Reduction of the Photon Index Γ₁ at the High Luminosity State

Z-sources Sco X-1 and GX 340+0 and atoll sources GX 3+1, 4U 1820-30, and 4U 1728-34 demonstrate a similar Γ versus T_e behavior in the sub-Eddington regime, namely, the quasi-constancy of the spectral index Γ, which is distributed around 2. It is important to emphasize that we consider the spectral behavior here, which is related to the Comptonization region, which in our scenario is the TL. According to FT11, ST11, ST12, and STF13, this result probably indicates that the gravitational energy release takes place in the whole TL, namely τ_⋆ = τ₀ for these five sources, and that is much higher than the cooling flow of the soft disk photons (see Equations (11) and (12)).

However, for Sco X-1 we test a wider range of luminosity than in other Z and atoll sources (see above). In particular, Sco X-1 allows us to establish the index behavior at the critical luminosity regime, when the emergent luminosity is even higher than the Eddington luminosity. We find that the photon index of the TL region Γ₁ significantly decreases when the source accretes close to the Eddington regime, which takes place in the FB (see Figures 10 and 12). Namely, in this mid-topFB stage, the hard Comptonization tail is characterized by the reduced value of the photon index (1.3 < Γ₁ < 2) and the high electron temperature of the TL (60 keV <kT_e < 200 keV). Despite its low level of normalization N_com1, the hard Comptonized component Comptb₁ is firmly detected at least up to 200 keV in the FB. Moreover, the fraction of the high-energy emission increases when kT_e increases and Γ₁ drops from 2 to 1.3. It should be emphasized that only Sco X-1 among other Z sources reaches the critical luminosity regime (see the dark blue points in Figure 12). In turn, it is reasonable to compare this result on atoll and Z sources with the spectral properties of the unique source XTE J1701-462 (LRH09), which involves both atoll and Z stages of evolution as well as reaching the Eddington luminosity. Whereas LHR09 apply different models to the spectral fit of XTE J1701-462 emission, in their model the so-called CBPL component (i.e.,a constrained BPL with E_b = 20 keV and Γ ⩽ 2.5) in the soft states and the BPL in the hard states assume the role of weak Comptonization. In the framework of that model the observations of XTE J1701-462 in the hard states are dominated by the BPL component with photon index Γ ∼ 2, while in the soft states the photon index often reaches its hard limit Γ ∼ 2 and ranges up to Γ ⩽ 2.5 in the spectral fit with the CBPL model, i.e., Γ is normally greater than 2. This discrepancy with our results for the atoll and Z sources (for which Γ ⩽ 2 in our model) can be related to the different model composition and different energy range used for the spectral fit. In fact, LRH09 analyzed the XTE J1701-462 spectrum only from 3 keV up to 80 keV.

**Figure 12.** Photon index Γ vs. *kT_e* for the Z-sources Sco X-1 (blue stars) and GX 340+0 (red triangles; taken from STF13) and atoll sources 4U 1728-34 (bright blue diamonds; taken from ST11), GX 3+1 (pink circles; taken from ST12), and 4U 1820-30 (green squares; taken from TSF13).
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4.3.2. Spectral Hardness and Electron Temperature Variability for Atoll and Z Sources: Comparison with XTE J1701-462

In order to compare the properties of the evolution of Sco X-1 and GX 340+0 with atolls and BHC sources we plot in Figure 13 (upper panel) HC (10–50 keV/3–50 keV) versus the luminosity in the 3–10 keV range (the hardness–luminosity diagram (HLD))for seven sources: Z-sources Sco X-1 and GX 340+0 (STF13); atoll sources GX 3+1(ST12), 4U 1820-30 (Titarchuk et al. (2013), hereafter TSF13), and 4U 1728-34 (ST11); and BHC sources SS 433 (Seifina & Titarchuk 2010, hereafter ST10) and 4U 1630-47 (Seifina et al. 2014, hereafter STS14).

As seen from Figure 13, upper panel, these NS and BH binaries trace specific tracks in this HLD. We find that various types of NS LMXB subclasses can be well traced by the soft X-ray luminosity. More specifically, the spectral hardness HC of different types of NS LMXB subclasses (atolls, GX atolls, Sco-like Z sources, and Cyg-like Z sources) is a function of the luminosity L_{3 − 10} in the soft energy range from 3 to 10 keV. In this way a Z source traces its Z branches at higher mass accretion rates, while atolls are observed at lower mass accretion rate values ( $\dot{M}$ ). Note that we assume that L_{3 − 10} is proportional to the mass accretion rate. We should point out that atolls and BHs are similar when their luminosities are relatively low while Z sources are entirely different from BHs. It is interesting that BHs span almost the whole X-ray luminosity range as it is covered by various types of NS LMXB subclasses. Figure 13 (bottom panel) shows that Z sources are more luminous than BHs in their soft states.

It is interesting that a Cyg-like Z source (e.g., GX 340+0) traces its Z branches at some higher $\dot{M}$ than Sco-like Z sources (e.g., Sco X-1). In turn, bright atolls (e.g., GX 3+1) trace their CCDs (usually between the lower banana to upper banana) at some higher $\dot{M}$ than ordinary atolls (e.g., 4U 1728-34, 4U 1820-30). In this respect it is interesting to review and investigate the spectral properties of XTE J1701-462 (see Homan et al. 2010). This unique X-ray source allows the study of its spectral characteristics along outburst phases with different properties of the NS systems versus its luminosity. It shows all flavors of the NS systems: first appearing as a Z source, then showing features of an atoll source, and finally fading. Homan at el. (2010) found that an initial Cyg-like behavior was followed by a Sco-like behavior as the luminosity fell. Thus, they concluded that Cyg-/Sco-like types depend on luminosity. They also compared the observed tracks for XTE J1701-462 with those found in the various NS LMXB subclasses and suggested that Z-sources and atolls can be linked through changes in a single variable parameter, namely, the mass accretion rate leading to the wide variety of behaviors observed in NS LXMBs with different luminosities.

We also compare the electron temperature variations along the spectral state changes for different NS LMXB subclasses (see Figure 13, bottom panel). One can see that kT_e is also traced by L_{3 − 10}. The electron temperature kT_e in atolls is usually related to relatively lower luminosity, while that in Z sources corresponds to the luminosity very close the Eddington one. In fact, this diagram demonstrates a clear difference between atoll and Z sources. Similar correlations were found by Lin et al. (2009) and Homan et al. (2010) for the case of XTE J1701-462. They claimed that for the 2006–2007 outburst events the luminosity L_{3 − 10} was a good parameter to track the gradual evolution of the CCD and HID tracks and allowed them to relate the observed properties to other NSs. In particular, they detected XTE J1701-462 with Z-source properties in terms of its CCD and HID when the source was at a high luminosity phase. On the other hand, XTE J1701-462 exhibited atoll properties when its luminosity becomes smaller.

5. CONCLUSIONS

In this paper, we study the correlations between the spectral and timing properties, and the mass accretion rate observed in the X-ray source Sco X-1 with RXTE. We find that the broadband energy spectra of Sco X-1 during all Z-states can be adequately reproduced by an additive model, consisting of two Comptonized components with different seed photon temperatures (for example, T_s1 = 0.7 keV and T_s2 = 1.6 keV). We also include an iron line represented by a Gaussian component to the model in order to obtain reliable fits.

Our approach to modeling the X-ray spectra of Sco X-1 allows us to separate the contributions of two distinct zones of spectral formation related to the hard and soft Comptonized components along the Z track which is possibly driven by the mass accretion rate $\dot{M}$ . In fact, the observed soft photon luminosity which is determined by normalization parameters of the Comptonized components (see Equation (1)) is proportional to $\dot{M}$ . We observe an increase in N_Com1 and N_Com2 (Figure 9) from the soft apex to the hard apex in the CCD (see Figure 1) which can indicate an increase of the mass accretion rate $\dot{M}$ from the lower normal branch to the upper normal branch.

The normalization parameter N_Com2 is related to the soft (NS) Comptonized componentand is related to total mass accretion rate $\dot{M}_{{\rm tot}}$ . One can see from Figure 9, panel b, how the total mass accretion rate, or N_Com2, increases when kT_e increases. Using Figure 1 one can also see how the hardness ratio increases from the lower FB to the upper FB. We should also point out that a comparative analysis using our model shows that various NS LMXBs are also well traced by soft luminosity in the energy range from 3 to 10 keV.

Our spectral analysis also allows us to reveal the stability of both photon indices Γ₁ and Γ₂ around 2 during the HB/NB/bot FB states, while the decrease of Γ₁ is observed in the mid-top FB. We interpret the detected quasi-stability of the indices of the Comptonized components about the value of 2 during the HB–NB–bot FBin the framework of the model in which the gravitational energy release occurs in the TL and when that is much higher than the soft (disk) flux. This index stability phase is now established for the Comptonized spectral components of Sco X-1 over HB–NB–bot FB. This result is similar to those previously found in the atoll sources 4U 1728-34, GX 3+1, and 4U 1820-30 and the Z-source GX 340+0 through all spectral states. We interpret the new index reduction phase detected over the FB in Sco X-1 for the hard Comptonized component in the framework of the model in which the gravitational energy release takes place only in some outer part of the TL. However, in its lower part, the soft photon illumination increases (mainly by NS soft photons), which is followed by a decrease of the plasma temperature. As a result, the electron cross-section increases and the radiation pressure reaches its critical value and thus it stops the accretion flow (see Section 4).

Note that during this index reduction stage the X-ray spectrum of Sco X-1 exhibits an electron temperature $T_e^{(1)}$ increase from 60 keV to 180 keV. It is important to emphasize that in BH sources the index increases up to a saturation level when the luminosity increases. This behavior is opposite to that seen in Sco X-1.

We are very grateful to the referee whose constructive suggestions help us to improve the quality of our paper.

X-RAY SPECTRAL AND TIMING BEHAVIOR OF SCORPIUS X-1. SPECTRAL HARDENING DURING THE FLARING BRANCH

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ABSTRACT

1. INTRODUCTION

2. DATA REDUCTION AND ANALYSIS

3. RESULTS

3.1. Color–color and Hardness–Intensity Diagrams of Sco X-1