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The Astrophysical Journal, 738:128 (20pp), 2011 September 10
C

doi:10.1088/0004-637X/738/2/128

2011. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

ON THE CONSTANCY OF THE PHOTON INDEX OF X-RAY SPECTRA OF 4U 1728-34 THROUGH ALL SPECTRAL STATES
Elena Seifina1 and Lev Titarchuk2
1 2

,3 ,4

Sternberg Astronomical Institute, Moscow State University, Universitetsky Prospect 13, Moscow 119992, Russia; seif@sai.msu.ru ` Dipartimento di Fisica, Universita di Ferrara, Via Saragat 1, I-44100 Ferrara, Italy; titarchuk@fe.infn.it, lev@milkyway.gsfc.nasa.gov 3 School of Physics, Astronomy, and Computational Sciences, George Mason University, Fairfax, VA 22030, USA 4 Goddard Space Flight Center, NASA, code 663, Greenbelt, MD 20770, USA Received 2011 January 5; accepted 2011 June 24; published 2011 August 18

ABSTRACT We present an analysis of the spectral properties observed in X-rays from neutron star X-ray binary 4U 1728-34 during transitions between the low- and high-luminosity states when the electron temperature kTe of the Compton cloud monotonically decreases from 15 to 2.5 keV. We analyze the transition episodes from this source observed with BeppoSAX and RXTE satellites. We find that the X-ray broadband energy spectra of 4U 1728-34 during all spectral states can be modeled by a combination of a thermal (blackbody-like) component, a Comptonized component (which we herein denote as COMPTB), and a Gaussian component. Spectral analysis using this model provides evidence that the photon power-law index is almost constant ( = 1.99 ± 0.02) when kTe changes from 15 to 2.5 keV during these spectral transitions. We explain this quasi-stability of the index by the model in which the spectrum is dominated by the strong thermal Comptonized component formed in the transition layer (TL) between the accretion disk and neutron star surface. The index quasi-stability takes place when the energy release in the TL is much higher than the flux coming to the TL from the accretion disk. Moreover, this index stability effect now established for 4U 1728-34 during spectral evolution of the source was previously suggested for a number of other neutron binaries. This intrinsic property of the neutron star is fundamentally different from that in black hole binary sources for which the index monotonically increases during spectral transition from the low state to the high state and saturates at high values of the mass accretion rate. Key words: accretion, accretion disks ­ black hole physics ­ radiation mechanisms: non-thermal ­ stars: individual (4U 1728-34) ­ stars: neutron Online-only material: color figures

1. INTRODUCTION The evolution of spectral parameters of compact objects in X-ray binaries is of great interest for understanding the nature of compact objects. It is well known that a number of black hole (BH) candidate sources demonstrate correlations between their 1­10 Hz quasi-periodic oscillation (QPO) frequencies L and photon power-law index during spectral transition when sources evolve from the low state (LS) to the high state (HS), see Shaposhnikov & Titarchuk (2009), hereafter ST09. Then the definition of the spectral state is related to the level of soft blackbody emission presumably related to the mass accretion rate. In the HSs of BHs, these index-QPO frequency correlations sometimes show a saturation of at high values of L . On the other hand, ST09 (see also Titarchuk & Seifina 2009, hereafter TS09) found that saturates with the mass accretion rate in almost any case of a BH binary. This saturation effect can be considered as a BH signature or as a signature of the converging flow (CF) into a BH (ST09 and TS09). The question that naturally arises is how the spectral index behaves as a function of the mass accretion rate or as a function of cutoff energy of the spectrum in neutron star (NS) sources. Recently, Farinelli & Titarchuk (2011, hereafter FT11), collected X-ray spectra obtained by BeppoSAX from quite a few NS sources: Sco X-1, GX 17+2, Cyg X-2, GX 340+0, GX 3+1, and GS 1826-238. Their results probably indicate that the value of the photon index slightly varies around 2 independently of the spectral state (or electron temperature of a Compton cloud) at least for this particular sample of NS spectra (see Di Salvo et al. 1

2000; Farinelli et al. 2008). However, the available data for those sources were taken when these sources were in the HS or in the low state (LS), but nobody has analyzed up to now the spectral evolution from the LS to the HS for any particular NS source. A suitable candidate for the study of the spectral evolution in an NS is the so-called atoll 4U 1728-34, which exhibits a remarkable spectral transition from the LS to the HS and vice versa. 4U 1728-34 (GX 354-0) was first resolved by UHURU scans of the Galactic center region in 1976 (see Forman et al. 1976 and Bradt et al. 1993). Then type I X-ray bursts from 4U 1728-34 were discovered during SAS-3 observations by Lewin et al. (1976) and Hoffman et al. (1976). Further, the bursting behavior was subsequently studied in detail using extensive observations by SAS 3, which accumulated 96 bursts in total. Using these data Basinska et al. (1984) presented evidence for a narrow distribution of peak burst fluxes, as well as a correlation between the peak flux and the burst phase. The distance to the source in the range of 4.2­6.4 kpc has been estimated by van Paradijs (1978) and confirmed by Basinska et al. (1984) and Kaminker et al. (1989) using measurements of the peak burst fluxes. A radio counterpart of 4U 1728-34 was detected during Very Large Array (at 4.86 GHz) observations with a variable flux density in the range of 0.3­0.6 mJy (Marti et al. 1998). The estimated extinction of the source is AV 14, and a precise position following from the detection of the radio counterpart allowed us to identify this source as a K = 15 infrared source (Marti et al. 1998). Long-term Ariel-5 measurements, as well as extensive monitoring by the All-Sky Monitor (ASM) on board RXTE, suggest the presence of a long-term quasi-periodicity about 63­72 days (Kong et al. 1998). RXTE/Proportional


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Counter Array (PCA) observations of the source in 1996 led to the discovery of nearly coherent millisecond oscillations during the X-ray bursts (Strohmayer et al. 1996). Titarchuk & Osherovich (1999) presented a model for the radial oscillations and diffusion of the perturbation in the transition layer (TL) surrounding the NS. Using dimensional analysis, they identified the corresponding radial oscillation and diffusion frequencies in the TL with the low-Lorentzian L and break frequencies b for 4U 1728-34. They predicted values for b , related to the diffusion in the boundary layer, that are consistent with the observed b . Subsets of the bursts observed during the PCA observations have also been studied by van Straaten et al. (2001) and Franco (2001) with particular attention to the relationship between the appearance of burst oscillations and a value of the mass accretion rate. Titarchuk & Shaposhnikov (2005, hereafter TS05) analyzed RXTE/PCA observations of 4U 1728-34 in the energy range from 3 keV to 40 keV and found that, using the model comprising two Comptonization components (BMC5 ), the photon index is consistent with being quasi-constant (around 2.2), while the low QPO frequency does not exceed 10 Hz. then monotonically increases to values of 6. Moreover, using broadband observations of 4U 1728-34 by BeppoSAX, Di Salvo et al. (2000) and Piraino et al. (2000) fitted the X-ray spectra of 4U 1728-34 in a wide energy range from 0.1 keV to 200 keV by a sum of Blackbody components plus a thermal Comptonization spectrum, usually described by the XSPEC COMPTT model (Titarchuk 1994; Hua & Titarchuk 1995). The TS05 model cannot fit the BeppoSAX data; moreover, this model has more parameters than does the model of Di Salvo et al. (2000), Piraino et al. (2000), and FT11. Naturally, we pose the question of whether the FT11 model can fit the BeppoSAX along with RXTE data and what dependence of index versus spectral state can be found. In this paper, we try to answer a fundamental question of the possibility of distinguishing a BH from NS systems, which others have extensively attempted to solve without considering the mass of the compact object as a main argument, in particular without using optical counterpart data to measure mass function. In this way, some methods have been proposed to identify systems that contain BHs using X-ray observational properties only. The strong rapid variability was first considered as a signature of the presence of BH (Oda et al. 1971), until the same rapid variability was detected in accreting NSs (Tennant et al. 1986). Now it is well established that Galactic BH candidates (BHCs) demonstrate two spectral states, the HS and LS, and transition between the two (Remillard & MacClintock 2006). However, sometimes the so-called atoll-NS sources6 also show the "high" and "low" spectral states (D' Ai et al. 2006; TS05). Therefore, this property requires more detailed investigations of BHs versus NSs. Specifically, the HS spectra of BHCs are characterized by thermal emission at 1 keV, presumably originated in the accretion disk, along with a steep power-law tail whose photon index ( = 2­3) monotonically increases with the mass accretion rate (see ST09). The LS spectra show much weaker disk emission than that in the HS spectra and
5

BMC is the so-called Bulk Motion Comptonization XSPEC Model (see details in Section 6.2.10 of "User's Guide of an X-Ray Spectral Fitting Package XSPEC v.12.6.0" and http://heasarc.gsfc.nasa.gov/ xanadu/xspec/manual/Additive.html). 6 Here, we use a term of the atoll-NS sources to specify NS X-ray binaries characterized by a specific " "-shaped track in a color­color diagram.

a harder power-law tail (the photon index of which is around 1.7). This hard component is generally believed to be a result of thermal Comptonization of soft (disk) photons in a hot gas (Compton cloud) in the vicinity of the compact object. BHs, in contrast with NSs, sometimes demonstrate a more complicate X-ray spectrum. For example, the RXTE spectra of BH GRS 1915+105 require two Comptonization components, soft and hard ones (see Titarchuk & Seifina 2009). In this case one can clearly see the evolution of two photon indices 1 = 1.7­3.0 and 2 = 2.7­4.2 for the hard and soft components, respectively. Titarchuk & Seifina (2009) argued that the index saturation effect of the hard component is due to Comptonization of the soft (disk) photons in the CF into BH and that of the soft component is due to the thermal Comptonization in the TL when the mass accretion rate increases. These conclusions were later supported by Monte Carlo simulations by Laurent & Titarchuk (2011). Moreover, in the description of BH and NS X-ray LS spectra with the thermal Comptonization model, there is an essential difference between these types of the compact sources. The electron temperature of the Compton (scattering) cloud kTe is usually lower for NSs, kTe < 25 keV, than that for BHs, kTe > 50 keV (see Churazov et al. 1997). The lower electron temperature in NSs is a consequence of the additional cooling provided by the NS surface, which reflects X-ray photons and ultimately determines the value of the Compton cloud electron temperature (Titarchuk et al. 1998 and see also Sunyaev & Titarchuk 1989; Kluzniak 1993). This fact of the observed difference between the BH and NSs was recently also discussed by Reynolds & Miller (2011). They conclude the observable difference of kTe in these types of the sources is evidence of the absence and presence of a solid surface in BHs and NSs, respectively, and this fact can be considered as indirect evidence for the existence of the event horizon in BHs. It is worth pointing out that Titarchuk et al. (1998) and Titarchuk & Fiorito (2004) previously came to similar conclusions based on the analysis of the Compton cooling of the X-ray emission region (TL) in the presence (NS) and absence (BH) of the reflection surface. Thus, the basic property that distinguishes BHs from NSs is the presence of the event horizon as well as a CF in the vicinity of a BH (Ebisawa et al. 1996). In fact, close to the event horizon, the strong gravitational force dominates the pressure forces and leads to an almost free fall CF of accreting material into a BH. The dynamic Comptonization of low energy photons off fastmoving electrons dominates the thermal Comptonization at a high-mass accretion rate and the plasma temperature of the CF is less than 10­15 keV; as a result, an extended steep power law is formed (see Titarchuk et al. 1997; Titarchuk & Zannias 1998; Laurent & Titarchuk 1999). These kinds of spectra are observed in the soft state of BH binaries (see, e.g., ST09 and TS09). On the other hand, in NS sources the radiation pressure forces become dominant close to their surface; thus, a free fall should be suppressed at high-mass accretion rates. Does the presence of the firm surface in the NS make any difference in the dependence of the photon index versus mass accretion rate with respect to that established in BHs (see ST09; TS09; ST10)? Furthermore, can the index saturation detected in many BHs with the mass accretion rate exist only in BH sources, since it has not yet been observed in NS sources? For example, Di Salvo et al. (2006), studying low-mass X-ray binaries hosting NSs, concluded that it is unlikely to distinguish BHs from NSs based on their X-ray spectra. However, FT11 argue that in NS sources the index 2


The Astrophysical Journal, 738:128 (20pp), 2011 September 10 Table 1 List of BeppoSAX Observations of 4U 1728-34 Used in the Analysis ObsID 20674001 20889003 Start Time (UT) 1998 Aug 23 19:15:27 1999 Aug 19 02:01:32 End Time (UT) 1998 Aug 24 09:14:15 1999 Aug 20 04:54:32

Seifina & Titarchuk

MJD Interval 51048.8­51049.41 51409.1­51410.22

References. 1 Di Salvo et al. 2000; 2 Piraino et al. 2000.

varies weakly until the soft photon illumination of the transition layer, Qd , is much smaller than the energy release in the TL, Qcor . We try to test further this kind of index behavior in the NS source using X-ray observations of the atoll source 4U 1728-34 and compare it, if possible, with the index dependence on the mass accretion rate established in BHs. In this paper, we present the analysis of the available BeppoSAX observations during 1998­1999 and RXTE/PCA/ HEXTE observations during 1996­2000 for 4U 1728-34. 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 an evolution of X-ray spectral and timing properties during the state transition in Sections 4 and 5. We discuss our results and make our conclusions in Sections 6 and 7. 2. DATA SELECTION Broadband energy spectra of the source were obtained combining data from three BeppoSAX Narrow Field Instruments (NFIs): the Low Energy Concentrator Spectrometer (LECS; Parmar et al. 1997) for 0.3­4 keV, the Medium Energy Concentrator Spectrometer (MECS; Boella et al. 1997) for 1.8­10 keV, and the Phoswich Detection System (PDS; Frontera et al. 1997) for 15­60 keV. The SAXDAS data analysis package was 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 were renormalized 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. After the fitting procedure we checked whether these normalizations were in a standard range for each instrument.7 Specifically, the LECS/MECS renormalization ratio is 0.92, and the PDS/MECS renormalization ratio is 0.97. In addition, spectra were rebinned according to energy resolution of the instruments in order to obtain significant data points. We rebinned the LECS spectra, applying a rebinning template for grouping (lecs_2.grouping) with an energy-dependent binning factor used in GRPPHA of XSPEC.8 We also rebinned the PDS spectra with a linear binning factor of two, grouping two bins together (resulting bin width is 1 keV). In Table 1 we list the BeppoSAX observations used in our analysis. We also analyzed the available data obtained with RXTE (Bradt et al. 1993), which were found in the time period from 1996 February to 2000 July (see also the review by Galloway et al. 2008). In our investigation we selected 127 observations made at different count rates (luminosity states) with a good coverage of rise­decay flare track. We performed an analysis of RXTE observations of 4U 1728-34 during four years for eight intervals, indicated by blue rectangles in Figure 1 (top). We also
7 8

analyzed two BeppoSAX observations, whose dates are marked by green triangles in Figure 1. Standard tasks of the HEASOFT/FTOOLS 5.3 software package were utilized for data processing. For spectral analysis we used PCA Standard 2 mode data, collected in the 3­20 keV energy range. The standard dead time correction procedure was applied to the data. The average dead time correction is in the range 3%­10% depending on the count rate value. HEXTE data were used in order to construct broadband spectra. We subtracted the background corrected in off-source observations. To exclude the channels with the largest uncertainties, we used only data in the 20­60 keV energy range for the spectral analysis. The HEXTE data were renormalized based on the PCA. Typical PCA/HEXTE renormalization factor is 0.98. We used the data that are available through the GSFC public archive (http://heasarc.gsfc.nasa.gov). In Table 2 we list the groups of RXTE observations that cover the source evolution from quiescent to flare events. Note that we did not use any normalization factor to normalize between BeppoSAX and RXTE data. We also used public 4U 1728-34 data from the ASM on board RXTE. We retrieved the ASM light curves (in the 2­12 keV energy range) from the public RXTE/ASM archive at MIT.9 In the bottom panel of Figure 1 we show a mean count rate (blue dashed line) during the 1996­2010 interval of ASM/RXTE monitoring observations of 4U 172834. In this panel one can also see a long-term quasi-periodic variability of mean soft flux during a cycle of six years. We investigate available periods of slow variability (indicated by green) during which we also have the BeppoSAX observations of 4U 1728-34 (see also the upper panel of Figure 1). We use definitions of the low- and high-luminosity states to relate these states to the source luminosity, and we demonstrate that during the high­low state transition the electron temperature of the Compton cloud changes from 2.5 keV to 15 keV, and vice versa, respectively. Thus, the "high spectral state" corresponds to the "low electron temperature state" and vice versa the "low spectral state" corresponds to the "high electron temperature state." During the flare seen in the ASM light curve the electron temperature kTe usually decreases from 15 keV to 2.5 keV. We introduce a definition of a "burst" to point out a significant increase in X-ray flux (about a factor of five) with respect to the persistent emission level. Specifically, we identify a "burst" when the ASM count rate is greater than 10 counts s-1 . We associate the count rate increase with the increase in the mass accretion rate. 3. SPECTRAL ANALYSIS In our spectral data analysis we use a model that consists of a sum of the Comptonization (COMPTB) component (COMPTB is the XSPEC Contributed model;10 see Farinelli et al. 2008,
9 10

http://heasarc.nasa.gov/docs/sax/abc/saxabc/saxabc.html http://heasarc.gsfc.nasa.gov/FTP/sax/cal/responses/grouping

http://xte.mit.edu/ASM_lc.html http://heasarc.gsfc.nasa.gov/docs/software/lheasoft/ xanadu/xspec/models/comptb.html

3


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- RXTE - BeppoSAX

4U 1728-34

R1- R8

Figure 1. Top: evolution of the ASM/RXTE count rate during 1996­2006 observations of 4U 1728-34. Blue rectangles indicate the RXTE/PCA & HEXTE data of pointed observations, and green triangles show BeppoSAX NFI data used for analysis. Bottom: ASM/RXTE 1 day-type light curve of 4U 1728-34 during 1996­2010. The blue dashed line shows a mean count rate and indicates the long-term quasi-periodic variability of mean soft flux during a cycle of six years. The green double arrow points out the 1996­2000 time interval of RXTE observations used in our analysis (see R1­R8 intervals). (A color version of this figure is available in the online journal.) Table 2 List of Groups of the RXTE Observation of 4U 1728-34 Used in the Analysis Number of Set R1 R2 R3 R4 R5 R6 R7 R8 Dates (MJD) 50128­50143 50710­50728 51086­51196 51409­51443 51237­51359 51198­51213 51667­51733 51652­51657 RXTE Proposal ID 10073 20083 30042 40019 40027 40033 50023 50029 Dates (UT) 1996 Feb 15­Mar 1 1997 Sep 19­Oct 1 1998 Sep 30­1999 Jan 18 1999 Aug 19­Sep 22 1999 Feb 27­Jul 10 1999 Jan 20­Feb 4 2000 Mar 7­Jul 8 2000 Apr 18­23 Rem. Ref. 1, 2, 3, 4, 5, 7, 8 3, 4, 5, 7, 8 4 8 6, 8 6, 8 6, 8 6, 8

BeppoSAX

References. (1) Strohmayer et al. 1996; (2) Ford & van der Klis 1998; (3) van Straaten et al. 2001; (4) Di Salvo et al. 2001; (5) Mendez et al. 2001; (6) Migliari et al. 2003; (7) Jonker et al. 2000; (8) TS05.

hereafter F08), a soft blackbody component of temperature TBB , and the Gaussian line component. The COMPTB spectral component has the following parameters: temperature of the seed photons Ts , energy index of the Comptonization spectrum (= - 1), electron temperature Te , Comptonization fraction f (f = A/(1 + A)), and the normalization of the seed photon spectrum NCOMPTB (see the Appendix for the definition of NCOMPTB ). 4

In Figure 2 we illustrate our spectral model as a basic model for fitting the BeppoSAX and RXTE spectral data for 4U 1728-34. We assume that accretion onto an NS takes place when the material passes through the main two regions, a geometrically thin accretion disk (standard Shakura­Sunyaev 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


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Transition layer

Neutron Star

Disk photons

Figure 2. Suggested geometry of the system. Disk and NS soft photons are upscattered (Comptonized) in the relatively hot plasma of the TL (between the accretion disk and the NS surface). Some fraction of these photons is seen directly by the Earth observer. Red and blue photon trajectories correspond to soft and hard (upscattered) photons, respectively. (A color version of this figure is available in the online journal.)

spectrum is formed in the TL region, where disk BB-like seed photons and NS soft photons are upscattered in the relatively hot plasma. Some fraction of these seed soft photons can also be seen directly by the Earth observer. Red and blue photon trajectories shown in Figure 2 correspond to soft (seed) and hard (upscattered) photons, respectively. We show examples of X-ray spectra in Figure 3 (for BeppoSAX data) and in Figures 4 and 5 (for RXTE data). Spectral analysis of BeppoSAX and RXTE observations indicates that X-ray spectra of 4U 1728-34 can be described by the model, while its Comptonization component can be presented by the COMPTB model. Moreover, for broadband BeppoSAX observations, this spectral model component is modified by photoelectric absorption at low energies. Also following the suggestions of Di Salvo et al. (2000) and Piraino et al. (2000), we add a Gaussian line at 6.7 keV and a thermal blackbody component at low energies (1­4 keV) to improve the fit statistics. Along with these components, Di Salvo et al. (2000) included a narrow Gaussian line to fit an excess in the residuals around 1.7 keV. We also test the presence of this line feature, but the addition of this component to the model does not improve the quality of the model fit. It is worth noting that D' Ai et al. (2006) analyzed simultaneous Chandra and RXTE observations of 4U 1728-34 (2002 March 2­5). They fitted the 1.2­35 keV continuum spectrum with a blackbody plus a Comptonized component, and they fitted large residuals at 6­10 keV by a broad (FWHM 2keV) Gaussian emission line or, alternatively, by two absorption edges associated with low ionized iron and Fe xxv/xxvi. However, in the framework of this model, D' Ai et al. (2006) found no evidence of broad or narrow Fe K lines between 6 and 7 keV. However, using our model wabs*(blackbody+COMPTB+Gaussian) we found an iron line feature during all BeppoSAX and RXTE observations. 5

On the top of Figure 3 we demonstrate the best-fit BeppoSAX spectrum using our model, and in the bottom right panel we show the best-fit spectrum along with for the model (reduced 2 = 1.16 for 445 dof). In particular, we find that the addition of the soft blackbody-like component of temperature TBB = 0.5­0.7 keV to the model significantly improves the fit quality of the BeppoSAX spectra. The line emission is clearly detected in the range from 5 to 8 keV, as one can see from the left bottom panel of Figure 3. We show that this line is quite broad, and it is much wider than the instrumental response whose width is smaller than 0.02 keV.11 Thus, we include in the model asimple Gaussian component whose parameters are a centroid line energy Eline , the width of the line line , and the normalization Nline to fit the data in the 6­8 keV range. We also include in the model the interstellar absorption with a column density NH . It should be mentioned that we fixed certain parameters of the COMPTB component: = 3 (low energy index of the seed photon spectrum) and = 0 because we neglect the efficiency of the bulk inflow effect versus the thermal Comptonization in the case of NS source 4U 1728-34. For the BeppoSAX data (see Tables 1 and 3) we find that the spectral index is of 1.03 ± 0.04 (or the corresponding photon index = + 1 is 2.03 ± 0.04). While the temperature of the seed photons Ts of the COMPTB component changes from 1.2 to 1.3 keV, the color temperature of the soft Blackbody component TBB is around 0.6 keV. Unfortunately, RXTE detectors cannot provide wellcalibrated spectra below 3 keV, while the broad energy band of BeppoSAX telescopes allows us to determine the parameters of blackbody components at soft energies. Thus, in order to fit the RXTE data we have to fix the temperature of the blackbody component at a value of TBB = 0.7 keV, obtained as an upper
11

See ftp://heasarc.gsfc.nasa.gov/sax/cal/responses/98_11.


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keV (keV/cm2 s keV)

10

-4

10

-3

0.01

0.1

1

1

10 channel energy (keV)

100

10

10

1

1

-1

normalized counts s-1 keV

0.01

normalized counts s-1 keV
S
2

-1

0.1

0.1

0.01

10

-3

10

-3

10

-4

10

-4

10

-5

10

-5

10

-6

4 2
â

2 0 -2

2

â

S

0 -2 -4 2 5 10 Energy (keV) 20 50

2

5

10
Energy (keV)

20

50

100

Figure 3. Top: best-fit spectrum of 4U 1728-34 in E F (E ) units using BeppoSAX observation 20889003 carried out on 1999 April 19. The data are presented by crosses and the best-fit spectral model wabs*(blackbody+COMPTB+Gaussian) by the green line. The model components are shown by red, crimson, and blue lines for blackbdody, COMPTB, and Gaussian components, respectively. Bottom panels: spectrum in units of counts along with . Left bottom panel: best-fit spectrum and for the model fit without the line component (reduced 2 = 2.15 for 445 dof). Right bottom panel: same as that on the left one but with the addition of the Gaussian (K -line) component (reduced 2 = 1.16 for 445 dof). The best-fit model parameters are = 2.07 ± 0.04, Te = 3.29 ± 0.04 keV, Eline = 6.0 ± 0.1 keV, and EWline = 51 ± 11 eV (see more details in Table 3). (A color version of this figure is available in the online journal.)

6


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Figure 4. Best-fit RXTE spectrum of 4U 1728-34 for the low-luminosity state in units E F (E ) (top) and the spectra in count units (bottom panels) with 2 for the 30042-03-01-00 observation. Left bottom panel: fit of the model wabs COMPTB,(red = 2.1 for 61 dof). Right bottom panel: same as the latter one but with 2 the addition of an iron Gaussian line and the blackbody component, namely, using the model wabs (blackbody + COMPTB + Gaussian) (red = 1.18 for 57 dof). The best-fit model parameters are = 1.99 ± 0.02, Te = 10.4 ± 0.3 keV, and Eline = 6.54 ± 0.03 keV (see more details in Table 4). Red, violet, and blue lines stand for blackbody, COMPTB, and Gaussian components, respectively. (A color version of this figure is available in the online journal.)

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Figure 5. Best-fit RXTE spectrum of 4U 1728-34 for the high-luminosity state in units E F (E ) 2 for the 50023-01-12-00 observation. Left bottom panel: fit of the model wabs COMPTB (red = 1.79 the addition of an iron Gaussian line and the Blackbody component, namely, using the model wabs The best-fit model parameters are = 1.99 ± 0.03, Te = 5.5 ± 0.1 keV, and Eline = 6.75 ± 0.04 keV for Blackbody, COMPTB, and Gaussian components, respectively. (A color version of this figure is available in the online journal.)

(top) and the spectra in count units (bottom panel) with for 61 dof). Right bottom panel: same as the latter one but with 2 (blackbody + COMPTB + Gaussian) (red = 1.2 for 57 dof). (see more details in Table 4). Red, violet, and blue lines stand

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 Te of the COMPTB component varies from 2.5 to 15 keV, while photon index is 8

almost constant ( = 1.99 ± 0.02) for all observations. It is worth noting that the width line of the Gaussian component does not vary much and is in the range of 0.3­0.6 keV. Color temperature Ts of the COMPTB component is around 1.3 keV,


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Table 3 Best-Fit Parameters of the Spectral Analysis of BeppoSAX Observations of 4U 1728-34 in the 0.3­60 keV Energy Rangea Observational ID 20674001 20889003 MJD (day) 51048.70 51409.50 TBB (keV) 0.47(3) 0.62(5) NBB
b

Ts (keV) 1.30(3) 1.21(5)

= -1 0.99(7) 1.07(4)

Te (keV) 3.76(8) 3.29(4)

log(A) 0.10(4) 1.06(6)

N

COMPTB

Eline (keV) 7.4(1) 6.0(1)

Nline

b

EWline (eV) 52(16) 51(11)



2 red

(dof)

2.65(2) 1.61(1)

4.18(3) 3.56(2)

0.55(4) 0.43(4)

1.25(457) 1.16(445)

Notes. Parameter errors correspond to the 1 confidence level. a The spectral model is wabs (blackbody + COMPTB + Gaussian), normalization parameters of blackbody and COMPTB components are in units 2 of L37 /d10 erg-1 s-1 kpc-2 , where L37 is the source luminosity in units of 1037 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 â total photons cm-2 s-1 in line.

which is consistent with that using the BeppoSAX data set of our analysis (Table 3) and previous studies by Di Salvo et al. (2000) and Piraino et al. (2000). We fixed the value of the COMPTB parameter log(A) to 1 when the best-fit values of log(A) 1, because in any case of log(A) 1 a Comptonization fraction f = A/(1 + A) is approximately 1 and variations of A 1 do not further improve the fit quality. We use a value of hydrogen column NH = 2.73 â 1022 cm-2 , which was found by Piraino et al. (2000). A systematic error of 0.5% has been applied to all analyzed RXTE spectra. In Figure 4 we show an example of the best-fit RXTE spectrum of 4U 1728-34 for the low-luminosity state in units of E F (E ) (top) and the spectrum in count units (bottom panels) with for the 30042-03-01-00 observation. On the left bottom panel 2 we demonstrate a fit of the model wabs COMPTB (red = 2.1 for 61 dof) and on the right, the same as the latter one, adding an iron Gaussian line and the blackbody component using the model wabs (blackbody + COMPTB + Gaussian) for which 2 we obtain red = 1.18 for 57 dof. The best-fit model parameters for this observation are = 1.99 ± 0.02, Te = 10.4 ± 0.3 keV, and Eline = 6.54 ± 0.03 keV (see more details in Table 4). Red, violet, and blue lines denote blackbody, COMPTB, and Gaussian components, respectively. We also apply the same procedure to the spectrum during the high-luminosity state, and in Figure 5 we present the results for the 50023-01-1200 observation. On the left bottom panel we show a fit of the 2 model wabs COMPTB (red = 1.79 for 61 dof) and on the right we present the same as the latter one, adding an iron Gaussian line and the blackbody components using the model 2 wabs (blackbody + COMPTB + Gaussian), for which red = 1.2 for 57 dof. The best-fit model parameters in this case are = 1.99 ± 0.02, Te = 5.5 ± 0.1 keV, and Eline = 6.75 ± 0.04 keV (see more details in Table 4). The adopted spectral model shows a very good performance throughout all data sets used in our analysis. Namely, the value 2 of reduced red = 2 /Ndof , where Ndof is the number of degrees of freedom (dof), is around 1.0 or less for most observations. For a small fraction (less than 3%) of spectra with high counting 2 statistics red reaches 1.5. However, it never exceeds a rejection limit of 1.7. Note that the energy range for the cases, in which we obtain the poor fit statistic (2 among 127 spectra with 2 = 1.7 for 44 dof), is related to the iron line region. It is possible that the shape of the Fe line is more complex than a simple Gaussian (i.e., there may be a blend of different energies, the presence of an 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. Moreover, recent analysis of high-resolution XMM-Newton spectra of 4U 1728-34 (Ng et al. 2010; Egron et al. 2011) us9

ing different spectral models also reveals evident residuals at 6­7 keV, which are attributed to the presence of a broad iron emission line. This feature can be fitted equally well by a composition of the pure iron line and the corresponding absorption edge as well as Laor instead of the Gaussian line profile (Ng et al. 2010) and also by a relativistically smeared line component or by a relativistically smeared reflection model component (Egron et al. 2011). This variety of the line models used in the data analysis for 4U 1728-34 demonstrates complexity of the line appearance in this source. It is worth noting that we find some differences between our values for the best-fit model parameters and those in the literature. In particular, the photon index , estimated by Di Salvo et al. (2000) for ObsID = 20674001, is 1.60 ± 0.25 while our value of = 1.9 ± 0.2. This difference in the index values can be explained using slightly different models. Di Salvo et al. (2000) included a narrow Gaussian line around 1.7 keV (radiative recombination emission from Mg xi) in order to fit an excess of the residuals of the continuum model. However our model result, using the BeppoSAX observation (ID = 20889003), confirms the result of Piraino et al. (2000), although we apply a slightly different spectral model. Our bestfit photon index = 1.9 ± 0.2 is very close to that obtained by Piraino et al. (2000) using the best-fit parameters of the COMPTT model (see Titarchuk 1994) electron temperature kTe = 3.16 ± 0.03 keV and optical depth (for spherical geometry) 0 = 11.4 ± 0.2. Using broadband BeppoSAX observations we can well determine all parameters of our spectral model, while due to the extensive observations of 4U 1728-34 by RXTE we are able to investigate the overall pattern of the source behavior during the spectral transitions in the 3­60 keV energy range. 4. EVOLUTION OF X-RAY SPECTRAL PROPERTIES DURING SPECTRAL STATE TRANSITIONS We have established common characteristics of the rise­decay spectral transition of 4U 1728-34 based on their spectral parameter evolution of X-ray emission in the energy range from 3 to 60 keV using RXTE/PCA and HEXTE data. In Figures 4 and 5 we present typical examples of the RXTE LS and HS spectra for 4U 1728-34. In fact, one can clearly see from these figures that the normalization of the thermal (blackbodylike) component is a factor of two higher in the HS than that in the LS, although photon indices for each of these spectra are slightly variable from 1.8 to 2.1, mostly concentrated around = 2 (see that distribution of on the left-hand panel of Figure 6). We test the hypothesis of appr 2 using 2 2 statistic criterion. We show the distribution of red (appr ) = i -appr 2 N 1 versus appr in the right-hand panel of i =1 N i


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk

Table 4 Best-Fit Parameters of the Spectral Analysis of PCA & HEXTE/RXTE Observations of 4U 1728-34 in the 3­60 keV Energy Rangea Observational ID Start Time Exposure Rate (MJD) Time (s) (counts s-1 ) 9632 12180 9488 9840 11550 9488 12540 9664 4160 9600 14560 16000 2992 7888 16510 7968 12530 9520 4464 4928 11500 3264 12770 3520 15650 16780 16420 6736 12580 3360 16540 8432 9712 1920 2352 4624 6608 2048 3312 6672 3376 6752 5296 4432 2656 1013 16640 9824 880 2432 2160 13700 14940 3200 9488 2432 9568 4608 10030 9792 16420 1824 1752 2071 1927 2040 2071 1493 1387 994 1021 1035 972 1058 1030 1090 1095 1191 2013 2043 1998 1183 1908 1657 2281 2431 1644 1388 1002 999 936 1511 1795 2421 1528 1525 1584 1583 1589 1599 1595 1719 1670 1637 1787 1730 1752 1776 1765 2059 2033 2194 1989 1787 1686 1232 1253 1286 1365 1124 1219 1293 = -1 0.98(6) 1.00(3) 1.00(2) 1.11(7) 1.02(3) 1.05(4) 0.99(2) 0.95(2) 0.91(7) 0.90(8) 0.90(9) 0.86(3) 0.98(2) 0.89(9) 0.91(8) 0.82(9) 0.99(2) 1.0(2) 0.99(7) 1.00(5) 0.99(7) 1.00(5) 1.00(8) 0.99(9) 1.12(9) 0.99(4) 0.99(2) 0.99(3) 0.99(7) 0.99(6) 0.99(6) 0.99(2) 0.97(5) 0.94(3) 0.85(9) 0.89(9) 0.85(8) 0.86(9) 0.85(9) 0.88(7) 0.89(9) 0.88(6) 0.89(7) 0.93(3) 0.92(2) 0.96(3) 0.98(2) 0.99(1) 0.9(1) 1.00(9) 0.99(6) 1.00(3) 1.00(5) 1.00(3) 0.997(9) 1.000(8) 0.99(3) 0.99(4) 0.99(7) 0.99(5) 0.99(6) Te (keV) 3.54(3) 3.71(4) 2.91(2) 3.18(7) 3.16(4) 3.17(4) 4.64(3) 5.2(1) 8.1(3) 8.2(2) 8.6(3) 8.4(1) 8.5(4) 8.1(2) 8.4(1) 6.9(1) 12.2(3) 3.01(4) 2.96(5) 2.89(3) 3.02(4) 3.06(2) 3.02(3) 2.96(2) 2.85(2) 3.22(7) 4.21(8) 3.02(3) 2.96(4) 2.95(4) 3.08(5) 10.4(3) 3.16(4) 11.1(6) 9.6(2) 9.8(2) 9.6(1) 9.7(2) 9.9(2) 10.2(1) 9.6(2) 9.6(1) 10.10(2) 8.2(2) 7.9(2) 8.4(3) 7.95(9) 8.13(9) 4.4(1) 4.46(7) 4.09(2) 4.79(3) 5.48(3) 6.9(2) 14.4(3) 14.3(5) 14.1(3) 12.06(4) 13.3(3) 9.8(2) 7.93(8) log(A)
b

N

COMPTB

c

NBbody

c

Eline (keV) 6.6(1) 6.68(8) 6.63(1) 6.64(3) 6.58(2) 6.58(7) 6.53(5) 6.50(3) 6.50(2) 6.51(2) 6.50(3) 6.48(5) 6.45(4) 6.60(2) 6.48(3) 6.62(2) 6.61(5) 6.6(1) 6.7(1) 6.7(1) 6.58(8) 6.5(1) 6.6(1) 6.7(1) 6.7(1) 6.59(9) 6.5(1) 6.5(1) 6.6(1) 6.7(1) 6.6(1) 6.54(3) 6.53(2) 6.58(8) 6.53(4) 6.55(3) 6.55(2) 6.54(2) 6.53(2) 6.57(3) 6.50(1) 6.53(4) 6.57(1) 6.51(2) 6.53(4) 6.46(2) 6.49(4) 6.47(3) 6.49(5) 6.62(3) 6.60(3) 6.55(6) 6.54(1) 6.54(4) 6.49(2) 6.53(2) 6.54(1) 6.51(2) 6.67(1) 6.63(1) 6.64(2)

Nline

c

EWline (eV) 100(30) 106(20) 120(20) 110(20) 150(20) 130(10) 90(10) 90(10) 50(8) 40(10) 40(10) 40(10) 40(10) 40(10) 50(10) 70(10) 50(20) 120(20) 160(30) 110(20) 110(10) 130(10) 130(8) 140(10) 130(10) 100(10) 90(10) 100(10) 100(10) 90(10) 100(10) 50(20) 140(8) 30(20) 40(20) 40(20) 40(20) 60(20) 50(20) 70(20) 70(10) 70(20) 50(30) 60(20) 50(30) 70(30) 60(30) 80(30) 160(20) 150(20) 160(20) 120(20) 120(20) 120(20) 30(20) 40(20) 50(20) 50(10) 70(8) 60(10) 60(8)



2 red

(dof)

F1 /F2

d

10073-01-01-00 50128.49 10073-01-01-000 50128.494 10073-01-02-00 50129.27 10073-01-02-000 50129.27 10073-01-03-000 50129.66 10073-01-03-00 50129.93 10073-01-04-000 50131.46 10073-01-04-00 50131.79 10073-01-06-000 50135.48 10073-01-06-00 50135.78 10073-01-08-000 50136.88 10073-01-07-000 50136.89 10073-01-07-00 50137.22 10073-01-08-00 50138.06 10073-01-09-000 50138.86 10073-01-09-00 50139.20 10073-01-10-01 50143.00 20083-01-01-00 50710.24 20083-01-01-01 50710.51 20083-01-01-02 50711.31 20083-01-01-020 50712.24 20083-01-02-000 50712.35 20083-01-02-01 50712.65 20083-01-03-00 50714.98 20083-01-03-000 50715.01 20083-01-04-00 50717.51 20083-01-04-01 50718.38 20083-01-03-02 50721.18 20083-01-03-020 50721.19 20083-01-04-02 50722.25 20083-01-04-020 50722.26 30042-03-01-00 51086.30 30042-03-02-00 51093.21 30042-03-01-01 51109.94 30042-03-02-01 51110.01 30042-03-03-01 51110.08 30042-03-04-00 51113.01 30042-03-01-03 51112.94 30042-03-01-04 51115.07 30042-03-05-00 51115.14 30042-03-07-01 51119.94 30042-03-07-00 51120.00 30042-03-08-00 51122.17 30042-03-10-00 51127.77 30042-03-10-01 51127.88 30042-03-11-00 51127.93 30042-03-12-00 51128.60 30042-03-13-00 51128.93 30042-03-14-02 51133.27 30042-03-14-01 51133.34 30042-03-14-00 51133.41 30042-03-15-00 51133.55 30042-03-16-00 51134.00 30042-03-17-00 51134.54 30042-03-18-00 51193.32 30042-03-19-01 51195.20 30042-03-19-00 51195.26 30042-03-20-00 51196.94 40033-06-01-00 51198.12 40033-06-02-00 51200.19 40033-06-02-01 51201.91

0.8(1) 0.7(1) 1.00b 0.94(6) 0.41(3) 0.41(4) 0.2(1) 0.18(5) 0.27(2) 0.30(2) 0.33(1) 0.29(2) 0.39(3) 0.31(2) 0.33(1) 0.18(1) 0.84(1) 0.59(5) 0.4(1) 0.6(1) 0.3(1) 0.28(5) 0.3(1) 0.5(2) 1.00b 0.15(5) 0.09(3) 0.28(4) 0.4(1) 0.8(2) 0.3(1) 0.71(3) 0.41(5) 1.0(2) 0.52(4) 0.60(3) 0.50(2) 0.56(4) 0.53(3) 0.69(3) 0.53(2) 0.59(2) 0.67(3) 0.46(2) 0.51(6) 0.55(3) 0.52(2) 0.53(4) 0.3(3) 0.3(3) 0.3(2) 0.3(1) 0.35(5) 0.40(8) 1.07(1) 1.01(1) 0.96(5) 0.83(6) 1.00b 0.61(3) 0.44(2)

3.4(1) 3.4(2) 4.05(6) 3.7(2) 4.53(5) 4.56(7) 3.25(2) 3.12(3) 2.3(2) 2.34(6) 2.32(4) 2.25(5) 2.43(6) 2.39(3) 2.51(2) 2.66(3) 2.40(4) 3.8(3) 5.0(3) 4.65(4) 4.3(3) 4.2(1) 4.6(1) 5.45(3) 5.69(8) 3.5(3) 3.1(1) 3.54(3) 3.51(4) 3.1(1) 3.4(2) 3.92(5) 5.35(8) 3.19(2) 3.52(3) 3.64(4) 3.85(2) 3.79(5) 3.68(2) 3.52(4) 4.03(3) 3.92(2) 3.67(3) 4.35(3) 3.96(8) 4.07(3) 4.14(4) 4.09(2) 4.73(3) 4.61(5) 5.12(4) 4.5(2) 4.28(7) 3.91(6) 2.58(3) 2.47(4) 2.58(3) 3.13(2) 2.87(3) 3.35(4) 3.89(2)

2.4(2) 2.09(4) 2.85(5) 2.56(2) 3.19(2) 3.28(2) 2.67(2) 2.36(3) 1.19(3) 1.18(2) 1.05(1) 1.06(3) 1.05(2) 1.07(1) 1.08(3) 1.64(2) 0.92(3) 2.75(6) 2.01(2) 2.6(3) 2.1(1) 2.3(1) 2.1(2) 2.8(6) 2.19(1) 2.2(1) 1.85(9) 2.15(6) 2.17(3) 2.4(3) 2.1(1) 0.99(8) 3.34(4) 1.05(9) 0.93(2) 0.85(2) 1.12(3) 0.89(2) 0.94(3) 0.92(1) 0.9(2) 0.89(4) 0.92(3) 1.19(3) 1.13(4) 1.15(2) 1.21(2) 1.23(2) 2.71(2) 2.72(9) 2.97(8) 2.71(4) 2.32(4) 1.79(7) 0.97(6) 0.95(9) 0.9(1) 0.90(6) 0.86(2) 0.75(4) 1.04(3)

1.2(1) 0.7(1) 0.57(1) 0.73(2) 0.32(1) 0.30(1) 0.38(1) 0.32(1) 0.30(2) 0.31(1) 0.32(1) 0.31(1) 0.33(2) 0.32(1) 0.34(1) 0.16(1) 0.44(5) 0.5(2) 1.0(1) 0.5(1) 0.33(8) 0.6(3) 0.3(1) 0.4(1) 0.3(1) 0.33(9) 0.5(3) 0.4(1) 0.28(9) 0.3(1) 0.3(1) 0.61(1) 0.55(2) 0.53(7) 0.49(3) 0.49(2) 0.49(2) 0.52(3) 0.51(2) 0.54(2) 0.47(2) 0.51(2) 0.55(2) 0.52(2) 0.69(9) 0.75(5) 0.69(4) 0.72(5) 0.57(7) 0.54(4) 0.62(4) 0.55(2) 0.55(2) 0.55(4) 0.60(3) 0.54(2) 0.55(1) 0.56(2) 0.30(4) 0.43(4) 0.40(4)

1.16(64) 1.1(64) 0.98(65) 1.28(64) 1.39(64) 1.15(64) 1.32(64) 1.07(64) 1.4(64) 1.1(64) 1.12(64) 0.96(64) 1.17(64) 1.56(64) 1.54(64) 1.05(64) 1.09(64) 0.86(57) 0.79(57) 0.8(57) 1.15(57) 0.81(57) 0.89(57) 0.72(57) 0.93(58) 0.92(57) 1.39(57) 0.87(57) 0.96(57) 0.73(57) 0.98(57) 1.21(57) 1.29(57) 1.1(57) 0.96(57) 1.06(57) 1.07(57) 1.22(57) 1.07(57) 0.93(57) 0.92(57) 1.15(57) 1.09(57) 1.3(57) 0.88(57) 0.95(57) 0.97(57) 0.76(57) 0.93(57) 1.12(57) 1.18(57) 1.3(57) 0.96(57) 1.2(57) 1.12(57) 1.15(57) 0.94(57) 1.21(57) 1.29(58) 1.16(57) 1.04(57)

2.82/1.43 2.69/1.49 3.26/1.31 3.03/1.34 3.21/1.28 3.22/1.27 2.08/1.46 2.08/1.46 1.45/1.60 1.43/1.71 1.50/1.81 1.41/1.73 1.54/1.76 1.49/1.75 1.58/1.89 1.73/1.74 1.49/2.46 4.65/4.3 3.33/1.2 3.25/1.17 3.03/1.15 3.09/1.14 3.27/1.20 3.71/1.36 3.96/1.44 2.65/1.01 2.19/1.10 2.57/0.95 2.56/0.95 2.39/0.88 2.45/0.92 2.62/3.67 3.90/1.60 2.19/3.44 2.19/3.39 2.28/3.48 2.27/3.54 2.29/3.56 2.29/3.64 2.28/3.60 2.48/3.73 2.40/3.66 2.40/3.66 2.62/3.34 2.54/3.17 2.58/3.23 2.63/3.08 2.61/3.08 3.23/1.88 3.18/1.04 3.46/1.90 3.10/1.90 3.75/2.10 3.75/2.10 1.78/2.79 1.82/2.83 1.86/2.90 1.98/2.95 1.99/3.20 2.20/2.94 2.37/2.68

10


The Astrophysical Journal, 738:128 (20pp), 2011 September 10 Table 4 (Continued) Observational ID 40033-06-02-03 40033-06-02-04 40033-06-02-07 40033-06-02-05 40033-06-02-06 40033-06-03-00 40033-06-03-06 40033-06-03-01 40033-06-03-02 40033-06-03-07 40033-06-03-03 40033-06-03-05 40027-06-01-01 40027-06-01-02 40027-06-01-04 40027-06-01-05 40027-06-01-06 40027-06-01-03 40027-06-01-07 40027-06-01-08 40027-08-01-02 40019-03-02-02 40019-03-02-01 40019-03-02-00 40019-03-03-01 40019-03-03-00 40019-03-01-03 40019-03-01-07 40019-03-01-04 40019-03-01-01 40019-03-01-02 40019-03-01-00 40019-03-01-06 50023-01-01-00 50023-01-02-00 50023-01-03-00 50023-01-04-00 50023-01-05-00 50023-01-06-00 50023-01-07-00 50029-23-01-00 50029-23-01-01 50029-23-02-00 50029-23-02-01 50029-23-02-02 50029-23-02-03 50023-01-12-00 50023-01-13-00 50023-01-14-00 50023-01-15-00 50023-01-17-00 50023-01-18-00 50023-01-19-00 50023-01-20-00 50023-01-21-00 50023-01-22-00 50023-01-23-00 50023-01-24-00 50023-01-25-00 50023-01-26-00 50023-01-27-00 50023-01-28-00 Start Time Exposure Rate (MJD) Time (s) (count s-1 ) 51203.98 51205.92 51206.06 51206.12 51206.19 51207.18 51207.27 51208.92 51210.12 51211.78 51211.91 51213.91 51237.04 51237.18 51238.36 51238.49 51238.56 51238.76 51239.90 51240.04 51359.15 51409.17 51409.23 51409.55 51410.16 51410.23 51442.39 51442.49 51442.60 51442.67 51442.74 51442.80 51443.19 51610.70 51613.69 51615.89 51619.81 51622.81 51625.73 51628.85 51652.4 51652.46 51657.13 51657.19 51657.58 51657.73 51663.96 51667.55 51669.55 51673.61 51679.72 51682.51 51685.50 51688.76 51691.71 51695.33 51697.45 51709.69 51712.35 51715.41 51718.93 51721.86 13230 6576 2784 2704 3120 3264 864 6608 1856 2368 12350 5152 4528 3360 3392 2720 2720 9616 3200 1136 1056 1984 2400 14370 2048 11760 8800 1200 1440 1152 848 12610 6288 2656 2544 3376 3296 3328 2992 2928 2256 2224 2464 2480 5664 7408 1792 2592 2528 2048 2688 2656 2720 2608 3056 2720 2112 2560 2672 2528 3024 2880 1084 1685 1634 1716 996.9 1491 911.7 1207 1635 1379 1112 1601 1023 1087 851.8 1044 1110 1054 657.9 1270 934.7 2078 2102 1268 1911 2321 438.6 457.6 692.9 705.3 708.7 758.2 759.2 551.7 801.5 788.8 520 773.5 536.6 1896 280.5 417.3 906.8 1027 773.8 384.3 1195 1715 961.9 313.9 368.7 372.2 632.4 613.7 654.4 476.1 248 188.5 803.3 576.4 655.6 238.6 = -1 1.00(3) 0.99(4) 0.99(2) 1.00(3) 1.00(4) 1.00(2) 1.00(3) 0.99(2) 0.99(3) 1.00(2) 1.00(1) 0.99(3) 1.06(2) 0.99(3) 0.99(1) 0.91(9) 0.97(4) 0.999(9) 0.99(2) 1.00(4) 1.00(4) 1.00(3) 0.94(6) 0.94(7) 0.96(8) 0.99(3) 1.00(6) 0.99(5) 0.99(4) 1.01(6) 1.00(4) 0.99(3) 0.99(2) 0.95(3) 0.96(4) 0.89(6) 0.93(3) 0.94(6) 0.98(7) 0.97(9) 1.00(3) 0.89(6) 0.89(3) 0.97(6) 0.96(2) 0.99(8) 0.99(3) 1.02(4) 1.0(2) 1.00(4) 1.01(6) 0.89(6) 0.97(5) 0.94(4) 1.01(9) 1.01(9) 0.99(2) 0.97(4) 0.90(4) 0.99(7) 0.99(3) 1.00(2) Te (keV) 5.44(3) 5.43(5) 5.81(9) 5.37(6) 5.55(8) 6.6(2) 6.8(3) 5.91(7) 4.27(3) 5.46(9) 5.71(5) 3.98(2) 7.8(3) 7.3(2) 7.9(3) 8.2(4) 8.3(4) 9.6(2) 8.9(3) 7.1(3) 7.2(3) 3.02(3) 3.04(6) 2.94(2) 2.87(5) 3.02(2) 5.7(3) 5.6(2) 5.3(2) 5.2(1) 5.4(2) 4.57(8) 4.80(5) 10.07(6) 10.4(2) 8.5(2) 7.8(3) 6.7(3) 5.5(2) 4.1(2) 13.6(8) 9.9(5) 8.7(4) 7.8(3) 7.9(2) 8.6(2) 5.5(1) 2.95(4) 4.07(9) 10.1(6) 9.4(4) 7.9(3) 7.3(2) 8.1(3) 9.4(4) 8.6(2) 7.8(3) 9.5(6) 7.8(2) 13.8(7) 9.9(5) 9.3(3) log(A)
b

Seifina & Titarchuk

N

COMPTB

c

NBbody

c

Eline (keV) 6.66(3) 6.65(2) 6.61(3) 6.64(3) 6.69(5) 6.61(3) 6.58(6) 6.69(2) 6.68(3) 6.74(3) 6.68(1) 6.68(2) 6.56(4) 6.57(3) 6.51(3) 6.58(3) 6.60(3) 6.61(1) 6.62(3) 6.72(3) 6.58(5) 6.64(3) 6.67(3) 6.64(2) 6.62(4) 6.62(1) 6.64(6) 6.75(6) 6.73(5) 6.69(5) 6.70(7) 6.73(1) 6.72(3) 6.56(3) 6.62(3) 6.56(3) 6.58(3) 5.99(7) 6.58(4) 6.73(2) 6.50(5) 6.54(5) 6.57(3) 6.63(3) 6.62(2) 6.58(2) 6.75(4) 6.64(3) 6.72(5) 6.51(4) 6.55(4) 6.63(5) 6.70(4) 6.57(4) 6.56(3) 6.59(4) 6.68(6) 6.64(5) 6.72(3) 6.59(4) 6.67(3) 6.56(4)

Nline

c

EWline (eV)



2 red

(dof)

F1 /F2

d

0.35(6) 0.33(7) 0.32(9) 0.4(1) 0.4(1) 0.35(7) 0.8(1) 0.31(6) 0.24(6) 0.34(9) 0.30(6) 0.25(6) 0.59(2) 0.38(8) 0.39(7) 0.36(4) 0.37(6) 0.43(3) 0.41(7) 0.36(9) 0.2(1) 0.52(8) 0.32(7) 0.43(5) 0.8(1) 0.40(4) 0.3(1) 0.3(1) 0.3(1) 0.4(1) 0.4(2) 0.26(9) 0.24(9) 0.63(6) 1.00(1) 0.40(2) 0.42(4) 0.22(2) 0.32(5) 0.05(5) 0.7(1) 0.34(5) 0.39(3) 0.46(4) 0.38(2) 0.40(4) 0.3(1) 0.48(9) 0.2(4) 0.47(9) 0.6(1) 0.32(3) 0.35(3) 0.38(3) 0.62(7) 0.56(6) 0.52(8) 0.7(2) 0.30(1) 0.51(4) 0.7(1) 0.6(1)

4.33(8) 4.3(1) 4.2(1) 4.3(2) 3.8(1) 3.69(6) 3.5(1) 3.68(8) 3.81(5) 3.4(1) 3.37(7) 3.74(5) 2.38(4) 2.69(6) 2.42(4) 2.46(5) 2.63(4) 2.45(3) 2.41(3) 3.1(1) 2.89(4) 5.7(2) 6.7(1) 7.54(9) 7.36(7) 7.21(6) 2.6(1) 2.6(1) 2.7(1) 3.0(1) 3.0(1) 3.0(1) 3.1(1) 4.04(5) 2.93(4) 3.21(3) 2.96(4) 3.49(3) 3.11(5) 6.5(1) 1.4(2) 1.68(4) 2.17(5) 2.51(6) 2.49(3) 2.28(4) 2.9(1) 3.8(1) 3.07(6) 1.73(3) 2.15(4) 2.61(3) 2.8(3) 2.67(5) 2.80(3) 3.02(4) 2.89(6) 1.96(3) 2.63(4) 2.36(3) 2.58(5) 2.54(4)

1.98(4) 1.96(5) 1.88(3) 1.73(8) 1.89(3) 1.48(6) 1.33(9) 1.74(6) 2.16(6) 1.98(4) 1.54(3) 2.07(4) 0.78(2) 0.89(4) 0.84(2) 0.86(2) 0.85(4) 0.73(3) 0.85(6) 0.94(3) 1.47(4) 3.16(6) 3.5(3) 3.1(2) 3.2(1) 3.16(4) 2.7(6) 2.6(3) 2.1(4) 2.7(6) 5.5(2) 2.9(2) 3.4(4) 0.93(5) 0.85(4) 0.9(3) 1.07(5) 3.69(4) 1.5(2) 3.9(2) 0.63(4) 0.62(6) 0.68(5) 0.9(1) 1.2(2) 1.3(3) 2.6(4) 2.3(3) 2.95(9) 0.74(4) 0.40(5) 1.5(4) 1.9(2) 1.0(3) 0.58(7) 0.81(3) 0.92(4) 0.5(2) 1.8(5) 0.8(3) 0.61(6) 0.61(4)

0.36(1) 40(10) 0.38(2) 40(10) 0.35(3) 40(10) 0.44(3) 50(10) 0.49(3) 50(10) 0.39(3) 30(10) 0.39(6) 40(10) 0.33(2) 30(10) 0.41(4) 40(10) 0.35(3) 30(10) 0.36(1) 30(10) 0.39(2) 30(10) 0.54(4) 70(10) 0.38(3) 40(10) 0.39(3) 40(10) 0.41(3) 50(10) 0.32(3) 40(10) 0.31(1) 40(10) 0.30(2) 40(10) 0.21(3) 40(10) 0.29(4) 40(10) 0.64(3) 100(20) 0.39(4) 150(10) 0.59(2) 170(8) 0.44(2) 160(10) 0.53(2) 170(6) 0.28(2) 40(10) 0.22(2) 40(10) 0.28(4) 40(10) 0.26(4) 40(5) 0.21(4) 40(8) 0.26(4) 40(10) 0.23(2) 40(10) 0.46(3) 50(8) 0.45(3) 50(10) 0.36(3) 40(8) 0.35(3) 40(10) 0.07(1) 30(10) 0.31(3) 40(8) 0.72(3) 150(6) 0.29(3) 40(10) 0.19(3) 30(10) 0.27(3) 40(10) 0.26(3) 40(8) 0.27(2) 40(10) 0.26(2) 40(10) 0.28(3) 40(10) 0.36(3) 50(8) 0.27(3) 40(6) 0.25(4) 40(10) 0.32(3) 50(10) 0.23(4) 40(10) 0.26(3) 40(6) 0.28(3) 50(8) 0.32(3) 60(10) 0.31(4) 60(10) 0.23(5) 40(10) 0.30(4) 40(10) 0.19(2) 30(10) 0.16(2) 30(10) 0.24(2) 40(10) 0.35(2) 50(6)

1.07(57) 0.96(57) 0.98(57) 0.87(57) 1.19(57) 1.19(57) 1.2(57) 0.97(57) 1.16(57) 0.93(57) 1.37(57) 1.32(57) 1.17(57) 0.74(57) 1.09(57) 1.72(57) 0.91(57) 0.95(57) 1.13(57) 1.09(57) 0.93(57) 1.37(57) 1.09(57) 1.12(57) 1.07(57) 1.05(57) 0.83(57) 1.09(57) 1.53(57) 1.17(57) 1.34(57) 1.28(57) 0.91(57) 1.03(57) 1.52(57) 1.75(57) 1.07(57) 0.76(57) 1.04(57) 0.88(57) 1.2(57) 0.91(57) 0.95(57) 1.29(57) 0.94(57) 0.81(57) 1.2(57) 1.1(57) 1.24(57) 1.09(57) 0.78(57) 0.92(57) 0.81(57) 0.92(57) 1.19(57) 1.1(57) 0.89(57) 1.29(57) 1.09(57) 1.19(57) 0.95(57) 1.07(57)

2.64/2.08 2.63/2.06 2.54/2.07 2.68/2.06 2.45/1.92 2.30/2.12 2.22/2.10 2.28/1.88 2.62/1.49 2.15/1.64 2.10/1.64 2.58/1.59 1.58/1.57 1.67/1.66 1.68/1.65 1.57/1.85 1.68/1.88 1.60/1.93 1.58/1.82 1.95/1.99 1.81/1.69 4.43/1.71 4.47/1.71 5.09/1.95 5.20/2.18 4.95/1.87 1.72/1.35 1.74/1.36 1.79/1.33 1.83/1.33 1.84/1.36 1.99/1.25 2.06/1.33 1.99/2.83 1.98/2.74 1.96/2.55 1.91/2.21 1.98/1.89 2.04/1.56 4.01/2.02 1.03/1.44 1.04/1.42 1.38/1.77 1.57/1.80 1.52/1.72 1.43/1.64 1.90/1.43 2.88/1.08 2.01/1.06 1.16/1.42 1.41/1.74 1.55/1.86 1.72/1.76 1.63/1.92 1.73/2.19 1.82/2.22 1.83/2.14 1.38/1.83 1.56/1.84 1.52/2.26 1.72/2.28 1.74/2.23

11


The Astrophysical Journal, 738:128 (20pp), 2011 September 10 Table 4 (Continued) Observational ID 50023-01-29-00 50023-01-30-00 50023-01-31-00 50023-01-32-00 Start Time (MJD) 51724.57 51727.50 51730.42 51733.41 Exposure Time (s) 3344 3088 2768 2912 Rate (count s-1 ) 1063 950.2 226 817.7 = -1 0.99(3) 0.99(2) 0.99(4) 1.0(2) Te (keV) 5.92(9) 6.4(2) 6.7(3) 3.7(1) log(A)
b

Seifina & Titarchuk

N

COMPTB

c

NBbody

c

Eline (keV) 6.57(3) 6.71(3) 6.58(5) 6.61(4)

Nline

c

EWline (eV) 50(10) 30(10) 40(10) 50(8)



2 red

(dof)

F1 /F2

d

0.27(9) 0.24(7) 0.3(1) 0.2(1)

3.4(1) 3.1(1) 2.62(8) 3.4(1)

1.7(2) 2.1(3) 0.9(1) 1.9(2)

0.28(2) 0.16(2) 0.28(5) 0.35(4)

1.1(57) 1.18(57) 1.02(57) 1.05(57)

2.13/1.71 1.90/1.62 1.71/1.59 1.36/1.11

Notes. The count rate corresponds to 5 PCA units and corrected for background. Parameter errors correspond to the 1 confidence level. a The spectral model is wabs (blackbody + COMPTB + Gaussian), where N is fixed at a value 2.73 â 1022 cm-2 (Piraino et al. 2000); color temperatures T and H s TBB are fixed at 1.3 and 0.7 keV, respectively (see comments in the text). b When parameter log(A) 1, it is fixed at 1.0 (see comments in the text). c Normalization parameters of blackbody and COMPTB components are in units of L /d 2 erg-1 s-1 kpc-2 ,where L is the source luminosity in units of 1037 erg s-1 , 37 10 37 d10 is the distance to the source in units of 10 kpc, and the Gaussian component is in units of 10-2 â total photons cm-2 s-1 in line. d Spectral fluxes (F /F ) in units of â10-9 ergs s-1 cm-2 for (3­10) and (10­60) keV energy ranges, respectively. 1 2

Figure 6. Left panel: histogram (frequency distribution) of the best-fit photon power-law index obtained using a model wabs (blackbody + COMPTB + Gaussian) for RXTE data (1996­2000). Right panel: function 2 (appr ) = (see comments in the text). (A color version of this figure is available in the online journal.)
1 N N i =1 i -appr i 2 2 vs. appr . A dashed horizontal line indicates the critical residual level red = 1

Figure 6. One can clearly see a sharp minimum of func2 tion red (appr ) around 1, which takes place in the range of appr = 1.99 ± 0.01 with a confidence level of 67% and appr = 1.99 ± 0.02 with a confidence level of 99% for 127 dof. It is important to emphasize that the photon index is also independent of the luminosity of the blackbody component of 2 COMPTB L39 /d10 and the plasma temperature of Compton cloud Te (see Figures 7 and 8). Using BeppoSAX data FT11 suggested that the photon index is about 2 for quite a few NS sources that are observed in the different spectral states. FT11 data characterize the spectral state by a value of electron temperature Te and they show that = 2 ± 0.2 (or = 1 ± 0.2) when kTe changes from 2.5 to 25 keV. A number of X-ray flaring episodes of 4U 1728-34 have been detected with RXTE during 1998­1999 (R3, R4 sets) and 2000 (R7, R8 sets) with good rise­decay 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 9 and 10. The RXTE/ASM count rate is shown in the top panel. Further, from the top to the bottom, we show the model flux in two energy bands 3­10 keV (blue points) and 10­60 keV (crimson points). In the next panel 12

we show a change of the TL electron temperature kTe . One can clearly see the spectral transition from the HS to the LS during the time period from MJD 51070 to MJD 51215 when electron temperature kTe varies from 3 keV to 15 keV. Normalizations of the COMPTB (crimson points) and blackbody components (blue points) are shown in the next panel of Figures 9 and 10. In particular, one can see from Figures 9 and 10 how COMPTB normalization NCOMPTB correlates with the variations of the ASM count rate and the model flux in the 3­10 keV energy band. On the other hand, the normalization of the blackbody component NBB is almost constant except at the flaring episode peak, when NBB increases from 0.09 to 0.27 (see blue points in Figure 9 at MJD = 51093 and 51133). Moreover, these flare spectral transitions are related to a noticeable increase in soft flux, in the energy range 3­10 keV, and decrease in hard flux, that in 10­60 keV (see the second panels from the top in Figures 9 and 10). The spectral index ( = - 1) is presented in the bottom panels of Figures 9 and 10. The index slightly varies around 1 (or 2). Photon index variation over the entire set of the observations is presented in Figure 6. The electron temperature kTe steadily decreases during the burst rise (see blue vertical strips in Figures 9 and 10). Equivalent width of iron line EWline and the normalizations of COMPTB NCOMPTB and blackbody components NBB steadily increase when the electron temperature decreases (see Figure 11).


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk

2 Figure 7. Plotted on the left is photon index vs. COMPTB normalization NCOMPTB = L39 /D10 and on the right that vs. Comptonized fraction f = A/(1 + A)using our spectral model wabs (blackbody + COMPTB + Gaussian) (see details in Tables 3 and 4). Blue and red points correspond to BeppoSAX and RXTE observations of 4U 1728-34, respectively. (A color version of this figure is available in the online journal.)

Figure 8. Photon index plotted vs. electron temperature Te (in keV) in the framework of our spectral model wabs (blackbody + COMPTB + Gaussian) (see details in Tables 3 and 4). Blue and red points correspond to BeppoSAX and RXTE observations of 4U 1728-34, respectively. (A color version of this figure is available in the online journal.)

In fact, a decrease in electron temperature Te of the Compton cloud (TL) with an increase in the (disk) soft flux is a wellknown effect, explained in detail by Titarchuk et al. (1998) and Titarchuk & Fiorito (2004). As shown on the right-hand panel of Figure 7, the Comptonization fraction f varies from 0.6 to 0.9. This means that in most cases the soft disk radiation of 4U 1728-34 is subjected to reprocessing in the Compton cloud, and only a small fraction of the disk emission component (1 - f ) is directly seen by the Earth observer. Thus, the energy spectrum of 4U 1728-34 during all states is dominated by a Comptonized component, while the direct disk emission is always weaker and detectable in the flaring episodes only (see Figures 9 and 10). Note that for BHs a definition of spectral transition is related to a change in photon index (see, e.g., ST09). However, there is no one-to-one correspondence between and cutoff (or e-fold) energy Efold . Titarchuk & Shaposhnikov (2010) demonstrate 13

using RXTE data for BH binary XTE J1550-564 that Efold decreases when increases from 1.4 to 2.1 - 2.2 until reaches 2.2 and then Efold increases. Thus, for a BH the main parameter used for the spectral transition definition is a variable photon index , which monotonically increases when a BH source goes to the HS. It is important to emphasize once again that in the NS binary 4U 1728-34 the transition from the LS to the HS takes place when the electron (plasma) temperature changes from 15 keV to 2.5 keV. Thus, following the FT11 suggestion, we define the spectral state transition in an NS source in terms of the electron temperature Te of the Compton cloud (TL). In this case the LS is characterized by high electron temperature Te , while the HS is related to low Te . Note that the electron temperature Te is a directly measurable quantity, and it corresponds to cutoff energy of the spectrum. Not all NSs show flares. Only a few NS binaries (such as Z and atoll sources) display spectral transitions during the bursts. Atoll sources, such as 4U 1728-34, usually show the flare transitions. One can establish a substantial difference between NSs and BHs due to these flare episodes when a source evolves from the LS to the HS and when plasma temperature of the Comptonized region changes remarkably (like in 4U 1728-34 from 2.5 keV to 15 keV). Thus, the NS low-mass X-ray binary 4U 1728-34 shows a steady decrease in electron temperature Te from the LS to the HS, while the photon index stays around 2. In contrast, in BH sources we see a steady monotonic growth of , which is followed by its saturation (see, e.g., ST09). 5. CORRELATIONS BETWEEN SPECTRAL AND TIMING PROPERTIES DURING SPECTRAL STATE TRANSITIONS The RXTE light curves have been analyzed using the powspec task from FTOOLS 5.1. The timing analysis RXTE/PCA data were performed in the 13­30 keV energy range using the event mode. The time resolution for this mode is 1.2 â 10-4 s. We generated power density spectra (PDS) in the 0.1­500 Hz frequency range with a 0.001 s time resolution. We subtracted the contribution due to Poissonian statistics. To model PDS we used QDP/PLT12 plotting package.
12

http://heasarc.gsfc.nasa.gov/ftools/others/qdp/qdp.html.


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk

Figure 9. From top to bottom: evolution of the RXTE/ASM count rate, model flux in 3­10 keV and 10­60 keV energy ranges (blue and crimson points, respectively), electron temperature kTe in keV, and COMPTB and blackbody normalizations (crimson and blue, respectively) during 1998 and 1999 flare transition set (R3, R5). In the last bottom panel, we present an evolution of the spectral index = - 1. The rising phases of the burst are marked with blue vertical strips. The peak burst times are indicated by the arrows at the top of the plot. (A color version of this figure is available in the online journal.)

Previously, timing analysis of 4U 1728-34 was carried out by Di Salvo et al. (2001) as a function of source position in a color­color diagram for RXTE data (R1, R2 sets in our terms). In the island part of the color­color diagram (corresponding to the hardest energy spectra), the power spectrum of 4U 1728-34 shows several features such as a band-limited noise component presented up to a few tens of Hz, a low frequency quasi-periodic oscillation (LFQPO) at frequencies between 20 and 40 Hz, a peaked noise component around 100 Hz, and one or two QPOs at kHz frequencies. During burst evolution (moving along the color­color diagram) in the lower banana (corresponding to the softer energy spectra) they found a very low frequency noise (VLFN) component below 1 Hz. In the upper banana (corresponding to the softest energy spectra) the power spectra are dominated by the VLFN with a peaked noise component around 20 Hz. 14

We find a similar timing behavior of 4U 1728-34 in our data set along with the energy spectra. In particular, in Figure 12, we show the details of a typical evolution of X-ray timing and spectral characteristics during X-ray flares. The evolution of the RXTE/ASM count rate during the 1998 (R3) outburst transition is presented at the top. Red/blue points A, B, and C mark moments at MJD = 51122/51128, 51133.27/51133.34, and 51196/51193 before, during, and after the X-ray outburst, respectively. In the lower panels (left column) we show PDSs for the 13­30 keV energy band along with the energy spectral diagram E F (E ) (right column) for A (top), B (middle), and C (bottom) points of the X-ray light curve. The strong noise components with a break at 1­3 Hz and broad QPOs centered in the range 7­10 Hz are seen before and after the burst, but the latter feature is not seen at the B moment (see panel B1), i.e., at the X-ray flare peak. During the B1-burst event one can


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk

Figure 10. Similar to that presented in Figure 9 but for the RXTE 2000 flare transition set (R7, R8). (A color version of this figure is available in the online journal.)

see a noise component with the power peak shifted to higher frequency with respect to that at A1/C1 events. In other words, the burst power spectrum, in this case, consists of the "high frequency" white­red noise component with a break at 40 Hz. On the right-hand side we present the E F (E ) spectral diagrams (panels A2, B2, and C2) related to the corresponding power spectra (panels A1, B1, and C1). The data are shown by red points, and the spectral model components are displayed by blue, black, and dashed purple lines for COMPTB, blackbody, and Ga ussia n components, respectively. Specifically, before the burst (A1 red; the 30042-03-08-00 RXTE observation, MJD = 51122) one can see a broken powerlaw noise component with a break at 1 Hz, broad QPO at 20 Hz (described by Lorentzian with FWHM = 11.7 ± 4.5 Hz, rms = 6.3 ± 1.0%, 2 =131 for 102 dof for a 67% confidence level). Later, just before the burst (A1 blue; 30042-03-11-00, MJD = 51128), break frequency of the broken power-law noise component shifts from 1 Hz to 3 Hz and QPO becomes less evident, but still visible at the 10­20 Hz range. The lowfrequency part of the â power diagram below 1 Hz increases 15

right before the burst (A1, blue). During the burst (B1 red, 30042-03-14-02, MJD = 51133.27; B1 blue, 30042-03-14-01, MJD = 51133.34) one can see a white­red noise component with the break frequency shifted to higher frequency at about 40 Hz. The QPO component is not seen in the power spectrum during the burst at frequencies 80 Hz and lower. We should point out once again that a similar behavior of 4U 1728-34 was detected previously by Di Salvo et al. (2001) during the 1996­1997 transition from island to banana states in the color­color diagram which we call a "burst" transition in this paper. Note that according to Di Salvo et al. (2001) the power spectrum at the upper banana state (at the maximum of the burst) consists of two noise components, namely, VLFN and high frequency noise (HFN). In addition, we have detected a particular burst when the power spectrum is presented only with a single HFN component (see panel (B1) of Figure 12). After the outburst (C1 blue, 30042-03-18-00, MJD = 51193; C1 red, 30042-03-20-00, MJD = 51196) one can see the same features in the â power plot as in that before the burst, but


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completeness of our presentation, we review the main points of the FT11 explanation in terms of the transition layer model. The energy balance in the TL is dictated by Coulomb collisions with protons (gravitational energy release), while inverse Compton and free­free emission are the main cooling channels (see the formulation of this problem in the pioneer work by Zel'dovich & Shakura 1969 as well as a similar consideration in Bisnovatyi et al. 1980). In fact, for the characteristic electron temperature (3 keV kTe 30 keV) and density values ( 10-5 g cm-3 ) of these regions in low-mass X-ray binaries, Compton cooling dominates over free­free emission; the relation between the energy flux per unit surface area of the corona Qcor , the radiation energy density ( ), and electron temperature Te is given by (see also Titarchuk et al. 1998) Qcor 20.2( )Te ( ), 0 (1)

where 0 is the Thomson optical depth of the TL. The distribution ( ) is obtained as a solution of the diffusion equation d 2 3Qtot =- , (2) d 2 c0 where Qtot = Qcor + Qdisk is the sum of the corona (TL) and intercepted disk fluxes, respectively. Combination of Equation (2) with two boundary conditions at the NS surface and the outer TL boundary leads us to the formulation of the TL boundary problem (see details in FT11). The solution for ( ) is then given by 2Qtot 3 2 ( ) = . (3) 1+ 0 -2 c 2 0 20
Figure 11. Equivalent width of the iron line (in eV, top), normalizations of COMPTB (middle) and Blackbody (bottom) components plotted vs. electron temperature Te (in keV) in the framework of our spectral model wabs (blackbody + COMPTB + Gaussian) during flare transitions (see also Tables 3 and 4). Green points correspond to BeppoSAX observations of 4U 1728-34. (A color version of this figure is available in the online journal.)

In order to establish the average plasma temperature Te we estimate the mean energy density in the TL as ( ) = 1 0
0
0

( )d =

Qtot (2 + 0 ). c

(4)

with slightly different parameters: br 1, 2 Hz and QPO 6, 10 Hz (described by Lorenzian with FWHM = 6.0 ± 2.1/15.0 ± 2.9 Hz, rms = 8.1 ± 0.4/10.6 ± 1.4%, and 2 = 139/143 for 102 dof; all parameter errors correspond to the 1 confidence level). In Figure 13 we present the â power plot observed on 2000 March 7 (the 50023-01-01-00 RXTE observation, MJD = 51610) during the quiet state in order to compare it with the typical sample of PDS during the X-ray flare event (see panel (B1) of Figure 12). 6. DISCUSSION We show the quasi-constancy of the photon (spectral) index in quite a few observations of the NS source 4U 1728-34 using BeppoSAX and RXTE observations. In Figures 7 and 8 we present plots of the photon index as functions of our model parameters: electron temperature Te (in keV), the COMPTB normalization (which equals the normalization of NS blackbody seed photons), and the Comptonization fraction f = A/(1 + A). We obtain these results using an application of the first principle spectral model to extensive BeppoSAX and RXTE observations of the NS binary source 4U 1728-34. FT11 give an explanation of this index stability, which was also revealed in other observations of NS binaries. In this paper, for the 16

If we now substitute the result of Equation (4) into Equation (1), after a bit of straightforward algebra we obtain 0.25 kTe 0 (2 + 0 ) = 2 me c 1+ Qdisk /Q .
cor

(5)

One should use a formula for spectral index 3 =- + 2 9 +, 4 (6)

where kTe /me c2 , and the -parameter is as defined in Titarchuk & Lyubarskij (1995). If we replace with its diffusion limit diff 1 diff = (7) 0 (2 + 0 ) and using Equation (5), we as 3 diff = - + 2 or diff 1+0.8Qdisk /Qcor obtain the diffusion spectral index 9 1+ Qdisk /Q + 4 0.25 and
disk cor

,

(8)

diff 1+ diff = 2+0.8Q for Q
disk

/Q

cor

(9)

/Q

cor

< 1.


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk

BB A A

C C

A1

A2 B1

B2 C1

C2
Figure 12. Upper panel: RXTE/ASM count rate during the 1998­1999 (R3, R5) outburst transition. Red/blue points A, B, and C mark moments at MJD = 51122/ 51128, 51133.27/51133.34, and 51196/51193 (before, during, and after X-ray outburst, respectively). Lower panels: PDSs for the 13­30 keV energy band (left column) are plotted along with energy spectral diagram E F (E ) (right column) related to the A, B, and C points of the X-ray light curve (upper panel). The strong noise component related to the break at 1­3 Hz and broad QPOs centered at 7­10 Hz are present before and after the burst (see panels (A1) and (C1)). At the X-ray flare peak (see panel (B1)) one can see a white­red noise PDS with the break at about 40 Hz. On the right-hand side panels we present the E F (E ) spectral diagrams (panels A2, B2, and C2) related to the corresponding power spectra (panels A1, B1, and C1). The data are shown by red points, and the spectral model components are displayed by blue, black, and dashed purple lines for COMPTB, blackbody, and Gaussian components, respectively. (A color version of this figure is available in the online journal.)

Thus, until Qdisk /Qcor 1 photon index 2. This is precisely what we see in the observations of NS 4U 1728-34 (see Figures 6­8). However, in BHs we observe that the photon index monotonically increases with QPO frequency and the mass accretion rate and finally saturates (see ST09, TS09, and ST10). Recently, Laurent & Titarchuk (2011), hereafter LT11, made Monte Carlo simulations of X-ray spectral formation in the Compton cloud that surrounds a BH. They reproduced the observed correlation index versus mass accretion rate. They also demonstrated that the index saturation observed in BH sources is a result of two effects, namely, cooling of the CF by the soft disk photons along with the photon capture by a BH. In fact, spectral index is the inverse of the Comptonization parameter Y, which is proportional to mean number of upscattering Nsc and efficiency of upscattering . But in the relatively cold CF photons (when mass accretion rate m in Eddington units is much greater than 1) mostly upscatter of electrons in the direction of the flow for 17

which Nsc is proportional to CF optical depth CF (or m) and is inverse proportional to CF (m). Thus, the spectral (photon) index saturates when the mass accretion rate increases. This is precisely what was reproduced in the MC simulations by LT11. Hence, one can conclude that the monotonic growth of the photon index with the mass accretion rate followed by its saturation is the observational signature of a BH while the constancy of (around 2) versus m (or electron temperature) is the NS signature. Recently Soria et al. (2011) found that in ultra luminous Xray source HLX1 photon index changes from 1.8 to 2.95 but they were unable to find an argument as to whether this source is intermediate-mass BH or foreground NS. Comparison of our and FT11 results for NSs and ST09 results for BHs (see also LT11) indicates that HLX1 is probably a BH because its photon index changes in the wide range from 1.8 to 2.95 (see Figure 14) but in an NS case the index does not vary and has almost a constant value around 2 (see Figures 6­8).


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk

l sl
b

Figure 13. â power diagram of 4U 1728-34 in the 0.1­150 Hz range, observed on 2000 March 7 (50023-01-01-00, MJD = 51610). The blue solid line shows the best fit of the power spectrum, which typically consists of three components: the broadband noise with break b (broken power law), low-frequency QPOs fit by Lorentzians (sl , l ), and 100 Hz bump noise (see Di Salvo et al. 2001). (A color version of this figure is available in the online journal.)

7. SUMMARY We presented our analysis of the spectral properties observed in X-rays from the NS X-ray binary 4U 1728-34 during transitions between the LS and the HS. We analyzed a number of transition episodes from this source observed with BeppoSAX and RXTE satellites. For our analysis we used a good spectral coverage and resolution of BeppoSAX detectors from 0.1 to 200 keV along with extensive RXTE observations in the energy range from 3 to 60 keV. We show that the X-ray broadband energy spectra during all spectral states can be adequately fitted by the composition of the Blackbody, Comptonized component (COMPTB), and Gaussian component. We also show that photon index of the best-fit Comptonized component in 4U 1728-34 is almost constant, about 2 (see Figure 6) and consequently al2 most independent of COMPTB normalization L39 /D10 , which is proportional to the disk mass accretion rate m, (see the left hand panel of Figure 7) and plasma temperature of Compton cloud Te (see Figure 8). Note the soft (disk) photon luminosity L39 is in units of 1039 erg s-1 and the distance to the source D10 is in units of 10 kpc. This index stability has been recently suggested using a quite a few number of other NS sources, Cyg X-2, Sco X-1, GX 17+2, GX 340+0, GX 3+1, GX 349+2, X 1658-298, GS 1826-238, and 1E 17243045, which were observed by BeppoSAX at different spectral states (see details in FT11). A relatively high value of Comptonized fraction f = 0.6­0.9, obtained in the framework of our spectral model, indicates significant reprocessing of X-ray disk emission in the Compton cloud in 4U 1728-34. 18

Using BeppoSAX observations, we also find that there are two sources of blackbody emission. One is presumably related to the accretion disk, and the other 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 the photon index 2 is almost constant when the source moves from the LS to the HS, i.e., when the plasma temperature of the Comptonized region varies from15to2.5 keV(seeFigure 8). We present strong theoretical arguments that the dominance of the energy release in the TL with respect to the soft flux coming from the accretion disk, Qdisk /Qcor 1, leads to almost constant photon index 2. Thus, we argue that this index stability is the intrinsic signature of an NS binary source, while in BHs the index monotonically changes with the mass accretion rate and ultimately saturates (see ST09). In Figure 14 we demonstrate the index correlation versus mass accretion rate for a number of BH sources and that the index depends on the mass accretion rate in NS 4U 1728-34. Photon indices of BHC sources (GRS 1915+105, GX 339-4, SS 433, and GRO J1655-40) show clear correlation with mass accretion rate m or with soft photon normal 2 ization L39 /D10 , which is proportional to m. This correlation is followed by the index saturation when m exceeds a cer tain level. The behavior of the index for the considered NS 4U 1728-34 is clearly different from that for the sample of BHC sources. We thank Chris Shrader and Cristiano Guidorzi for careful reading and editing of this paper. We are very grateful to the


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk

Figure 14. Examples of diagrams of photon index vs. mass accretion rate for BHC sources (GRS 1915+105 (taken from TS09), GX 339-4 (ST08), SS 433 (ST10), and GRO J1655-40 (ST08)) along with that for atoll NS 4U 1728-34. One can see a noticeable change of followed by saturation plateau for BHs as for NS 4U 1728-34 the index slightly varies about 2 (see also Figure 6). The level for = 2 is indicated by the blue dashed line. (A color version of this figure is available in the online journal.)

19


The Astrophysical Journal, 738:128 (20pp), 2011 September 10

Seifina & Titarchuk Bisnovatyi, G. S., Khlopov, M. Yu., Chechetkin, V. M., & Eramzhyan 1980, SvA, 24, 716 Boella, G., Chiappetti, L., Conti, G., et al. 1997, A&AS, 122, 327 Bradt, H. V., Rothschild, R. E., & Swank, J. H. 1993, A&AS, 97, 355 Churazov, E., Gilfanov, M., Sunyaev, R., et al. 1997, Adv. Space Res., 19, 55 D' Ai, A. R., Iaria, R., Di Salvo, T., et al. 2006, A&A, 448, 817 Di Salvo, T., Iaria, R., Burderi, L., & Robba, N. R. 2000, ApJ, 542, 1034 Di Salvo, T., Iaria, R., Robba, N. R., & Burderi, L. 2006, Chin. J. Astron. Astrophys., 6, 183 Di Salvo, T., Mendez, M., van der Klis, M., Ford, E., & Robba, N. R. 2001, ApJ, 546, 1107 Ebisawa, K., Titarchuk, L., & Chakrabarti, S. K. 1996, PASJ, 48, 59 Egron, E., Di Salvo, T., Burderi, L., et al. 2011, A&A, 530, A99 Farinelli, R., & Titarchuk, L. 2011, A&A, 525, 102 (FT11) Farinelli, R., Titarchuk, L., Paizis, A., & Frontera, F. 2008, ApJ, 680, 602 (F08) Ford, E., & van der Klis, M. 1998, ApJ, 506, L39 Forman, W., Tananbaum, H., & Jones, C. 1976, ApJ, 206, L29 Franco, L. 2001, ApJ, 554, 340 Frontera, F., Costa, E., dal Fiume, D., et al. 1997, Proc. SPIE, 3114, 206 Galloway, D. F., Muno, M. P., Hartman, J. M., Psaltis, D., & Chakrabarty, D. 2008, ApJS, 179, 360 Hoffman, J. A., Lewin, W. H. G., Doty, J., et al. 1976, ApJ, 210, L13 Hua, X.-M., & Titarchuk, L. 1995, ApJ, 449, 188 Jonker, P. G., Mendez, M., & van der Klis, M. 2000, ApJ, 540, L29 Kaminker, A. D., Pavlov, G. G., Shibanov, Y. A., et al. 1989, A&A, 220, 117 Kluzniak, W. 1993, A&AS, 97, 265 Kong, A. K. H., Charles, P. A., & Kuulkers, E. 1998, New Astron., 3, 301 Laurent, P., & Titarchuk, L. 1999, ApJ, 511, 289 (LT99) Laurent, P., & Titarchuk, L. 2011, ApJ, 727, 34 (LT11) Lewin, W. H. G., Clark, G., & Doty, J. 1976, IAU Circ., 2922, 1 Marti, J., Mirabel, I. F., Rodriguez, L. F., & Chaty, S. 1998, A&A, 332, L45 Mendez, M., van der Klis, M., & Ford, E. 2001, ApJ, 561, 1016 Migliari, S., van der Klis, M., & Fender, R. P. 2003, MNRAS, 345, L35 Ng, C., Daz, T. M., Cadolle, B. M., & Migliari, S. 2010, A&A, 522, A96 Oda, M., Gorenstein, P., Gursky, H., et al. 1971, ApJ, 166, L1 Parmar, A. N., Martin, D. D. E., Bavdaz, M., et al. 1997, A&AS, 122, 309 Piraino, S., Santangelo, A., & Kaaret, P. 2000, A&A, 360, L35 Remillard, R. A., & MacClintock, J. E. 2006, ARA&A, 44, 49 Reynolds, M. T., & Miller, J. M. 2011, ApJ, 734, L17 Seifina, E., & Titarchuk, L. 2010, ApJ, 722, 586 (ST10) Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337 Shaposhnikov, N., & Titarchuk, L. 2009, ApJ, 699, 453 Soria, R., Zampieri, L., Zane, S., & Wu, K. 2011, MNRAS, 410, 1886 Strohmayer, T. E., Zhang, W., Swank, J. H., et al. 1996, ApJ, 469, L9 Sunyaev, R. A., & Titarchuk, L. G. 1989, in Proc. 23rd ESLAB Symp. on Two Topics in X-Ray Astronomy, ed. J. Hunt & B. Batrick (ESA SP-296; Noordwijk: ESA), 627 Tennant, A. F., Fabian, A. C., & Shafer, R. A. 1986, MNRAS, 219, 871 Titarchuk, L. 1994, ApJ, 434, 570 Titarchuk, L., & Fiorito, R. 2004, ApJ, 612, 988 Titarchuk, L., Lapidus, I. I., & Muslimov, A. 1998, ApJ, 499, 315 Titarchuk, L., & Lyubarskij, Y. 1995, ApJ, 450, 876 Titarchuk, L., Mastichiadis, A., & Kylafis, N. D. 1997, ApJ, 487, 834 Titarchuk, L., & Seifina, E. 2009, ApJ, 706, 1463 Titarchuk, L., & Shaposhnikov, N. 2005, ApJ, 626, 298 Titarchuk, L., & Shaposhnikov, N. 2010, ApJ, 724, 1147 Titarchuk, L., & Zannias, T. 1998, ApJ, 493, 863 Titarchuk, L. G., & Osherovich, V. A. 1999, ApJ, 518, L95 van Paradijs, J. 1978, Nature, 274, 650 van Straaten, S., van der Klis, M., Kuulkers, E., & Mendez, M. 2001, ApJ, 551, 970 Zel'dovich, Ya. B., & Shakura, N. I. 1969, SvA, 13, 175

referee for his/her valuable comments and corrections to the content of this paper. L.T. acknowledges the support of this paper by the ADP NASA grant, NNX09AF02G. APPENDIX ON THE DEFINITION OF THE NORMALIZATION OF THE COMPTB AND BMC MODELS The COMPTB and BMC models describe the outgoing spectrum as a convolution of the input "seed" blackbody-like spectrum, whose normalizations are NCOMPTB and NBMC and color temperature is kT , with Comptonization Green's function. Similar to the ordinary bbody XSPEC model, bolometrical luminosity L
bol

=
0



E â A(E )dE,

(A1)

where A(E ) is the photon flux density of blackbody radiation A(E ) = 8.052 â K â E2 E -1 â exp (kT )4 kT
-1

,

(A2)

and K = NCOMPTB NBMC is the normalization of the seed blackbody photon spectrum, defined in the same way as the XSPEC bbody model. Thus, one can calculate the emergent luminosity of the source as an integral L
bol

= 8.052 â K
0



4 z3 dz = 8.052 â K â . ez - 1 15

(A3)

2 On the other hand NBMC ,NCOMPTB = K = L39 /D10 (see Section 6.2.10 of "User's Guide of an X-Ray Spectral Fitting Package XSPEC v.12.6.0"13 and Farinelli et al. 200814 ), where L39 is the source luminosity in units of 1039 erg s-1 and D10 is the distance to the source in units of 10 kpc. If we know K we can find L39 having D10 . Thus, similar to the ordinary bbody XSPEC model, the normalizations NCOMPTB and NBMC are a ratio of the source (disk) luminosity to the square of the distance:

NBMC ,NCOMPTB =

L 39 erg s 10

-1

10 kpc D

2

.

(A4)

This implies an important BMC models. Namely, using evaluate the normalization of which is presumably a correct

property of both COMPTB and these models one can correctly the original "seed" component, mass accretion rate indicator.

REFERENCES
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https://heasarc.gsfc.nasa.gov/docs/software/lheasoft/ xanadu/xspec/XspecManual.pdf 14 http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/models/comptb.html

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