SUZAKU AND BeppoSAX X-RAY SPECTRA OF THE PERSISTENTLY ACCRETING NEUTRON-STAR BINARY 4U 1705-44

Suzaku made seven observations of 4U 1705-44 in 2006–2008. Detailed information of these observations is given in Table 1. Both the X-ray Imaging Spectrometer (XIS, 0.2–12 keV; Koyama et al. 2007) and the Hard X-ray Detector (HXD, 10–600 keV; Takahashi et al. 2007) instruments were used during these observations. There are four XIS detectors, numbered as 0 to 3. XIS0, 2, and 3 all use front-illuminated CCDs and have very similar responses, while XIS1 uses a back-illuminated CCD. XIS2 was damaged in 2006 November, and its data are analyzed only for the first three observations. The HXD instrument includes both PIN diodes (10–70 keV) and GSO scintillators (30–600 keV). Both the PIN and GSO are collimated (non-imaging) instruments.

We reprocessed each observation using the aepipeline tool provided by Suzaku FTOOLS version 15 and applying the latest calibration available as of 2010 February. We then applied the publicly available tool aeattcor.sl by John E. Davis to obtain a new attitude file for each observation. This tool corrects the effects of thermal flexing of the Suzaku spacecraft and obtains more accurate estimate of the spacecraft attitude. For all our seven observations, the above attitude correction produced sharper point-spread function (PSF) images. With the new attitude file, we updated the XIS event files using the FTOOLS xiscoord program.

Since 4U 1705-440 is a relatively bright source, window and burst options were adopted during each observation to limit the effects of event pile-up (Table 1). Despite this, pile-up was still present in the image center. We estimated the pile-up fractions at different positions of the CCD using the publicly available tool pileup_estimate.sl by Michael A. Nowak. The pile-up fraction refers to the ratio of events lost via grade or energy migration to the events expected in the absence of pile-up. The unfiltered pile-up fractions integrated over the whole CCDs are about 10%–15% for all observations except for the observation 401046010 (∼3%). Table 1 lists the radii of the central circular regions that contain most of the XIS CCD pixels with local pile-up fractions that exceed 5% and 10%, respectively. We used annular regions to extract spectra (circular regions are used for observation 401046010). The outer radius was set to be 120 pixels, while two cases of inner radii were used, corresponding to the 5% and 10% pile-up exclusion regions, respectively. The corresponding integrated pile-up fractions of all annular regions are ∼3% and ∼5%, respectively. Using the models for the soft-state spectra, which include MCD and BB components, we find that the spectral fitting results using 10% pile-up exclusion regions show systematic decrease in the soft-component (MCD) flux and increase in the hard-component (BB) flux, by about 3%, compared with the results using 5% pile-up exclusion regions. The differences in most cases are within the error bars at a 90% confidence level, and the conclusions of this paper hold for either case. For simplicity and increased accuracy, we only show results using the 5% pile-up exclusion regions below.

4U 1705-44 is in the direction toward the Galactic ridge, and the background consists of non-X-ray (particle) background, absorbed cosmic X-ray background, and Galactic ridge emission. Even though our source can be regarded as a point source, there is no region of the detector plane that is free from the source emission to estimate the pure background. This is because the PSF of the XIS is quite spread out and our source during these seven observations was bright enough to dominate over the background (1–10 keV) throughout the 1/4 window. We compared results using two methods of estimating the background. In the first method, we set the background region to be the whole 1/4 window excluding a circular region of radius 350'' around the source. In the second method, we estimated the non-X-ray background, which varies with time, using the xisnxbgen tool based on the night Earth data by Suzaku. We estimated the X-ray background, including the cosmic X-ray background and Galactic ridge emission, using observation 100026030 by Suzaku. It is specific for observing the background emission around the supernova remnant RX J1713-3946, and the pointing direction of this observation has a 184'' offset from 4U 1705-44. Both of the methods turn out to give very similar spectral fit results, and we only show results using the second method below.

The response files of the XIS for each observation were generated using the xisresp script which uses the xisrmfgen and xissimarfgen tools (specifying 1% accuracy). They take into account the time variation of the energy response and the specific extraction region for each observation and each XIS detector. As the responses of XIS0, 2, and 3 on the whole are very similar, we combined their spectra and responses using the script addascaspec.

We also extracted the PIN spectra. The non X-ray and cosmic X-ray backgrounds are taken into account. The non X-ray background is calculated from the background event files distributed by the HXD team. The cosmic X-ray background is from the model by Boldt (1987), and its flux is about 5% of the background for PIN. The response files provided by the HXD team were used. The GSO data were not used, considering the large uncertainty in calibration and low signal-to-noise ratios above 40 keV.

The CD/HID of these observations are shown in Figure 2. We defined soft and hard colors as the ratios of the count rates in the (3.6–5.0)/(2.2–3.6) keV bands and the (11.0–20.0)/(5.0–8.6) keV bands, respectively. The count rates of the lowest three energy bands were from XIS0, 1, and 3 combined. We first obtained the count rates using the 5% pile-up exclusion regions and then converted to the value corresponding to the whole integrated PSF. They are background subtracted and dead time in burst option corrected. XIS2 was not used for this because it was not on for all observations. The count rates in the energy band 11.0–20.0 keV were from the PIN with the background subtracted and the dead time correction made. The CD and HID in Figure 2 use the 128 s data. The intensity is from the energy band 2.2–8.6 keV. Two type-I X-ray bursts were found in observation 401046010, and data around them are not included in Figure 2 or our spectral analysis. The data points with hard color larger than 0.2 (square symbols) are all from observation 401046010, indicating that only this observation was in the hard state while all other observations (cross symbols) were in the soft state.

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Most observations show little variation (the average and standard deviation of colors are given in Table 1), and we created one spectrum each observation for spectral modeling. Each spectrum has three instrumental components, i.e., XIS023 (combination of XIS0, 2, and 3), XIS1, and PIN. In the end, we have seven spectra from Suzaku observations and they are denoted as suz1–suz7 hereafter (Table 1). We rebinned the spectra by factors of 8 and 16 for energies below and above 2.55 keV, respectively, and further rebinning was made so that every bin has at least 40 counts and χ² minimization criterion can be used in our spectral fitting.

There are two pointed observations of 4U 1705-44 with BeppoSAX, one on 2000 August 20 in the soft state and the other on 2000 October 3 in the hard state (Table 2; Fiocchi et al. 2007). The publicly available data are from three narrow field instruments: the Low Energy Concentrator Spectrometer (LECS, 0.1–10 keV; Parmar et al. 1997), the Medium Energy Concentrator Spectrometer (MECS, 1.3–10 keV; Boella et al. 1997), and the Phoswich Detection System (PDS, 15–300 keV; Frontera et al. 1997). There are three MECS units (MECS1, 2, 3), but no data from MECS1 are available during these two observations. Thus we used only data from MECS2 and 3. We extracted two spectra, one for the soft-state observation and the other for the hard-state observation, and they are denoted as sax1 and sax2 hereafter (Table 2). The LECS and MECS data were extracted from circular regions of 8' radius centered on the source position. As our source is in the direction of the Galactic ridge, we cannot use "blank fields" measurement for background subtraction for the LECS. Instead, we used the semi-annuli method described in Parmar et al. (1999). For the MECS, we used the "blank fields" method for the MECS as described in the instrument analysis guide. The PDS spectra were also extracted, with the background rejection method based on fixed Rise Time thresholds. The background for the PDS spectra was obtained using observations during off-source intervals. All the spectra for each instrument were finally rebinned using the publicly available template files to sample the instrument resolution with the same number of channels at all energies.

We fit all nine spectra, suz1–suz7 from Suzaku and sax1–sax2 from BeppoSAX. For Suzaku, we jointly fit spectra from XIS023, XIS1, and the PIN. We used the energy bands with good calibration and high signal-to-noise ratios for each instrument: 1.2–1.7, 1.9–2.2, and 2.3–10 keV for XIS detectors, and 11.0–40.0 keV for the PIN. Their relative normalizations were left free, and the spectral fit results quoted later are all from XIS023 (results from XIS1 differ by <3% generally). For BeppoSAX spectra, we jointly fit the LECS, MECS2, MECS3, and PDS. We utilized the 1.0–3.5 keV energy band for the LECS, 1.7–10.0 keV for the MECS, and 15.0–40.0 keV for the PDS (15.0–150.0 keV for the hard-state spectrum sax2). Their relative normalizations are also left free, but that of PDS relative to MECS was constrained to the range 0.77–0.93, a 90% confidence interval advised by the instrument analysis guide. The spectral fit results quoted later are all referenced to MECS2 (results from MECS3 differ by <2%). The fit of the Crab Nebula from the MECS using a single power law gives the photon index 2.1 and normalization 9.23, while the XIS gives 2.1 and 9.55, respectively. Thus the normalizations from both observatories appear to differ by less than 5%. For all spectral fits, we set the model systematic error to be 1%.

For the soft-state spectra, we tested three models for the continuum spectra: MCD+BB, MCD+BB+PL, and, SIMPL(MCD)+BB, respectively, where PL is a power law and SIMPL is a simple-Comptonization model by Steiner et al. (2009). MCD (diskbb in XSPEC) has two parameters: the temperature kT_MCD at the apparent inner disk radius R_MCD, and the other is the normalization N_MCD ≡ (R_MCD,km/D_10 kpc)²cos i, where D_10 kpc is the distance to the source in unit of 10 kpc and i is the disk inclination. BB (bbodyrad in XSPEC) assumes an isotropic BB spherical surface with radius R_BB and has two parameters, i.e., the temperature kT_BB and the normalization N_BB ≡ (R_BB,km/D_10 kpc)². SIMPL (in XSPEC12) is an empirical convolution model of Comptonization in which a fraction of the photons from an input seed spectrum is scattered into a power-law component. This model has only two free parameters, i.e., the photon power-law index Γ_SIMPL and the scattered fraction f_SC. In addition, there is a flag parameter to control whether all the scattered photons are up-scattered in energy or are both up- and down-scattered. We specified that all the scattered photons are up-scattered in energy. We found that inclusion of down-scattering only changed our results within error bars. We assumed that the Comptonization seed photons are from the disk. The fit results of the MCD and BB are consistent within error bars if we assumed both the MCD and BB contribute to the Comptonization seed photons instead, thanks to low Comptonization for all our soft-state observations. The best-fitting photon power-law index Γ_SIMPL turns out to be high (>4) in most cases, a regime where the model is not suitable (Steiner et al. 2009). Thus, we constrained Γ_SIMPL to be less than 2.5, a value typically seen in the black hole cases. No constraint on the photon index Γ_PL in the PL model was used.

The two hard-state continuum spectra sax2 and suz1 were fit with a BB plus a Comptonized component. We tested three choices of the Comptonization component: a broken power law (BPL; bknpower in XSPEC), a cutoff power law (CPL; cutoffpl in XSPEC), and the Comptonization model by Titarchuk (1994; CompTT in XSPEC). CompTT is an analytic model describing Comptonization of soft photons in a hot plasma.

All models included an absorption component (we use model wabs in XSPEC). There are strong broad Fe lines in most spectra (see also Reis et al. 2009). They were modeled by the diskline model (Fabian et al. 1989), which describes line emission from a relativistic accretion disk. Its parameters are: the line energy E_line in unit of keV, the power law dependence of emissivity (β), the disk inner and outer radii in units of GM/c², the disk inclination i, and the normalization (photons cm⁻² s⁻¹). Figure 3 shows some examples of unfolded spectra at different states using different models, with the Fe lines modeled by the diskline model. The top panel shows the hard-state spectrum sax2 using model CPL+BB. The lower two panels show the soft-state spectrum suz2 using models MCD+BB+PL and SIMPL(MCD)+BB, respectively.

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We scaled the luminosity and radius related quantities using a distance of 7.4 kpc (Haberl & Titarchuk 1995), unless indicated otherwise. The flux and its error bars are all calculated for an energy band of 0.001–200 keV (1.5–200 keV for CPL/PL components) using the cflux model in XSPEC12. As there is little emission of the thermal components outside the above energy band, the values are essentially bolometric for thermal components. For the MCD component, we assume the inclination to be 24°, from the fitting of Fe lines (see below).

We test three models for the soft-state continuum spectra: MCD+BB, MCD+BB+PL, and SIMPL(MCD)+BB. Our practice is to use a fixed value of the interstellar column density (N_H) for all spectral fits of each model. To determine for the appropriate value, we fit all soft-state spectra (suz2 − suz7 and sax1) simultaneously with each model, while tying their N_H to a common value. The best-fitting values of N_H for MCD+BB, MCD+BB+PL, and SIMPL(MCD)+BB are (1.69 ± 0.01), (1.88 ± 0.06), and (1.71 ± 0.01) × 10²² cm⁻², respectively. The above values are obtained from fits with the Fe line region 4.0–8.0 keV excluded, although the fits with the Fe line modeled by the diskline model give very similar values. We see that models MCD+BB and SIMPL(MCD)+BB yield similar values of N_H, but they are smaller than that from model MCD+BB+PL. This is consistent with the results of Steiner et al. (2009), i.e., fits with PL tend to infer higher values of N_H than fits with SIMPL, a systematic effect of different ways of handling the Comptonization. Considering this issue, we do not require a common value of N_H for all models, but use N_H = 1.71 × 10²² cm⁻² for models MCD+BB and SIMPL(MCD)+BB, and 1.88 × 10²² cm⁻² for model MCD+BB+PL. In the latter case, the choice of either value of N_H does not affect the spectral parameters for the MCD and BB components very much, but there are obvious differences for the PL component, as will be discussed below.

The spectral fit results of the thermal components (MCD and BB) in the soft state from all tested models with the Fe line included are shown in Figure 4, and results of all spectral components are tabulated in Tables 3 (MCD+BB+PL+diskline) and 4 (SIMPL(MCD)+BB+diskline). The details of fitting the Fe line with the diskline model are given in Section 3.4. The red crosses and the black triangles in Figure 4 are for soft-state spectra suz2–suz7 and sax1, respectively, and the panels from the top to the bottom correspond to continuum models MCD+BB, MCD+BB+PL, and SIMPL(MCD)+BB, respectively. For model SIMPL(MCD)+BB, the MCD component shown is the original value before scattering. The dotted lines in Figure 4 correspond to the NS burst radius of R_burst ∼ 7.4 km (at a distance of 7.4 kpc), assuming L_X = 4πR²σT⁴. The NS radius was derived from spectral fitting to Type I X-ray bursts of this source using RXTE data (see also Gottwald et al. 1989). The dashed lines correspond to R = 2.2 km, which is about the average visible BB emission size.

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From Figure 4, we see that the MCD and BB components in the soft state roughly follow the L ∝ T⁴ tracks for all models, which implies relatively constant apparent emission areas. We discuss the extent of deviation in Section 4. The inner disk radius is comparable with the NS radius, while the visible BB emission area is about 1/11 of the NS surface. The kT_MCD has values from ∼0.8 to 1.7 keV, and kT_BB from ∼1.8 to 2.4 keV. These values are roughly similar to those seen in Aql X-1, 4U 1608-52, and XTE J1701-462 in the atoll soft state (Lin et al. 2007, 2009). Fits with the Fe line region excluded from the fit generally give consistent results for the MCD and BB components, to within 10% for the normalization parameter N_MCD and within 20% for the N_BB. Spectrum sax1 gives larger differences (∼40% for N_BB), probably because of its narrower energy band and lower energy resolution (only five channels above 10 keV and none in the energy band of 10–15 keV).

Results of the thermal components from both models MCD+BB+PL and SIMPL(MCD)+BB are generally similar, but differences of >20% can occur in some cases (e.g., 30% for N_MCD from the spectrum suz2; compare Tables 3 and 4). Due to weak Comptonization in the soft state, model MCD+BB in general also gives similar results of the thermal components (e.g., flux differs <5% and N_BB by <20%) and acceptable reduced χ² values (<2.0; but 2.6 for sax1). The largest differences in best-fitting spectral parameters from model MCD+BB compared with those from models MCD+BB+PL and SIMPL(MCD)+BB are from BeppoSAX spectrum sax1 (N_BB differs by ∼50%).

We first investigate the performance of different Comptonization models. Using spectrum sax2, which extends to 150 keV (instead of 40 keV for spectrum suz1), we obtained values of χ²/ν 190.2/226, 287.1/224, and 339.9/225 for models CPL+BB, BPL+BB, and CompTT+BB, respectively (N_H was allowed to have different values for different models). The result for CompTT+BB quoted above is just one possible solution with a local χ² minimum. The best-fitting input seed photon temperature τ₀ is <0.2 keV (the cold seed photon model; Lin et al. 2007). All the above models give similar results in terms of kT_BB (∼1.5 keV), N_BB (≲20), and the Comptonization fractions (>90%). There is another solution for CompTT+BB, which has χ²/ν = 252.5/225. It has τ₀ = 0.9 ± 0.1 keV (the hot seed photon model; Lin et al. 2007). For this case, the inferred BB component is quite different from the models above, with kT_BB = 0.5 ± 0.1 keV and N_BB = 256 ± 110. The fit residuals of all the above models are shown in Figure 5. We see that CPL+BB gives the best fit over the whole energy range, while other models tend to have large residuals at high energy (>15 keV). Hereafter, we focus on model CPL+BB only.

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The fit of the CPL model to the BeppoSAX hard-state 15.0–150.0 keV spectrum (the BB contributes little at energies above 15.0 keV) gives a cutoff energy of 44 ± 4 keV. The cutoff energy cannot be well constrained in the case of spectrum suz1, for which we use energies only up to 40 keV. Thus, we fixed the cutoff energy to be 44 keV when we fit spectra sax2 and suz1. The simultaneous fit of sax2 and suz1 gives a best-fitting value of N_H = (1.89 ± 0.04) × 10²² cm⁻² from model CPL+BB, close to the value of 1.88 × 10²² cm⁻² obtained from model MCD+BB+PL for the soft state. For comparison, we fit the hard-state spectra using both N_H = 1.88 and 1.71 × 10²² cm⁻², and the results are given in Table 5. We see no large different between these two sets of solutions. Using N_H = 1.88 × 10²² cm⁻² tends to give a smaller BB emission area and a higher photon index of the CPL model. The values of the photon index are more similar between spectra sax2 and suz1 than using N_H = 1.71 × 10²² cm⁻². Both values of N_H give high fractions of Comptonization (>90%).

The results using N_H = 1.88 × 10²² cm⁻² are shown in Figure 4, the blue squares and the black diamonds for suz1 and sax2, respectively. They are repeated in the middle and bottom panels. They are not shown in the top panel, because this panel is reserved for solutions free of Comptonization and such a model is unacceptable for observations of the hard state. From Figure 4, we see that the boundary layer emission areas in the hard state are comparable to those in the soft state. Although L_BB changes over 50 times, the values of N_BB are always in the range of ∼5–15.

One of our main goals of using the broadband spectra is to search for detectable thermal emission from the accretion disk in the hard state. We added the MCD component while analyzing the two hard-state spectra (suz1 and sax2), i.e., using model CPL+MCD+BB, with either the Fe modeled with the diskline model or with the Fe region excluded in the fit. N_H is either fixed at 1.71 or 1.88 ×10²² cm⁻², or left free in the fit. The best-fitting disk temperature tends to go below 0.2 keV, with an upper limit <0.25 at a 90% confidence level. The normalizations of the MCD component N_MCD are not well constrained. For all cases, the unscattered flux of the MCD component is <2% of the total flux (absorbed or unabsorbed; 1–200 keV). Thus, if we assume a physically visible disk, then we cannot exclude either possibility, i.e., the disk in the hard state might be truncated at a very large radius and/or the temperature is below 0.2 keV. Alternatively, the disk may be rendered invisible by very high Comptonization.

Figure 6 shows the fraction of Comptonized luminosity versus the total luminosity, using SIMPL(MCD)+BB for the soft state and CPL+BB for the hard state. The total luminosity is normalized by the Eddington luminosity L_Edd, which is derived from the type I X-ray bursts showing photospheric radial expansion and corresponds to an average peak flux of about 4 × 10⁻⁸ erg cm⁻² s⁻¹ (Galloway et al. 2006). Figure 6 shows that Comptonization only constitutes <15% of the emission in the soft state, but >90% in the hard state. For the soft-state data, the fractional contribution of Comptonized luminosity decreases with luminosity on the whole, which is consistent with the behavior of atoll-type transients (Lin et al. 2007). The MCD+BB+PL model also gives low-Comptonization solutions for the soft state (<15%), with N_H either 1.71 or 1.88 ×10²² cm⁻². One main difference between these two choices of N_H is that fits with N_H = 1.88 × 10²² cm⁻² give higher values of Γ_PL (∼2.7) than fits with N_H = 1.71 × 10²² cm⁻² (Γ_PL ∼ 2.2).

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The BB component, which describes the emission from the boundary layer in our model, is present in both the hard and soft states. We can compare this component with the other spectral components to investigate the impact of different accretion processes in different states. We plot in Figure 7 the luminosity of the MCD component plus Comptonization (SIMPL/CPL) versus the BB luminosity from model SIMPL(MCD)+BB. Model MCD+BB+PL gives similar results. The hard-state data (diamond and square symbols) are from model CPL+BB. The dashed and dotted lines correspond to the ratios of 1 and 0.05 of the BB luminosity versus the MCD component plus Comptonization luminosity, respectively. They are about the average values for the soft- and hard-state observations, respectively. If we assume that the Comptonization emission is not from the boundary layer, the above result means that there is a much lower portion of energy seen in the visible portion of the boundary layer in the hard state than in the soft state. Similar results were suggested to be a possible consequence of a strong jet in the hard state in Lin et al. (2007).

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We first fit the Fe line with a Gaussian line. A broad Gaussian line with the line width σ around 0.6 is generally required, while fits with a narrow line (σ < 0.1 keV) are mostly unacceptable, with χ² values increased by >100 for ∼700 degrees of freedom in the soft state. The diskline model can in general improve the fits further, compared with a broad Gaussian line, with the χ² values decreased by about 30 on average in the soft state. In the hard state, the diskline model still gives the best fits, though the improvement is much less. We also fit the spectra with a smeared edge (smedge in XSPEC) in our continuum model, with the lower limit of the threshold energy set to be the neutral Fe K edge 7.1 keV. We obtain fits with χ² values larger than those using the diskline model by about 30 on average, and the threshold energy in most fits reaches the lower limit 7.1 keV. Thus the broad line feature in the spectra is probably not completely due to the Fe absorption edge. The more complicated model combining both a Gaussian line and a smeared edge can give fits with similar χ² values as those using the diskline model, but we choose to focus on the results using the simpler model, i.e., the diskline model.

While fitting the Fe line with the diskline models, we initially fit all soft-state spectra simultaneously, with the inclination parameter i tied to a common value. Different continuum models turn out to give quite similar best-fitting values of i: 243 ± 08, 233 ± 10, and 242 ± 08 from models MCD+BB, MCD+BB+PL, and SIMPL(MCD)+BB, respectively. Thus we fix the disk inclination to be i = 24°. For most of the soft-state spectra, the inner disk radius inferred from the diskline model reaches 6 GM/c², the innermost stable circular orbit (ISCO). Thus in the final fitting, we fix it to be 6 GM/c². For the hard-state spectra, the Fe lines are much weaker, and the best-fitting inner disk radius in the diskline model is quite uncertain. The lower error bar reaches 6 GM/c² for the two observatories using both N_H = 1.88 and 1.71 × 10²² cm⁻². For simplicity, we then fixed the inner disk radius in the diskline model to be 6 GM/c² for the hard-state spectra to derive the final results. The obtained Fe line flux and equivalent width are not sensitive to such details.

The results of fitting Fe lines with the diskline model are shown in Figure 8. It can be seen that the Fe emission line is detected in all spectra, and most of them show a broad feature (see also Reis et al. 2009). Tables 3–5 contain best-fitting parameters of the Fe line for each spectrum, with the equivalent width also included. The best-fitting value of E_line reaches the allowed upper limit 6.97 keV in most cases. The equivalent width is around 170 eV for most of the soft-state spectra, and it is around 100 eV in the hard state. The power-law dependence of emissivity β is generally steeper in the soft state (∼−3.5) than in the hard state (∼−2.5). We note that our detection of these relativistic Fe lines, mostly in the soft state, cannot be due to the pile-up effect (Ng et al. 2010), as we have excluded enough pile-up regions when we extract the Suzaku spectra. Moreover, the BeppoSAX detectors have no pile-up problem, and its spectrum sax1 also shows the relativistic feature.

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Fe emission lines in X-ray binaries are the most obvious signature of an accretion disk irradiated by an external source of hard X-rays, due to a combination of high fluorescent yield and large cosmic abundance (Miller 2007). To investigate the irradiation source of the Fe lines, we show in Figure 9 the dependence of the bolometric Fe energy line flux on the BB energy flux (upper panel) and Comptonization (SIMPL/CPL) flux (lower panel), both integrated over 6.4–200 keV. The soft-state data show that the Fe line flux increases monotonically with the BB flux, but has no clear dependence on the Comptonization flux. This might imply that it is the boundary layer emission that illuminates the accretion disk and produces the Fe line, in agreement with the conclusions of Cackett et al. (2009a). The Fe line energy flux is about 4% of the BB energy flux (solid lines).

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The hard-state data in Figure 9 (diamond/square symbols) in the upper panel show that there is much higher Fe line flux relative to the BB continuum in the hard state compared to the soft state. This might indicate that the BB emission is not the (major) source illuminating the accretion disk to produce the Fe line in the hard state. From the lower panel, we can see that there is strong Comptonization flux available in the hard state. However, using the reference lines and comparing the upper and lower panels, we see that the Comptonization emission is not as efficient as the BB emission to illuminate the accretion disk and produce the Fe line. This can be explained if the Comptonization emission is located farther away from the accretion disk than the boundary layer. We also caution that some BB flux may be screened from the observer's view by the accretion disk.

We have shown that 4U 1705-44 exhibits two distinct spectral states. The hard-state spectra span from ∼1 to 150 keV, while the soft-state spectra are mostly confined below 40 keV (see also Fiocchi et al. 2007). Such two distinct states have been observed in other atoll-type NS LMXBs (Barret 2001; van der Klis 2006). On the whole, these two spectral states are very similar to the thermal and hard states (but not the steep power-law state) of accreting black holes (Remillard & McClintock 2006; Done et al. 2007). In addition, atoll-type NS LMXBs and accreting black holes also have many similarities in timing properties. All this motivates the speculation that the accretion process is quite similar between atoll-type NS LMXBs and accreting black holes (Barret 2001; Done et al. 2007; Lin et al. 2007). This implies that the presence of the boundary layer in atoll-type NS LMXBs probably does not strongly interfere with the accretion disk, at least at luminosities below ∼0.5 L_Edd. However, the boundary layer is still an important spectral component in atoll-type NS LMXBs. Figure 7 shows that the boundary layer emission flux is comparable with that from the disk. Because the boundary layer is hotter than the disk (Mitsuda et al. 1984), the soft-state spectra tend to cover a broader energy band and extend to higher energies in atoll-type NS LMXBs than in the thermal state of accreting black holes (compare our Figure 3 and Figure 2 in Remillard & McClintock 2006). The relatively weak contribution of the boundary layer in the hard state, as shown in Figure 7, can be interpreted as the consequence of mass ejection in this state (Lin et al. 2007). This seems to be in alignment with the jet model for the hard state in accreting black holes (Fender 2006; Done et al. 2007).

In Lin et al. (2007), our spectral modeling of two atoll sources Aql X-1 and 4U 1608-52, using the MCD+BB model plus weak Comptonization showed the MCD behavior close to the L_MCD ∝ T⁴_MCD track. In contrast, classical two-component models resulted in constant or slightly decreasing temperatures of the thermal component (MCD or BB) with increasing luminosity. We note, however, that in that study we used RXTE data and the MCD component in the low-luminosity soft state could not be well constrained. In this study, we used Suzaku and BeppoSAX spectra, which extend the energy range down to 1 keV, and the MCD components are well constrained for all soft-state spectra. As the result of the better low-energy coverage, we did not need to put additional constraints on the PL component, as was necessary in Lin et al. (2007). This motivates us to evaluate more quantitatively how closely the MCD component follows the L_MCD ∝ T⁴_MCD track.

Our spectral modeling of broadband spectra of 4U 1705-44 shows a track that is flatter than the L_MCD ∝ T⁴_MCD relation, with nearly an order of magnitude variation in luminosity. There is a slight decrease of R_MCD at higher luminosity. Spectral fitting with Comptonization modeled by PL suggests L_MCD ∝ T^{3.3 ± 0.2}_MCD, while fitting by SIMPL results in L_MCD ∝ T^{3.1 ± 0.1}_MCD. Such deviations have been seen in several black-hole X-ray binaries, and it is normally believed to be due to a spectral hardening effect, instead of a real change in the inner disk radius (Shafee et al. 2006; Davis et al. 2006; McClintock et al. 2007, 2009). Spectral hardening arises when the electron scattering dominates over absorption as the main opacity source. In such a situation, the local specific flux in the disk appears as a simple dilute BB with a color temperature higher than the effective temperature by a factor of f_col (Shimura & Takahara 1995). This factor slightly increases with luminosity/temperature. Based on a simple analytic estimate of the hardening factor, Davis et al. (2006) suggested a L_MCD ∝ T³_MCD relation. It should be noted that the extent to which the hardening factor depends on luminosity can vary with the inclination, the mass of the compact object, etc. A detailed numeric simulation to obtain how the hardening factor behaves for an accreting NS or direct accretion modeling to infer the real inner disk radius with more realistic spectral models incorporating many effects could provide further insights. We further note that there are possibly other factors causing the above deviation. We cannot exclude the possibility of real change of the inner disk radius in some part of the soft state. It is also possible that the above deviation is due to our simple descriptions of the weak Comptonization and the boundary layer.

We perform a rough estimate of the magnetic field in 4U 1705-44, under the assumption that the disk is truncated at the ISCO in our soft-state observations. This requires the magnetic field to be dynamically unimportant for these soft-state observations. That is, the Alfvén radius r_A, the radius at which the magnetic pressure is roughly the sum of the ram and gas pressure, should be smaller than the ISCO. Based on Equations (6.19–6.20) in Frank et al. (1985), we have

$$\begin{eqnarray} r_{\rm A} &\sim & 7.5 \left(\frac{k_{\rm A}}{0.5}\right) \left(\frac{M_{\rm NS}}{M_{\odot }}\right)^{1/7} \left(\frac{R_{\rm NS}}{10\ {\rm km}}\right)^{10/7}\nonumber\\ &&\times\left(\frac{L}{10^{37}\ {\rm erg\, s^{-1}}}\right)^{-2/7} \left(\frac{B}{10^{8}\ {\rm G}}\right)^{4/7}\ {\rm km}, \end{eqnarray} \tag{ 1 }$$

where B is the magnetic field strength at the surface of the NS and k_A is the correction from the spherical accretion to disk accretion and is about 0.5. This formula assumes a dipole magnetic field. We further assume M_NS = 1.4 M_☉ (such that R_in = 12.4 km), and R_NS = 10 km. The above expression shows that the obtained value of B will only weakly depend on the NS mass (a power of 1/4). Using L = 10³⁷ erg s⁻¹, from the faintest soft-state spectrum suz3, and the constraint r_A < R_in, we find B < 1.9 × 10⁸ G. We can also assume that r_A is less than R_NS, which would decrease the above limit by 30%.

We see that the apparent emission of the boundary layer, modeled by BB, roughly follows L_BB ∝ T⁴_BB, from the hard to the soft states with the luminosity of the boundary layer covering ∼0.003–0.12 L_Edd. The apparent area of the boundary layer is about 1/11 of the the NS surface, as inferred from Type I X-ray bursts. The actual area of the boundary layer might be larger due to a special geometry of the boundary layer, which has been attributed to be an equatorial belt (Lin et al. 2007). Using Equation (3) in Lin et al. (2007) and using the inclination obtained from the Fe line fit (i = 24°), the latitude range (from the NS equator) of the boundary layer is about 13°, corresponding to an emission area of 23% of the NS surface. Accordingly L_BB should be 1.6 times larger than shown in Section 3, which assumes isotropic emission of the boundary layer. Thus, L_BB/L_{MCD+Comptonization} is not around 1 in the soft state, as shown in Figure 7, but is about 2.6. If i = 60°, the latitude range of the boundary layer is about 7°, corresponding to an emission area of 12% of the NS surface. In this case, L_BB should be 30% larger than shown in Section 3. L_MCD should increase by 80% (i.e., adjusting for i = 60°) so that L_BB/L_{MCD+Comptonization} would be around 0.7 in the soft state.

Whether the above results imply that the real boundary layer area is small and nearly constant further depends on the radiative transfer process in the atmosphere above the boundary layer, i.e., the hardening effect as discussed above for the disk spectra. The small BB emission area is reminiscent of the well known spectral modeling problem of the NS thermal emission in quiescence, i.e., the BB fit of its thermal component produced inferred radii too small for theoretical NS size estimate, whereas models taking into account the radiative transfer in the hydrogen atmosphere give radius estimate much closer to theoretical expectation of the size of NSs (e.g., Rutledge et al. 1999). However, all our observations are quite bright (≳10³⁷ erg s⁻¹), and the emission should be due to active accretion. At such a high accretion rate, a pure hydrogen atmosphere is not expected (Brown et al. 1998), and the above problem might not apply to our case. Our conclusion of the small size of the boundary layer is based on the assumption that the modification of the bursting atmosphere on burst emergent spectra is similar to that of the boundary layer emission. This assumption might be valid if most of the heat in the boundary layer is generated in a layer as deep as that for burst nuclear burning. We note that the small inferred size of the boundary layer agrees with the theoretical expectation of most of the boundary layer models at sub-Eddington accretion rates (Kluzniak & Wilson 1991; Inogamov & Sunyaev 1999; Popham & Sunyaev 2001). Thus it is quite possible that the boundary layer emission area is indeed small for our observations.

If the behavior of the hardening factor for the boundary layer is similar to that for the burst emission, then one might conclude that the boundary layer emission area is constant if L_BB ∝ T⁴_BB is measured, as the hardening factor is quite independent of the temperature for burst emission in sub-Eddington limit (Madej et al. 2004; Özel 2006). For example, for an NS with mass 1.4 M_☉ and radius 10 km, Table 2 from Madej et al. (2004) suggests an approximate relation of L_BB ∝ T^3.7_BB for T_BB within 1.1–2.5 keV (most of our observations fall into this range). Thus, our results of roughly following L_BB ∝ T⁴_BB from the hard to soft states might imply little change of the real boundary layer emission area for our observations.

We note that there is scatter in the inferred apparent emission area of the boundary layer. The fractional variation is about 40%, larger than the typical error bars (10%). There are also systematic differences in the inferred boundary layer emission area between BeppoSAX and Suzaku, both in the hard and soft states (see Tables 3–5). Whether all this is real or affected by systematic problems related to spectral models and/or instrumentation is unclear. If we do a simple power-law fit as we did for the MCD component, the BB component seems to follow L_BB ∝ T^{5.0 ± 0.2}_BB from fit to all data combined and L_BB ∝ T^{4.3 ± 0.1}_BB from fit to Suzaku data only. Because of the above uncertainties, we did not treat these deviations from L_BB ∝ T⁴_BB as significant. A better understanding of our luminosity vs. temperature results for the disk and boundary layer of an accreting NS may be gained from further theoretical work on each component, and from additional observations, e.g., with improved statistics and dynamic range for samples of the hard state.