Broad-band X-ray emission and the reality of the broad iron line from the neutron star–white dwarf X-ray binary 4U 1820−30 Free

Abstract

Broad relativistic iron lines from neutron star X-ray binaries are important probes of the inner accretion disc. The X-ray reflection features can be weakened due to strong magnetic fields or very low iron abundances such as is possible in X-ray binaries with low mass, first generation stars as companions. Here, we investigate the reality of the broad iron line detected earlier from the neutron-star low-mass X-ray binary 4U 1820−30 with a degenerate helium dwarf companion. We perform a comprehensive, systematic broad-band spectral study of the atoll source using Suzaku and simultaneous NuSTAR and Swift observations. We have used different continuum models involving accretion disc emission, thermal blackbody and thermal Comptonization of either disc or blackbody photons. The Suzaku data show positive and negative residuals in the region of Fe K band. These features are well described by two absorption edges at 7.67 ± 0.14 keV and 6.93 ± 0.07 keV or partial covering photoionized absorption or by blurred reflection. Though, the simultaneous Swift and NuSTAR data do not clearly reveal the emission or absorption features, the data are consistent with the presence of either absorption or emission features. Thus, the absorption based models provide an alternative to the broad iron line or reflection model. The absorption features may arise in winds from the inner accretion disc. The broad-band spectra appear to disfavour continuum models in which the blackbody emission from the neutron-star surface provides the seed photons for thermal Comptonization. Our results suggest emission from a thin accretion disc (kT_disc ∼ 1 keV), Comptonization of disc photons in a boundary layer most likely covering a large fraction of the neutron-star surface and innermost parts of the accretion disc, and blackbody emission (kT_bb ∼ 2 keV) from the polar regions.

1 INTRODUCTION

A low-mass X-ray binary (LMXB) system consists of a low-mass companion star (≲1 M_⊙) and a primary compact star [a neutron star (NS) or a black hole] rotating around each other. For such a system, in the course of evolution when the companion star fills its Roche lobe, matter is transferred from the companion star to the compact star. This matter follows a slow spiral path and forms an accretion disc around the primary (Frank, King & Raine 2002). For the supermassive as well as the stellar-mass black holes, X-ray emission lines specifically, Fe Kα line ∼6.4 keV, from the inner part of the accretion disc are well known (Miller 2007). With the advance in X-ray spectroscopy, asymmetry in the Fe Kα line profile has been observed in many sources including persistent NS LMXBs. Several authors have discussed the inner disc origin of such a line from the different NS LMXBs and attributed the line asymmetry to relativistic blurring (Bhattacharyya & Strohmayer 2007; Cackett et al. 2008; Pandel, Kaaret & Corbel 2008; Papitto et al. 2009; Reis, Fabian & Young 2009).

4U 1820−30 is an extensively studied source because of its extraordinary properties. It is an ultracompact NS X-ray binary with an orbital period of 11.4 min (Stella, Priedhorsky & White 1987). Thermonuclear X-ray bursts from this source were first discovered by Grindlay & Gursky (1976) and confirmed that the compact object as an NS which resides in the metal-rich globular cluster NGC 6624. Based on optical observation of this cluster, Hesser & Shawl (1985) estimated the distance to be 7.6 kpc. The binary system has a low mass (∼0.07 M_⊙), Roche lobe filling, degenerate Helium (He) dwarf as a companion and the accreted matter likely has a very high He abundances (Rappaport et al. 1987). Based on theoretical modelling, Cumming (2003) showed that the bursts from 4U 1820−30 are consistent with a picture of accumulation and burning of He-rich material. The mass of the NS in this binary is not very well known. Güver et al. (2010) estimated the mass of the NS to be ∼1.6 M_⊙ based on the spectral analysis of multiple thermonuclear X-ray bursts. However, García, Zhang & Méndez (2013) found that the decaying phase of those thermonuclear bursts did not satisfy the relation |$F\propto T_{\text{bb}}^4$| which was a crucial assumption to estimate the mass of the NS. Anderson et al. (1997) reported the system inclination angle i to be in the range of 35° ≤ i ≤ 50°.

Rossi X-ray timing explorer (RXTE) observation of the atoll source 4U 1820−30 have shown kilohertz (kHz) quasi-periodic oscillations (QPOs) at different frequencies in its power density spectrum. Zhang et al. (1998) reported the highest QPO frequency to be 1060 ± 20 Hz from 4U 1820−30 which may be the signature of the marginally stable orbit. The source also exhibited a 176 d periodic modulation in the X-ray flux (Priedhorsky & Terrell 1984). Photospheric radius expansion X-ray burst has been reported for this source from the analysis of RXTE data (Galloway et al. 2008). On 1999 September, a remarkable 3 h superburst was observed from 4U 1820−30, during which its peak isotropic luminosity was ∼3.4 × 10³⁸ erg s⁻¹ assuming a distance of 6.6 kpc. Spectral analysis of this superburst revealed the evidence of a broad emission line between 5.8 and 6.4 keV and an absorption edge at 7–9 keV (Strohmayer & Brown 2002). Costantini et al. (2012) fitted the broad-band continuum with a blackbody and a Comptonization model obtained from XMM–Newton EPIC-PN and INTEGRAL data taken during 2009 April. However, they found no clear evidence of iron emission line in the 6.4 keV region.

Cackett et al. (2008) performed the spectral analysis of the Suzaku data taken on 2006 September 14 using the X-ray Imaging Spectrometer (XIS) in the 1–9 keV band and the 12–25 keV band of the Hard X-ray Detector (HXD)/positive intrinsic negative (PIN) [ignoring 1.5–2.5 keV region]. By using a variety of continuum models, Cackett et al. (2008) detected a significant iron line and fitted it to a relativistic iron line model by restricting the line energy to be between 6.4 and 6.97 keV. Cackett et al. (2010) reanalysed the data with improved calibration after combining all the spectra obtained with the front illuminated CCDs (for higher signal-to-noise ratio) and reported significant (but weaker than before) detection of the emission line at ∼6.4 keV. While Cackett et al. (2008) reported the presence of iron line profile at energies ∼6.4 keV from the Suzaku spectral fitting, Costantini et al. (2012) found no significant evidence of iron emission line at energies ∼6.4 keV in the spectra obtained from combined INTEGRAL and XMM–Newton data. As the source 4U 1820−30 is an NS and He white dwarf binary, the presence of the iron Kα emission line provides crucial information on the nature of the white dwarf and hence it is important to verify the reality of any iron line features in its X-ray spectra.

A disadvantage of the X-ray CCD detectors is that the photon pile-up can distort the shape of the spectra especially in the Fe K band. Thus, it is important to test the spectral properties using broad-band spectra, that are either free of photon pile-up distortions or properly pile-up corrected. NuSTAR with its pile-up free operation in the ∼3–79 keV provides such an opportunity. In this work, we re-analyse the spectra obtained from Suzaku and test the results using the new simultaneous NuSTAR and Swift data. The Suzaku data and the combined NuSTAR and Swift data provide broad-band coverage from 0.3 to 30 keV allowing us to constrain the different broad spectral components as well as an iron line feature. We organized the paper as follows. In Section 2, we describe the observation details and data reduction, in Section 3 we discuss the temporal behaviour of the source and in Section 4 we discuss the details of spectral modelling. Finally, we summarize our results and conclusions in Section 5.

2 OBSERVATION AND DATA REDUCTION

2.1 Suzaku XIS and HXD/PIN

The Suzaku observation of the source 4U 1820−30 was performed on 2006 September 14 at the XIS (Koyama et al. 2007) nominal pointing position with XIS detectors operating in 1/4 window mode. The net exposure after instrumental deadtime were about 13 and 29.6 ks for XIS and PIN, respectively. The observation details are summarized in Table 1. The data reduction was performed using the convenient and straightforward analysis tool xselect V2.4c.

As 4U 1820−30 is one of the brightest known X-ray sources, there may be some significant pile-up (up to 20 per cent or so) in the XIS detectors. Therefore, we checked for the presence of a significant pile-up. We applied the attitude correction using the tool aeattcorr.sl to reduce the pointing determination error for this bright source and used the attitude-corrected event file for further analysis. We also ran another routine pile-estimate.sl which allowed us to create a region file that excluded the most piled up areas and then to estimate the effective pile-up fraction of the remaining events. We selected an annulus region of outer radius 140 arcsec and inner radius 30 arcsec and then gradually increased the inner radius. We found that when we excluded the region of 60 arcsec radius, the effective pile-up fraction was ∼5 per cent. We extracted the source spectrum after selecting an annulus region of outer radius 140 arcsec and inner radius 60 arcsec. Similarly, we extracted a background spectrum from a 127 arcsec source free circular region. We then created the response files accordingly for each XIS detector, after which we combined the spectra of all front-illuminated detectors (XIS0, XIS2 and XIS3) to get higher signal-to-noise ratio using the tool addascaspec. Finally, the spectra were rebinned by a factor of 4 to enhance the signal-to-noise ratio by a factor ∼2.

In the case of HXD (Takahashi et al. 2007) PIN data, we downloaded the latest tuned background file from the Suzaku web site.¹ We ran the ftool hxdpinxbpi to produce the deadtime corrected PIN source spectrum as well as the PIN background spectrum.

2.2 NuSTAR FPMA and FPMB

NuSTAR observed the source 4U 1820−30 on 2013 July 11 (Obs. ID: 80001011002). NuSTAR data were collected with the focal plane module telescopes (FPMA and FPMB). The net exposure after instrumental deadtime was about 1.8 ks. Table 1 lists the observation details.

The data reduction was performed using the NuSTAR data analysis software (nustardas v1.4.1) with the latest calibration version 20141020. We filtered the event file and applied the default depth correction using the nupipeline task. The source region was extracted from a 100 arcsec circular region centred on the source position. The background region was taken from the corner of the same detector as close as possible to the source without including the source photons. Source and background light curves and spectra were extracted from the FPMA and FPMB data and response files were generated using the nuproduct task. The data from the two FPM were modelled simultaneously in order to minimize systematic effects. Initially, we rebinned the spectra by a minimum of 100 counts per bin but the data appeared to be noisy for such a rebinning and we finally rebinned after taking a minimum of 800 counts per bin.

2.3 Swift/XRT

The source was also observed by Swift nearly simultaneously with the NuSTAR observation, the details of which are provided in Table 1. Following standard procedure for filtering and screening, Swift X-ray ray telescope (XRT) data were reduced using the xrtpipeline v 0.13.0 tool. The data obtained from photon counting (PC) mode were found to be severely piled up. Data extracted from a ∼30 arcsec circular region in the image had an average count rate of 102.3 ± 5.4 counts s⁻¹. Therefore, the PC mode data was not useful. Swift also observed this source using Window Timing (WT) mode with an exposure of ∼1.9 ks. The background-subtracted average count rate in this mode was found to be 81.7 ± 2.5 counts s⁻¹ which is well below the prescribed photon pile-up limit for the WT mode data (∼100 counts s⁻¹; Romano et al. 2006). Therefore, source and background spectra were extracted using rectangular boxes with xselect v 2.4. The latest Swift/XRT spectral redistribution matrices were used. The xrtmkarf tool was used along with exposure map file to generate an auxiliary response file for the current observation.

3 HARDNESS–INTENSITY DIAGRAM

Following García et al. (2013), we generated hardness–intensity diagram by calculating the hard colour as a flux ratio in the 6–9.7 keV and 9.7–16 keV bands and the intensity as the 2–10 keV flux. We extracted the spectrum of the Crab from the RXTE/Proportional Counter Array data (Obs. ID: 92802 − 02 − 05 − 00) taken close to our observations and calculated the fluxes in the above-mentioned energy bands and used those to normalize the fluxes in each energy band for proper comparison. By such a procedure, we compared the spectral states during the Suzaku and the NuSTAR observations in the same hardness–intensity diagram as shown in Fig. 1. For both the Suzaku and the NuSTAR observations, the source was observed in the so-called banana branch (soft/high) spectral states of the atoll sources (Hasinger & van der Klis 1989). In the hardness–intensity diagram, we found that during Suzaku and NuSTAR observation the spectral changes occur mostly in flux and only little change in spectral hardness (see Fig. 1).

4 SPECTRAL ANALYSIS

4.1 Suzaku spectra

We analysed the spectra using xspec version 12.8.1g (Arnaud 1996). We fitted the combined XIS(0, 2, 3) data in the 0.8–10 keV band and the HXD/PIN data in the 15–35 keV band simultaneously. We ignored the 1.5–2.5 keV band due to known calibration uncertainties. We used a constant factor to account for absolute flux calibration offset between the XIS and HXD/PIN.

4.1.1 Continuum shape

X-ray continuum of NS LMXBs can be equally well explained by different continuum models. Apart from a power-law or Comptonized component, the soft component can arise from the NS surface or the boundary layer. The soft component can also arise from the accretion disc around the NS (Lin, Remillard & Homan 2007). We first tested a two component model; blackbody plus a diskbb (bbody and diskbb in xspec, respectively, Mitsuda et al. 1984). We accounted for the absorption by multiplying the absorption model TBabs with abundance set to wilm (Wilms, Allen & McCray 2000). We also used a constant factor to account for any differences in the cross-calibration normalization between different instruments. We fixed this constant to 1 for the combined XIS and varied for HXD/PIN. The combination of these two models did not yield a good fit to the data (χ²/dof = 1116/333 where dof stands for degrees of freedom). Hence, we used the following continuum models which we describe below in details.

• Model 1: TBabs×(diskbb + bbody + powerlaw)

• Model 2: TBabs×(diskbb + bbody + cuttofpl)

• Model 3: TBabs×(diskbb + bbody + nthcomp)

• Model 4: TBabs×(diskbb + bbody + CompTT)

Model 1 provided an improved fit (Δχ² = −537 for the addition of two parameters) compared to the two component model TBabs×(diskbb + bbody). This implied that the power law played a significant role in fitting the continuum but the fit was formally not acceptable (χ²/dof = 579/331). The best-fitting power-law slope was Γ = 2.6 ± 0.05. The diskbb and the bbody temperature obtained were kT_disc = 1.27 ± 0.02 keV and kT_bb = 2.53 ± 0.02 keV, respectively. In the residuals we found an absorption feature at ∼7.5 keV and an emission feature at ∼6.4 keV. The spectral data with residuals are shown in the top and lower panel of Fig. 2(a), respectively.

Following Bloser et al. (2000), we tried to fit the continuum using a power law with exponential cut-off (cutoffpl in xspec, an analytical approximation of unsaturated Comptonization) model along with the two thermal components diskbb and bbody i.e. model 2. This model TBabs ×(bbody + diskbb + cutoffpl) fitted the continuum well (χ²/dof = 475/331), but resulted in residuals in the 6–9 keV band which is shown in Fig. 3.

Next, we used a physical thermal Comptonization model nthcomp (Zdziarski, Johnson & Magdziarz 1996; Życki, Done & Smith 1999). The physical picture is that the hot electrons Compton upscatter seed photons with a (quasi-)blackbody spectrum e.g. from an NS surface or an accretion disc. Either of these shapes can be selected via the model parameter input type with both being parametrized by a seed photon temperature (denoted by kT_seed). From the model 1, we replaced the power-law component by the Comptonized model nthcomp (model 3). We first tied the temperature of the nthcomp model (kT_seed) to the temperature of the diskbb (kT_disc) model (defined as model 3A). This model provided χ²/dof = 473/330. We performed the fit again after tying the nthcompkT_seed to the single temperature blackbodykT_bb (defined as model 3B). This model resulted in χ²/dof = 479.6/330. Both the above choices for the seed photon temperature in the nthcomp model resulted in an absorption-edge-like signature ∼7.5 keV and an emission line feature at ∼6.4 keV [see Fig. 2(b) and (c), lower panel].

We also examined the continuum with another thermal Comptonization model CompTT (Titarchuk 1994) along with the same thermal components. The model 4, TBabs ×(bbody + diskbb + CompTT) with kT_seed = kT_disc provided us a consistent fit (χ²/dof = 472.6/330) with what we obtained earlier with other continuum models.

Apart from the main continuum models discussed above, we tried some additional models to fit the continuum. We tested the combination of one thermal component and one Comptonized component. We combined either diskbb or bbody to the nthcomp component. We defined the combination of the diskbb and the nthcomp as model 0A and the combination of the bbody and the nthcomp as model 0B.

• Model 0A: TBabs ×(diskbb + nthcomp)

• Model 0B: TBabs ×(bbody + nthcomp)

It may be noted that both the models provided us a significantly worse fit (χ²/dof = 500/332 and 496/332 for the model 0A and 0B, respectively) compared to the two thermal component model.

4.1.2 Modelling of the features seen ∼6–8 keV region

When we fitted the continuum with different combinations of phenomenological and physical models, in each case the residuals showed an absorption edge at ∼7.5 keV which might be the Fe K edge and an emission line feature at ∼6.4 keV. We applied the absorption based models as well as the relativistic reflection model to fit the excess observed at ∼6–8 keV band.

1. Absorption based models

   In order to include these features, we used an absorption-edge component (edge in xspec) which improved the fit by Δχ² = −41 for the continuum model 3A and Δχ² = −28 for the continuum model 3B for two additional parameters. Examination of the fit residuals suggested another absorption feature at ∼7 keV. By the application of a second absorption edge, the fit was improved by Δχ² = −28 for the continuum model 3A and Δχ² = −22 for the continuum model 3B along with the first edge (for two additional parameters). The two edges at ∼7.65 and ∼6.92 keV were comparable in their depths. The best-fitting parameters of the new models 3A(+2 edges) and 3B(+2 edges) [see Table 2 for description] are listed in Table 3. The spectral data and deviations of the observed data from the best-fitting models with the χ value multiplied with a single and double edges are shown in Fig. 2(b) and (c).

   Two absorption-edge models were also employed with the continuum model 2. The new model reads as model 2(+2 edges), see Table 2 for description. Here also two absorption edges with energies 7.7 ± 0.13 keV and 6.9 ± 0.07 keV provided us a satisfactory fit (χ²/dof = 406/327). The best-fitting cut-off power-law Γ and high-energy cut-off values were found to be 1.0 ± 0.4 and |$6.1_{-1.1}^{+2.5}\,{\rm keV}$|⁠, respectively. Next, we added two edge models with the continuum model 4 and the new model 4(+2 edges) [see Table 2 for description] resulted in χ²/dof = 405/326 with the best-fitting seed photon temperature |$kT_{\text{seed}}=0.91_{-0.10}^{+0.06}\,{\rm keV}$|⁠, electron temperature |$kT_{\text{e}}=3.4_{-0.15}^{+0.27}\,{\rm keV}$| and optical depth τ ≲  11.7. Here also edge parameters were similar to those found in the case of other continuum models. All the best-fitting parameter values of the model 2(+2 edges) and model 4(+2 edges) are reported in Table 4. We also applied two edge component to the continuum model 0A and this model 0A(+2 edges) [see Table 2], provided χ²/dof = 436.6/328. Thus, model 3A(+2 edges), 2(+2 edges) or 4(+2 edges) provided significantly better fit (χ²/dof = 405/326, 406/327 and 405/326, respectively) than the model 0A(+2 edges) [χ²/dof = 436.6/328]. Since the bbody model component is included in all our best-fitting models, we estimated blackbody area fraction (A_bb) using the best-fitting blackbody normalization. A_bb is defined as the fraction of the NS surface area that is emitting as a blackbody (assuming a 10 km radius for the NS.)

    Since the models involving two absorption edges provided a good description of the data, we employed a physical photoionized absorption model. We used the zxipcf model in xspec (Miller et al. 2007; Reeves et al. 2008) after assuming that it covered some fraction of the X-ray source. We replaced the edge components of the model 3A(+2 edges) and 3B(+2 edges) with a single zxipcf model. According to this model, a power-law source illuminates the photoionized gas of the turbulent velocity of 200 km s⁻¹ and reproduces absorption. The addition of this model to the data improved the fit by Δχ² = −54 and −43 for three additional parameters, compared to the fit with the model 3A and 3B, respectively (corresponding χ²/dof values are 419/327 and 437/327, respectively). The addition of the same model led to an improvement of Δχ² = −55 for three additional parameters (corresponding χ²/dof = 417/327) compared to the fit with the model 4. In particular, the fit was improved at the energy ranges 6–9 keV and broad residuals were no longer present in the above-mentioned energy range (see Fig. 4, right-hand panel). We found the best-fitting column density of the photoionized plasma lying in the range N_H ∼ (0.6–1.8) × 10²³ cm⁻². The best-fitting ionization parameter (logξ) and the covering fraction lay in the range 0.32–0.90 and 0.21–0.49, respectively. During the fitting with the zxipcf model the redshift parameter was frozen to zero.

    However, we noted that our best-fitting reduced χ² values were still high because of the residuals present at ∼3 keV. In both the cases, the model fits were significantly improved by the addition of a narrow Gaussian at ∼3 keV. Thus, the new χ²/dof values for the models 3A(+2 edges) and 3B(+2 edges) became 358/323 and 383/323, respectively. The 2σ upper limit of the Gaussian width (σ) was <0.088 with the best-fitting line energy 3.2 ± 0.03 keV.

2. Relativistic reflection models

   We also examined if the features in the Fe K band were better described by relativistic broad iron line than the edges. For this, we removed the two edge components from the model 3A(+2 edges) and added a LAOR line component (LAOR in xspec, Laor 1991). The fit resulted in χ²/dof = 426.6/325 with best-fitting line parameters |$E_{\text{LAOR}} = 6.93_{-0.06}^{+0.34}\,{\rm keV}$|⁠, inner radius |$R_{\text{in}} = 4.2_{-0.6}^{+0.8}R_g$|⁠, emissivity index |$\beta =3.2_{-0.2}^{+0.4}$|⁠, equivalent width ∼45 eV. The inclination was not well constrained (>14 deg).

    The irradiation of hard ionizing flux on to the accretion disc leads to the line emission. In order to model the broad Fe Kα line along with reflection continuum, it is necessary to employ a reflection model. Following Cackett et al. (2010), here we employed a reflection model where the blackbody component provides the illuminating flux instead of a power-law spectrum. We used the reflection model (bbrefl_Hestar.fits)² appropriate for an He-star donor, provided by Ballantyne & Strohmayer (2004) where a constant density slab is illuminated by a blackbody. The reflection model was relativistically blurred by rdblur model in xspec. We applied this reflection model with the continuum model 1 and this model, TBabs×(bbody + diskbb + rdblur×bbrefl_Hestar.fits + powerlaw) provided us a good fit (χ²/dof = 429/326) with the best-fitting parameters: inner radius |$R_{\text{in}} = 8.3_{-1.5}^{+1.0}R_g$|⁠, inclination i = 27 ± 2 deg, ionization parameter logξ = 3.1 ± 0.4, emissivity index β > 4.7. These parameters are consistent within errors with that obtained by Cackett et al. (2010). The spectral data and residuals (in units of σ) are shown in Fig. 4 (left-hand panel). However, the reported χ²/dof value was high because of the residuals at ∼3.2 keV. If we removed the energy band 2.5–3.5 keV from the spectral fitting, the same model provided χ²/dof = 316/290 without changing the spectral parameters significantly.

    We employed the same reflection model convolved with rdblur to the continuum model 2 which resulted in χ²/dof = 420/325 with the best-fitting parameters: inner radius |$R_{\text{in}} = 8.5_{-1.6}^{+2.5}R_g$|⁠, inclination |$i=26.4_{-3.0}^{+2.6}$| deg, ionization parameter logξ = 2.6 ± 0.2. So far the reflection model was not applied with the continuum models which contains thermal Comptonization model (nthcomp or CompTT). Therefore, the same reflection model with rdblur was applied along with the continuum model 4 also. It resulted in χ²/dof = 435/325 with the best-fitting parameters: inner radius |$R_{\text{in}} = 7.5_{-1.4}^{+0.6}R_g$|⁠, inclination |$i=28.3_{-3.7}^{+2.6}$| deg, ionization parameter logξ = 3.1 ± 0.3.

Finally, in the Table 5, we enlisted χ²(dof) values that we obtained after addition of line model or absorption based model or reflection model with different continuum models in the Suzaku spectra of 4U 1820−30. However, we found that the emission/absorption features observed ∼6–8 keV is moderately better described by two absorption-edge models compared to the blurred reflection model or partially covering absorption model. The weak absorption features seen at ∼1 keV, ∼2.5 keV and ∼3 keV (see Fig. 2) in the Suzaku spectrum were unidentified features and the origin of these features may be instrumental. We did not try to model these weak absorption features as any support for the absorption based model from these features is unexpected.

4.2 NuSTAR and Swift spectra

We simultaneously fitted spectral data of NuSTAR FPMA and FPMB in the 3–79 keV energy band and Swift/XRT spectrum in the 0.3–8 keV energy band. To fit both the soft and hard components in the spectra, we selected a model consisting of the blackbody (bbody) and the power-law model (powerlaw). As before, we used the TBabs model to account for the Galactic absorption. A constant was used to account for relative normalization between different instruments. This model failed to describe the spectrum with χ²/dof of 856/702. To see whether multiple soft components were required, we added the disc blackbody component (diskbb). The overall fit improved significantly and this model (model 1) resulted in χ²/dof = 742/700. To check whether a cut-off exists in the spectrum, we replaced the power-law model with a cu-toff power law (cutoffpl). Although the model (model 2) provided an acceptable fit (χ²/dof = 711/699), the power-law photon index became negative and the cut-off energy was below 5 keV, which were unacceptable.

Low reduced χ² with cut-off power law is most likely a signature of the presence of thermal Comptonization. Therefore, we replaced the cut-off power-law model by the thermal Comptonization model (nthcomp). The combination of this thermal Comptonization model and blackbody (model 0B) provided an exceptionally good fit (χ²/dof = 716/701), with the seed photon temperature tied to the blackbody kT_bb ∼ 0.53 ± 0.04 keV and Γ ∼ 1.8 ± 0.03. When we replaced the blackbody model with the multicolour disc blackbody model, the fit still held equally well along with nthcomp model (model 0A). However, we retained both the blackbody and the multitemperature disc blackbody models for two reasons : (1) Suzaku spectral fitting requires disc component with high significance; (2) the origin of multicolour disc blackbody component is due to photons from accretion disc while the origin of the blackbody component is at the surface of the NS. In many cases, both of these are required to fit the spectrum. The temperature of seed photons was tied either to multitemperature disc (model 3A) or to surface blackbody temperature (model 3B). Both of these provided an equally good fit while differences in fluxes were observed. As done before for Suzaku spectrum, we tried to fit the spectrum with another thermal Comptonization model CompTT by Titarchuk (1994) along with two thermal components (model 4). This fit resulted in similar electron temperature (kT_e) and the seed photon temperature (kT_seed) as derived by the nthcomp model with an optical depth (τ) of the Comptonizing cloud ∼9.5 (see Table 4). Table 3 lists the best-fitting parameters of the best-fitting model 0A, 0B, 3A and 3B for the joint NuSTAR and Swift spectra and Fig. 5 shows the simultaneous FPMA, FPMB and XRT spectral fitting, the best-fitting model and χ residuals. Addition of an absorption edge or a Gaussian or a diskline did not improve the fit. However, we introduced two edges at energies which were within the ranges consistent with that obtained from the Suzaku spectral fitting keeping optical depth (τ) as a free parameter. In both the models 3A and 3B, for the edge in the energy range 7.54–7.80 keV, 90 per cent upper limit on the optical depth (τ) was 0.094 which was within errors of the depth measured with Suzaku. For the second edge in the energy range 6.86–6.98 keV, the 90 per cent upper limit on the optical depth (τ) was <0.042. The upper limit of τ in the fits appeared to be consistent with each other.

5 DISCUSSION

We examined the continuum behaviour as well as the presence of the broad iron line in the X-ray spectra of 4U 1820−30 using broad-band observations with Suzaku, NuSTAR and Swift. We used a number of continuum models to the data and investigated the presence of discrete features in the Fe K band. Studies of Fe fluorescence in X-ray binaries are not trivial and issues regarding statistics, bandpass and competing physical processes play vital roles in the interpretation of the results. Our spectral components included the emission from the NS surface and an accretion disc around the NS, thermal Comptonization in a corona of hot electrons, reflection off the accretion disc and photoionized absorption from material in the vicinity of the system. From our spectral analysis, we did not observe any trace of Fe Kα emission line in the energy range 5.8–7.0 keV using simultaneous spectroscopy of NuSTAR and Swift. But at the same time, the Suzaku XIS data clearly showed absorption or emission features in the Fe K band (see Figs 2 and 3). These features can be described in two ways – (i) absorption edges or absorption from photoionized gas, and (ii) blurred reflection. The absorption features observed in the data at ∼6.9 keV and ∼7.6 keV, when fitted with two edge components, yielded a better fit statistically. It may be noted that, Cackett et al. (2010) detected a significant broad iron line in the Suzaku observations of the source 4U 1820−30 but the combined XMM–Newton and INTEGRAL spectrum did not find clear evidence of iron emission lines (see Costantini et al. 2012). Using RXTE data of the source 4U 1820−30, Titarchuk, Seifina & Frontera (2013) reported a broad Fe emission line during both the soft and the hard states, although RXTE is much less sensitive in detecting emission lines compared to high-resolution instruments like NuSTAR or Suzaku.

It is important to note that same edge energies (E_edge) were recovered from the different continuum models. Thus, the choice of continuum did not affect the values of the absorption-edge-related parameters. We discuss here alternative interpretations of the broad feature seen ∼6.4 keV in the Suzaku spectrum of 4U 1820−30. A broad emission line was no longer required if we introduced two absorption edges at energies above 6.9 keV. D’ Ai et al. (2005) applied two absorption-edge models, instead of a broad emission line, to fit broad line feature observed ∼6.5 keV in the chandra and RXTE observation of another atoll type low-mass NS X-ray binary 4U 1728−34. The broad features seen in the Suzaku spectra at ∼6–9 keV were also well described by a blurred reflection model. From the reflection model fit, the inner disc radius and the source inclination were found to be ∼8 GM/c² and ∼28 deg, respectively. Thus, it is clear that the presence of absorption edges may mimic the broad iron line like feature or vice-versa (see also Egron et al. 2011).

It may also be noted that the Fe K edge is observed in the 7.1–9.1 keV range, and our observed energy for one edge at 6.92 ± 0.07 keV was marginally lower than the K-edge energy of neutral iron. Thus, the edge must arise close to the surface of the NS which might then be gravitationally redshifted to observed energies. The required redshifts for ∼6.9 keV and ∼7.7 keV edges are 0.025 and 0.20, respectively. For the aforesaid redshifts, the absorbing material must be located at a distance 3.4–20.7 R_S from the NS. This suggests that the absorption edge must arise from close to the NS. Since there was no evidence for X-ray bursts during the Suzaku observation, the absorption features were unlikely to be the burst-driven wind. On the other hand, since the absorption features were described by photoionized zxipcf model (N_H ∼ (0.6–1.8) × 10²³ cm⁻² and log ξ ∼ 0.32–0.90), the absorption features might arise due to the winds from the inner accretion disc (Boirin et al. 2005). The source was observed in a high/soft state during the Suzaku observation and the luminosity of the source lies ∼(7–8) × 10³⁷ erg s⁻¹ (as bright as persistent atolls, e.g. GX 13+1, GX 9+1). The accretion rate on to the compact object is very high ∼1.1 × 10¹⁸ gm s⁻¹ (Heinke et al. 2013), which is comparable to the bright atoll GX 13+1 (∼10¹⁸ gm s⁻¹, Ueda et al. 2004) and ultracompact binary 4U 1916−053 (∼0.6 × 10¹⁷ gm s⁻¹, Heinke et al. 2013) for whom disc winds were detected (Díaz Trigo et al. 2012, 2006). This suggests that the high accretion rate may give rise to massive, radiatively driven winds. However, it may be noted that the absorption by a photoionized disc wind was also observed in sources that accretes matter lower than those of GX 13+1 and GX 9+1 (Boirin et al. 2005; Díaz Trigo et al. 2006)

The Suzaku and Swift+NuSTAR broad-band data sets also allowed us to investigate the continuum models. It is well known that a number of different continuum models describe the observed spectra of NS LMXBs (White, Stella & Parmar 1988; Mitsuda et al. 1989; Barret 2001; Cackett et al. 2010). Our analysis of broad-band Suzaku data showed that the continuum model consisting of an accretion disc blackbody, a simple blackbody and thermal Comptonization of disc photons best described the observed data statistically (see Table 3). The same model also described the NuSTAR data but it was not possible to distinguish statistically the models with diskbb and blackbody seeds for thermal Comptonization (compare with Lin et al. 2007).

In the Comptonization model, we assumed two different origins of the input seed photons for thermal Comptonization to investigate the emission geometry of the source (as done by Sanna et al. 2013; Lyu et al. 2014). For the models 0A, 0A(+2 edges), 3A and 3A(+2 edges), we assumed that the input photon distribution was due to multicolour disc blackbody (diskbb) component (kT_seed = kT_disc) and for the rest of the models we assumed it due to single temperature blackbody (bbody) component (kT_seed = kT_bb). We calculated the inner accretion disc radius from the normalization parameter of the disc blackbody (diskbb) component. It gave us physically acceptable inner disc radius for all the models ( ≳ 10 km). We also calculated the fraction of the NS surface area that was emitting as blackbody emission by assuming that the NS had a radius of 10 km. Clearly, in this scenario the blackbody area could not exceed the NS surface area, and models 0B and 3B(+2 edges) with fractional BB area of 1.45 and 3.68, respectively, were ruled out. Thus, it is unlikely that the blackbody is providing the seed photons for the thermal Comptonization.

In all the models where we set kT_seed = kT_disc, the seed photon flux was consistently less than the diskbb flux (f_seed/f_diskbb < 1). It was a good consistency check as in all the models we assumed that the input photon arises from the accretion disc. In these models, the blackbody emission is arising from a small fraction (8 per cent to 14 per cent) of the NS surface. This was similar to the result obtained by Lin et al. (2007) based on RXTE observations of Aql X−1 and 4U 1608−52. These results indicated that a standard thin accretion disc impacted the NS where the colliding gas formed the boundary layer covering a substantial area of the NS surface and radiated efficiently via thermal Comptonization. In this scenario, the blackbody emission might arise from the uncovered polar regions as the energy deposited by the impact of the disc would quickly get distributed due to thermal conduction. This scenario was supported by the small inner disc radii R_in ∼ 10 km inferred from the models 0A(+2 edges) and 3A(+2 edges). In a geometry in which the disc provided the seed photons for thermal Comptonization in a boundary layer between the innermost disc and the surface of the NS, the ratio of seed flux to the disc flux could not exceed unity and it was expected to be substantially less than one if the boundary layer was confined in a narrow ring in equatorial plane. For the model 3A, we found f_seed/f_diskbb ∼ 0.79 (Suzaku) and ∼0.28 (Swift + NuSTAR), it was possible that the Comptonizing corona might be covering substantial part of the NS surface as suggested by the blackbody emission from the polar regions or additionally the corona might be covering the innermost part of the disc which in turn resulted in highly Comptonized spectrum as observed.

The size and geometry of the boundary layer is an open issue which is not satisfactorily understood (see e.g. Syunyaev & Shakura 1986; Inogamov & Sunyaev 1999; Popham & Sunyaev 2001; Grebenev & Sunyaev 2002). Numerical calculations in the classical theory of boundary layers predict that boundary layer can inflate in a radial direction in order to radiate away excess luminosity during high accretion rate state. However, at low accretion rate which is usually observed during hard state, inflation because of radiation pressure is negligible and the boundary layer can be assumed to be compact within the size of the fraction of the NS radius (Popham & Sunyaev 2001). However, the amount of seed photon flux and the Comptonized flux obtained in this work is not consistent with a narrow and thin boundary layer region. Additionally, for a face-on system, boundary layer emission is supposed to be very strong during hard state but the present system is more edge on.

In an alternative and more realistic formalism by Inogamov & Sunyaev (1999), the boundary layer is found to spread on to the surface of the NS covering a fraction depending on the mass accretion rate. Unlike the standard model where the accretion energy is concentrated in a small radius, the Inogamov & Sunyaev (1999) model allows the dissipation of energy in a sufficiently broad region of NS surface. This is in fair agreement with the high-Comptonized flux as well as seed photon flux as reported in this paper. Broad-band X-ray observations such as those would be possible with the upcoming Astrosat mission will play an important role in further understanding the geometry of the X-ray emitting regions in accreting NS LMXB.

We are thankful to the anonymous referee whose detail in-depth comments helped us in improving the paper. This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Centre (HEASARC). ASM would like to thank Inter-University Centre for Astronomy and Astrophysics (IUCAA) for hosting him during subsequent visits. BR likes to thank IUCAA for hospitality and other facilities extended to him during his visit under their visiting Associateship programme.

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