A detailed spectral study of intermittent-accreting millisecond X-ray pulsar Aql X-1 during pulse-on and pulse-off stages

ABSTRACT

We present a detailed spectral study of an intermittent-AMXP Aql X-1 during the pulse-on and pulse-off stages by using the archival Rossi X-ray Timing Explorer (RXTE) data. We first perform temporal analysis by using Z|$_n^2$| technique in three different energy bands, 3.0–13.0, 13.0–23.0, and 23.0–33.0 keV, for the last 128 s time segment of the RXTE data including pulse-on region. We show that the pulse is the most significant in the softest band. We, then, show that the spectrum is represented the best via combination of absorbed blackbody, disc blackbody, and a Gaussian line. We modelled the last four segments of the data 30188-03-05-00 to better compare pulse-on and pulse-off stages. We found a vague residual in the spectral fit of the pulse-on segment between |$\sim$|3.0 and 13.0 keV, which agrees with the result of temporal analysis. We show that the residual may be represented with an extra blackbody component with the temperature of 1.75 keV and the radius of 0.75 |$\pm$| 0.49 km. For deeper analysis, we performed phase-resolved spectroscopy to the last 128 s, pulse-on, segment. We obtain two separate spectra for the spin phase ranges of 0.75–0.25 (pulse-high) and 0.25–0.75 (pulse-low), and followed the same procedure. We display that the residual becomes more clear for pulse-high compared to the pulse-low. We report that the additional blackbody component, which models the residual, indicates a hotspot from the surface of the neutron star with the radius of 1.65 |$\pm$| 0.74 km whose temperature is 1.65 keV.

1 INTRODUCTION

The predominant X-ray sources within the Milky Way Galaxy are low-mass X-ray binaries (LMXBs) comprising a compact object – a black hole or a neutron star (NS) – nearly centrally located within the system, with a low-mass main sequence star (⁠|$M_{\mathrm{c}}\lesssim 1\, {\rm M}_{\odot }$|⁠). These systems represent the older, accreting population of the Galaxy and often exhibit extended accretion episodes (Bahramian & Degenaar 2023). LMXBs are further classified into various subclasses based on their X-ray properties, such as variability or luminosity, the characteristics of their donor stars, and the nature of the compact object. Mass transfer in LMXBs primarily occurs through Roche lobe overflow, where the low-mass companion star fills its Roche lobe, leading to material transfer from the first Lagrange point to the Roche lobe of the compact object. Due to the angular momentum of the transferring material and the morphology of the system, it forms an accretion disc around the compact object (Pringle & Rees 1972).

When an NS is born in a supernova explosion, it possesses the highest rotational velocity of its lifetime. However, it loses angular momentum and decelerates. Yet, within LMXBs, the mechanism of mass transfer also transfers angular momentum to the NS, thereby boosting its rotational speed. Consequently, LMXBs is believed to be the environment where millisecond pulsars are generated. This process is known as the recycling scenario (Alpar et al. 1982; Bhattacharya & van den Heuvel 1991).

Due to the lack of coherent pulsations, the rotation periods of NSs in almost all LMXB systems cannot be monitored (Vaughan et al. 1994; Dib et al. 2004; Messenger & Patruno 2015). The explanation of the absence of pulsations is summarized as follows: (i) The magnetic field of the compact object might be too weak to canalize the material in the inner radius of the disc through the poles of the NS. (ii) The Gravitational lensing effect could blur the illumination from the polar caps, then the amplitude of the signals could decrease to the undetectable level. (iii) The periodic changes in the flux could be annihilated as a result of that X-ray light being scattered from the comptonized coronae.

Two groups differ from other LMXBs with the appearance of X-ray pulsations. The first is nuclear-powered X-ray pulsars (NXPs) that exhibit quasi-periodic burst oscillations during the observed thermonuclear X-ray bursts. The second is accreting millisecond X-ray pulsars (AMXPs) that emit coherent X-ray pulses, with a period of milliseconds, originating from infalling plasma to the magnetic poles of the rotating NS from the inner layers of the accretion disc. Only 23 AMXPs have been detected so far (Strohmayer & Keek 2017; Campana & Di Salvo 2018; Di Salvo & Sanna 2022; Patruno & Watts 2021; Sanna et al. 2022; Bult et al. 2022). The AMXP family has a subclass, so-called intermittent-AMXPs, which exhibit discontinuous pulse phenomena with pulse-on and pulse-off stages. They are unique labs to comprehend the absence of the pulse behaviour in LMXB systems. This subclass has only four members yet, HETE J1900.1-2455, SAX J1748.9-2021, Aql X-1, and MAXI J0911-655, respective to their discovery.

Aql X-1 is an NS-LMXB whose donor is a K4 |$\pm$| 2 main-sequence star that rotates with a period of 18.95 h (Chevalier & Ilovaisky 1991) in a 36°–47° inclined orbit (Mata Sánchez et al. 2017). In the light of Rossi X-ray Timing Explorer (RXTE) data, it has been reported that the distance of the source is 4.4–5.9 kpc derived from type-I photospheric radius expansion bursts, assuming the Eddington limit is 2.0–3.8 |$\times 10^{38}$| erg s|$^{-1}$| (Jonker & Nelemans 2004). It is also classified as a soft X-ray transient due to its almost annual cyclic outbursts with a recurrence time of 60–140 d and a duration of 25–60 d (Šimon 2002; Güngör, Ekşi & Göğüş 2017). In the quiescent state, the X-ray luminosity is |$L_{\rm X} \approx 10^{33}$| erg s|$^{-1}$| (Verbunt et al. 1994), while the outburst peak luminosity could reach up to |$L_{\rm X} \approx 10^{37}$| erg s|$^{-1}$| (Campana, Coti Zelati & D’Avanzo 2013). Aql X-1 is a unique member of the intermittent-AMXPs (Koyama et al. 1981) with 550.27 Hz pulse frequency, consistent with the burst oscillations (Casella et al. 2008), which has been detected only for 150 s overall 20 yr in the peak of 1998 outburst.

In this work, to enlarge our knowledge about pulse phenomena, we applied simultaneous timing and spectral analysis to the pulsation episode of Aql X-1. We explain the detailed data reduction, timing, and spectral analysis using the RXTE data covering the pulse episode in Section 2. We discuss and conclude our present results of the timing and spectral analysis in Section 3.

2 DATA ANALYSIS AND RESULTS

We used the data of RXTE/Proportional Counter Array (PCA) detector (Jahoda et al. 2006), operating within its most sensitive energy range of 3.0–30.0 keV. The PCA (2.0–60.0 keV; Bradt, Rothschild & Swank 1993) is particularly suited for studying spectral variation on short time-scales, such as pulsations or X-ray bursts, thanks to its large collecting area (⁠|$\simeq$|6500 cm|$^2$|⁠) and high time resolution down to |$\mu$|s. Our analysis involved systematic timing and spectrum evaluations focused on the pulsed episode of Aql X-1. Additionally, we examined the spectral evolution before, during and after the pulsation. Essential details regarding the data used in this study are summarized in Table 1.

The All-Sky Monitor (ASM; Lochner & Remillard 1995) light curve of the 1998 outburst of Aql X-1, whose duration is about 8 months, is displayed in Fig. 1. The hard count rates are derived from ASM C band data in the energy range of 5.0–12.0 keV, while the soft count rates are computed using the sum of the data of ASM A and B bands in the energy range of 1.5–3.0 and 3.0–5.0 keV, respectively. The lower panel of Fig. 1 illustrates the evolution of the hardness ratio. Notably, the range delimited by the red line on the hardness curve indicates the soft-high state during the outburst. This state signifies accretion dominance, with the observed pulse phenomena within this regime.

These three consecutive data given in Table 1 are split into 128 s time windows for both temporal and spectral analysis. One of the reasons for this segmentation strategy is to avoid computational obstacles by choosing a binary number to create spectra that result to get response and background files in the same length with extra effort. Beside this, although the pulse duration is reported as slightly longer than 150 s, the power spectrum given in Casella et al. (2008) is also for 128 s long though our results would be comparable with the ones in the literature in which our search is performed via Z|$_n^2$| technique while the mentioned one in the literature is via classical Fourier method.

2.1 Temporal analysis

We began with employing the faxbary task in ftools¹ package to apply the barycentering correction to photon arrival times, before performing temporal analysis to the observations listed in Table 1.

For the first step, we utilized the Z|$^{2}_{n}$| statistic (Buccheri et al. 1983). This approach is preferred over alternatives because it operates directly on photon arrival times rather than on binned data. The power of Z|$^{2}_{n}$| statistic is defined as

where Z|$^{2}$| represents the power, N denotes the total number of photons in the search interval, n stands for the number of harmonics (here, it is set to be 1), and |$\Phi$| represents the phase of the photons.

Subsequently, we computed Z|$_1^{2}$| power spectra within the 3.0–30.0 keV energy band for each segment of the three observation sets, each lasting 128 s. The |$Z_1^2$| technique can perform a direct temporal analysis on the arrival time of the photons and allows us to reach the time resolution limit of the detector, 1 |$\mu$|s for PCA, as long as there are enough photons in the sample set. We used the previously reported frequency of |$550.27~\text{Hz}$| for the source and performed the scan in |$10^{-4}~\text{Hz}$| steps in the frequency range of 550.0–|$550.5~\text{Hz}$|⁠. This frequency resolution is sufficient to accurately determine the detected pulse frequency.

Our analysis identified a significant power at 550.27 Hz only in the last segment of ObsID 30188-03-05-00, consistent with the report in Casella et al. (2008). The maximum Z|$_1^{2}$| power of the signal is 104.79, with a single trial probability of 1.7 |$\times 10^{-23}$| calculated by assuming a Poisson noise distributed as |$\chi ^2$| with two degrees of freedom. Considering the number of trials, the number of frequency bins multiplied by the number of power spectra, we determined the chance occurrence probability of the signal at 550.27 Hz to be 3.6|$\times 10^{-18}$|⁠.

Same as in the literature, we did not detect any sign of possible pulse in the power spectra generated for the previous and latter data of the pulse detected ObsID. For a more detailed analysis of the pulsation, we computed a dynamic power spectrum using a search time window of 25 s, shifting by 1 s along the entire observation. We again performed our search in the frequency range of 550.0–550.5 Hz with a resolution of 10|$^{-4}$| Hz. Since the most spectrally effective energy range of PCA is 3.0–30.0 keV, we performed all temporal analysis starting from 3.0 keV to be consistent with the further spectral analysis. Besides this, sub-setting the data for 25 s time windows decreases the photon count to make good Z|$_1^2$| statistic. Therefore, as a semi-arbitrary optimal choice, we divided the energy range into equal three parts, 3.0–13.0, 13.0–23.0, and 23.0–33.0 keV, to get an idea about the energy range that the pulse is the most significant. We track the Z|$_1^2$| power values instead of pulse fractions that might be misleading since the count rates are very low for higher energies. The pulse with the maximum power was observed in the energy range of 3.0–13.0 keV. The resulting dynamic spectrum in 3.0–13.0 keV is presented in the left panel of Fig. 2. It is noticed that the power has increased significantly in the last 150 s, as depicted in the inset. We also displayed the pulse profile derived by folding the light curve with the 550.27 Hz frequency in the upper right panel of the figure. The green region indicates pulse-high, while the pink denotes pulse-low which will be used to perform our further ‘phase-resolved spectroscopy’ discussed later in Section 2.2. The lower right panel illustrates the time evolution of pulse power in the three energy ranges. We would like readers to pay attention to that the power is substantially higher in the 3.0–13.0 keV energy band compared to the other bands.

2.2 Spectral Analysis

We utilized the ‘saextrct’ task in ftools to extract clean light curves and spectra. We independently generated response matrices for the three data sets provided in Table 1 using pcarsp version 11.7. heasoft version 6.30.1 is used to analyse all data sets. We generated background spectra using the module file for bright sources, pca-bkgd-cmbrightvle-eMv20051128.mdl. Spectra were obtained by classifying all channels of at least 20 counts. To take into account instrumental uncertainties, we added a systematic error of 1.0 per cent. We applied abundances from Wilms, Allen & McCray (2000) to take into account the interstellar medium, interstellar grains, and the H|$_{2}$| molecule. In xspec version 12.0, we used phabs as a photoelectric absorption model with the default cross-section (Verner et al. 1996). The neutral hydrogen column densities were fixed to |$N_{\rm H}~=~3.4\times 10^{21}~{\rm cm}^{-2}$| following Maccarone & Coppi (2003). We employed the distance of 5 kpc to transform normalization values to radii (Jonker & Nelemans 2004).

2.2.1 Step 1: model selection

Unlike non-pulsating LMXBs, which typically show transitions between hard and soft spectral states, AMXPs are often characterized as hard X-ray transients. The X-ray continuum generally consists of one or two blackbody-like components and an unsaturated comptonization component (Gierliński, Done & Barret 2002; Gierliński & Poutanen 2005; Poutanen 2006). In the hard state, the spectrum is dominated by a hard/comptonized component along with a soft/thermal component, whereas in the soft state, the spectrum is primarily dominated by the soft/thermal component (Lin, Remillard & Homan 2007).

One of the main objectives of this study is to understand the spectral effect of the origin of the pulsation. The most important step is to model the pulse-off spectrum with very high accuracy, possibly even more than what model is used, to get the discrepancy with the pulse-on. To have a sense of which model would best describe the data, we first tracked hardness evolution and established the source’s spectral state. Given the time evolution of hardness (Fig. 1), we considered three models commonly used to describe the source in the soft state: phabs|$^\ast$|(discbb + nthcomp + gau) (Raichur, Misra & Dewangan 2011; Sakurai et al. 2012; Abdelfatah et al. 2021), phabs|$^\ast$|(discbb + comptt + gau) (Lin et al. 2007; Göǧüş, Alpar & Gilfanov 2007), and phabs|$^\ast$| (discbb + bbodyrad + gau) (Güngör et al. 2020). We then applied these models to each 128 s segment of the data listed in Table 1.

We started with a fundamental model of bbodyrad + discbb to explain a simple accretion scenario and noticed the model efficiently works as previously mentioned in the literature (Güngör et al. 2020). Previous studies (Mitsuda et al. 1989; Gierliński et al. 2002; Lin et al. 2007) have shown that residuals above 15.0 keV indicate reverse Compton effects to take into account up-scattering photons by possible corona. We, though, proceeded a combination of a comptonization model (compTT in xspec; Titarchuk 1994) with a disc blackbody in which the Wien temperature is linked to the temperature of the disc blackbody model under the assumption of that photons from the inner accretion disc are seeds for the inverse Compton process. The plasma temperature of compTT is fixed to a reasonable value of 15.0 keV (Lin et al. 2007). The geometry is chosen as a disc (see Titarchuk & Lyubarskij 1995, for details). We also attempted nthcomp (Zdziarski, Johnson & Magdziarz 1996; Życki, Done & Smith 1999) as a comptonization model that allows us to switch blackbody and disc blackbody as the seed photons and to investigate relatively larger range of optical depths. Following the studies in the literature with similar strategy (Raichur et al. 2011; Sakurai et al. 2012; Abdelfatah et al. 2021), we applied the model as discbb + nthcomp|$_{\text{bb}}$|⁠, which approves the two optically thick components, T|$_{\text{in}}$| and T|$_{\text{bb}}$|⁠. This implies the situation of where the blackbody emission from the NS surface is fully comptonized, while the disc emission is observable. The electron temperature is again fixed to 15.0 keV, while T|$_{\text{in}}$|⁠, T|$_{\text{bb}}$|⁠, and |$\Gamma$| are kept as free-fit parameters.

After constructing all of the models, we identified the most efficient model with best |$\chi ^{2}$| and reasonable physical parameters such as temperature, normalization, etc. Among these, we identified the phabs|$^\ast$| (discbb + bbodyrad + gau) model as the most suitable and as simple as possible to well fit the data. In this model, the bbodyrad component represents the boundary layer emission from the NS surface, discbb represents the emission from the accretion disc, and gau represents the broad iron line originating from the accretion disc. As noted in Lin et al. (2007) and Asai et al. (2000), the line energy can be constrained to 6.2–7.3 keV with |$\sigma$| ranging from 0.1 to 1.0 for the Gaussian model. To reduce the number of free parameters in our analysis, we fixed the line energy at 6.4 keV with a |$\sigma$| of 0.8 for all segments. To test the hypothesis that a Compton Cloud could be responsible for the absence of the pulse, we added a comptt model (Titarchuk 1994) to our chosen model and examined the variation in the parameters. Comparing the model combinations, we found no significant differences in the evolution of the model parameters statistically. The results suggest that high accretion may disperse the Compton cloud, supporting the conclusion that the phabs|$^\ast$| (discbb + bbodyrad + gau) model is the most reliable for our study. Therefore, we conclude that the lack of a detectable pulse is not due to scattering by the comptonized corona, and this scenario does not directly explain the pulse phenomena.

2.2.2 Step 2: segmented sequential spectral analysis

Sources like Aql X-1 exhibit rapidly varying spectral characteristics. To detect potential variability caused by the pulse, we performed a simultaneous fit for the last four segments (9th, 10th, 11th, and 12th segments of ObsId 30188-03-05-00) of the data including pulse-on region. Notably, only the final segment (12th) shows pulsation. The results of the simultaneous fit for these four segments, as well as the normalization values with blackbody temperature when included, are summarized in Table 2 and shown in Fig. 3.

First, we simultaneously fit the pulse-off segments (9th, 10th, and 11th) and then we used the results as input fit parameters to the pulse-on segment (12th). As can be seen in Fig. 3(a), the residuals in the pulse-on segment (blue pluses) show slightly higher scatter than the other segments in the softer energy. It is seen in the first row of Table 2 that the |$\chi ^2$| value of this scatter is above 3. Remembering the energy range where the pulse is the most powerful is 3.0–13.0 keV, the picture in Fig. 3(a) strengthen the idea that the spectrum needs an extra component for pulse-on characteristic.

Secondly, apart from the first approach, we only set the blackbody and disc blackbody parameters of the pulse-on segment free in order to determine any variation between the pulse-on and pulse-off regions. As can be seen in the second row of Table  2, model values of both pulse-off and pulse-on segments are statistically consistent to each other (Fig. 3b). We, then, refitted the segments by adding an extra blackbody component only on pulse-on one, assuming this excess is caused by the area where the pulse is generated. We set the temperature and normalization of the additional ‘bbodyrad’ component unfrozen for the pulse-on segment. We obtained the temperature to be |$1.75\pm {0.20}$| keV from the additional blackbody. In the light of this approach, which can be seen in the last row of Table 2 and the panel (c) of Fig. 3, the parameters were improved physically and statistically to make them consistent. It is interpreted that the NS boundary layer provided the blackbody component, the pulse provided the secondary blackbody, and the accretion disc provided the disc blackbody.

2.2.3 Step 3: phase-resolved spectroscopy

To put forward more clear picture about the effect of the pulse-on to the spectrum, we performed phase-resolved spectroscopy within millisecond resolutions. We used only the last 128 s within the last 150 s where the pulse is seen, neglecting 10 s from the end. Since the detection of the pulse takes place at the end of the observation, neglecting the last 10 s minimizes the amount of possible errors that may arise from instrumental effects. With this preference, we also eliminated the transitional effects at the beginning and terminal. Though, the time segment of the pulse with higher and relatively constant amplitude is used for phase-resolved spectroscopy. We created the pulse profile as an output of our temporal analysis. The phase range of 0.25–0.75 and 0.75–0.25 are chosen as pulse-high and pulse-low regions, as can be seen as green and pink coloured areas in the right-upper panel of Fig. 2, respectively. We then created two independent spectra for both pulse-high and pulse-low from last 128 s segment, so each has 64 s duration.

Following the similar procedure as in Section 2.2.2, we first fitted the pulse-low (the pulse-off in the case of Fig. 3) spectra by using the model of phabs*(bbodyrad + discbbody + gau). Then, we used the best-fitting parameters as frozen inputs adding an extra blackbody component to fit the pulse-high (the pulse-on in the case of Fig. 3). Therefore, the panel (a) of Fig. 4 shows the residuals without the extra blackbody, comparing the pulse-high spectrum to the best model of pulse-low without free normalization, since these are intertwined data. This strategy allows us to determine the residuals with greater precision. Also, as it can be seen in the first approximation of Table 3, the value of |$\chi ^2$| is determined as 20.35 which indicates much higher residuals. We set the blackbody and disc blackbody parameters only of the pulse-high free in order to specify any differences between the pulse-high and pulse-low spectra. The results of the free parameter deviation for both segments are given in the Table 3 as the second approach. The model parameters for both pulse-low and pulse-high segments are statistically consistent with each other, as can be seen in the residuals shown in panel (b) of Fig. 4. We finally refitted only the pulse-high segment by adding an extra blackbody component assuming that the extra radiation comes from the hotspot that is the cause of the observed coherent pulsation. The temperature of the extra blackbody component is obtained to be about  |$1.65\pm {0.06}$| keV whose radius of  |$1.65\pm 0.54$| km indicated by its normalization. Based on this approach, as presented in the last row of Fig. 3 and panel (c) of Fig. 4, the parameters were improved both physically and statistically comparing to the second approach.

3 DISCUSSION AND CONCLUSIONS

In this study, we have applied a three-step analysis to demonstrate the existence of the spectral effects of the pulse phenomenon. We present the output of the spectral analysis of three Aql X-1 observations obtained by RXTE in Section 2.2.1. First, we modelled the spectra of Aql X-1 in the energy range of 3.0–30.0 keV with the models previously used in the literature and determined the most appropriate model.

Then, for more detailed analysis, we compared the pulse-on segment with the pulse-off ones. Due to the high spectral variability of sources like Aql X-1, we modelled the last four segments simultaneously, in which the last is the pulse-on and the rest is pulse-off. In the spectral fit of the last segment, we detected a discrepancy, which we thought as the effect of the pulse, so we added another blackbody to the model. By setting the added blackbody parameters free, we obtained the temperature of about 1.75 keV. In this case, the blackbody component came from the NS boundary layer, the secondary blackbody is from the pulse while the disc blackbody component is the contribution of the inner layers of the accretion disc. Casella et al. (2008) stated that a combination of disc black body with a component representing the boundary layer is sufficient to model the whole spectrum of Aql X-1. Our spectral analysis agrees with that a combination of two physical models may well fit the data. At this point, we prefer to use the blackbody component to express the boundary layer and the disc blackbody for the disc by adding a Gaussian to represent the iron line. We also present two model solutions in panels (b) of Figs 3 and 4. However, especially in phase-resolved spectroscopy, spectra for pulse-low and pulse-high are constructed from data intertwined in millisecond intervals. Though, any difference would not be expected in the fit parameters, even the normalization. Under this assumption, we followed the strategy of adding an extra blackbody component and found that the |$\chi ^{2}$| values well improved.

Finally, in Section 2.2.3, we applied phase-resolved spectroscopy to the 128 s pulse-on segment. For this reason, using the spin frequency and ephemeris values of the source obtained from the temporal analysis, we created pulse-high and pulse-low spectra for the phase ranges of 0.25–0.75 and 0.75–0.25, respectively. The residual detected in the previous step becomes more clear revealed, as shown in Fig. 4. In agreement with the results we obtained in the previous step, we added a blackbody component for the pulse-high and obtained that the pulse could have a source with a temperature of about 1.65 keV. We utilized the bbodyrad task in xspec to simulate the difference between the pulse-low and pulse-high spectra using a single additional blackbody component. The hotspot is assumed to be circular in this task. Although only spectral results cannot clearly confine the location, the intermittency of the pulse suggests the location to be at very high latitudes with very low angles between the rotating axis (Lamb et al. 2009).

Examining Fig. 1, we see that the pulsation becomes visible near the outburst peak when the source is in the soft state. The unabsorbed flux for 3.0–30.0 keV is calculated as |$8.6\times 10^{-9}$| erg s|$^{-1}$| cm|$^{-2}$|⁠. This corresponds to a total amount of flux that describes the model we used, and also the contribution attributed to the pulsation blackbody component is calculated as |$7.4 \times 10^{10}$| erg s|$^{-1}$| cm|$^{-2}$|⁠, meaning it corresponds to 8.62 per cent of the total flux. This value is also related to the pulse profile as well as the peak -or pulse fraction- of the flux. In the meanwhile, the difference between the pulse-low and pulse-high spectra depends on the definition of the spin phase, which are 0.75-0.25 and 0.25–0.75, respectively. We obtained the pulse fraction as |$\sim$|4.5 per cent. Although Casella et al. (2008) reported that the pulse fraction varies between |$\sim$|2 per cent and |$\sim$|10 per cent, the pulse profile given in the inner panel of Fig. 1 of Casella et al. (2008) indicates a pulse fraction of |$\sim$|4.0–4.2 with the minimum of the pulse profile is |$\sim$|4750 cnt/s and the maximum is |$\sim$|4950 cnt s⁻¹. Our estimation of the pulse fraction is consistent with this value. Given the sinusoidal shape of the pulse profile, it may not be very easy to just relate the pulsed fraction to the fraction of the flux of the blackbody component to the total flux. Furthermore, while the blackbody model flux contributes to some extend to the whole energy band that RXTE is sensitive, the pulsed fraction is only calculated within a limited energy range we defined. In addition to these observational effects there should be other factors that needs to be taken into account as well. For example our spectral analysis do not take into account the gravitational redshift or the very fast rotation of the NS into account. These should also need to be taken into account if we aim to directly compare the flux ratio to the pulsed fraction.

ACKNOWLEDGEMENTS

This work has made use of ASM data of NASA’s RXTE satellite. This work is partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK) Grant No. 120F094. CG acknowledges support from Bilim Akademisi -– The Science Academy, Turkey under the BAGEP programme and TK acknowledges support from TUBITAK-BIDEB 2210 fellowship.

DATA AVAILABILITY

This study utilized observational data that is publicly available from the RXTE/PCA Master Catalogue of the NASA/HEASARC archive.

Footnotes

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