Study of Complex Absorption and Reflection in a Unique Intermediate Polar Paloma

We have implemented two methods to search for the period: the Lomb–Scargle method (Lomb 1976; Scargle 1982) and the CLEAN algorithm (Roberts et al. 1987). The first one is widely used to find the frequencies present in an unevenly sampled time series. The later one uses the algorithm to deconvolve the effect of the window function from the discrete Fourier transform (DFT) spectra and thereby minimize the effect of spectral leakage. This method has been used efficiently for other IP sources with unevenly sampled data (Norton et al. 1992, 1997).

In the NuSTAR-FPMA power spectra using the Lomb–Scargle method (top panel of Figure 2), we can clearly identify the peak at orbital frequency Ω, corresponding to a period value of 9384 ± 229 s, present in all the energy bands (3–40 keV, 3–10 keV, and 10–40 keV). We notice that the peaks are stronger in the 3–10 keV band compared to the 10–40 keV band. This period is also identified by Schwarz et al. (2007) at ∼9430.35 s in their optical photometric campaign and Thorstensen et al. (2017) at ∼9434.88 s using radial velocity spectroscopy. We see the spin frequency peak ω, corresponding to a period value of 8365 ± 181 s, immediately next to the orbital frequency in the Lomb–Scargle power spectra. This value agrees with one of the spin period candidate (∼8175.37 s) by Schwarz et al. (2007) and spin period (∼8229 s) detected by Littlefield et al. (2022). We notice another weak peak at 2ω − Ω, with a period value of 7545 ± 148 s. In the FPMA power spectra, these two peaks (ω, 2ω − Ω) appear with a much lower power compared to the Ω. Joshi et al. (2016) obtained two low-power peaks for ω and 2ω − Ω adjacent to the strongest peak at orbital period in their power spectra, obtained using previous XMM-Newton observation, but with smaller period values (7800 and 6660 s, respectively) than ours. In Figure 2 we have also marked the expected positions of several harmonics and sideband frequencies. We notice a relatively strong peak (2850 ± 21 s) near Ω + 2ω (expected at 2893 ± 48 s). We also observe peaks at 4474 ± 52 s and 4183 ± 46 s, which respectively agree with Ω + ω (expected at 4423 ± 72 s) and 2ω (expected at 4182 ± 90 s) within error bars. Note that the resolution of our power spectra, which depends on the total observation duration, data gaps, etc., creates a hindrance to resolve all the harmonics and sidebands precisely. Another possible candidate of spin period at ∼8758.12 s according to Schwarz et al. (2007), which is very close to peak Ω, could not be confirmed owing to the limitation of the resolution of the power spectra. We also notice that the peaks in the FPMA power spectra are stronger in the 3–10 keV band compared to the 10–40 keV band.

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In the bottom panel of Figure 2, we have plotted the CLEANed power spectra. Before performing the CLEAN operation, we have detrended the light curve for the presence of dc bias, if any, by subtracting a mean value and dividing by the standard deviation. The CLEANed algorithm requires two parameters—number of iterations and loop gain—to deconvolve the window power spectra from the DFT spectra iteratively with the gain fraction in each iteration. We chose gain 0.1, typically used (Norton et al. 1992; Rana et al. 2004) for this algorithm. Iteration number was set at 1000. We find that the strong Ω peak and the Ω + 2ω peak are present; however, other weak peaks at ω, 2ω − Ω, and 2ω, which were in seen in the Lomb–Scargle power spectra, are almost diminished in the CLEANed power spectra.

A similar exercise is done for the XMM-Newton PN power spectra (Figure 3). Though the PN light curves are continuous, the power spectral resolution is poor owing to the shorter duration of the observation. We have found that the peak corresponding to Ω is evidently present, with a period value of 9400 ± 761 s, agreeing with that of the FPMA value. We are unable to distinguish either ω or 2ω − Ω in the PN power spectra because of the broad peak of Ω. It is interesting to note that the peak strength of Ω is much lower in the 0.3–3.0 keV band than in the 3–10 keV band. However, for all other peaks in the power spectra, peak strength decreases in the higher energy band. By our previous definition of orbital and spin periods from FPMA, we have marked their expected positions in the PN power spectra, along with harmonics and sideband frequencies. We notice that there is significantly strong power near the position marked by Ω + 2ω, as we found from FPMA power spectra.

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Based on our measured orbital period (9384 ± 229 s), we have folded the PN and FPMA light curves to study the rotational properties of the source. The folding is performed based on the ephemeris TJD = 19,275, chosen arbitrarily close to the start time of the NuSTAR observation. The folded light curves in different energy bands and the hardness ratios (HRs) are shown in Figure 4. In the soft X-rays, the 0.3–3.0 keV band obtained from PN (left panel of Figure 4), there is strong modulation in the light curve; however, the entire light curve can be described by one broad hump (ϕ = 0.7–1.7), with several dips in between. There are three prominent minima, appearing at ϕ ∼ 0.16, 0.50, and 0.70, with the first one being the strongest. In the 3.0–10.0 keV band, the similar broad hump-like feature is visible, with the minimum at ϕ ∼ 0.70 being the strongest one. A direct comparison of PN light curve with the FPMA light curve (right panel of Figure 4) in the same energy band, 3–10 keV, shows the similar nature of the hump and the presence of an overall minimum at ϕ ∼ 0.70. The pulse fraction (PF) of modulation in the 3–10 keV energy band is 72% ± 4% and 72% ± 6% from PN and FPMA, respectively, using the definition PF $=({I}_{\max }-{I}_{\min })/({I}_{\max }+{I}_{\min })$, where I denotes the count rate. The hard X-ray in the 3–10 keV band of FPMA follows the same pattern of the light curve as that of 10–40 keV.

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As we inspect the hardness ratio 1 (HR1), defined as HR1 = I_{3−10 keV}/I_{0.3−3.0 keV}, obtained from the PN light curve, we notice a strong peak around ϕ ∼ 0.16 (bottom left panel of Figure 4). This corresponds to the dip at the same phase, seen in the 0.3–3.0 keV and 3.0–10.0 keV bands of the PN light curve. HR1 can roughly be divided into four intervals: (a) ϕ ∼ 0.10–0.22, (b) ϕ ∼ 0.22–0.50, (c) ϕ ∼ 0.50–0.80, and (d) ϕ ∼ 0.80–1.10. In HR1, phase interval (a) shows the strong peak, whereas interval (c) covers the lowest valley region. Intervals (b) and (d) represent the phase intervals before and after the peak region in the HR1, respectively.

Hardness ratio 2 (HR2), defined similarly to HR1, but for the 10–40 keV and 3–10 keV bands of FPMA, exhibit a rather flat profile (bottom right panel of Figure 4). We have fit a constant model that gives a mean value of 0.34, with an acceptable fit statistic of χ²(dof) = 141.5(100).

We did not attempt detailed analysis based on the period ω, since this period appears very weakly in the FPMA power spectra and could not be resolved in PN power spectra.

The FPMA and FPMB data in the 3–40 keV range are employed for probing the shock temperature of the PSR and the presence of the Compton reflection hump. Beyond 40 keV the background dominates over the source counts; hence, it is not included for the spectral analysis. Initially we have used an absorbed bremsstrahlung model, with a single Gaussian component for modeling the iron line complex, which could not be resolved by NuSTAR data. We obtain a good fit with χ²/dof = 463(439). The column density of the absorber is ${3.76}_{-1.27}^{+1.32}\times {10}^{22}\,{\mathrm{cm}}^{-2}$. This value is larger than the total galactic column density along the direction of the source, 0.42 × 10²² cm⁻² (HI4PI Collaboration et al. 2016). This indicates that a strong absorption specific to the source is present in the spectra. The obtained continuum temperature is ${19.9}_{-1.7}^{+1.9}$ keV. The Gaussian component shows a line energy of ${6.59}_{-0.05}^{+0.05}$ keV, with a $\sigma ={247}_{-59}^{+67}$ eV, indicating the presence of significant ionized Fe Kα lines.

Since the PSR is multitemperature in nature, the obtained bremsstrahlung temperature indicates an average temperature of the entire PSR. Therefore, we used the isobaric cooling flow model mkcflow (Mushotzky & Szymkowiak 1988) to model the PSR (Mukai et al. 2003). This model also incorporates the ionized line emissions, including the ionized Fe Kα lines (He-like and H-like). We kept the switch parameter set at 2 to determine the spectra based on AtomDB 3.0.9. ³ The redshift parameter is fixed at 1.35 × 10⁻⁷ following the Gaia DR2 distance of 578 ± 35 pc (Gaia Collaboration et al. 2018). We have also incorporated the absorption component tbabs. For the neutral Fe Kα line at 6.4 keV, we have added a Gaussian component with line central energy fixed at 6.4 keV and line width σ fixed at 0 (as suggested by spectral analysis of XMM-Newton EPIC data, discussed in the next section). We obtained an acceptable fit with χ²(dof) = 470(440). The overall absorber column density remains similar to that of the bremsstrahlung fit within statistical uncertainty. The lower temperature reached the lower limit allowed by the model, so we fixed it at 0.0808 keV. The upper temperature comes out to be ${42.9}_{-5.0}^{+5.5}$ keV. To check the presence of Compton reflection, we convolved the reflect component with the multitemperature cooling flow model. It slightly improves the fit statistic to χ²(dof) = 464(439), but the reflection amplitude gives a high value ${0.93}_{-0.65}^{+0.87}$ with large uncertainty associated with it. The upper temperature is somewhat lowered in this case, standing at ${27.9}_{-5.1}^{+8.6}$ keV. The values of the other parameters remain similar to the no-reflection fit within statistical uncertainty. A strong and complex absorption can affect the spectra beyond 7 keV, and thereby the continuum itself. Therefore, we can comment on reflection only after properly modeling the absorption in the source by including soft X-rays from XMM-Newton data.

First, we have utilized the EPIC (PN, MOS1, and MOS2) spectra in the 5–8 keV range to study the Fe Kα emission lines. We have used the absorbed bremsstrahlung model to fit the underlying continuum. We have added three Gaussians to model the three Fe Kα lines: neutral, He-like, and H-like. The best-fit parameter values are reported in Table 1, with the spectral fitting plotted in Figure 5. The line widths are kept fixed at 0 since all the Fe Kα lines are consistent with the instrumental resolution limit of EPIC (∼120 eV at 6.0 keV). This shows that lines are narrow. We have fixed the bremsstrahlung temperature and column density of the absorber at 19.9 keV and 3.76 × 10²² cm⁻², as obtained with the NuSTAR-only fit using the bremsstrahlung model (see Section 3.2.1), which otherwise could not be constrained. We notice that the best-fit values of the line central energies are slightly redshifted; however, that is not statistically important, since they agree with their expected theoretical values within error bars.

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Table 1. Probing Iron Lines Using EPIC Data (5.0–8.0 keV)

Parameter	Unit	Value
nH,tb	×1022 cm−2	3.76f
Tbr	keV	19.9f
Nbr	×10−3	${1.82}_{-0.05}^{+0.05}$
EL, Neutral	keV	${6.35}_{-0.04}^{+0.05}$
σNeutral	eV	0f
eqwNeutral	eV	${66}_{-18}^{+30}$
NL, Neutral	×10−5	${0.7}_{-0.2}^{+0.2}$
EHe−Like	keV	${6.66}_{-0.02}^{+0.02}$
σHe−Like	eV	0f
eqwHe−Like	eV	${182}_{-23}^{+28}$
NHe−Like	×10−5	${1.9}_{-0.2}^{+0.2}$
EH−Like	keV	${6.93}_{-0.03}^{+0.02}$
σH−Like	eV	0f
eqwH−Like	eV	${137}_{-24}^{+24}$
NH−Like	×10−5	${1.3}_{-0.2}^{+0.2}$
χ2(dof)		123(93)

Note. n_H,tb represents column density of the absorber. T_br and N_br denote the temperature and normalization of bremsstrahlung continuum, respectively. E_L , σ, N_L , and "eqw" represent line central energy, line width, normalization, and equivalent width of the corresponding Fe Kα line, respectively. f denotes that the line parameter is fixed.

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We have next looked into the RGS spectra. The spectra from RGS1 and RGS2 are simultaneously fit in the range of 0.45–2.0 keV. The signal-to-noise ratio of the spectral data is poor, with only 47% of the total count being contributed from source. However, the ionized oxygen line (O vii) in the spectra is clearly present. To get an overview of the ionized line, we fitted the line with a Gaussian component on top of an absorbed bremsstrahlung continuum. The spectra are shown in Figure 6. The line center appears at ${0.568}_{-0.004}^{+0.004}$ keV, with a line width (σ) of ${6}_{-2}^{+5}$ eV and an equivalent width of ${117}_{-77}^{+70}$ eV. We note that the O vii line is composed of fine atomic transition lines (intercombination, resonance, and forbidden lines), which RGS cannot resolve, thereby giving rise to a broad line width. There is visibly some excess residual around 0.5 keV, expected from the N vii line. But a poor signal-to-noise ratio for that line makes it statistically unimportant.

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In order to constrain the absorption parameters, as well as the nature of the multitemperature PSR, the spectral data from all three EPIC cameras were simultaneously fit in the 0.3–10.0 keV band. We have used ISM absorption model tbabs for modeling the overall absorption near the source, as well as any intervening galactic absorption. The multitemperature plasma of the PSR has been modeled with the cooling flow model, implemented by mkcflow. The neutral Fe Kα line is described by a narrow (σ = 0) Gaussian component. The absorbed cooling flow model with a Gaussian component gives an extremely poor fit statistic χ²(dof) = 5447(424). Inclusion of a partial covering absorber dramatically improves the fit, with χ²(dof) = 604(421). The overall column density appears to be ∼6.3 × 10²⁰ cm⁻². The column density of the partial covering absorber comes out as ∼6.08 × 10²² cm⁻² with a covering fraction of ∼65%. However, the upper temperature of the cooling flow model remains unconstrained (79 keV), the overall abundance is very large (∼3.77), and the fit statistic is still poor and deserves further improvement. Inclusion of a reflect model substantially improves the fit to χ²(dof) = 501(420), but the reflection amplitude turns out to be unphysically large (∼8.24). A poor fit with a single partial covering component suggests that absorption should require more elaborate modeling. In addition, getting such a high value of reflection amplitude indirectly shows that absorption has an extended effect until the energy range 7 keV and beyond, which can also be mimicked by the tail of the reflection hump for an alleged strong Compton reflection. Therefore, instead of reflect, we introduced another partial covering absorber (pcfabs ₁ ∗pcfabs ₂ ). Two partial covering absorbers mathematically describe abosorbers with three column densities and corresponding covering fraction (Equation (1))

$$\begin{eqnarray}&&\begin{array}{l}[{f}_{\mathrm{pc}1}{e}^{-{n}_{{\rm{H}},\mathrm{pc}1}\sigma (E)}+(1-{f}_{\mathrm{pc}1})]\\ \times \,[{f}_{\mathrm{pc}2}{e}^{-{n}_{{\rm{H}},\mathrm{pc}2}\sigma (E)}+(1-{f}_{\mathrm{pc}2})]\\ =\,A+{{Be}}^{-{n}_{{\rm{H}},\mathrm{pc}1}\sigma (E)}+{{Ce}}^{-{n}_{{\rm{H}},\mathrm{pc}2}\sigma (E)}\\ +\,{{De}}^{-({n}_{{\rm{H}},\mathrm{pc}1}+{n}_{{\rm{H}},\mathrm{pc}2})\sigma (E)}.\end{array}\end{eqnarray} \tag{ 1 }$$

Here σ(E) stands for photoelectric cross section, and n_H,pc1, f_pc1 and n_H,pc2, f_pc1 represent column densities and covering fraction contributed from each partial absorber model component. B, C, and D are the functions of f_pc1 and f_pc2 and represent the respective fraction of each of the resulting three column densities, and A = 1 − (B + C + D).

The fit with two partial covering absorbers improves the fit statistic significantly (χ²(dof) = 478(419)) in comparison to the single partial absorber model. The column density of the overall absorber is ${3.42}_{-1.09}^{+1.13}\times {10}^{20}\,{\mathrm{cm}}^{-2}$. The column density and covering fraction of the two pcfabs components become ${2.55}_{-0.39}^{+0.46}\times {10}^{22}\,{\mathrm{cm}}^{-2}$ with 65% ± 3% and ${22.65}_{-4.20}^{\,+5.40}\times {10}^{22}\,{\mathrm{cm}}^{-2}$ with 50% ± 5%, respectively. The upper temperature of the cooling flow model is constrained with a value of ${43.2}_{-12.2}^{+15.7}$ keV. Though the error bars are large, it is expected owing to the limited coverage of hard X-rays by XMM-Newton data. The lower temperature of ${0.86}_{-0.24}^{+0.29}$ keV represents some mean temperature near the bottom region of the PSR. At this point we observe slight excess in the soft X-rays, possibly arising as a result of line emissions of low Z and Fe L-shell emissions. The main excess is around 0.57 keV, representing the O vii line, which is also observed from RGS spectra. To model that, we introduced an extra optically thin plasma emission component (mekal), appearing with a temperature ${0.17}_{-0.05}^{+0.04}$ keV, which decreased the fit statistic further to χ²(dof) = 466(417). The corresponding F-statistic probability for inclusion of this extra component is 4.9 × 10⁻³.

It is evident that the source spectra involve a complicated absorption scenario, where it is paramount to model it appropriately. Motivated by the fact that a single partial absorber is not enough to model the local intrinsic absorber, which indicated a distribution of column densities, we introduced the pwab (Done & Magdziarz 1998) component to model the intrinsic absorber. This component assumes a power-law distribution of the covering fraction as a function of column density of neutral absorbers. The fit statistic is χ²(dof) = 470(418), closely similar to the fit statistic obtained from the previous two partial absorber fits. We kept the ${n}_{{\rm{H}},\min }$ of the power-law absorber fixed to 1 × 10¹⁵ cm⁻², which could not be constrained otherwise. The ${n}_{{\rm{H}},\max }$ provides a value of ${32.09}_{-6.78}^{+15.61}\times {10}^{22}\,{\mathrm{cm}}^{-2}$, along with a power-law index of $-{0.60}_{-0.01}^{+0.01}$. We could not constrain the column density of the overall absorber either, which provided us with an upper limit of <7.0 × 10¹⁹ cm⁻². However, in this fit, the emission components parameters remain similar with that of the two partial covering absorber fit scenario within statistical uncertainty. Here we notice that the F-test probability of introducing the extra optically thin component to model the emission features below 1 keV is 1.5 × 10⁻¹⁸, indicating a much stronger necessity for this component than the case of two partial absorbers.

Given the complex intrinsic absorber scenario of Paloma and emission features in soft X-rays, we have also performed an alternate modeling using zxipab (Islam & Mukai 2021). This component can describe the absorption in the pre-shock flow as the power-law distribution of the warm photoionized absorber, hence providing an alternate description of the soft X-ray features. In this case, we do not introduce an extra low-temperature plasma emission component. We obtain a similarly good fit statistic as in previous cases, χ²(dof) = 467(420). The overall absorber presents itself with a column density of ${4.03}_{-1.25}^{+1.42}\,\times {10}^{20}\,{\mathrm{cm}}^{-2}$, consistent with the two-partial-absorber scenario. The warm absorber shows a column density value of ${31.76}_{-6.68}^{+10.25}\,\times {10}^{22}\,{\mathrm{cm}}^{-2}$ for ${n}_{{\rm{H}},\max }$, and we kept the ${n}_{{\rm{H}},\min }$ frozen at the lowest value permissible for this parameter (10¹⁵ cm⁻²), because of it becoming unconstrained. The low temperature of the cooling flow component now goes to the lower limit allowed by the model, so fixed at 0.0808 keV. The upper temperature (${34.5}_{-7.3}^{+14.9}$keV) is consistent with the value obtained from the previous two scenarios within statistical uncertainty.

Equipped with our understanding of the complex absorber and the overall continuum from the XMM-only and NuSTAR-only fits, we devised three model variants M₁, M₂, and M₃ to model the broadband spectra in the range of 0.3–40.0 keV. The description of the model variants is given in Table 2.

We have quoted the best-fit values of the parameters in Table 3. For representation, the spectral and ratio (data/model) plots using model M1 are shown in the top and middle panels of Figure 7. The spectral parameters agree within the statistical uncertainty for all three models. However, for model M2 we could not constrain the column density of the overall absorber, and an upper limit (<0.7 × 10²⁰ cm⁻²) is obtained. For a low value of the overall absorber that includes the galactic absorption, it may be hard to constrain this parameter, given that we already have a complex intrinsic absorber component to describe the spectra. Note also that the neutral power-law distribution of absorber pwab and the ionized version zxipab have significant differences in predicting the model flux below <0.8 keV (Figure 1 of Islam & Mukai 2021). This gives rise to differences in the obtained column densities of the overall absorber between models M2 and M3. M1, M2, and M3 give us consistently statistically acceptable fits, with a χ²(dof) = 952(859), 956(862), and 952(863), respectively. In addition, the emission parameters for all three model variants give statistically similar values.

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Table 3. Best-fit Parameters Using Simultaneous Broadband Spectra in the 0.3–40.0 keV Range

Parameter d	Unit	M1	M1-R	M2	M2-R	M3	M3-R
nH,tb	1020 cm−2	${4.5}_{-1.2}^{+1.2}$	${4.5}_{-1.2}^{+1.2}$	<0.7	<0.7	${4.7}_{-1.3}^{+1.3}$	${4.5}_{-1.3}^{+1.4}$
nH,pc1	1022 cm−2	${2.2}_{-0.4}^{+0.4}$	${2.1}_{-0.2}^{+0.4}$	⋯	⋯	⋯	⋯
pcf1/log(xi) a		${0.66}_{-0.03}^{+0.02}$	${0.66}_{-0.02}^{-0.02}$	⋯	⋯	${0.6}_{-0.1}^{+0.1}$	${0.6}_{-0.1}^{+0.1}$
nH,pc2/${n}_{{\rm{H}},\max }$ b	1022 cm−2	${20.0}_{-3.1}^{+3.1}$	${19.0}_{-2.8}^{+3.2}$	${27.6}_{-4.1}^{+7.3}$	${25.2}_{-4.1}^{+6.8}$	${30.5}_{-5.4}^{+7.3}$	${28.8}_{-4.6}^{+7.9}$
pcf2/β c		${0.54}_{-0.04}^{+0.03}$	${0.54}_{-0.03}^{+0.03}$	$-{0.59}_{-0.01}^{+0.01}$	$-{0.58}_{-0.02}^{+0.01}$	$-{0.55}_{-0.01}^{+0.01}$	$-{0.58}_{-0.02}^{+0.02}$
Tme	keV	${0.18}_{-0.05}^{+0.03}$	${0.18}_{-0.05}^{+0.03}$	${0.19}_{-0.02}^{+0.02}$	${0.19}_{-0.02}^{+0.02}$	⋯	⋯
Nme	10−4	${1.7}_{-0.1}^{+1.1}$	${2.0}_{-0.9}^{+1.2}$	${4.5}_{-1.0}^{+1.7}$	${5.5}_{-1.3}^{+1.5}$	⋯	⋯
T1,mkc	keV	${0.67}_{-0.17}^{+0.18}$	${0.67}_{-0.16}^{+0.19}$	${0.68}_{-0.19}^{+0.17}$	${0.69}_{-0.17}^{+0.18}$	0.0808f e	0.0808f
T2,mkc	keV	${34.2}_{-2.5}^{+4.2}$	${29.6}_{-4.9}^{+4.9}$	${33.6}_{-4.2}^{+1.9}$	${27.9}_{-3.9}^{+5.8}$	${31.7}_{-3.5}^{+3.3}$	${28.5}_{-3.6}^{+5.4}$
Nmkc	10−11	${11.1}_{-1.3}^{+1.0}$	${12.0}_{-1.4}^{+1.5}$	${10.6}_{-1.1}^{+1.9}$	${11.8}_{-1.5}^{+1.6}$	${11.8}_{-1.4}^{+1.9}$	${12.3}_{-1.8}^{+1.7}$
Z	Z⊙	${1.4}_{-0.2}^{+0.2}$	${1.2}_{-0.2}^{+0.2}$	${1.2}_{-0.2}^{+0.2}$	${1.1}_{-0.2}^{+0.2}$	${1.2}_{-0.2}^{+0.2}$	${1.1}_{-0.2}^{+0.2}$
Ω/2π		⋯	${0.39}_{-0.25}^{+0.48}$	⋯	${0.47}_{-0.35}^{+0.43}$	⋯	${0.26}_{-0.26}^{+0.45}$
EL	keV	${6.36}_{-0.02}^{+0.04}$	${6.36}_{-0.04}^{+0.03}$	${6.36}_{-0.04}^{+0.04}$	${6.37}_{-0.05}^{+0.04}$	${6.34}_{-0.01}^{+0.06}$	${6.36}_{-0.04}^{+0.04}$
σ	eV	0f	0f	0f	0f	0f	0f
N L	10−5	${1.0}_{-0.2}^{+0.2}$	${0.9}_{-0.2}^{+0.2}$	${0.9}_{-0.2}^{+0.2}$	${0.8}_{-0.2}^{+0.2}$	${0.9}_{-0.2}^{+0.2}$	${0.8}_{-0.2}^{+0.2}$
χ2(dof)		952(859)	948(858)	956(862)	952(861)	952(863)	951(862)

Notes.

^a pcf1 (covering fraction for first partial absorber) for model M1 or log(xi) (ionization parameter of warm power-law absorber) for model M3. ^b n_H,pc2 (column density of second partial absorber) for model M1 or ${n}_{{\rm{H}},\max }$ (maximum column density of the neutral (and warm) power-law absorber) for model M2 (and M3). ^c pcf2 (covering fraction for second partial absorber) for model M1 or β (power-law index of neutral (and warm) absorber) for model M2 (and M3). ^d n_H,tb and n_H,pc1, respectively, denote column density of the overall and first partial absorber. T_me and N_me are temperature and normalization of the optically thin cold plasma emission component. T_1,mkc , T_2,mkc , and N_mkc denote upper and lower temperature and normalization of the isobaric cooling flow component. Z stands for overall abundance. E_L , σ, and N_L represent line energy, line width, and normalization of the Gaussian component for the neutral Fe Kα line, respectively. ^e f denotes that the parameter is fixed.

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Once our spectral model has satisfactorily constrained the absorption parameters and the continuum, we attempted to find the contribution of Compton reflection. We adopted model variants M1-R, M2-R, and M3-R (for model description, see Table 2), with the abundance parameters of the reflect component linked to that of emission components. We used the default value of the inclination angle (i), set at $\mu =\cos i=0.45$. The three models produced a reflection amplitude of ${0.39}_{-0.25}^{+0.48}$, ${0.47}_{-0.35}^{+0.43}$, and ${0.26}_{-0.26}^{+0.45}$, along with an improvement in fit statistic, however not large, of Δχ²(Δdof) = 4(1), 4(1), and 1(1), respectively (Table 3). The ratio (data/model) plot using model M1-R is shown in the bottom panel of Figure 7. Though mutually agreeing values of reflection amplitudes are obtained in all three models, the large statistical uncertainty and small improvement in fit-stat put us in a delicate situation to comment about its "robust" presence in our spectra.

Our orbit-folded light curve (Figure 4) showed prominent variation in the HR1, indicating the presence of the change in the complex intrinsic absorber. We extracted phase-resolved spectra in the four phase intervals as defined in Section 3.1.2. We have quoted the best-fit parameters for the phase-resolved spectra in Table 4. We kept the column density of the overall absorber fixed at the best-fit value from the phase-averaged spectral fitting. The temperatures of the plasma emission components remain the same within statistical uncertainty for all the phases, as well as with the phase-averaged value, for any particular model variant. Though the column density of the complex absorbers also remains the same within error bars, our spectral fitting clearly reveals the change in the covering fraction parameters. For phase (a) model M1 shows the highest value of the covering fraction (pcf1 and pcf2) for the intrinsic absorbers (${0.79}_{-0.04}^{+0.04}$ and ${0.73}_{-0.06}^{+0.05}$), whereas for phase (c) the lowest values of those parameters are obtained (${0.49}_{+0.06}^{-0.11}$ and ${0.31}_{-0.16}^{+0.12}$). The parameter values (pcf1 and pcf2) for the other two phases, phase (b) (${0.67}_{-0.04}^{+0.05}$ and ${0.50}_{-0.06}^{+0.05}$) and phase (d) (${0.70}_{-0.04}^{+0.03}$ and ${0.54}_{-0.06}^{+0.04}$), are consistent with each other. Models M2 and M3 follow the same trend with the power-law index for the complex absorber. We obtain the highest value of the power-law index (∼−0.3) for phase (a) and the lowest value (∼−0.7) for phase (c), whereas phases (b) and (d) give intermediate values (∼−0.5), similar to each other. For model M₃, we also obtain a low value of ionization parameter (∼−1.3) during phase (c), compared to the other three phases (∼0.7, 0.7, and 0.5 for (a), (b), and (d), respectively).

Table 4. Best-fit Parameters for Phase-resolved Spectra in the 0.3–40.0 keV Range

Parameter	Unit	M1				M2				M3
		(a)	(b)	(c)	(d)	(a)	(b)	(c)	(d)	(a)	(b)	(c)	(d)
		0.10–0.22	0.22–0.50	0.50–0.80	0.80–1.10	0.10–0.22	0.22–0.50	0.50–0.80	0.80–1.10	0.10–0.22	0.22–0.50	0.50–0.80	0.80–1.10
nH,tb	1020 cm−2	4.5f	4.5f	4.5f	4.5f	0.7f	0.7f	0.7f	0.7f	4.7f	4.7f	4.7f	4.7f
nH,pc1	1022 cm−2	${2.3}_{-0.8}^{+0.7}$	${1.8}_{-0.3}^{+0.5}$	${2.9}_{-1.5}^{+1.4}$	${1.9}_{-0.5}^{+0.4}$	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
pcf1/log(xi)		${0.79}_{-0.04}^{+0.04}$	${0.67}_{-0.04}^{+0.05}$	${0.49}_{-0.11}^{+0.06}$	${0.70}_{-0.04}^{+0.03}$	⋯	⋯	⋯	⋯	${0.66}_{-0.16}^{+0.16}$	${0.68}_{-0.12}^{+0.12}$	$-{1.30}_{-0.19}^{+0.21}$	${0.46}_{-0.09}^{+0.10}$
nH,pc2/${n}_{{\rm{H}},\max }$	1022 cm−2	${20.9}_{-4.3}^{+5.6}$	${16.3}_{-4.3}^{5.7}$	${21.2}_{-20.2}^{+21.5}$	${18.3}_{-4.1}^{+5.4}$	${34.6}_{-10.0}^{+17.7}$	${18.1}_{-4.7}^{+9.3}$	${20.1}_{-8.8}^{+15.3}$	${21.7}_{-5.7}^{+10.7}$	${38.9}_{-10.2}^{+17.0}$	${20.2}_{-4.3}^{+7.0}$	${18.6}_{-10.2}^{+39.1}$	${22.8}_{-4.8}^{+9.2}$
pcf2/β		${0.73}_{-0.06}^{+0.05}$	${0.50}_{-0.06}^{+0.05}$	${0.31}_{-0.16}^{+0.12}$	${0.54}_{-0.06}^{+0.04}$	$-{0.36}_{-0.02}^{+0.04}$	$-{0.59}_{-0.03}^{+0.03}$	$-{0.74}_{-0.03}^{+0.03}$	$-{0.57}_{-0.02}^{+0.02}$	$-{0.32}_{-0.04}^{+0.04}$	$-{0.55}_{-0.02}^{+0.02}$	$-{0.77}_{-0.02}^{+0.03}$	$-{0.52}_{-0.02}^{+0.02}$
Tme	keV	<0.27	<0.19	0.18f	${0.12}_{-0.04}^{+0.05}$	${0.18}_{-0.08}^{+0.04}$	${0.17}_{-0.03}^{+0.03}$	<${0.22}_{-0.06}^{+0.05}$	${0.12}_{-0.02}^{+0.04}$	⋯	⋯	⋯	⋯
Nme	10−4	${4.4}_{-3.7}^{+4.5}$	${3.4}_{-1.6}^{+2.1}$	${0.4}_{-0.4}^{+0.7}$	${3.7}_{-2.6}^{+5.8}$	${16.8}_{-8.6}^{+23.2}$	${5.2}_{-1.7}^{+3.2}$	${1.3}_{-0.6}^{+0.9}$	${8.0}_{-3.4}^{+7.8}$	⋯	⋯	⋯	⋯
T1,mkc	keV	<1.28	<0.98	<0.90	<0.86	<1.41	${0.72}_{-0.35}^{+0.53}$	<0.87	${0.58}_{-0.24}^{+0.30}$	0.0808f	0.0808f	0.0808f	0.0808f
T2,mkc	keV	${41.2}_{-10.4}^{+17.5}$	${35.4}_{-6.2}^{+5.7}$	${38.2}_{-9.3}^{+13.9}$	${43.6}_{-7.4}^{+11.2}$	${35.7}_{-10.8}^{+17.6}$	${36.8}_{-7.7}^{+9.4}$	${38.0}_{-10.0}^{+13.0}$	${44.2}_{-8.6}^{+11.1}$	${33.3}_{-10.2}^{+17.0}$	${33.7}_{-6.1}^{+9.6}$	${28.3}_{-16.0}^{+11.6}$	${40.3}_{-8.3}^{+9.0}$
Nmkc	10−11	${12.1}_{-3.7}^{+4.2}$	${12.0}_{-2.3}^{+2.8}$	${4.6}_{-1.2}^{+1.9}$	${10.9}_{-2.0}^{+2.4}$	${13.1}_{-4.5}^{+8.6}$	${10.6}_{-2.1}^{+3.6}$	${4.4}_{-0.1}^{+0.2}$	${9.9}_{-2.0}^{+3.4}$	${14.9}_{-4.8}^{+9.2}$	${11.8}_{-2.6}^{+3.2}$	${6.5}_{-1.7}^{+2.8}$	${11.1}_{-2.1}^{+3.6}$
Z	Z⊙	${1.6}_{-0.6}^{+0.6}$	${1.8}_{-0.4}^{+0.5}$	${1.3}_{-0.4}^{+0.6}$	${1.6}_{-0.4}^{+0.7}$	${1.2}_{-0.6}^{+0.8}$	${1.7}_{-0.4}^{+0.6}$	${1.3}_{-0.4}^{+0.6}$	${1.5}_{-0.4}^{+0.5}$	${1.2}_{-0.5}^{+0.6}$	${1.6}_{-0.4}^{+0.5}$	${0.8}_{-0.3}^{+0.3}$	${1.3}_{-0.4}^{+0.4}$
LineE	keV	${6.48}_{-0.12}^{+0.08}$	${6.32}_{-0.03}^{+0.03}$	${6.44}_{-0.10}^{+0.07}$	${6.38}_{-0.05}^{+0.05}$	${6.48}_{-0.08}^{+0.09}$	${6.32}_{-0.03}^{+0.03}$	${6.43}_{-0.09}^{+0.07}$	${6.38}_{-0.05}^{+0.06}$	${6.48}_{-0.07}^{+0.09}$	${6.32}_{-0.03}^{+0.04}$	${6.45}_{-0.05}^{+0.10}$	${6.38}_{-0.05}^{+0.05}$
σ	eV	0f	0f	0f	0f	0f	0f	0f	0f	0f	0f	0f	0f
Nline	10−5	${1.5}_{-0.7}^{+0.8}$	${1.6}_{-0.4}^{+0.4}$	${0.5}_{-0.2}^{+0.3}$	${1.1}_{-0.4}^{+0.4}$	${1.4}_{-0.7}^{+0.8}$	${1.4}_{-0.4}^{+0.4}$	${0.5}_{-0.2}^{+0.2}$	${1.0}_{-0.3}^{+0.4}$	${1.3}_{-0.7}^{+0.8}$	${1.4}_{-0.4}^{+0.4}$	${0.5}_{-0.3}^{+0.3}$	${10.1}_{-3.5}^{+3.4}$
χ2(dof)		200(203)	393(427)	347(304)	503(463)	203(205)	399(429)	345(305)	506(465)	210(207)	405(431)	355(307)	502(467)

Note. Symbols carry the same meaning as in Table 3.

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