Relativistic X-ray reflection and highly ionized absorption in the spectrum of NS LMXB 1A 1744-361

A Neutron star Low-mass X-ray binary (NS LMXB) consists of an NS and a low-mass ($\lesssim 1M_{\odot}$) donor star. In NS LMXB systems, mass accreting from the donor star onto the NS by Roche-lobe overflow forms structures such as an accretion disc. It emits electromagnetic radiation in a wide range of wavelengths, from radio to X-rays. NS LMXBs may be persistent accreator or transient systems based on their long-term variabilities. Persistent NS LMXBs are characterized by persistent luminosity in X-rays and may have an X-ray luminosity of $L_{X}\gtrsim 10^{36}{\rm~{}erg\ s}^{-1}{}$ (Ludlam et al. 2019, 2017). Whereas some NS LMXBs exhibit an outburst, a sudden and explosive brightening phenomenon, and such LMXBs are called X-ray Transients. Transient LMXBs undergo recurrent bright ($L_{X}\gtrsim 10^{36}{\rm~{}erg\ s}^{-1}{}$) outbursts lasting from days to weeks and then return to long intervals of X-ray quiescence ($L_{X}\lesssim 10^{34}{\rm~{}erg\ s}^{-1}{}$) lasting from months to years (Degenaar & Wijnands, 2010). Persistent and transient NS LMXBs are classified into two classes: Z and Atoll sources based on their behavior on the X-ray hardness intensity diagram (HID) and color-color diagram (CCD) (Hasinger & van der Klis, 1989). Z sources are usually very bright and sometimes radiate at Eddington luminosity ($L_{Edd}$). Atoll sources are generally less bright ($L\lesssim 0.5L_{Edd}$). Based on their luminosity, the state of Atoll sources is further divided into ‘banana branch’ and ‘island branch’, and usually, they correspond to the High-soft (HS) and Low-hard (LH) state, respectively. The banana branch has been further divided into lower banana and upper banana at lower and higher luminosities.

The source 1A 1744-361 is a transient NS LMXB discovered by the Ariel V satellite in 1976 during its outburst state (Davison et al., 1976; Carpenter et al., 1977). Since then, several outbursts have been observed from the source between the years 1989 and 2005 with a number of missions like RXTE, Chandra, and INTEGRAL. Emelyanov et al. (2001) discovered 33 likely type-I bursts in the field containing 1A 1744-361 in 2001. However, those were not unambiguously identified as thermonuclear bursts. At a later time, the first thermonuclear (Type I) burst from 1A 1744-361 was discovered by Bhattacharyya et al. (2006a) using the 2005 RXTE PCA data. It confirmed the suggestion of Emelyanov et al. (2001) that the source harbors a rapidly rotating NS as a compact object. During this burst Bhattacharyya et al. (2006a) discovered millisecond period brightness oscillation, which provided the spin frequency of the NS of $\sim 530$ Hz. The lack of strong indication of photospheric radius expansion during the burst suggested a 9 kpc upper limit of the source distance (Bhattacharyya et al., 2006a). From the studies of energy-dependent dips in the 2003 PCA data Bhattacharyya et al. (2006a) also found that this source is a dipping LMXB. The binary orbital period of the source estimated by Bhattacharyya et al. (2006a) is $97\pm 22$ minutes. From the timing analysis, Bhattacharyya et al. (2006b) found that the source 1A 1744-361 shows Atoll behavior during the outbursts. After July 2005, the source’s outburst activities were detected on June 2008, November 2009, and August 2013 (Bahramian et al., 2013). Recently, MAXI/GSC detected an outburst from the field, including 1A 1744-361 on 30th May 2022 (Kobayashi et al., 2022). SWIFT/XRT subsequently confirmed the outburst originating from the known neutron star low-mass X-ray binary 1A 1744-361 (Kennea et al., 2022). At later times, the source was observed by the missions NICER and NuSTAR during 3rd June 2022 and 8th June 2022, respectively (Ng et al., 2022; Pike et al., 2022).

Spectral studies of 1A 1744-361 were performed in the past using data from the satellites RXTE and Chandra (Bhattacharyya et al., 2006b; Gavriil et al., 2012). Bhattacharyya et al. (2006b) performed the spectral analysis of this source using the RXTE/PCA data, and they found that a Comptonized blackbody model describes the persistent spectrum of this source well. They reported the first detection of a broad ($\sim 0.6{\rm~{}keV}{}$) iron emission feature at $\sim 6$ keV and an iron absorption edge at $\sim 8$ keV. They mentioned that the energies of the absorption edge are consistent with those expected from ionized iron. Gavriil et al. (2012) reported on the Chandra High Energy Transmission Grating (HETG) spectra of this source during its 2008 July outburst. They found that its persistent emission is well modeled by a blackbody ($kT\sim 1.0{\rm~{}keV}{}$) plus power law ($\Gamma\sim 1.7$) with an absorption edge. They also found a significant absorption line at $6.961\pm 0.002$ keV, consistent with the Fe XXVI (hydrogen-like Fe) $2-1$ transition. They placed an upper limit on the velocity of a redshifted flow of $v<221$ km s^-1. They further confirmed the suggestion of Bhattacharyya et al. (2006b) that this source is an Atoll source. The mission NuSTAR observed the source on 8th June 2022, and the preliminary spectral results have been reported by Pike et al. (2022). They found that the $3.0-40.0{\rm~{}keV}{}$ energy spectrum is well-described by a combination of relativistic disk reflection of a power law with a high energy cut-off, with an intervening warm absorber. They also reported the detection of narrow absorption lines at $6.95\pm 0.02$ keV and $8.01\pm 0.03$ keV. The time-averaged $0.5-10.0$ keV NICER spectrum during its 2022 outburst is well-fitted by an absorbed cut-off power law and blackbody component with a Gaussian absorption line component (Ng et al., 2022). The Gaussian absorption line has centroid energy $6.988^{+0.012}_{-0.015}$ keV and width $\sim 0.004{\rm~{}keV}{}$ .

In this work, we represent a systematic and in-depth spectral and timing analysis of this source using the available NuSTAR observation performed on 8th June 2022. We aim to characterize the shape of the X-ray spectrum accurately and search for any emission and/or absorption features in it, as there was a hint of the same from the previous analysis. Studies of the same allow us to derive information on the physical and geometrical parameters of the system. We have organized the paper as follows: in Section 2 we describe the observation and data reduction. In Section 3 and Section 4 we present the details of the timing and spectral analysis, respectively. In section 5, we discuss the results obtained from the analysis.

Nuclear Spectroscopic Telescope ARray (NuSTAR; Harrison et al. 2013) observed the source 1A 1744-361 only once on 8th June 2022 for a total exposure of $\sim 34$ ks. We have used this observation (obsID: 90801312001) for our analysis.

The NuSTAR data were collected in the $3-79$ keV energy band using two identical co-aligned telescopes equipped with the focal plane modules FPMA and FPMB. We reduced the data using the standard data analysis software NUSTARDAS v2.1.1 task included in HEASOFT v6.29 and using the latest CALDB version available. We used the task nupipeline to generate the calibrated and screened event files. For the source, we extracted events from a circular region centered on the source, with a radius of $100^{\prime\prime}$ for both the FPMA and FPMB. We also extracted background events from a circle of the same radius from the area of the same chip with the lowest apparent source contamination for both instruments. We then used the tool nuproducts to build the filtered event files, the background subtracted light curves, the spectra, and the arf and rmf files. This nuproducts software ensures that all the instrumental effects, including loss of exposure due to dead-time, are correctly accounted for. We grouped the FPMA and FPMB spectral data with a minimum of $50$ counts per bin which allows the use of $\chi^{2}$ statistics. Finally, we fitted spectra from the FPMA and FPMB simultaneously, leaving a floating cross-normalization constant.

The left panel of Figure 1 shows the 100s bin-size NuSTAR light curve of the source in the $3-79$  keV energy band. The light curve exhibits variations in intensity throughout the observation and a short flare at an elapsed time around $20$ ks. The variability of the X-ray flux is commonly explained by the partial covering of the NS system by ionized absorbers (Buisson et al., 2021; Ducci et al., 2023; Saavedra et al., 2023). We did not observe either Type-I X-ray bursts or absorption dips in the NuSTAR light curve of this source, although those have been detected earlier (Bhattacharyya et al., 2006a). The average count rate of the source during this observation is $\sim 80$ count s^-1, while a small increment (factor of $\sim 1.4$) in the count rate is observed during the flaring. We further constructed the colour-colour diagram (CCD) of the source using light curves in the $3-6$ keV, $6-10$ keV, and $10-20$ keV energy bands. We defined the soft-colour as the ratio of count rates in $6-10$ keV and $3-6$ keV, and hard colour as the ratio of count rates in $10-20$ keV and $6-10$ keV. We present the resulting diagram in the right panel of Figure 1. It is evident from the CCD that the source is in the ’upper-banana’ state during this observation. The CCD of this source is very similar to the other known Atoll source 4U 1608-522 and GX 9+9 (Takahashi et al., 2011; Chatterjee et al., 2023). In addition, we extracted light curves with 100s bins in the $3-10$  keV and $10-79$  keV energy bands and calculated the hardness ratio (HR). The variation of the $3-10$ keV and $10-79$ keV count rates and HR as a function of time are shown in the top, middle, and lower panel of Figure 2, respectively. We note that the HR remains roughly constant with time throughout this observation except for the short time interval near the elapsed time of $\sim 20$ ks where flaring occurs. It further establishes the commonly observed fact that in the banana state of the Atoll sources, the hardness is relatively constant over a wide range of luminosity (van der Klis, 1995; Church et al., 2014).

We used the spectral analysis package XSPEC $v12.12.0$ (Arnaud, 1996) to fit the NuSTAR FPMA and FPMB spectra simultaneously between $3.0$ to $50.0$  keV energy band, while above $50$ keV is dominated by the background. We added a model constant to account for cross-calibration of the two instruments FPMA and FPMB. The value of constant for FPMA was fixed to $1$ and allowed it to vary for the FPMB. We used TBabs to model the Galactic absorption along the line of sight with wilm abundances (Wilms et al., 2000) and vern (Verner et al., 1996) photoelectric cross section. Spectral uncertainties are quoted at the $90$ percent confidence intervals (e.g., $\Delta\chi^{2}=2.7$ for one interesting parameter) unless otherwise stated.

We present the spectral and timing analysis results of the accreting neutron star 1A 1744-361 from the NuSTAR observation during its 2022 outbursts. During this observation, the source is detected with an average count rate of $\sim 80{\rm~{}count\ s}^{-1}$. A small flaring activity occured at $\sim 20$ ks after the start of the observation. The CCD indicates that the source was in the banana branch of the atoll track during this observation. The HR of the source lies in the range $0.05-0.15$, also indicative of the banana state of the source. The unabsorbed bolometric X-ray flux during this observation in the energy band $0.1-100{\rm~{}keV}{}$ is $4.0\times 10^{-9}$ erg s^-1 cm^-2. This implies an unabsorbed bolometric luminosity of $3.9\times 10^{37}$ erg s^-1, assuming a distance of $9$ kpc. This value corresponds to $\sim 10\%$ of the Eddington luminosity ($L_{Edd}$) which is $\sim 3.8\times 10^{38}$ erg s^-1 for a canonical $1.4\>M_{\odot}$ NS (Kuulkers et al., 2003). The luminosity is consistent with those of the atoll sources in the banana branch. All these observed characteristics indicate that the source was neither in the extremely low-hard state nor the very high-intensity (high-soft) state. We found that the continuum X-ray emission is well described by a blackbody ($kT_{bb}\sim 1.3{\rm~{}keV}{}$) plus power-law ($\Gamma\sim 1.2$) with a cut-off energy at $\sim 5.0{\rm~{}keV}{}$. The observed cut-off energy is typical for the atoll sources in the banana states. The spectrum of this source exhibited the presence of broad Fe-K emission line in $6-7{\rm~{}keV}{}$, a Compton hump $10-20{\rm~{}keV}{}$, and robust absorption features in $7-9{\rm~{}keV}{}$. The broad Fe-K emission line and Compton hump are commonly explained by the disc reflection of the coronal emission (i.e., hard X-ray photons) subject to the strong relativistic distortion (Fabian et al., 1989). The strong absorption features indicate the presence of a local partially ionized absorber in the line of sight. The absorption by the plasma from the accretion disc generates absorption lines (Neilsen & Lee, 2009). Therefore, in our spectral modeling, we employed disc reflection of hard X-ray emission and absorption of the incoming radiation in the photo-ionized plasma.

We found that the $3.0-50.0{\rm~{}keV}{}$ source spectrum is adequately fitted using a model combination consisting of an absorbed single-temperature blackbody model (bbody) and a reflection model (relxill) along with the addition of a warm absorber model (zxipcf). In this combination of model, the inner-disk radius, $R_{in}$, obtained from the relxill is $\sim(1.61-2.86)R_{ISCO}=(8.4-14.9)R_{g}$ ($17.6-31.2$ km for a $1.4M_{\odot}$ NS), where $R_{ISCO}=5.2R_{g}$ for a spinning NS with $a=0.25$). The source shows comparatively a larger inner disc radius and is consistent with other NS LMXBs (Miller et al. 2011; Papitto et al. 2013; King et al. 2016; Iaria et al. 2016; Mondal et al. 2021). The value of $R_{in}$ indicates that the accretion disc is neither truncated very close to nor far from the NS consistent with the observed flux/mass accretion rate. The photon index ($\Gamma=1.18\pm 0.03$) obtained from the final spectral fit further shows that the source is neither in the soft nor in the very hard spectral state. The best-fitting model gives a relatively low inclination $\sim 35^{0}$, not consistent with the dipping features previously observed in the light curve of this source. The reflection spectrum revealed that the accretion disc is highly ionized with log$\xi\sim 4.4$, and the iron abundance is high comparable to the solar composition ($A_{Fe}=6.40\pm 0.92$). The relativistic reflection model relxill yielded values fully compatiable with those from the previous phenomenologica modeling with gabs and edge.

Apart from the disc reflection features, this observation showed the presence of prominent Fe absorption features between the energy ranges $6.9-8.8{\rm~{}keV}{}$ (see Figure 4). We used the Gaussian absorption model gabs to estimate the features of the lines. The centroid energies of these lines are measured at $\sim 6.90{\rm~{}keV}{}$ and $\sim 7.99{\rm~{}keV}{}$. We further measured an absorption edge at energy $\sim 8.79{\rm~{}keV}{}$. The strength of the absorption lines is measured in terms of the equivalent width (EW). The EW of the $\sim 6.90{\rm~{}keV}{}$ Fe line was $60\pm 2$ eV, and for the $\sim 7.99{\rm~{}keV}{}$ Fe line was $40\pm 1$ eV. The most abundant elements seen in absorption in the X-ray spectra of LMXBs are Fe XXV (rest-frame energy $6.70{\rm~{}keV}{}$) and Fe XXVI (rest-frame energy $6.97{\rm~{}keV}{}$), which can be red/blue shifted in case of an in/outflow. Thus, the line detected $\sim 6.90{\rm~{}keV}{}$ could represent absorption in a modest inflow or in a strong outflow. The in/outflow velocity ($v$) of the absorbing material can be determined via $(E_{0}-E_{i})/E_{i}=v/c$, where $E_{i}$ and $E_{0}$ are the observed and rest energy of the line, respectively. If the strong absorption feature we detect $\sim 6.90{\rm~{}keV}{}$ is indeed the blueshifted Fe XXV K$\alpha$ line (rest energy $E_{0}=6.70{\rm~{}keV}{}$), then we measure an outflow velocity of $\sim 8700$ km s^-1. In addition, we estimated the full-width half-maximum (FWHM) of the intrinsic $\sim 6.90{\rm~{}keV}{}$ absorption line of $\sim 0.306$  keV. It corresponds to an equivalent resolved velocity of $\sim 13280$ km s^-1. However, considering $\sim 6.90$  keV line as blueshifted Fe XXV predicts a strong Fe XXVI at commensurate blueshift ($\sim 7.18$  keV), which is not seen. Thus, the observed line at $\sim 7.99{\rm~{}keV}{}$ probably is the blueshifted line from the K$\beta$ transition of He-like, Fe XXV ion, compatible with rest energy $\sim 7.78{\rm~{}keV}{}$. We found that the absorption edge at energy $\sim 8.79{\rm~{}keV}{}$ is consistent with a He-like Fe XXV absorption edge.

The prominent absorption features are suggestive of the presence of a local partially ionized absorber. For this reason, we implemented the model zxipcf that accounts for the contribution of the partially ionized local absorber. Moreover, the line-by-line fitting is not sufficient to address the question of inflow/outflow to the system; a physical self-consistency is required (Miller et al., 2016). We found that the partially covering absorber has a significant absorbing column density of $N_{H}=2.94_{-0.42}^{+0.34}\times 10^{22}$ cm^-2. The absorbing material covers a fraction of $\sim 90\%$ of the central X-ray source, characterized by a high ionization parameter (log$\xi\sim 3.6$). The value of the ionization parameter is consistent with Gavriil et al. (2012), determined by the XSTAR simulations. This model further gives a redshift of $z=-0.021_{-0.003}^{+0.001}$, i.e. implying an outflow velocity of $\simeq 6000-7200$ km s^-1. This indicates that the absorption is best associated with a moderate outflow from the NS system.

We note that relativistic X-ray reflection and photoionized absorption have been simultaneously detected in bright Z-type NS LMXB GX 13+1 (Ueda et al. 2004; Díaz Trigo et al. 2012; Saavedra et al. 2023). The spectral behavior of the source 1A 1744-361 is very similar, as observed for the atoll source GX 13+1 by Saavedra et al. (2023). They detected broad ($\sigma\sim 0.15$) absorption lines around $\sim 6.87$ and $\sim 8.03{\rm~{}keV}{}$ from the NuSTAR spectrum of GX 13+1 and attributed those to the Fe XXVI K$\alpha$ and Ni XXVIII absorption line, respectively. If the observed line energies are compared to the rest energies of Fe XXVI K$\alpha$ and Ni XXVIII absorption line, it indicates a redshifted flow. However, from the modeling with a physically motivated warm absorber model, they suggested an outflow from the system with a velocity $\lesssim 1000$ km s^-1. They attributed the absorption features to a photo-ionized plasma emanating from the accretion disc in the form of wind/jets. Blueshifted narrow absorption lines have been previously observed in many NS LMXBs and are interpreted as outflowing disc winds (Ueda et al., 2004; Miller et al., 2011; Degenaar et al., 2014; Bozzo et al., 2016). The amount of blueshift ($\sim 6300$ km s^-1) observed for the source 1A 1744-361 is comparatively larger than the typically observed values i.e., $400-3000$ km s^-1 (Díaz Trigo & Boirin, 2016). However, the highest velocities claimed for NS LMXBs so far are $\sim 9000-14000$ km s^-1 (Degenaar et al., 2014; Miller et al., 2016). For the NS LMXB 1RXS J180408.9-342058, Degenaar et al. (2016) measured an outflow velocity as high as $\sim 25800$ km s^-1 even at a low inclination angle of $i\sim 30^{0}$. Whereas redshifted flow, i.e., inward to the NS systems, is not commonly observed, and the origin of the same is still poorly understood. Kubota et al. (2018) reported a redshift of $\sim 4000\pm 1400$ km s^-1 for the high-mass X-ray binary SMC X-1 and discussed some possibilities of the astrophysical origin of the absorption lines.

A rough estimation of the distance of the ionized absorbing material ($r$) from the centre of the system could be evaluated by means of the ionization parameter $\xi$. According to Díaz Trigo et al. (2012), the distance $r$ is defined as

where $L$ is the unabsorbed luminosity in ergs s^-1, $n_{e}=N_{H,warmabs}/d$ is the electron density of the ionized plasma, and $d$ is the thickness of the slab of ionizing absorbing material. Using the spectral-fitting results and considering typical values of $d/r$ ranging from $0.1$ to $1$, we estimate $r$ between $\sim 1.0\times(10^{5}-10^{6})$ km. This value is in excellent agreement with the value previously obtained by Gavriil et al. (2012) using the Chandra data. Moreover, this value for $r$ is safely within the accretion disc radius found earlier by Gavriil et al. (2012). It suggests that the absorption features are most likely emanating from a disc wind far from the central source. However, the complete geometry of the putative absorber in 1A 1744-361 needs to be clearly understood.

The best-fit spectral parameters were further used to compute physical properties like mass accretion rate ($\dot{m}$), the maximum radius of the boundary layer ($R_{BL,max}$), and magnetic field strength ($B$) of the NS in the system. We first estimated the mass accretion rate per unit area, using Equation (2) of Galloway et al. (2008)

The above equation yields a mass accretion rate of $4.4\times 10^{-9}\;M_{\odot}\;\text{y}^{-1}$ at a persistent flux $F_{p}=2.35\times 10^{-9}$ erg s^-1 cm^-2, assuming the bolometric correction $c_{bol}\sim 1.38$ for the nonpulsing sources (Galloway et al., 2008). Here we assume $1+z=1.31$ (where $z$ is the surface redshift) for an NS with mass ($M_{NS}$) 1.4 $M_{\odot}$ and radius ($R_{NS}$) $10$ km. To estimate the maximum radial extension of the boundary layer from the NS surface based on the mass accretion rate, we used Equation (2) of Popham & Sunyaev (2001). We found the maximum value of the boundary layer to extend to $R_{BL}\sim 6.53\;R_{g}$, assuming $M_{NS}=1.4\>M_{\odot}$ and $R_{NS}=10$ km. The actual value may be larger than this if we account for the viscous effects and the spin of this layer. The radial extent of the boundary layer regions is consistent with the disc position.

An upper limit of the magnetic field strength of the NS can be estimated using the upper limit of $R_{in}$ measured from the reflection fit. Equation (1) of Cackett et al. (2009) gives the following expression for the magnetic dipole moment,

We assumed a geometrical coefficient $k_{A}=1$, an anisotropy correction factor $f_{ang}=1$, and the accretion efficiency in the Schwarzschild metric $\eta=0.2$ (as reported in Cackett et al. 2009 and Sibgatullin & Sunyaev 2000) and used $0.1-100$ keV flux as the bolometric flux ($F_{bol}$) of $\sim 4.0\times 10^{-9}$ erg s^-1 cm^-2. Cackett et al. (2009) modified $R_{in}$ as $R_{in}=x\>GM/c^{2}$ introducing a scale factor $x$. Using the upper limit of $R_{in}$ ($\lesssim 15\>R_{g}$), we obtained $\mu\leq 0.47\times 10^{27}$ G cm³. This corresponds to an upper limit of the magnetic field strength of $B\lesssim 0.94\times 10^{9}$ G at the magnetic poles (for an NS mass of $1.4\>M_{\odot}$, a radius of $10$ km, and a distance of $9$ kpc). To the best of our knowledge, there has not been any previous estimation of the $R_{in}$, $\dot{m}$, $\mu$, $B$ of this NS system. Hence, there exists no scope for comparison of the results obtained in the present analysis with other previous works.

In this work, we aimed to focus on detecting disc reflection and absorption, thereby constraining its accretion geometry through spectro-timing analysis. We note that the continuum emission can alternatively be described with different combinations of model components. Apart from the presence of the Comptonization component, previous studies detected the presence of a broad emission line and absorption features in the spectra of 1A 1744-361 (Bhattacharyya et al., 2006b; Gavriil et al., 2012) and we focused on these features. We primarily inspected that the reflection and absorption features were insensitive to the specific choice of the continuum models. However, the choice of reflection and absorption model may have some impact on the spectral parameters. In our spectral fitting, we have found that power law is dominant in the phenomenological fit and provided most of the hard X-ray flux. This flux illuminates the accretion disc and produces the reflection spectrum. The choice of the reflection model is based on this observed fact. However, different reflection models based on different illuminating spectra may be tested in the reflection fits. We note that it is challenging to constrain all the reflection parameters if we implement the reflection models, which assumes different illuminating spectra. In addition, a further correlation between the ionization and column density of the absorber and the equivalent width of the broad iron line can be drawn in future studies.

This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Centre (HEASARC). This research also has made use of the NuSTAR data analysis software (NuSTARDAS) jointly developed by the ASI Space Science Data Center (SSDC, Italy) and the California Institute of Technology (Caltech, USA). ASM and BR would like to thank Inter-University Centre for Astronomy and Astrophysics (IUCAA) for their facilities extended to him under their Visiting Associate Programme.

This research has made use of data obtained from the HEASARC, provided by NASA’s Goddard Space Flight Center. The observational data set with Obs. IDs $90801312001$ (NuSTAR) dated 8th June 2022 is in public domain put by NASA at their website https://heasarc.gsfc.nasa.gov.