Evidence for the Photoionization Absorption Edge in a Photospheric Radius Expansion X-Ray Burst from GRS 1747–312 in Terzan 6

Neutron stars (NSs) in low-mass X-ray binaries (LMXBs) can accrete matter transferred from their companions through the Roche-lobe overflow. Depending on the mass density and temperature of the accreted gas, unstable thermonuclear burning of hydrogen, helium, or their mixture on the surface of the NSs gives rise to the phenomena known as type I X-ray bursts (e.g., see, Lewin et al. 1993; Strohmayer & Bildsten 2006 for reviews). Three main branches of type I X-ray bursts, i.e., normal bursts, intermediate-duration bursts, and superbursts, are distinguishable based on their duration (see Figure 7 in Falanga et al. 2008 and references therein). The light curves of these bursts showed a fast rise and approximately exponential decay with a duration of a few seconds for normal bursts, tens of minutes for intermediate-duration bursts, and up to several hours for superbursts, depending on the ignition depth. In particular, the superbursts are likely triggered by carbon burning in the deep NS ocean (Cumming & Bildsten 2001; in't Zand 2017).

X-ray burst spectra can usually be well fitted by a diluted blackbody, with temperature kT_bb ∼ 1–3 keV (Lewin et al. 1993). Some bursts show photospheric radius expansion (PRE), which is believed to be a result of the luminosity approaching the Eddington value, when the radiation pressure lifts the NS surface layers (Lewin et al. 1993). During the subsequent cooling phase of PRE bursts, the photosphere is likely located at the NS surface. This fact allows us to use PRE bursts as a tool to measure NS masses M and radii R (e.g., see Ebisuzaki 1987; Sztajno et al. 1987; Damen et al. 1990; van Paradijs et al. 1990; Lewin et al. 1993; Özel et al. 2009; Suleimanov et al. 2011a; Poutanen et al. 2014; Li et al. 2015, 2017). In particular, the NS LMXBs in globular clusters are ideal targets to constrain the equation of state of matter at supranuclear density, because the distance to the objects can be determined independently using optical observations (e.g., Kuulkers et al. 2003; Guillot et al. 2013; Li et al. 2015; Özel et al. 2016).

Although most X-ray burst spectra can be well described by the Planck function, deviations from the blackbody have been observed in several cases. in't Zand et al. (2013) found soft and hard X-ray excesses in the spectra of an X-ray burst from SAX J1808.4−3658, which was interpreted as a result of enhanced persistent emission during the burst. Many other LMXBs showed the same phenomenon (Worpel et al. 2013). Moreover, the reflection component from the photoionized accretion disk has been observed from the superburst in 4U 1820−30 (Ballantyne & Strohmayer 2004), 4U 1636−536, and IGR J17062−6143 (Keek et al. 2014, 2017).

Photoionization absorption features in the range 6–11 keV have also been identified in 4U 0614 + 091, 4U 1722−30, and 4U 1820−30 (in't Zand & Weinberg 2010), and HETE J1900.1−2455 (Kajava et al. 2017) due to the bound–bound or bound–free transitions of the newborn heavy elements in the X-ray burst photospheres. The observed spectral features can be associated with the hydrogen-like Fe edge at 9.278 keV, or hydrogen/helium-like Ni edges at 10.8/10.3 keV. The presence of the spectral features potentially allows to measure the gravitational redshift for the NS surface (Lewin et al. 1993; Özel 2006) which gives additional constraints on the NS mass and radius.

GRS 1747−312 is a transient LMXB located in the globular cluster Terzan 6 (Predehl et al. 1991; Pavlinsky et al. 1994; Verbunt et al. 1995; in't Zand et al. 2003a, 2003b). Thermonuclear X-ray bursts occurred in GRS 1747−312, establishing that the binary system hosts a NS. GRS 1747−312 is known to be an eclipsing binary in a 12.360 ± 0.009 hr orbit observed at an inclination of >745 with an eclipse duration of ∼43 min (in't Zand et al. 2000, 2003b). The optical counterpart has not yet been identified.

The distances to globular clusters can be measured from the relations (Harris 1996, 2010),

$$\begin{eqnarray}&&{(m-M)}_{0}={V}_{\mathrm{HB}}-{M}_{{\rm{V}}}(\mathrm{HB})-3.1E(B-V),\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&{M}_{{\rm{V}}}(\mathrm{HB})=0.16[\mathrm{Fe}/{\rm{H}}]+0.84\end{eqnarray} \tag{ 2 }$$

and V_HB, E(B − V) and [Fe/H] are referred to as the apparent magnitude of the horizontal branch stars in a globular cluster, the foreground reddening, and the metallicity, respectively. We calculate the distance to Terzan 6 using the values and typical errors V_HB = 22.16 ± 0.20, E(B − V) = 2.35 ± 0.20, and [Fe/H] = −0.62 ± 0.20 (Fahlman et al. 1995; Barbuy et al. 1997; Kuulkers et al. 2003; Valenti et al. 2007). Then, the distance uncertainty can be estimated from Equations (1) and (2) by propagating errors. The distance modulus (m − M)₀ is 14.13 ± 0.65 and the distance to Terzan 6 is ${6.7}_{-1.7}^{+2.3}\,\mathrm{kpc}$ at 1σ conficence level.

Non-Planckian spectra have also been observed in the peculiar PRE burst from GRS 1747−312 (in't Zand et al. 2003a). The time-resolved spectra showed a strong PRE phase occurring in the first 50 s after the burst trigger. The spectra around the peak of the radius expansion and during the decay phase are biased from the blackbody profile since the reduced chi-square (${\chi }_{\mathrm{red}}^{2}$) are systematically larger than 2. in't Zand et al. (2003a) added a Gaussian line to account for the possible Fe line emission, which can improve the fitting. But the Fe line has a broad feature and a low central energy of 4.9 keV. The authors claimed that this is hard to explain from Fe–K emission within reasonable shifts, especially the larger ${\chi }_{\mathrm{red}}^{2}$ appears around the peak height of the photosphere where the gravitational redshift is negligible.

In this work, we investigate the possible presence of an absorption edge in this peculiar X-ray burst from GRS 1747−312 (in't Zand et al. 2003a). The analysis of the spectral properties of the burst is given in Section 2. We discuss the origin and variations of the absorption edge energy in Section 2.2. The direct cooling method is applied to estimate the NS mass and radius in Section 3. The discussion of the results is presented in Section 4 and we summarize in Section 5.

The Proportional Counter Array (PCA; Jahoda et al. 2006; Shaposhnikov et al. 2012) on board the Rossi X-ray Timing Explorer (RXTE), which has an energy resolution of 17% at 6 keV, is a powerful instrument to study X-ray bursts. During the RXTE pointing to the source XTE J1751−305 (Obs. ID. 70131-02-17-00), the PCA observed an intense type I X-ray burst, which is believed to originate from GRS 1747−312 located 40' off-axis. We re-analysed this PRE burst following in't Zand et al. (2003a). Three proportional counter units (0, 2, 3) were active during that burst. From Standard 2 PCA data, in order to guarantee roughly the same signal-to-noise ratio for all spectra, the data were extracted with the exposure time varying from 1 to 4 s. Around 24 s after the burst trigger, the exposure time was set to 0.25 s to catch the rapid spectral variations. Following the method introduced by in't Zand et al. (2003a), the correction to the collimator response was made due to off-axis pointing by RXTE. The background spectrum was extracted from 440 to 40 s before the burst trigger. Dead-time corrections were carried out according to instructions from the RXTE team.¹⁰ All spectra were binned to ensure each channel had at least 15 photons, and a 0.5% systematic error was added.

The spectrum of the burst shows clear deviations from the Planckian shape. An additional absorption edge improves the fits significantly (see also in't Zand & Weinberg 2010; Kajava et al. 2017). The edge model wabs×bbodyrad×edge in xspec (version 12.8.2) (Arnaud 1996) is applied to fit the spectra in the energy range 3–20 keV. The blackbody component, bbodyrad, has two parameters, the blackbody temperature, kT_bb, and normalization, K_bb ≡ (R_bb/D_10kpc)², to account for emission from the photosphere, where R_bb and D_10kpc are the blackbody radius and the distance to the source in units of 10 kpc, respectively. The multiplicative model edge is expressed as M(E) = exp[−τ (E/E_Edge)⁻³] for photon energies E > E_Edge and M(E) = 1 otherwise, where τ and E_Edge are the absorption depth and the threshold energy, respectively. During the fitting, we fixed the hydrogen column density at N_H = 6 × 10²² cm⁻² (in't Zand et al. 2003a). The blackbody model wabs×bbodyrad is also used as a comparison to the edge model. We illustrate in Figure 1 how these two models fit the spectrum extracted during the PRE phase in the interval 28–29 s after the burst onset. We see a clear improvement in χ² and in the structure of the residuals when using the edge model. The bolometric flux is calculated using cflux command in the energy range 0.001–200 keV. The 1σ errors of kT_bb, K_bb, E_Edge, τ and flux are determined from the xspec command error.

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2.1. Results

The results of the fitting of the time-resolved spectra are shown in Figure 2, where the red crosses and black crosses are obtained from the edge model and blackbody model respectively. The ${\chi }_{\mathrm{red}}^{2}$ are displayed in the bottom panel of Figure 2. It should be noticed that the blackbody model cannot fit the data around the peak flux (t ∼ 10–40 s) and the decay phase (t ∼ 110–160 s) very well, but we still plot the best-fitted values without errors. The blackbody model fits to the data have dozens of spectra with ${\chi }_{\mathrm{red}}^{2}\gt 2$. From the edge model, only two spectra have ${\chi }_{\mathrm{red}}^{2}\gt 2$ without trends in the residuals. For the multiplicative edge component, an F-stat test is appropriate to estimate the probability of chance improvement (Orlandini et al. 2012; DeCesar et al. 2013). We obtained the probability in the range 0.05–8 × 10⁻⁶, which is a statistically significant improvement. Generally, the bolometric flux, the blackbody temperature, and the blackbody radius have small differences and almost the same trends compared with the blackbody model (see also Figure 3 in in't Zand et al. 2003a).

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From the spectral fitting, the touchdown flux is F_TD = (2.12 ± 0.07) × 10⁻⁸ erg cm⁻² s⁻¹. Another three PRE bursts from GRS 1747−312 have lower touchdown fluxes. The two bursts observed by RXTE (Galloway et al. 2008) have $(1.00\,\pm 0.03)\times {10}^{-8}$ and (1.67 ± 0.04) × 10⁻⁸ erg cm⁻² s⁻¹, while the burst observed by Suzaku (Iwai et al. 2014) has (1.85 ± 0.28) × 10⁻⁸ erg cm⁻² s⁻¹. Because of the strong PRE and the plateau of bolometric flux during the PRE phase, the type I X-ray burst we analyzed has been regarded as reaching its Eddington limit in previous works (e.g., in't Zand et al. 2003a; Kuulkers et al. 2003; Galloway et al. 2008). The 3σ upper limit of the persistent luminosity for our analyzed burst is 6 × 10³⁵ erg s⁻¹ in the energy range 0.1–200 keV (in't Zand et al. 2003a), which belongs to the quiescent state. In this case, the accretion disk is not expected to affect the NS atmosphere and the evolution of the spectra and the burst satisfies criteria from Suleimanov et al. (2016), i.e., the accretion luminosity less than 5% of the Eddington luminosity.

2.2. Absorption Edge

We took the advantage of the direct cooling method to determine the NS mass and radius of GRS 1747−312 as proposed by Suleimanov et al. (2017). The procedure is described briefly here. We use two NS atmosphere models from Nättilä et al. (2015), with the atmosphere composition of X = 0.352, Y = 0.118, Z = 40 Z_⊙ (Z_⊙ = 0.0134) for the abundances of hydrogen, helium, and metals, respectively, and the pure iron model. In these models the NS surface gravity, $\mathrm{log}g$, varies from 13.7 to 14.9 with a step of 0.1 for the pure iron and 0.15 for the Z = 40 Z_⊙ models. The models at intermediate $\mathrm{log}g$ were obtained by linear interpolation.

The direct cooling method suggests minimizing the function

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i=1}^{{N}_{\mathrm{obs}}}\left[\displaystyle \frac{{(w{\rm{\Omega }}-{K}_{i})}^{2}}{{({\rm{\Delta }}{K}_{i})}^{2}}+\displaystyle \frac{{({{wf}}_{c}^{4}{\ell }{F}_{\mathrm{Edd}}-{F}_{i})}^{2}}{{\rm{\Delta }}{F}_{i}^{2}}\right].\end{eqnarray} \tag{ 3 }$$

Here w, f_c, and ℓ, are the model spectral dilution factor, the color correction factor, and the flux (or luminosity) in units of the Eddington limit, respectively; Ω = (R(1 + z)/D)² is the angular dilution factor and F_Edd = GMc/(1 + z)κ_TD² is the observed Eddington flux, where κ_T = 0.2(1 + X) is the Thomson electron scattering opacity and X is the hydrogen mass fraction. The K_i and F_i are the ith observed blackbody normalization and flux during the cooling tail, where ΔK_i and ΔF_i are the corresponding errors. For each observed point (K_i, F_i) we take the minimum value of the normalized distance estimated in the square brackets of Equation (3) to the dense set of points along the model curve $(w{\rm{\Omega }},{{wf}}_{c}^{4}{\ell }{F}_{\mathrm{Edd}})$.

We consider a grid of masses M from 1 to 3 M_⊙ with a step of 0.01 M_⊙ and a grid of radii R from 9 to 18 km with a step of 0.01 km. The pairs (M, R) are ignored if the causality condition $R\gt 2.9{GM}/{c}^{2}$ is not satisfied (Lattimer & Prakash 2007). For a given pair (M, R) the surface gravity $\mathrm{log}g$ and the gravitational redshift z are computed. Then w and f_c are determined from the theoretical models (Nättilä et al. 2015) for the given atmosphere composition. We interpolate the sets of models to find the theoretical curve $w-{{wf}}_{c}^{4}{\ell }$ for the corresponding $\mathrm{log}g$. Then we fit the data in the time interval 68 ≤ t ≤ 96 s (see Figure 2), i.e., after the touchdown down to the flux level of 10⁻⁸ erg cm⁻² s⁻¹. We do not use the data at lower fluxes, because the model clearly deviates from the data (see Figure 3). We also note that the selected spectra corresponding to rather high flux and temperature are well fitted with the model without the edge (see Figure 2). This allows us to use atmosphere model spectra that have been fitted with the blackbody only to obtain w and f_c. The best-fit theoretical model computed for $\mathrm{log}g=14.3$ together with the observed K_bb–F_bb relation are shown in Figure 3.

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We note that for a given (M, R) and chemical composition the only fitting parameter in Equation (3) is the distance to the source, D. The minimum χ² for each pair of (M, R) and the global minimum together with the best-fit D are obtained with the regression method. We find the best-fit χ² = 13.78 for Z = 40 Z_⊙ and χ² = 14.66 for pure iron (both for 12 dof). In the M–R plane, Δχ² can be transferred to find the confidence regions, which are shown in Figure 4. It is clear that NS radii can lie within a reasonable range of 10 < R < 14 km (see e.g., Steiner et al. 2013; Nättilä et al. 2017) only for models with very high metal abundance, i.e., pure iron in our case. The obtained fits also limit the possible distance to the source (see the dotted curves in Figure 4).

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For illustrative purposes, we can draw a curve on the (M, R) plane corresponding to the observed Eddington temperature obtained from the best-fit parameters F_Edd = 1.90 × 10⁻⁸ erg cm⁻² s⁻¹ and Ω = 199 (km/10 kpc)² for the pure iron model shown in Figure 3. From the definition of the Eddington temperature (which is independent of the distance) we get (Suleimanov et al. 2011a):

$$\begin{eqnarray}&&{T}_{\mathrm{Edd},\infty }=9.81{({F}_{\mathrm{Edd},-7}/{\rm{\Omega }}[{(\mathrm{km}/10\mathrm{kpc})}^{2}])}^{1/4}\,\mathrm{keV}\end{eqnarray} \tag{ 4 }$$

where F_Edd,−7 = F_Edd/10⁻⁷ erg cm⁻² s⁻¹. The contour of constant Eddington temperature ${T}_{\mathrm{Edd},\infty }=1.72\,\mathrm{keV}$ is shown in Figure 4 by the red dashed curve for the pure iron model. It is in a good agreement with the M–R confidence regions (we do not expect that they fully overlap, because the value of ${T}_{\mathrm{Edd},\infty }$ is computed for $\mathrm{log}g=14.3$ only and in reality varies across the (M, R) plane). Moreover, the region of constant gravitational redshift 1 + z = 1.34 ± 0.11 overlaps with the 68%, 90%, and 99% M–R confidence regions for the pure iron model, which means a good consistency. However, for the Z = 40 Z_⊙ model, the redshift constraints are inconsistent with the M–R confidence region (see the lower contours in Figure 4) for reasonable NS radii.

In this work, we analyze the peculiar type I X-ray burst from GRS 1747–312, which showed strong discrete feature in the burst spectra. in't Zand et al. (2003a) fitted the feature by a broad emission line and claimed that two radius expansion phases, which correspondingly lasted 70 s for the slow one and 8 s for the fast one, occurred in GRS 1747–312. However, the broad emission line and the fast radius expansion phase are both difficult to explain. We found that the burst spectra are fitted well using the blackbody component with an additional photoionization edge from heavy elements. Then the presence of the fast radius expansion phase is not needed (see Figure 2).

During the cooling tail, the edge energies showed fluctuations, which cannot be solely from the limited energy resolution of RXTE/PCA. We note that the edge energies for the H-like Fe and H-like Ni are 9.278 keV and 10.8 keV, respectively. So we may observe gravitational redshifted edge energies between 9.278/(1 + z) − 10.8/(1 + z), i.e., 7.4–8.6 keV for 1 + z = 1.26, for a mixture of Fe/Ni. These values are close to the fluctuations, i.e., between 7.0 ± 0.4 and 9.0 ± 0.4 keV. In the PRE phase, the edge energies are systematically larger than those during the cooling tail, which may indicate changes in edge energy from the gravitational redshift variations.

4.1. Reason for the Vanishing of the Photoionization Edge around the Touchdown

4.2. Possibility of an Expansion Phase in the Cooling Tail

4.3. Effect of Ignorance of NS Spin

4.4. M–R of the NS in GRS 1747–312

4.5. Distance to GRS 1747−312/Terzan 6

The PRE burst we studied is the most intense of all bursts from GRS 1747−312 (in't Zand et al. 2003b; Galloway et al. 2008; Iwai et al. 2014). We find that the edge observed during the PRE phase and the cooling tail correspond to absorption from hydrogen-like Fe, Ni, or a mixture of Fe and Ni. The presence of the edge is confirmed by fits to the observed flux-normalization relation with the theoretical model, which requires a high metal abundance.

We showed that the M–R confidence region for even such a high metal abundance as 40 Z_⊙ is inconsistent with the recent constraints on the NS radius of <13.6 km coming from tidal deformability during an NS–NS merger. However, the M–R constraints obtained for pure iron are well consistent with this limit, giving an upper limit on the mass of the NS of 1.8 M_⊙. These constraints are also consistent with the gravitational redshift measurements from the absorption edge. The data then limit the distance to the source to D = 11 ± 1 kpc. Future measurements of the mass function and type of the companion star would help to improve the constraints on the NS mass and radius in GRS 1747−312.

We appreciate the referee for the comments and suggestions for improving our work. Z.L. thanks Tadayasu Dotani for the useful discussions. Z.L. was supported by the Swiss Government Excellence Scholarships. Z.L. thanks the International Space Science Institute and University of Bern for the hospitality. Parts of this work have been done during Z.L.'s visits to the University of Turku and the University of Tübingen. This work was supported by the National Key R&D Program of China (No. 2017YFA0402602), the National Natural Science Foundation of China (Grant Nos. 11703021, 1673002 and U1531243), and Hunan Provincial Natural Science Foundation of China (Grant Nos. 2017JJ3310 and 2018JJ3495). This research has been supported in part by the grant 14.W03.31.0021 of the Ministry of Education and Science of the Russian Federation (J.P., V.F.S.) and by the Deutsche Forschungsgemeinschaft grant WE 1312/51-1 (V.F.S.).

Software: Xspec (v12.8.2; Arnaud 1996).