POSSIBLE DETECTION OF AN EMISSION CYCLOTRON RESONANCE SCATTERING FEATURE FROM THE ACCRETION-POWERED PULSAR 4U 1626−67

Suzaku is the fifth Japanese X-ray satellite (Mitsuda et al. 2007) to be launched and is equipped with two different instruments. One instrument is an X-ray imaging spectrometer (XIS; Koyama et al. 2007), a charge-coupled device camera at the focus of the X-ray telescope (XRT; Serlemitsos et al. 2007), covering the 0.2–12 keV energy range. There are four XIS units; three of them (XIS-0, XIS-2, and XIS-3) are front-illuminated (FI) while the other one (XIS-1) is back-illuminated (BI). The other instrument is an HXD (Takahashi et al. 2007), which consists of PIN silicon diodes (HXD-PIN; 10–70 keV) and Gd₂SiO₅Ce (GSO; 50–600 keV) scintillators. 4U 1626−67 was observed by Suzaku on 2006 March 9 UT 01:18 through March 11 19:38 at "XIS nominal" pointing position. The XIS operated in standard clocking mode and included the "1/8 window" option in order to have a time resolution of 1 s, without a charge injection function.

We used data produced by Suzaku pipeline processing version 2.0.6.13 with the calibration versions hxd-20090515, xis-20090403, and xrt-20080709, and the software version HEADAS 6.5.1.

XIS and HXD events were screened by using standard criteria. We discarded events collected when Earth's limb was less than 5°, when Earth's day–night boundary angle from the line of sight was less than 25°, or when the spacecraft was in an orbit phase within 436 s (for the XIS) or 500 s (for the HXD) of the South Atlantic Anomaly ingress/egress. For XIS-1, we also excluded events in the time interval between 2006 March 10 UT 06:58:30 and 07:20:54, because the cooling system was not properly working during this period. We accepted only XIS events with standard grades (0, 2, 3, 4, and 6) in the analysis.

XIS spectra and light curves were extracted from a circle with a radius of 4.3 arcmin centered at the source. Spectra from the three FI XIS sensors were summed together and the XIS intensity in the 0.4–10.0 keV energy band was ∼5 counts s⁻¹ for each sensor. We accumulated the XIS background spectra from a source-free region having the same exposure area as that of the corresponding sensors. The derived background spectra exhibited an intensity of ∼0.02 counts s⁻¹ for each sensor in the 0.4–10.0 keV range, and are considered negligible.

HXD screened events were used to obtain spectra and light curves for the PIN and GSO sensors. The HXD-PIN simulated non X-ray background (NXB) model was provided by the Suzaku HXD team, and we used the METHOD = LCFITDT and METHODV = 2.0 data sets (Fukazawa et al. 2009). The systematic uncertainty of the NXB model is estimated to be 2.31% for a 10 ks exposure in the 15–40 keV energy band (Fukazawa et al. 2009). Hereinafter, we assume 3% systematic errors in the HXD-PIN analyses, and the cosmic X-ray background spectra were subtracted by using data acquired by HEAO-1 (Boldt 1987). However, the source was not detected by the HXD-GSO. The NXB-subtracted HXD-GSO light curve and spectrum exceeded the HXD-GSO NXB by ∼1%, and the latter were within typical systematic uncertainties (Fukazawa et al. 2009). Net exposures were 102.7 ks for XIS-0, 2, and 3, 101.4 ks for XIS-1 and 87.6 ks for the HXD.

For the arrival time of each XIS and HXD-PIN event, barycenter correction was performed with the tool aebarycen (Terada et al. 2008). We surveyed the HXD-PIN data by using a folding technique to obtain a best spin period of P_(Suzaku) = 7.67795(9) s. This period is consistent with the spin-down trend that started to be observed from 1990 onwards, and that is calculated by using the spin-down rate of $\dot{\nu } \sim -4.8 \times 10^{-13}$ Hz s⁻¹ measured with the Swift satellite over the period 2004–2007 (Chakrabarty et al. 1997; Camero-Arranz et al. 2010).

XIS and HXD background-subtracted light curves of 4U 1626−67 are shown in Figure 1. The light curves are plotted using a time bin of 7678 s, a multiple of P_(Suzaku). The XIS and HXD light curves have an intensity variation of less than 7%, and the hardness ratio between them is approximately constant; the reduced chi-squared (χ²) value is about 1 when fitting a constant model to the hardness ratio. The average and the 3σ level are shown in Figure 1. As a result, we confirmed that there is no significant spectral variation. Thus, X-ray spectra were extracted by using data over the entire observation.

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The top panel of Figure 2 shows the broadband 4U 1626−67 phase-averaged raw count rate spectrum normalized by a Crab Nebula spectrum that was observed for calibration purposes. XIS source data were normalized by using a canonical model of the Crab Nebula spectrum, since spectra from the Crab Nebula suffer from pile-up. HXD data were normalized by an HXD Crab Nebula spectrum observed on 2006 March 30 taken for the same observation parameters—position of the source with respect to the instrument FoV, grade criteria, and PIN threshold file (ae_hxd_pinthr_20060727.fits)—as for 4U 1626−67. The 4U 1626−67 source intensity is about 20 mcrab at 20 keV, and the normalized spectrum is characterized by three main features: a soft X-ray excess below ∼3 keV, as reported by several authors (Angelini et al. 1995; Schulz et al. 2001; Krauss et al. 2007), a power-law continuum, and a dip feature at ∼35 keV.

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To model the phase-averaged spectrum, we fit the data with a ∼0.24 keV blackbody for the soft excess, a negative and positive power-law times exponential (NPEX) model (Mihara 1995; Makishima et al. 1999) and a Gaussian-absorption (GABS) model (Soong et al. 1990) for the continuum above 3 keV, and a standard photoelectric absorption. The NPEX model

$$\begin{equation} {f(E) = (A_{n}E^{-\alpha }+A_{p}E^{+\beta }) \exp \left(-\frac{E}{kT}\right), } \end{equation} \tag{ 2 }$$

where E is the energy of an incident photon and kT is a plasma temperature (also called the cutoff energy), has two power-law components with indices α and β. The negative α term describes the spectrum at low energy, and the positive β term, which dominates as the energy increases, simulates the Wien peak in the unsaturated Comptonization regime when β = 2.0.

The best-fit model and its residuals are plotted in the lower panel of Figure 2. Above 3.5 keV only 1% of the NPEX negative term is contributed by the blackbody component. Therefore, hereinafter, we ignore XIS data below 3.5 keV and exclude the blackbody component from the fit.

To evaluate the statistical significance of the CRSF in the phase-averaged spectrum, first, we fit the spectrum with only NPEX continuum or NPEX × GABS model. The residuals of the NPEX with GABS model for energy bands above 3.5 keV are shown in Figure 3(a), and the best-fit parameters are listed in Table 1. Second, we tested the significance using the F test routine of Press et al. (2007). In this case, the F statistical value is defined as

$$\begin{equation} {F = \frac{\chi _{1}^{2}/\nu _{1}}{\chi _{2}^{2}/\nu _{2}}, } \end{equation} \tag{ 3 }$$

where χ²₁ and χ²₂ are statistical chi-squared, ν₁ and ν₂ are degrees of freedom corresponding to the results of fittings using models 1 and 2 (in this case model 1 is only NPEX continuum and model 2 is NPEX with multiplicative component), respectively. The derived F statistical value is 3.1, which indicates that the probability of chance improvement of the χ² is 3.7 × 10⁻¹². Thus, the CRSF is a statistically significant feature in the phase-averaged spectrum. We also found that the residuals in Figure 3(a) have a complex structure near the Fe-emission line energy around 6.6 keV. The fit improves by the addition of a Gaussian Fe-line model with an energy of 6.62 keV, a width (σ_Fe) of 0.37 keV, and an equivalent width (EW) of 33.3 eV (Figure 3(b) and Table 1). These values are statistically consistent with the ASCA EW upper limit of <33 eV for an Fe-emission line in the 6.4–6.9 keV range (Angelini et al. 1995). The broad width may indicate the presence an Fe-line complex. If we use three narrow Gaussian Fe lines, the Fe-line energies are 6.37^+0.07_{− 0.08}, 6.61^+0.05_{− 0.07}, and 6.92^+0.04_{− 0.04} keV with corresponding EWs of <11.1, <12.2, and <17.4 eV, although the fit is not improved significantly and we would not be able to distinguish whether the Fe-emission line structure is made by three lines or not, due to the energy resolution of XIS (∼150 eV). The X-ray unabsorbed fluxes in the 3.5–10 keV and 10–60 keV energy bands are 1.27^+0.01_{− 0.16} × 10⁻¹⁰ erg cm⁻² s⁻¹ and 4.02^+0.46_{− 0.88} × 10⁻¹⁰ erg cm⁻² s⁻¹, respectively, and the hard X-ray flux is consistent with the BeppoSAX observation (Orlandini et al. 1998). Exchanging the GABS model with a cyclotron absorption model (CYAB; Mihara et al. 1990) also fits the data well (Figure 3(c) and Table 1).

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If we replace the NPEX model by an exponential cutoff power-law model (ECUT, which is the powerlaw*highecut model in Xspec; White et al. 1983) and fit the data with a GABS model, we obtain an acceptable χ² value (see Table 1), but substantial residual structures are seen above 20 keV (Figure 3(d)). Although the CRSF energy agrees with BeppoSAX observations (Orlandini et al. 1998), the best-fit continuum model is inconsistent with BeppoSAX results.

Phase-resolved spectra acquired by HEAO-1, Tenma, and RXTE (Pravdo et al. 1979; Kii et al. 1986; Coburn 2001) show a strong phase dependence in the continuum emission of 4U 1626−67. Suzaku XIS and HXD folded light curves also indicate changes across the pulse (Figure 4). Specifically, while the 10–30 keV/3.5–10 keV ratio maintains the characteristics of the individual light curves, the 30–50 keV/10–30 keV ratio indicates spectral differences between phases 0.0–0.3 and the other phases.

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To investigate spectral changes across the pulse, we divided the events into eight phase-resolved spectra (Figure 5) and normalized these spectra by the Crab Nebula spectrum by using the method described in Section 3.2 (Figure 6). The Crab Ratios show that the ∼20 keV peak is more prominent at higher pulse flux. Additionally, the ratios flatten at lower pulse flux and the energy of the resonance feature changes. The resonance features are particularly outstanding in the dim phase spectrum (ϕ = 0.125–0.250), where the hardness ratio (Figure 4) shows a large change in these features.

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We then performed spectral fitting to the phase-resolved spectra with the NPEX continuum and the Fe-emission line model in order to establish the pulse-phase dependence of the continuum and the CRSF. The Fe-line energy and the width of the Gaussian function were fixed at values obtained from the averaged spectrum. The parameters from the spectral fitting are listed in Table 2, and the ratios between the original data and the best-fit model are shown in Figure 7. We found that the ratio for the dim phase (ϕ = 0.125–0.250) spectrum exhibits a monotonic increase above 30 keV, and the residuals show evidence for the existence of an emission feature rather than an absorption (Figure 8(a)). In contrast, the other phases have a V-shaped ratio caused by a CRSF absorption feature. Moreover, the fitting results for the dim phase spectrum show that the A_p parameter is unconstrained, strongly suggesting that the continuum spectrum at the dim phase requires only the upper limit of the high-energy cutoff component. In other words, the result makes the NPEX model effectively a power-law times exponential cutoff model (cutoffpl in Xspec). The result is consistent with the trend that the 20 keV peak in the Crab Ratios is less prominent at lower pulse flux. We also tried other empirical models applied to an accretion-powered pulsar, ECUT, and a power law with Fermi–Dirac cutoff (Tanaka 1986), and find that their best-fit cutoff energies are consistent with 0. In other words, a power-law times an exponential cutoff model is the only one able to fit the dim phase spectrum. For this reason we fit the dim phase spectrum by using the NPEX model with fixed A_p = 0. As we can see in Table 2, the difference between the χ² values for freely selected A_p and for fixed A_p = 0 is negligible. Therefore, we henceforth fix A_p = 0 for the NPEX model when fitting the dim phase spectrum.

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Next, we included the GABS model and refit the phase-resolved spectra. The resulting parameterized models fit all of the phase-resolved spectra well (see Table 3 and Figure 9), and residuals above 30 keV in the dim phase were eliminated (see Figure 8(b)). We also evaluate the significance of including a GABS component using the same method discussed in Section 3.1. The derived probabilities are summarized in Table 3, which shows that the absorption factor is not statistically significant in the dim phase. This significance did not change even when we adopted the CYAB model (as opposed to the GABS model as the cyclotron feature model) for spectral fitting.

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Since the GABS model reproduces an absorption feature, we fit the phase-resolved spectra by the NPEX plus a Gaussian model in which we allowed the Gaussian normalization to be both positive and negative. The derived parameters are shown in Table 4 and Figure 10. The results indicate that the emission line produces the residuals from the NPEX fitting in Figure 8(a). We can evaluate how much the additional term improved the fit using the F test for additional terms (Bevington 1969). The F statistical value, hereafter called F_χ, is defined as

$$\begin{equation} {F_\chi = \frac{\big(\chi _{1}^{2} - \chi _{2}^{2}\big)/(\nu _{2} - \nu _{1})}{\chi _{2}^{2}/\nu _{2}}. } \end{equation} \tag{ 4 }$$

Each suffix denotes model 1 and 2, NPEX only and NPEX + Gaussian model, respectively. The derived probability from F_χ also summarized in Table 4. The results show that the data support the presence of the emission line in the dim phase with F_χ of 7.688, corresponding to a probability of chance improvement of the χ² of 1.9 × 10⁻⁴. The residuals of the fitting are shown in Figure 8(c). The obtained resonance energy, E_a = 40.5^+13.7_{− 14.7} keV, is statistically consistent with those observed in the other phases.

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To examine the chance probability of improvement of the derived F value, we simulate the spectra following a procedure similar to Section 5.2 of Protassov et al. (2002). First, we simulate 10,000 data sets using "fakeit" in XSPEC Version12 according to the NPEX (A_p = 0) model with parameters fixed at best-fit values listed in Table 2, same instrumental response, background files, and same exposure time. Each data set is binned using same binning as that used for real data. Second, we fit the simulated data using only NPEX (A_p = 0) and NPEX (A_p = 0) + Gaussian model allowing their normalization to be negative. Third, we calculate the F_χ derived by these two model fittings. Last, we evaluated the number of simulated spectra with F_χ exceeding the 7.688, which is derived by fitting of real data to estimate the approximate probability. The derived histogram of the F_χ is shown in Figure 11 and the evaluated chance probability is 3.0 × 10⁻⁴ which is consistent with the F_χ value obtained from real data using Equation (4). In order to evaluate the effect of systematic error of the HXD-PIN NXB model, we also refit the dim phase spectrum taking into account the 3% systematic errors of HXD-PIN. The F_χ is 7.688^+2.523_{− 2.490} and the probability is between 2.91 × 10⁻³ and 1.53 × 10⁻⁵. Therefore, even though the NXB level of HXD-PIN is underestimated, we have possibly detected the emission line at the cyclotron resonance energy in the dim phase. Although there is a ∼85% possibility that the structure in the dim phase is produced by an absorption feature, we stress that the continuum requires a hard component with a large cutoff energy, in addition to a wide and deep absorption feature, as seen in Figure 12. Furthermore, the kT value at the dim phase matches those at the other phases with the emission model, whereas a large jump in the value is required with the absorption model, as shown in Figure 9.

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