New measurements of the cyclotron line energy in Cen X-3

X-ray binaries are the brightest X-ray sources in our galaxy. High mass X-ray binaries (HMXBs) are the binary star systems consisting of a neutron star or a black hole and a donor star with mass $\geq$ 10M_⊙. The persistent X-ray binaries are mostly powered by capture of matter from strong stellar wind of the companion star. For accretion onto a high magnetic field neutron star, the accreted material is channeled along the magnetic field lines onto the magnetic poles at relatively large distance from the surface of the compact object creating accretion funnels, where the X-ray emission is originated due to conversion of the gravitational potential energy of the infalling material to kinetic energy which is then released as X-rays due to shocks and dissipations into the accretion column and on the hot spots (Basko & Sunyaev 1975).
Cyclotron resonant scattering features (CRSF) or simply, cyclotron lines are usually seen in absorption against the continuum spectrum in many of these sources. In such strong magnetic fields, the energies of the electrons are quantized into equi-spaced Landau levels. Resonant scattering of hard X-ray photons on such electrons in line-forming region, results in cyclotron lines. CRSFs allow a direct measurement of the magnetic field since the energy of the former is directly related to the magnetic field as $E_{\rm{C}}=11.6\frac{B}{10^{12}\,\rm{G}}(1+z)^{-1}$n keV, where B₁₂ is the magnetic field strength in units of 10¹² G, n is the Landau level number, and z is the gravitational redshift at the line-forming region. n=1 and n=2, 3, 4.. correspond to the fundamental and harmonic cyclotron lines, respectively.
For a given source, the cyclotron line energy is often found to depend on X-ray luminosity L_X. The correlation between the two was first observed in the transient source V 0332+53, in which the line energy decreases with increasing X-ray flux (Tsygankov et al. 2006). A positive correlation of CRSF energy with luminosity was first discovered in Her X-1 by Staubert et al. (2007). Since then, several other X-ray pulsars have been studied for the CRSF energy-L_X relationship and it has been established that CRSF energy-luminosity relation is bimodal with source luminosity (Becker et al. 2012a) with the majority of sources showing a positive correlation (Staubert et al. 2019). Although, an unambiguous explanation is still lacking, different theoretical models have been proposed to explain these dependencies for e.g the shock-height model Becker et al. (2012a), or the reflection model of Poutanen et al. (2013).
In this paper, we focus on one of the most luminous persistent accreting X-ray pulsars in our galaxy, Cen X-3, first discovered with a rocket-borne detector (Chodil et al. 1967). Extensive follow-up observations with Uhuru revealed the binary and pulsar nature of the system (Giacconi et al. 1971, Schreier et al. 1972). The system is an HMXB consisting of a neutron star of mass 1.21$\pm$0.21 M_⊙ which emits pulsed X-rays every 4.8 s while orbiting an O-type supergiant v779 Cen (Krzeminski 1974) of mass and radius of 20.5$\pm$0.7 M_⊙ and 12 R_⊙, respectively every 2.1 days. Although a strong stellar wind emanates from the supergiant, an accretion disk fed by Roche lobe overflow was inferred from optical light curves by Tjemkes et al. (1986) in 1986, which supply most of the accretion fuel. The high luminosity of the star ( 5.0 $\times 10^{37}$erg s^-1; Suchy et al. 2008) also suggests that the predominant mode of accretion is via a disk, as does the detection of QPO from the source (Takeshima et al. 1991, Raichur & Paul 2008). The distance to the binary system is estimated to be $\sim$ 8 kpc (Krzeminski 1974).
The pulse phase averaged spectrum of X-ray pulsars is generally characterized by a flat power law with an energy index of 0.5-1.5 upto a high-energy cutoff at 10.0-20.0 keV. The analysis of BeppoSAX data shows that the broadband ( 0.12 - 100 keV ) spectrum of Cen X-3  is well fitted by an absorbed power-law continuum (photon index $\sim$ 1.2) modified by a high-energy rollover (with cutoff energy $\sim$ 14 keV and e-folding energy $\sim$ 8 keV) smoothed around the cutoff energy with a soft excess below 1 keV interpreted as a blackbody with kT $\sim$ 0.1 keV (Burderi et al., 2000). Additionally, iron K-emission lines at 6.4 keV, 6.67 keV and 6.97 keV are also clearly resolved (Ebisawa et al. 1996, Naik & Paul 2012). The 6.4 keV emission line is identified with the fluorescent iron K$\alpha$ line due to reprocessing by cold circumstellar matter surrounding the binary system (Nagase 1989), whereas 6.67 keV and 6.97 keV lines are considered to be originated in the highly photoionized accretion disk corona(Kallman & White 1989). The analysis of Ginga data (Nagase et al., 1992) showed that the spectrum at high energy is better fitted with a Lorentzian shape high energy turn over which resembles the effects of cyclotron scattering feature, the presence of CRSF at $\sim$ 28 keV has been confirmed by Santangelo et al. (1998) which implies a magnetic field at the surface of the neutron star of B = 2.98 $\times$ 10¹² G taking into account the effects of the gravitational field close to it.
In spite of being one of the brightest X-ray sources in the galaxy and one of the most studied accretion powered X-ray pulsars, the cyclotron line feature in Cen X-3, and especially its luminosity dependence is not studied extensively. Cen X-3 shows luminosity variation by a factor of upto 40 though it is a persistent X-ray source. Here we present timing and spectral analysis of two observations of Cen X-3 with the broadband X-ray missions Suzaku and NuStar. Along with detection of the cyclotron line in these two observations, we also compared the line energies with the previous reports, covering an X-ray luminosity range of 1.1-5.4 $\times 10^{37}$ ergs s^-1.

Cen X-3 was observed once each with the Suzaku observatory Mitsuda et al. (2007) and the NuSTAR (The Nuclear Spectroscopic Telescope Array; Harrison et al. 2013). The observation log is given in Table 1. An orbital phase resolved spectroscopy was carried out using the same Suzaku  observation that reported many pre-eclipse dips (Naik et al. 2011).

NuSTAR (Harrison et al. 2013), launched in 2012 is the first hard X-ray focusing telescope operating in the energy band 3.0-79.0 keV. It consists of two co-aligned telescopes that focus X-ray photons onto their respective Focal Plane Modules (FPMA and FPMB). Each module consists of a two-by-two array of CdZnTe pixel detectors, each with 32$\times$32 0.6mm pixels which provide a 12’ field of view, an angular resolution of 18" (FWHM) and energy resolution of 400 eV at 10 keV and 900 eV at 60 keV (FWHM).
The NuSTAR  data was processed using NUSTARDAS (v1.8.0) along with CALDB v20190627. To extract the data products we used source-centered circular regions of 110" radius for both FPMA and FPMB. Background regions were extracted with an equivalent area away from the source. No contamination from stray light was observed. We then applied barycentric correction to the NuSTAR  clean science event files to correct for X-ray photon arrival times using FTOOL barycorr. Light curves were extracted with a bin size of 20 ms and spectra from the corrected event files using the task nuproducts. The timing and spectral analysis was performed with HEASOFT v6.26.1 package.
Suzaku consists of two main payloads: the X-ray Imaging Spectrometer (XIS, 0.2-12 keV; Koyama et al. 2007) and the Hard X-ray Detector (HXD, 10-600 keV; Takahashi et al. 2007). The XIS consists of four CCD detectors of which three (XIS 0, 2 and 3) are front illuminated (FI) and one (XIS 1) is back illuminated (BI). The HXD comprises PIN diodes and GSO crystal scintillator detectors.
The Suzaku observation was made in 1/4 window mode and data reduction was done on the filtered ‘cleaned’ event files¹¹1http://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/abc/ following the reduction technique mentioned in the Suzaku ABC guide. We applied barycentric correction to all event files using aepipeline. In case of CCD data as obtained by XIS, we had to take care of pile-up which is two photons of lower energy being read as one with higher energy which may cause artifical hardening of the X-ray spectrum. We discarded photons collected within the portion of the PSF where the estimated pile-up fraction was greater than 4 % (determined using the FTOOLS task pileest) by choosing a source region with an annulus of $3^{{}^{\prime}}$ radius and excluding the inner 15 arc-seconds of this annulus. Background for the XIS were extracted by selecting circular regions of the same size of $3^{{}^{\prime}}$ radius in a portion of the CCD that was not significantly contaminated by the source X-ray mission. XIS lightcurves and spectra were therefore extracted for these source and background regions.

Being a photon counting detector, data from PIN detector have to be corrected for deadtime which is the time interval for which the detector electronics are processing one photon and thus cannot yet detect the arrival of another. This dead time correction was done using FTOOLS task hxddtcor. For the HXD/PIN, simulated ‘tuned’ non X-ray background event files (NXB) corresponding to the month and year of the respective observations were used to estimate the non X-ray background ²²2http://heasarc.nasa.gov/docs/suzaku/analysis/pinbgd.html(Fukazawa et al., 2009).
The XIS spectra were extracted with 2048 channels and the PIN spectra with 255 channels. Response files for the XIS were created using the CALDB version ‘20150312’. For the HXD/PIN spectrum, response files corresponding to the epoch of the observation were obtained from the Suzaku guest observer facility³³3http://heasarc.nasa.gov/docs/heasarc/caldb/suzaku/.

We have presented results from a detailed timing and spectral analysis of the HMXB Cen X-3 with Suzaku and NuSTAR. The pulse profiles are found to vary with energy. Although similar dependence was presented in previous works by Suchy et al. (2008) and Raichur & Paul (2010), we observed an additional feature, a bump at $\phi\sim$ 0.05 below 25 keV in both Suzaku and NuSTAR observations. A similar bump at $\phi\sim$ 0.05 was observed in 0.1-1.8 keV energy range by Burderi et al. (2000).
We also presented measurements of the cyclotron line feature in the Suzaku and NuSTAR data. In both Suzaku and NuSTAR spectra, we use the gaussian absorption model GABS to find the cyclotron line at 30.29 keV and 29.22 keV respectively.
To look for any variation of cyclotron line with luminosity, we used the line measurements from earlier observations of Cen X-3 . The energy of cyclotron resonance scattering feature E_c in the pulse averaged X-ray spectrum of Cen X-3 as reported in several papers since its discovery is presented in Table 3. The flux for all the previous measurements were reported for 2-10 keV energy band except for GINGA-LAC . For the comparison, the 2-30 keV energy band flux reported for GINGA-LAC  measurement was corrected in 2.0-10.0 keV energy range using $f_{c}=f^{po}\times\frac{f_{R}}{f^{po}_{R}}$ where $f^{po}$ and $f^{po}_{R}$ are the power law model flux in 2-10 keV band and 2-30 keV energy range respectively with $\Gamma$=1.01 and norm${}_{po}=1$ and $f_{R}$ is the flux in the 2-30 keV energy range as reported in the paper. It is noted that different continuum and cyclotron line models were used to fit the spectra from different instruments. To allow a comparison of the values obtained with the previous measurements, we fitted the NuSTAR spectrum with the same models as adopted in these works for the spectrum obtained with GINGA-LAC,  RXTE  and BeppoSAX (see Table 3). We obtained a CRSF energy value of 29.2   keV with the models used for RXTE  and BeppoSAX  spectrum which is consistent with the value obtained with our NuSTAR  model. For the Nagase et al. (1992) model used for GINGA-LAC  spectrum, in the final fit, the high-energy cutoff was replaced by Lorentzian cyclotron line component (cylabs; Mihara et al. (1990), Makishima et al. (1990)). This model provided a value of 27.5   keV for NuSTAR  spectrum compared to the value 29.2   keV obtained with gabs. The CRSF energy measured with GINGA-LAC  has larger error and it is also less certain as the spectrum was just upto above 30   keV and barely covered the cyclotron line. We also note here that the GINGA-LAC  results showed a much larger optical depth of the CRSF compared to all the other observations. As the spectrum did not cover as high energy as the other instruments like RXTE , BeppoSAX , NuSTAR  and Suzaku , it also did not require a high energy cutoff. We notice that except one CRSF measurement with Beppo-SAX (Santangelo et al. 1998), all are consistent with a CRSF energy in the range of 29.5-30.0 keV over a luminosity range of 1.1-5.4$\times 10^{37}$ergs s^-1, while sources like V 0332+52 shows about 20$\%$ CRSF energy variation in the same luminosity range (Tsygankov et al. 2006). A lower CRSF value in one of the BeppoSAX  observations, however, corresponds to a luminosity that is in the middle of this entire luminosity range and therefore does not indicate a luminosity dependence of the line energy. An average value of E${}_{cyc}=$ 29.7 keV was calculated considering the minimum and the maximum observed cyclotron line energies with the respective uncertainties. Including all the reported results, the upper limit on CRSF energy variation between measurements is $\pm$ 7.7% ($\sim$ 2.3 keV) around the average value including the statistical errors and any systematic errors in each of the measurements. We do not find a correlation of the cyclotron line energy with luminosity (Fig.  5) for Cen X-3. While comparing spectral parameters like the CRSF using data from different observations, inter-calibration of different instruments also needs to be considered. In Cen X-3, the variation between different measurements is within 2.3 keV of the average value while in 4U 1538-52, the variation is within about 1.5 keV of the average value (Varun et al. 2019, Hemphill et al. 2019). Lack of detection of significant variation in the cyclotron line energy also indicates good inter-calibration of the different instruments within a few percent.
Such studies for the variation of cyclotron line with luminosity has been carried out earlier for other X-ray pulsars, notable ones being Her X-1 and Vela X-1 both of which show a positive correlation (see., Staubert et al. 2019 for review) with luminosity. Like in the case of V 0332+53, the energy of the fundamental CRSF in another brightest known CRSF source, SMC X-2 (Jaisawal & Naik 2016) is negatively correlated with L_X, while Her X-1 (Staubert et al. 2007), GX 304-1 (Klochkov et al. 2012; Malacaria et al. 2015;Rothschild et al. 2016), A 0535+26 (Sartore et al., 2015), Vela X-1 (Fürst et al., 2014), Cep X-4 (Vybornov et al., 2017) show a positive correlation. There are also X-ray pulsars with tentative evidence of correlation between CRSF energy and luminosity but so far not confirmed, such as 4U 0115+63 (Iyer et al., 2015) and 4U 1538-522 (Hemphill et al., 2014). It is now a general consensus that the variation of cyclotron line energy is due to the change in the line formation region above the neutron star surface with X-ray luminosity (Becker et al., 2012b). For typical luminosities less than 10³⁷ erg s^-1, the matter stops close to the stellar surface and therefore, the location of line forming region is independent of X-ray flux. Above this luminosity, matter is stopped well above the stellar surface because of shock formation (Coulomb interaction dominated). Since the ram pressure increase with increased accretion rate, it pushes the shock region towards the neutron star surface where the magnetic field is higher. This causes the positive correlation of line energy with flux (Staubert et al., 2007). Furthermore, if the Eddington luminosity exceed the critical luminosity ( $\sim$ 3 $\times$ 10³⁷ erg s^-1 ) for typical neutron star parameters, a radiation-dominated shock forms. With the increase in accretion rate, this shock formation region move away from the stellar surface and an anti-correlation of the CRSF energy with luminosity is expected.
A long-term decay in CRSF energy between 1992 to 2012 was assessed in Her X-1 (Staubert et al. 2014). Similar to Her X-1, long-term decrease was found in Vela X-1 (La Parola et al. 2016). The observed decrease could be attributed to the change of magnetic field configuration at the polar cap or the geometric displacement of the line forming region (Staubert et al. 2014). On the contrary, a positive trend with 5$\%$ increase in CRSF energy from 1996 to 2012 was observed in 4U 1538-52 (Hemphill et al. 2016). Although the evidence of a long-term change in CRSF energy has been seen in few sources until now, previous works have noted that the centroid line energy in Cen X-3 is stable over the past 14 years, at 31.6$\pm$ 0.2 keV as seen in the Swift/BAT data (Ji et al., 2019). The current work examines the possible variation of the cyclotron line energy of Cen X-3 over a period of close to 27 years and concludes that there is no evidence for a time variability of the CRSF nor a luminosity dependence.