Discovery of Two Cyclotron Resonance Scattering Features in X-ray Pulsar Cen X-3 by Insight-HXMT

The accreting X-ray pulsars have strong magnetic field, and when the magnetic pressure dominates the gas in the accretion disk, the flow of infalling gas is channeled along magnetic field lines to the surface of neutron star. Most of the gas fall on an area which is less than the whole surface area of the neutron and form the "hot spot" where the kinetic energy of gas is converted into radiation. Due to the magnetic axis and rotation axis of the neutron star may not be parallel, as the star rotates, the radiation from the hot spots forms a pulse profile with the same rotation period of neutron star (Davidson, 1973). The Larmor radius of infalling electrons becomes comparable to or smaller than the electrons’ de Broglie wavelength in such a strong magnetic field, then the quantum effects of electronic orbital radius and energy become unignorable (Mészáros, 1992). The photons are resonantly scattered by the electrons near the neutron star surface and absorption lines will appear on the X-ray spectra, the so-called cyclotron resonance scattering features (CRSFs). The energy of fundamental lines which correspond to the cyclotron scattering from the ground level to the first excited Landau level is relevant to the magnetic field as

where $B_{12}$ is the magnetic field in units of $10^{12}\ \rm G$, and $z$ is the gravitational redshift near the surface of a neutron star.

The neutron star system Cen X-3 discovered by Uhuru (Giacconi et al., 1971) has a spin period of $\sim 4.8\ \rm s$ (Schreier et al., 1972) and an orbital period of $\sim 2.08\ \rm d$ (Falanga et al., 2015), is a high-mass X-ray binary pulsar located at a distance of $\sim 6.9$ kpc based on the recent Gaia measurement (Van Den Eijnden et al., 2021). The system consists of a neutron star with the mass of 1.21±0.21 $M_{\odot}$ and an O-type supergiant v779 Cen of mass 20.5±0.7 $M_{\odot}$ (Ash et al., 1999) with radius of 11.4$\pm$0.7$R_{\odot}$ (Falanga et al., 2015). The eclipse lasts for 20$\%$ of the nearly circular orbit (Nagase, 1989) with the orbital eccentricity below 0.0016 (Bildsten et al., 1997). The mass transfer between the high luminosity of Cen X-3 and supergiant via Roche lobe overflow is inferred from the optical light curves of this system (Tjemkes et al., 1986). The pulse profile shape also changes with energy, the pulse profile is clearly single-peaked at high energy (roughly above 10 keV), and double peak at low energy observed by $Ginga$ (Nagase et al., 1992) and $BeppoSAX$ (Burderi et al., 2000). Cen X-3 is a bright X-ray source, with the observed X-ray average luminosity about $(0.1-1)\times 10^{38}$ erg s^-1 (White et al., 1983) and can sometimes locate in the low luminosity (Nagase et al., 1992).

The cyclotron absorption line near 30 keV has been observed in the spectrum of Cen X-3 through several X-ray missions. Nagase et al. (1992) reported the presence of an absorption line at $\sim$ 30 keV using the combination of the power law continuum and a Lorenzian shape by Ginga, which later was identified as cyclotron resonant scattering by BeppoSAX (Santangelo et al., 1998). RXTE observations (Suchy et al., 2008) also suggested a cyclotron resonance scattering feature at about 31 keV with a continuum described by the Fermi-Dirac cut-off model ($fdcut$, Tanaka 1986). Tomar et al. (2020) used the spectra of Suzaku and NuSTAR, and determined the cyclotron line energy $\sim$ 30.29 keV and 29.22 keV, respectively. This is also acknowledged that the spectrum of an X-ray pulsar varies with the pulse phase. Burderi et al. (2000) observed the cyclotron line energy decreasing from 36 to 28 keV along the peak of pulse profile. During the RXTE observations by Suchy et al. (2008), the cyclotron line energy of Cen X-3 increased during the early rise of the main peak, followed by a gradual decrease. The CRSF energy of Cen X-3 does not show a tendency of decrease/increase during the ten years of observations (Ji et al., 2019). It is still an open question whether there are multiple cyclotron features in Cen X-3, and there is no evidence of other absorption features in the spectrum for Cen X-3 in previous observations yet.

In this paper we report the results of a spectral analysis of the broad band spectrum ($2-105$ keV) of Cen X-3 observed with the Insight-HXMT. We confirm the presence of two cyclotron absorption features at $\sim 28$ and $\sim 47$ keV in the spectrum of Cen X-3 at the first time. In Section 2 we present the observations and the data extraction. Timing analysis and the X-ray spectral analysis including phase-averaged spectrum and phase-resolved spectroscopy are presented in section 3. We make a conclusion of the discovery of two cyclotron lines in Cen X-3 and a brief discussion is shown in Section 4.

Insight-HXMT is the first X-ray astronomical satellite in China, launched on 2017 June 15. Three kinds of main scientific payloads aboard the Insight-HXMT consist of the High Energy X-ray telescope (HE) operating in $20-250$ keV Liu et al. (2020), the Medium Energy X-ray telescope (ME) operating in $5-30$ keV Cao et al. (2020) and the Low Energy X-ray telescope (LE) operating in $1-15$ keV Chen et al. (2020). The detector areas of the three telescopes are 5100, 952, and 384 $cm^{2}$, respectively. HE detectors have the large area for hard X-ray studies, with the energy resolution of $\sim$15$\%$ at 60 keV.

For each observation, the Insight-HXMT Data Analysis Software (HXMTDAS) v2.04 is used to analyze data (more details on the analysis processes can refer to the previous work, e.g., Wang et al. 2021; Chen et al. 2021). In order to take advantage of the best screened event file to generate the high-level products including the energy spectra, response file, light curves and background files, we use tasks $he/me/lepical$ to remove spike events caused by electronic systems and $he/me/legtigen$ be utilized to select good time interval (GTI) when the pointing offset angle $<0.04^{\circ}$; the pointing direction above earth $>10^{\circ}$; the geomagnetic cut-off rigidity >8 GeV and the South Atlantic Anomaly (SAA) did not occur within 300 seconds.

Cen X-3 has been observed frequently by the pointing observations of Insight-HXMT. We concentrated on two observations identified as the Exposure IDs P010131100111 on July 26, 2017 and P010131101602 on June 27, 2018 when Cen X-3 reach a mean X-ray luminosity of $\sim 10^{38}$ ergs s^-1 from $2-105$ keV (also see the spectral analysis results in Section 3). The ExpID P010131100111 lasted for $\sim$ 25 ks from MJD 57960 13:49:17 to 20:43:47 with the mean HE count rate of $\sim 251.4$ cts/sec, and the ExpID P010131101602 lasted 6.7 ks from MJD 58296 05:41:09 to 07:34:09 with the HE count rate of $\sim 199.9$ cts/sec. Since the two observations have high flux levels, the high S/N ratio will increase sensitivity and spectral line studies, particularly for HE detectors, which makes it possible for us to measure the hard X-ray energy spectrum of the source with high accuracy. The final data analysis was performed with the XSPEC 12.11.1 version (Arnaud, 1996). All uncertainties are quoted at the 3$\sigma$ confidence level.

In this section we present the timing analysis and detailed spectral results including the phase-averaged and phase-resolved spectroscopy based on $Insight$-HXMT data, which aims to confirm two CRSFs discovered in Cen X-3.

In this work, we investigated the X-ray properties of accreting X-ray pulsar Cen X-3 from $2-105$ keV. In the both phase-average spectral analysis and phase-resolved spectroscopy, we not only confirm the CRSF at $\sim 28$ keV, in particular, we have detected one additional feature at $\sim 47$ keV with the high significance levels, thus making Cen X-3 be one of the X-ray pulsars with more than one cyclotron absorption line. The existence of two CRSFs in Cen X-3 is not dependent on the continuum spectral models (e.g., HighECUT and NPEX) and spectral line profile models (gabs and cyclabs). During the observations with two cyclotron absorption lines reported, Cen X-3 had the mean X-ray luminosity of $\sim 10^{38}$ erg s^-1 from 2 – 105 keV assuming a distance of $\sim$ 6.9 kpc. In the phase-resolved spectrum results in Fig. 5. The energies of both the fundamental and harmonic cyclotron lines evolve throughout the pulse phase, and similar to the shape of the pulse profile. Interestingly, the ratio of two line centroid energies does not change significantly and stabilizes in a narrow value range of $1.6-1.7$ over the pulse phase.

The observed X-ray luminosity varies over the pulse phase from $\sim(4-13)\times 10^{37}$ erg s^-1. In addition, the centroid line energies of the cyclotron absorption features versus the pulse phase is also derived. In Fig. 6, we presented energies of both the fundamental (blue point) and first harmonic (red point) of the cyclotron absorption lines detected in the spectrum of the pulsar Cen X-3 versus its luminosity, with the first harmonic line energy ranging from $\sim 43-50$ keV and the energy of fundamental line in the range of $\sim 25-32$ keV. The centroid line energies have no significant correlation with luminosity, and still show the possible trend of lower line energies at higher luminosity. This relation may connect to a critical luminosity which divides two accretion dynamic regions containing the super-critical and sub-critical cases in accreting pulsars (Becker et al., 2012). When $L_{X}>L_{\rm crit}$, plasma is decelerated by the radiation-dominated shock. Below the shock altitude, the photons which break down the balance between downward advection and upward diffusion of radiation are trapped by advection, although they eventually diffuse the column walls to form the observed X-ray spectrum. The emission height varies in proportion to X-ray luminosity in this case which results in an anti-correlation between $E_{\rm cyc}-L_{X}$. While in the subcritical case, the gas still makes its initial deceleration through a radiation-dominated shock, the final stopping occurs via direct Coulomb interactions caused by accreting ions lose energy to electrons close to the surface of the accretion column. Then the excited electrons return to the ground state via radiative dipole transition so that a significant fraction of these photons will escape through the walls of the column (Nelson et al., 1993), which makes a positive relation between $E_{\rm cyc}-L_{X}$. For the case of Cen X-3, we assume that neutron star mass and radius values $M_{*}=1.21M_{\odot}$ (Ash et al., 1999) and $R_{*}$ = 10 km, and $\varLambda$ = 0.1 and $w=1$ based on the theoretical considerations (Becker et al., 2012), $L_{\rm crit}\sim 3.5\times 10^{37}erg\cdot sec^{-1}$. Thus Cen X-3 is located in a super-critical regime during our observations, and generally an anti-correlation of $E_{\rm cyc}-L_{X}$ is expected. For the phase-resolved line energies versus the corresponding luminosity (Fig. 6), the relation is not obvious yet. At present the $E_{\rm cyc}-L_{X}$ relations are generally reported in the average spectrum of X-ray pulsars (Staubert et al., 2019), thus much more observational data would help to check the relation in Cen X-3 (work in preparation with the Insight-HXMT data from 2018-2021).

In spectral analysis of Insight-HXMT data, we perform the fit with the analytical models (e.g., NPEX, HighECut), deriving a photon index of $\sim 0.7-1.2$, and the cutoff energy of $\sim 13$ keV with a column density of $\sim(1.8-2.3)\times 10^{22}$ cm^-2. The observed spectral properties could be also compared with the physical model proposed by Becker & Wolff (2006) which calculates emitted spectra from an X-ray pulsar accretion column due to the bulk and thermal Comptonization of bremsstrahlung, cyclotron, and blackbody seed photons. They also modeled and fitted the spectrum of Cen X-3 taking a distance of 8 kpc (6.9 kpc in our case), using a hydrogen column density of $N_{H}=2\times 10^{22}\rm cm^{-2}$ in order to reproduce the observed low-energy turnover. The cut-off energy could be related to the electron temperature ($T_{e}\sim 3\times 10^{7}$ K) of the Comptonizing plasma, and the relatively flat shape at lower energies with $\Gamma<2$ can be ascribed to the contribution of thermal Comptonization. Our measurement on the fundamental cyclotron line energy around 28 keV is consistent with the previous studies and model spectrum of Becker & Wolff (2006), while the harmonic line around 45 – 48 keV is not included in their model.

The straightforward interpretation for two cyclotron absorption features is that the absorption line located in $\sim 47$ keV is the first harmonic of the identified 28 keV line as the fundamental CRSF. However, we find that the line energies of two cyclotron lines do not follow the relation $E_{2}=2E_{1}$, while $E_{2}/E_{1}\sim 1.6-1.7$ for the pulse phase-resolved spectra, and $\sim 1.7-1.8$ also for the average spectral cases (see Table 1). A few X-ray pulsars show a similar phenomenon, e.g., MAXI J1409-619 (Orlandini et al., 2012), GX 301-2 (Ding et al., 2021). This disagreement with the line energy scale relation can be explained by that the first harmonic line is produced by pure absorption (Nishimura, 2003), while for harmonic resonance scattering features, other effects such as multiple scattering and photon spawning also take place (Schönherr et al., 2007). It has been proposed that the absorption features are not due to one line, maybe form independently in different regions (Fürst et al., 2018; Ding et al., 2021), then the two absorption lines are expected to form at different heights above the surface of the neutron star, the harmonic line situated at the surface of the NS, while the fundamental line at the height ($h\sim 1.5-2$ km based on the ratio of $E_{2}/E_{1}$ for Cen X-3) of low the magnetic field strength. Another explanation is to consider by assuming that the center of the dipole magnetic field is offset relative to the center of the neutron star if we assume two absorption lines originate from the different poles of the neutron star (Rodes-Roca et al., 2009).

We are grateful to the referee for the useful comments to improve the manuscript. This work is supported by the National Key Research and Development Program of China (Grants No. 2021YFA0718500, 2021YFA0718503), the NSFC (12133007, U1838103). This work made use of data from the Insight-HXMT mission, a project funded by China National Space Administration (CNSA) and the Chinese Academy of Sciences (CAS).

Data that were used in this paper are from Institute of High Energy Physics Chinese Academy of Sciences(IHEP-CAS) and are publicly available for download from the Insight-HXMT website. To process and fit the spectrum and obtain folded light curves, this research has made use of XRONOS and FTOOLS provided by NASA.