Cyclotron Resonance Scattering Feature Research Articles

The high-energy cyclotron line in 2S 1417-624 discovered with Insight-HXMT during the 2018 outburst

We report a detailed timing and spectral analysis of the X-ray pulsar 2S 1417-624 using the data from Insight-HXMT during the 2018 outburst. The pulse profiles are highly variable with respect to both unabsorbed flux and energy. A double-peaked pulse profile from the low flux evolved to a multi-peaked shape in the high-flux state. The pulse fraction is negatively correlated to the source flux in the range of sim (1--6)$\ $ erg cm$^ $ s$^ $, consistent with Rossi X-ray Timing Explorer (RXTE) studies during the 2009 giant outburst. The energy-resolved pulse profiles around the peak outburst showed a four-peak shape in the low-energy bands and gradually evolved to triple peaks at higher energies. The continuum spectrum is well described by typical phenomenological models, such as the cut-off power law and the power law with high-energy cut-off models. Notably, we discovered high-energy cyclotron resonant scattering features (CRSFs) for the first time, which are around 100 keV with a statistical significance of sim 7sigma near the peak luminosity of the outburst. This CRSF line is significantly detected with different continuum models and provides very robust evidence for its presence. Furthermore, pulse-phase-resolved spectroscopy confirmed the presence of the line, whose energy varied from 97 to 107 keV over the pulse phase and appeared to have a maximum value at the narrow peak phase of the profiles.

A quantitative explanation of the cyclotron-line variation in accreting magnetic neutron stars of super-critical luminosity

Context. Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Cyclotron lines are believed to be generated in the radiative shock in the accretion column. High-luminosity NSs show a smooth anti-correlation between the cyclotron-line centroid (ECRSF) and X-ray luminosity (LX). Aims. It has been pointed out that the observed ECRSF − LX smooth anti-correlation in high-luminosity NSs is in tension with the theoretically predicted one, if the radiative shock is the site of cyclotron-line formation. The shock height increases approximately linearly with luminosity, while the dipolar magnetic field drops as the cubic power of distance, thereby implying that the cyclotron-line energy ought to decrease significantly when the luminosity increases by, say, an order of magnitude, which is contrary to observations. Since there is no other candidate site for the cyclotron-line formation, we re-examine the predicted rate of change of the cyclotron-line energy with luminosity at the radiative shock, taking a closer look at the Physics involved. Methods. We developed a purely analytical model describing the overall dependence of the observed cyclotron energy centroid on the shock front’s height, including both the relativistic boosting and the gravitational redshift effects in our considerations. The relativistic boosting effect is due to the mildly relativistic motion of the accreting plasma upstream with respect to the shock’s reference frame. Reults. We find that the cyclotron-line energy varies with (a) the shock height due to the dipolar magnetic field, (b) the Doppler boosting between the shock and bulk-motion frames, and (c) the gravitational redshift. We show that the relativistic effects noticeably weaken the predicted ECRSF − LX anti-correlation. We use our model to fit the data of the X-ray source V0332+53 that exhibits a weak negative correlation and demonstrate that the model fits the data impressively well, thereby alleviating the tension between observations and theory. Conclusions. The reported weak anti-correlation between cyclotron-line centroid and X-ray luminosity in the supercritical accretion regime may be explained by the combination of the variation of the magnetic-field strength along the accretion column, the effect of Doppler boosting, and the gravitational redshift. As a result of these effects, the actual magnetic field on the surface of the neutron star may be a factor of ∼2 larger than the naively inferred value from the observed CRSF.

Temporal and spectral variations of the X-ray pulsar Cen X-3 observed by NuSTAR

We report a time-resolved analysis of the accreting X-ray pulsar Cen X-3 using observations carried out by NuSTAR, which cover approximately two binary orbits in different intensity states. The pulse profile is relatively stable over the orbital phase and shows energy dependence. It has an obvious double-peaked shape in the energy band below 15 keV –with the second pulse peak decreasing as energy increases– and is gradually dominated by a single peak in higher energy bands. We find that the pulse profile in the energy band of 3–5 keV at high-intensity states shows a subtle triple-peaked shape, with the main peak divided into two subpeaks. We also find a positive correlation between the pulse fraction and both energy and flux. Our spectral analysis reveals that the spectra can be well described by the continuum of Fermi-Dirac cutoff and NPEX models, and the cyclotron line is detected with the centroid energies varying from 26 keV to 29 keV, along with the iron emission line around 6.4 keV. We investigated the dependence between the cyclotron resonant scattering feature (CRSF) centroid energy and luminosity and discuss the theoretical critical luminosity. Although the variation of Ecyc − LX is not distinct, there is a possibility that the critical luminosity lies within the range of ∼(0.5 − 4)×1037 erg s−1 in the band of 4–78 keV. The photon index shows a strong positive correlation with luminosity. Our orbital-phase analysis reveals that the spectral parameters show orbital variability, and the highly variable photoelectric absorption may indicate the existence of clumpy stellar winds.

Evidence for a Cyclotron Absorption Line and Spectral Transition in EXO 2030+375 during the 2021 Giant Outburst

Based on Insight-HXMT observations of EXO 2030+375 during its 2021 giant outburst, we report the analysis of pulse variations and the broadband X-ray spectrum, and find the presence of a potential cyclotron resonant scattering feature (CRSF) with the fundamental line at ∼47 keV from both average spectra and phase-resolved spectroscopy. During the outburst, the source reached an X-ray luminosity of ∼1038 erg s−1 from 2 to 105 keV at a distance of 7.1 kpc. The X-ray pulsar at the spin period of 41.27 ± 0.61 s exhibits complex timing and spectral variations with both energy and luminosity during the outburst. The shapes of the pulse profiles show the single main peak above ∼20 keV, while appearing to exhibit multipeak patterns in low-energy bands, and the transition of the 10–20 keV pulse profiles from multipeak to single peak is observed at ∼0.8 × 1038 erg s−1, which suggests the evolution from the subcritical luminosity (pencil-beam dominated) to the supercritical luminosity (fan-beam dominated) regime. A dip structure before the energy of the CRSFs is found in the pulse fraction–energy relation of EXO 2030+375 near the peak luminosity. A detailed analysis of spectral parameters showed that the power-law photon index exhibits three distinct trends as luminosity increases, and these spectral changes also signify a spectral transition from subcritical to supercritical regimes. The critical luminosity infers a magnetic field of ∼(4.8−6.0) × 1012 G, which supports the presence of the cyclotron line at ∼47 keV. A Comptonization model applied for the broad X-ray spectra during the outburst also suggests the surface magnetic field ranging from ∼(5−9) × 1012 G.

Polarization perspectives on Hercules X-1: further constraining the geometry

ABSTRACT We conduct a comprehensive analysis of the accreting X-ray pulsar, Hercules X-1, utilizing data from Imaging X-ray Polarimetry Explorer (IXPE) and Nuclear Spectroscopic Telescope Array. IXPE performed five observations of Her X-1, consisting of three in the Main-on state and two in the Short-on state. Our time-resolved analysis uncovers the linear correlations between the flux and polarization degree as well as the pulse fraction and polarization degree. Geometry parameters are rigorously constrained by fitting the phase-resolved modulations of Cyclotron Resonance Scattering Feature and polarization angle with a simple dipole model and Rotating Vector Model, respectively, yielding roughly consistent results. The changes of χp (the position angle of the pulsar’s spin axis on the plane of the sky) between different Main-on observations suggest the possible forced precession of the neutron star crust. Furthermore, a linear association between the energy of Cyclotron Resonance Scattering Feature and polarization angle implies the prevalence of a dominant dipole magnetic field, and their phase-resolved modulations likely arise from viewing angle effects.

Cyclotron line formation in the radiative shock of an accreting magnetized neutron star

Context. Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Accretion onto their magnetic poles is responsible for the emergence of X-rays, but the site of the CRSF formation is still a puzzle. A promising candidate for high-luminosity sources has always been the radiative shock in the accretion column. Nevertheless, no quantitative calculations of spectral formation at the radiative shock have been performed so far. Aims. It is well accepted that, in the accretion column of a high-luminosity, accreting magnetic NS, a radiative shock is formed. Here, we aim to explore the scenario where the shock is the site of the cyclotron-line formation. We studied spectral formation at the radiative shock and the emergent spectral shape across a wide range of the parameter space and determined which parameters hold an important role in shaping a prominent CRSF. Methods. We developed a Monte Carlo (MC) code based on the forced first collision numerical scheme to conduct radiation transfer simulations at the radiative shock. The seed photons were due to bremsstrahlung and were emitted in the post-shock region. We properly treated bulk-motion Comptonization in the pre-shock region, thermal Comptonization in the post-shock region, and resonant Compton scattering in both regions. We adopted a fully relativistic scheme for the interaction between radiation and electrons, employing an appropriate polarization-averaged differential cross-section. As a result, we calculated the angle- and energy-dependent emergent X-ray spectrum from the radiative shock, focusing on both the CRSF and the X-ray continuum, under diverse conditions. The accretion column was characterized by cylindrical symmetry, and the radiative shock was treated as a mathematical discontinuity. Results. We find that a power law, hard X-ray continuum, and a CRSF are naturally produced by the first-order Fermi energization as the photons criss-cross the shock. The depth and the width of the CRSF depend mainly on the transverse optical depth and the post-shock temperature. We show that the cyclotron-line energy centroid is shifted by ∼(20 − 30)% to lower energies compared to the classical cyclotron energy; this is due to the Doppler boosting between the shock reference frame and the bulk-motion frame. We demonstrate that a “bump” feature arises in the right wing of the CRSF due to the up-scattering of photons by the accreting plasma and extends to higher energies for larger optical depths and post-shock temperatures. Conclusions. We conclude that resonant Compton scattering of photons by electrons in a radiative shock is efficient in producing a power-law X-ray continuum with a high-energy cutoff accompanied by a prominent CRSF. The implications of the Doppler effect on the centroid of the emergent absorption feature must be considered if an accurate determination of the magnetic field strength is desired.

A Possible Cyclotron Feature of the Gamma-Ray Binary 4FGL J1405.1–6119

We reanalyzed the X-ray observations of the γ-ray binary candidate 4FGL J1405.1−6119 using the XMM-Newton observations. In the X-ray spectra, we find a weak absorption feature around 2 keV in the XMM-Newton observations, which could be the cyclotron resonant scattering feature (CRSF) or so called cyclotron line of the possible neutron star (NS) in the binary. The line energy of the CRSF is ∼2 keV, implying that the magnetic field on the surface of the NS is about B ≈ 1011 G or B ≈ 1014 G depending on the cyclotron line being generated by electron or proton, respectively. This suggest that 4FGL J1405.1−6119 hosts a weakly magnetized NS or a magnetar.

Studying the variations of the cyclotron line in Cen X-3 using Insight-HXMT

We investigate the cyclotron resonant scattering features (CRSFs) of the accreting X-ray pulsar Cen X-3 and significantly detect the 29 keV cyclotron line features in the hard X-ray averaged spectroscopy studies based on the recent Insight-HXMT observations in 2022, when Cen X-3 has X-ray luminosity LX>∼5×1037 erg s−1 in the bands of 2 – 60 keV. We do not find a harmonic line in the average spectra based on different continuum models. We showed that the CRSF energies have no correlation with time or luminosity in the average spectra. In addition, by performing a pulse phase-dependent spectral analysis, we revealed the fundamental line with the centroid energy ranging from 25 to 29 keV with a high significance over the spin phases. The evolution of the cyclotron line centroid energies over pulse phase is similar to the shape of pulse profiles, illustrating a positive correlation between the energy of CRSFs and the pulse phase flux.

Long-term evolution of cyclotron line energy in an eclipsing pulsar 4U 1538−522

ABSTRACT We present the timing and spectral analysis of the high-mass X-ray binary source 4U 1538−522 using Nuclear Spectroscopic Telescope Array (NuSTAR) observations. One of the observations partially covers the X-ray eclipse of the source along with eclipse ingress. The source is found to spin down at the rate of 0.163 ± 0.002 s yr−1 between ∼54973 and 58603 MJD. It is evident that at time ∼58620 MJD, a torque reversal occurred; thereafter, the source exhibited a spin-up trend at the rate −(0.305 ± 0.018) s yr−1 until 59275 MJD. A recent NuSTAR observation finds the pulse period of the source: (526.2341 ± 0.0041) s. The pulse profile exhibits a transition from double-peaked to single-peaked nature above ∼30 keV. We analysed the overall trend of the temporal evolution of fundamental cyclotron resonance scattering feature, Ecyc, incorporating recent NuSTAR measurements. Initially, during the time span ∼50452.16–55270.8 MJD, the cyclotron line energy is found to increase at a rate of 0.11 ± 0.03 keV yr−1, which is further followed by a decrease at a rate −0.14 ± 0.01 keV yr−1 between 55270.8 and 59267 MJD. The combined measurements in the time span 50452.16–59267 MJD reveal that the cyclotron line energy is increasing linearly at a rate of 0.08 ± 0.02 keV yr−1.

Nustar observation of the binary system 4U 0114 + 65

ABSTRACT The high-mass X-ray binary system 4U 0114 + 65 was observed by Nustar in October 2019 and by XMM-Newton in August 2015. Here we performed spectral and timing analysis of the Nustar observation and carry out timing analysis on the XMM-Newton data. We measured the spin period of the neutron star from both observations and found a spin-up rate $\dot{p}$ = 1.54 ± 0.38 × 10−6$\mathrm{s\, s}^{-1}$ . During the Nustar observation, two flares occurred, one shortly after the start of the observation and the other near the end separated by a long period of low/quiescent state. The large and sudden flares mostly resulted from accretion of corotating interaction region (CIR) material. A common spectral model to high mass X-ray binaries (HMXBs), powerlaw with high energy cutoff and absorption at low energy, gave a good fit to both flaring and quiescent states. A fluorescent iron line was not required in fitting any of the states. On the other hand, very tentative evidence of Cyclotron Resonant Scattering Feature (CRSF) at ∼17 keV was found during fitting using cyclabs model; however, fitting improvement was not significant enough to confirm its detection, plus a very narrow width (<1 keV) was obtained for the line and its first harmonic. Visual inspection of the spectra showed a deficiency of emission near the expected first and second harmonic. Another important feature visually noticed in the spectra is the presence of hard tail above 50 keV. This could be explained by the shocked material bounding the CIR.

Orbital- and Spin-phase Variability in the X-Ray Emission from the Accreting Pulsar Centaurus X-3

We present a time-resolved analysis using 39 ks NuSTAR observation data of the X-ray pulsar Centaurus X-3, covering an orbital-phase interval of Φ = 0.199–0.414. The orbital- and spin-phase variabilities are investigated through time-resolved spectra, light curves, and pulse profiles. The orbital-phase variability was due to the mixture of two comparable effects: intrinsic flux variability of ∼10% and obscuration by the clumpy stellar wind. The typical size and number density of the clumps are ∼9 × 1010 cm and ∼3 × 1012 cm−3, respectively. In the spin-phase-resolved analysis, we detected variations in the spectral features of the continuum, the Fe line, and the cyclotron resonance scattering feature (CRSF). The photon index ranged from 0.72 to 1.06, corresponding to the difference in the Comptonization optical depth by a factor of ∼1.6. The equivalent width and intensity of the Fe line had negative correlations with the continuum flux. The central energy and the strength of the CRSF increased at the pulse maximum. The former ranged from 26.0 to 28.7 keV, while the latter varied by a factor of ∼1.9. The pulse profile was double-peaked in the low-energy band, and it gradually shifted to being single-peaked with energy, indicating the existence of two distinct emission patterns, corresponding to the pencil and fan beams. Finally, we found that the pulse profiles were highly stable along the orbital phase, within a variation degree of ∼20%, which provides evidence of the highly stable accretion stream of the binary system.

Discovery of two cyclotron resonance scattering features in X-ray pulsar cen X-3 by Insight-HXMT

ABSTRACT We present the results of the neutron star X-ray binary system Cen X-3 performed by Insight-HXMT with two observations during 2017 and 2018. During these two observations, the source reached a X-ray luminosity of ∼1038 erg s−1 from 2–105 keV. The analysis of the broadband X-ray spectrum reports the presence of two cyclotron resonance scattering features (CRSFs) with the fundamental line at ∼ 28 keV and the harmonic line at ∼47 keV. The multiple lines exist by fittings with different continuum models, like the absorbed negative and positive power-law with an exponential cutoff (NPEX) model and a power-law with high energy exponential cutoff model. This is the first time that both fundamental and harmonic lines are detected in Cen X-3. We also show evidence of two cyclotron lines in the phase-resolved spectrum of Cen X-3. The CRSF and continuum spectral parameters show evolution with the pulse profile, and the two line centroid energy ratio does not change significantly and locates in a narrow value range of 1.6−1.7 over the pulse phase. The implications of the discovering two cyclotron absorption features and phase-resolved spectral properties are discussed.

Phase-dependent cyclotron line feature in XTE J1946 + 274: a NuSTAR view

ABSTRACT We report the results from a timing and spectral analysis of the Be/X-ray binary, XTE J1946 + 274 which underwent a Type II outburst in June 2018 and was observed with NuSTAR at a flux of ∼2.8 × 10−9 erg cm−2 s−1. The spectrum was described well with HighEC, NPEX, FDcut, and the CompTT models for the continuum. A cyclotron line is detected at ∼37.7 keV independent of the choice of the continuum model, confirming the previous detections. The pulse profile shows strong energy dependence with a double-peaked structure at low energies while evolving into a single-peaked structure at higher energies. Though the cyclotron line is detected in the phase-average spectra, from the phase-resolved analysis we find that it is unambiguously detected in only ∼50 per cent of the phases, where the second pulse peak disappears. In the remaining pulse phase, we find marginal evidence for the presence of a weak line at 36.5 keV. The cyclotron line centroid remains fairly constant with phase in the second peak but a significant variation of the Cyclotron Resonance Scattering Feature's depth with the pulse phase is evident. We compile the results from the previously published literature on this source and find that XTE J1946 + 274 has been observed over the flux range of ∼0.4–7.3 × 10−9 erg cm−2 s−1. Although there is no clear variation between the cyclotron line energy with luminosity, it is among a handful of the sources that have been observed over such a wide range of fluxes and may contain, within this range, the critical luminosity.

Insight-HXMT Discovery of the Highest-energy CRSF from the First Galactic Ultraluminous X-Ray Pulsar Swift J0243.6+6124

The detection of cyclotron resonance scattering features (CRSFs) is the only way to directly and reliably measure the magnetic field near the surface of a neutron star (NS). The broad energy coverage and large collection area of Insight-HXMT in the hard X-ray band allowed us to detect the CRSF with the highest energy known to date, reaching about 146 keV during the 2017 outburst of the first galactic pulsing ultraluminous X-ray source (pULX) Swift J0243.6+6124. During this outburst, the CRSF was only prominent close to the peak luminosity of ∼2 × 1039 erg s−1, the highest to date in any of the Galactic pulsars. The CRSF is most significant in the spin-phase region corresponding to the main pulse of the pulse profile, and its centroid energy evolves with phase from 120 to 146 keV. We identify this feature as the fundamental CRSF because no spectral feature exists at 60–70 keV. This is the first unambiguous detection of an electron CRSF from an ULX. We also estimate a surface magnetic field of ∼1.6 × 1013 G for Swift J0243.6+6124. Considering that the dipole magnetic field strengths, inferred from several independent estimates of magnetosphere radius, are at least an order of magnitude lower than our measurement, we argue that the detection of the highest-energy CRSF reported here unambiguously proves the presence of multipole field components close to the surface of the neutron star. Such a scenario has previously been suggested for several pulsating ULXs, including Swift J0243.6+6124, and our result represents the first direct confirmation of this scenario.

Phase-dependent Evolution within the Large Luminosity Range of 1A 0535+262 Observed by Insight-HXMT during 2020 Giant Outburst

We have performed phase-resolved spectral analysis of the accreting pulsar 1A 0535+262 based on observations of Insight-HXMT during the 2020 type II outburst of the source. We focus on the two-dimensional dependence of the cyclotron resonance scattering features (CRSFs) along the outburst time and at different phases. The fundamental CRSF line (f-CRSF) shows different time- and phase-dependent behaviors. At higher luminosity, the phase profile of the f-CRSF energy changes from a single peak to double peaks, with the transition occurring at MJD 59185. On the contrary, the first harmonic CRSF (first CRSF) at ∼100 keV is only detected within a narrow phase range (0.8−1.0) accompanied by a shallow f-CRSF line. Based on these results, we speculate that when the source enters the supercritical regime, the higher accretion column height can significantly enhance the harmonic line at a narrow phase through an “anti-pencil” beam at a higher energy band. At the same time, it will also affect the behavior of the fundamental line.

NuSTAR discovery of a cyclotron line in GRO J1750-27

ABSTRACT GRO J1750-27, discovered during an outburst in 1995 with CGRO-BATSE, is one of the farthest known Galactic Be/X-ray binary systems. This relatively poorly studied system recently went into an outburst in September 2021. The source was observed during the latest outburst using the NuSTAR telescope during the rising phase of the outburst. We estimate the spin period of the source to be 4.45 s using which we produced energy-resolved pulse profiles between 3 and 65 keV. We find that the profile is double-peaked at low energies (<18 keV), while evolving into a single peak at higher energies (>18 keV). The broad-band spectrum of this source was fitted well with a high energy cutoff power-law model and we report the discovery of a cyclotron resonant scattering feature (CRSF) in this source at 43 keV, indicating a magnetic field strength of 3.7 × 1012 G. Our estimate of the magnetic field strength, using the cyclotron line, is consistent with the estimates made earlier using the accretion torque model from measurements of spin-up rates and fluxes during the previous outbursts.

The symbiotic X-ray binaries Sct X-1, 4U 1700+24, and IGR J17329−2731

ABSTRACT Symbiotic X-ray binaries are systems hosting a neutron star accreting form the wind of a late-type companion. These are rare objects and so far only a handful of them are known. One of the most puzzling aspects of the symbiotic X-ray binaries is the possibility that they contain strongly magnetized neutron stars. These are expected to be evolutionary much younger compared to their evolved companions and could thus be formed through the (yet poorly known) accretion induced collapse of a white dwarf. In this paper, we perform a broad-band X-ray and soft γ-ray spectroscopy of two known symbiotic binaries, Sct X−1 and 4U 1700+24, looking for the presence of cyclotron scattering features that could confirm the presence of strongly magnetized NSs. We exploited available Chandra, Swift, and NuSTAR data. We find no evidence of cyclotron resonant scattering features (CRSFs) in the case of Sct X−1 but in the case of 4U 1700+24 we suggest the presence of a possible CRSF at ∼16 keV and its first harmonic at ∼31 keV, although we could not exclude alternative spectral models for the broad-band fit. If confirmed by future observations, 4U 1700+24 could be the second symbiotic X-ray binary with a highly magnetized accretor. We also report about our long-term monitoring of the last discovered symbiotic X-ray binary IGR J17329−2731 performed with Swift/XRT. The monitoring revealed that, as predicted, in 2017 this object became a persistent and variable source, showing X-ray flares lasting for a few days and intriguing obscuration events that are interpreted in the context of clumpy wind accretion.

Variations of magnetic multipoles in the X-ray binary pulsars Her X-1 and A 0535+26

ABSTRACT The X-ray binaries (XRBs) Her X-1 and A 0535+26 have been extensively studied over the years during outbursts and in deep quiescence. Cyclotron resonance scattering features (CRSFs) have been observed in absorption correlating with X-ray luminosities, though recently, an anticorrelation was seen in the 2020 giant outburst of A 0535+26 at higher luminosities. These types of behaviour have been observed in several other XRBs, yet there are sources showing extended periods of no correlation at all. Such aperiodic changes and periods of no change in CRSFs can be explained by changes in the surface magnetic fields of the X-ray pulsars. In particular, we show here that CRSF variations occur in Her X-1 and A 0535+26 due to corresponding changes in the strong nondipolar components of their surface magnetic fields, while the magnetic dipoles reaching out to the accretion discs remain largely unchanged.

Study of timing and spectral properties of the X-ray pulsar 1A 0535+262 during the giant outburst in 2020 November–December

ABSTRACT We made a detailed study of the timing and spectral properties of the X-ray pulsar 1A 0535+262 during the recent giant outburst in 2020 November and December. The flux of the pulsar reached a record value of ∼12.5 Crab as observed by Swift/BAT (15–50 keV) and the corresponding mass accretion rate was ∼6.67 × 1017 g s−1 near the peak of the outburst. There was a transition from the subcritical to the supercritical accretion regime which allows exploring different properties of the source in the supercritical regime. A q-like feature was detected in the hardness–intensity diagram during the outburst. We observed high variability and strong energy dependence of pulse profiles during the outburst. Cyclotron Resonant Scattering Feature (CRSF) was detected at ∼44 keV from the NuSTAR energy spectrum in the subcritical regime and the corresponding magnetic field was B ≃ 4.9 × 1012 G. The energy of the CRSF was shifted towards lower energy in the supercritical regime. The luminosity dependence of the CRSF was studied and during the supercritical regime, a negative correlation was observed between the line energy and luminosity. The critical luminosity was ∼6 × 1037erg s−1 above which a state transition occurred. A reversal of correlation between the photon index and luminosity was observed near the critical luminosity. The NuSTAR spectra can be described by a composite model with two continuum components, a blackbody emission, cut-off power law, and a discrete component to account for the iron emission line at 6.4 keV. An additional cyclotron absorption feature was included in the model.

Cyclotron line formation by reflection on the surface of a magnetic neutron star

Context. Accretion onto magnetic neutron stars results in X-ray spectra that often exhibit a cyclotron resonance scattering feature (CRSF) and, sometimes, higher harmonics of it. Two places are suspect for the formation of a CRSF: the surface of the neutron star and the radiative shock in the accretion column. Aims. Here we explore the first possibility: reflection at the neutron-star surface of the continuum produced at the radiative shock. It has been proposed that for high-luminosity sources, as the luminosity increases, the height of the radiative shock increases, thus a larger polar area is illuminated, and as a consequence the energy of the CRSF decreases because the dipole magnetic field decreases by a factor of two from the pole to the equator. This model has been specifically proposed to explain the observed anticorrelation of the cyclotron line energy and luminosity of the high-luminosity source V 0332+53. Methods. We used a Monte Carlo code to compute the reflected spectrum from the atmosphere of a magnetic neutron star, when the incident spectrum is a power-law one. We restricted ourselves to cyclotron energies ≪mec2 and used polarization-dependent scattering cross sections, allowing for polarization mode change. Results. As expected, a prominent CRSF is produced in the reflected spectra if the incident photons are in a pencil beam, which hits the neutron-star surface at a point with a well-defined magnetic field strength. However, the incident beam from the radiative shock has a finite width and thus various magnetic field strengths are sampled. As a result of overlap, the reflected spectra have a CRSF, which is close to that produced at the magnetic pole, independent of the height of the radiative shock. Conclusions. Reflection at the surface of a magnetic neutron star cannot explain the observed decrease in the CRSF energy with luminosity in the high-luminosity X-ray pulsar V 0332+53. In addition, it produces absorption lines much shallower than the observed ones.