Critical Luminosity Research Articles

Luminosity dependence of the multiple cyclotron lines in 4U 0115+63

Context. The Be X-ray binary 4U 0115+63 underwent a giant outburst in 2023 with the X-ray luminosity of the source reaching 1038 erg s−1. During the outburst, two target of opportunity observations were made with NuSTAR. Aims. The main goal of this work is to model the multiple cyclotron scattering features (CRSFs) present in 4U 0115+63 and study their dependence on the luminosity of the source. Methods. The 3–79 keV broadband X-ray coverage of NuSTAR allowed us to properly model the continuum and investigate the nature of the multiple cyclotron resonance scattering features present in the source spectrum. We used the epoch-folding technique to find the pulsation from the source and also studied the changes in the cyclotron line energy with an order of magnitude variation in the source luminosity. Results. We detected five cyclotron lines during the 2023 outburst near 12, 16, 24, 34, and 47 keV. The ∼16 keV cyclotron line cannot be harmonically related to the other cyclotron lines at ∼12 keV and ∼24 keV. This indicates the presence of two fundamental lines in the spectrum of 4U 0115+63 at 12 keV and 16 keV. Conclusions. With the inclusion of the two latest NuSTAR observations, we have expanded the data set of the CRSF line center to encompass a broad range of luminosity. This enables us to comprehensively investigate the relationship between the centroid energy of the cyclotron lines and luminosity. The CRSF line center shows no anticorrelation with luminosity, unlike previously reported. Instead, a weak positive correlation is found in four out of the five detected cyclotron lines of 4U 0115+63. The luminosity variation of the two fundamental CRSFs could be well explained with the prediction from the collisionless shock model. A tentative negative correlation was observed in the fundamental CRSF at 16 keV and its harmonics beyond a “critical luminosity” of 1038 erg/s. This behavior was not present for the 12 keV fundamental CRSF and its harmonic at 24 keV.

Spectral evolution of RX J0440.9+4431 during the 2022–2023 giant outburst observed with Insight-HXMT

In 2022–2023, the Be/X-ray binary X-ray pulsar RX J0440.9+4431 underwent a Type II giant outburst, reaching a peak luminosity of LX ∼ × 1037 erg s−1. In this work, we utilized Insight-HXMT data to analyze the spectral evolution of RX J0440.9+4431 during the giant outburst. By analyzing the variation in the X-ray spectrum during the outburst using standard phenomenological models, we find that as the luminosity approaches the critical luminosity, the spectrum becomes flatter, with the photon enhancement predominantly concentrated around ∼2 keV and 20–40 keV. The same behavior has also been noted in Type II outbursts from other sources. While the phenomenological models provide good fits to the spectrum, it is sometimes difficult to gain insight into details of the fundamental accretion physics using this approach. Hence, we also analyzed spectra obtained during high and low phases of the outburst using a new, recently developed physics-based theoretical model that allows us to study the variations in the physical parameters during the outburst, such as the temperature, density, and magnetic field strength. Application of the theoretical model reveals that the observed spectrum is dominated by Comptonized bremsstrahlung emission emitted from the column walls in both the high and low states. We show that the spectral flattening observed at high luminosities results from a decrease in the electron temperature, combined with a compactification of the emission zone, which reduces the efficiency of bulk Comptonization. We also demonstrate that when the source is at maximum luminosity, the spectrum tends to harden around the peak of the pulse profile, and we discuss possible theoretical explanations for this behavior. We argue that the totality of the behavior in this source can be explained if the accretion column is in a quasi-critical state at the time of maximum luminosity during the outburst.

Study of stellar properties under TESS satellite observations

This study employs data from the TESS satellite to investigate the properties of stars. TESS, the Transiting Exoplanet Survey Satellite, offers insights into star activity, periodic variations, and planetary transits by monitoring changes in stellar brightness. Our analysis of TESS data explores critical star attributes, including mass, luminosity, activity levels, and dynamic changes. By examining the relationship between these stellar properties and the presence of planets, we aim to uncover the intricate interplay between celestial bodies and unveil the universe's mysteries. This research encompasses data collection methods, processing techniques, and data analysis approaches, addressing star classifications, parameters, and periodic stellar activity. We also delve into flare energy, which reveals the energy released during stellar flares, and photoperiodic analysis, a tool for understanding periodic light changes in celestial bodies. The study concludes by highlighting the significance of newly discovered planets and the diversity of stars observed by TESS. It underscores the importance of comprehending the connections between stars and planets, shaping our understanding of celestial habitability. In summary, this study enriches our knowledge of star and planet properties, contributing to a broader comprehension of the universe. Through our analysis, we seek to illuminate the complex relationships between celestial entities and unveil the universe's enigmas.

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.

Searching for the Highest Energy of Pulsation and Critical Luminosity of Swift J0243.6+6124 Observed by Insight-HXMT

Owing to the broad energy coverage of Insight-HXMT in the hard X-ray band, we detected the highest energy of pulsation exceeding 200 keV around the 2017–2018 outburst peak of the first Galactic pulsating ultraluminous X-ray source (PULX) Swift J0243.6+6124, which is the highest energy detected from PULXs to date. We also obtained the highest energy of pulsation of every exposure during the outburst in 2017–2018, and found the highest energy is roughly positively correlated with luminosity. Using our newly developed method, we identified the critical luminosity being 4 × 1038 erg s−1 when the main peaks of the low and high energy pulse profiles became aligned, which separates the fan-beam dominated and pencil-beam dominated accretion regimes. Above the critical luminosity, the phase of the main peak shifted gradually from 0.5 to 0.8 until the outburst peak in all energy bands is reached, which is in agreement with the phase shift found previously at low energies. Our result is consistent with what is derived from spectral analysis.

The effect of thermal torques on AGN disc migration traps and gravitational wave populations

ABSTRACT Accretion discs in active galactic nuclei (AGNs) foster black hole (BH) formation, growth, and mergers. Stellar mass BHs migrate inwards under the influence of hydrodynamical torques unless they encounter a region where the torque flips sign. At these migration traps, BHs accumulate and merge via dynamical or gas-assisted interactions, producing high-frequency LIGO/Virgo/KAGRA (LVK) gravitational wave (GW) sources and potentially cutting off the supply of extreme mass ratio inspirals that would otherwise make low-frequency, LISA-band GWs. In this paper, we study the interplay between different types of migration torques, focusing especially on the ‘thermal torques’ generated by the thermal response of the AGN to embedded stellar-mass BHs that accrete through their own mini-discs. In contrast to previous work, we find that Type I torques cannot produce migration traps on their own, but thermal torques often do, particularly in low-mass AGN. The migration traps produced by thermal torques exist at much larger distances (∼103−5 gravitational radii) than do previously identified Type I traps, carrying implications for GW populations at multiple frequencies. Finally, we identify a bifurcation of AGN discs into two regimes: migration traps exist below a critical AGN luminosity, and do not at higher luminosities. This critical luminosity is fit as $\log _{10} L_{\rm AGN}^c = 45 {\!-\!} 0.32 \log _{10}{(\alpha /0.01)}$ where α is the Shakura–Sunyaev viscosity parameter, a range compatible with recent claims that LVK GWs are not preferentially associated with high-luminosity AGN.

Probing spectral and timing properties of the X-ray pulsar RX J0440.9 + 4431 in the giant outburst of 2022–2023

ABSTRACT The X-ray pulsar RX J0440.9 + 4431 went through a giant outburst in 2022 and reached a record-high flux of 2.3 Crab, as observed by Swift/BAT. We study the evolution of different spectral and timing properties of the source using NICER observations. The pulse period is found to decrease from 208 s to 205 s, and the pulse profile evolves significantly with energy and luminosity. The hardness ratio and hardness intensity diagram (HID) show remarkable evolution during the outburst. The HID turns towards the diagonal branch from the horizontal branch above a transition (critical) luminosity, suggesting the presence of two accretion modes. Each NICER spectrum can be described using a cutoff power law with a blackbody component and a Gaussian at 6.4 keV. At higher luminosities, an additional Gaussian at 6.67 keV is used. The observed photon index shows negative and positive correlations with X-ray flux below and above the critical luminosity, respectively. The evolution of spectral and timing parameters suggests a possible change in the emission mechanism and beaming pattern of the pulsar depending on the spectral transition to sub- and supercritical accretion regimes. Based on the critical luminosity, the magnetic field of the neutron star can be estimated in the order of 1012 or 1013 G, assuming different theoretical models. Moreover, the observed iron emission line evolves from a narrow to a broad feature with luminosity. Two emission lines originating from neutral and highly ionized Fe atoms are evident in the spectra around 6.4 and 6.67 keV (later is seen only in higher luminosities).

Temporal and spectral study of the X-ray pulsar 2S 1553–542 during the 2021 outburst

We study the timing and spectral properties of the X-ray pulsar 2S 1553–542 using the NuSTAR and NICER during the outburst in January–February 2021. During the outburst, the spin period of the neutron star was $$P\sim 9.2822$$ s based on NuSTAR data. The pulse profiles are studied using different NICER observations, which implies that the profile is more or less sinusoidal with a single peak and the beaming patterns are dominated mainly by the pencil beam. The NICER spectra of the source are studied for different days of the outburst. They can be well described by a model consisting of a blackbody emission, power law and photoelectric absorption component. The variation of spectral parameters with luminosity is studied over the outburst. The photon index shows anti-correlation with luminosity below the critical luminosity, which implies that the source was accreting in the sub-critical accretion regime during the NICER observations. We also report the anti-correlation between pulsed fraction (PF) and luminosity of the 2S 1553–542 using NICER observations. The evolution of spin-up rate with luminosity is studied during the outburst, which implies that both are strongly correlated. The torque-luminosity model is applied to estimate the magnetic field at different spin-up rates. The magnetic field is estimated to be $${\simeq }2.56 \times 10^{12}$$ G from the torque-luminosity model using the source distance of 20 kpc. The magnetic field is also estimated using the critical luminosity, consistent with our findings.

On the cyclotron absorption line and evidence of the spectral transition in SMC X-2 during 2022 giant outburst

ABSTRACT We report comprehensive spectral and temporal properties of the Be/X-ray binary pulsar SMC X-2 using X-ray observations during the 2015 and 2022 outbursts. The pulse profile of the pulsar is unique and strongly luminosity dependent. It evolves from a broad-humped into a double-peaked profile above luminosity 3 × 1038 erg s−1. The pulse fraction of the pulsar is found to be a linear function of luminosity as well as energy. We also studied the spectral evolution of the source during the latest 2022 outburst with NICER. The observed photon index shows a negative and positive correlation below and above the critical luminosity, respectively, suggesting evidence of spectral transition from the sub-critical to supercritical regime. The broad-band spectroscopy of four sets of NuSTAR and XRT/NICER data from both outbursts can be described using a cut-off power-law model with a blackbody component. In addition to the 6.4 keV iron fluorescence line, an absorption-like feature is clearly detected in the spectra. The cyclotron line energy observed during the 2015 outburst is below 29.5 keV, however latest estimates in the 2022 outburst suggest a value of 31.5 keV. Moreover, an increase of 3.4 keV is detected in the cyclotron line energy at equal levels of luminosity observed in 2022 with respect to 2015. The observed cyclotron line energy variation is explored in terms of accretion induced screening mechanism or geometrical variation in line forming region.

Evolution of disc and corona in MAXI J1348−630 during the 2019 reflare: NICER and Insight-HXMT view

ABSTRACT In this work, using Neutron star Interior Composition Explorer and Insight-Hard X-ray Modulation Telescope observations, we present a study of the broad-band spectral and timing evolution of the source throughout the first reflare, which occurred about 4-month after the major outburst. Our findings suggest that during the reflare, below a critical luminosity Lcrit ∼ 2.5 × 1036 (D/2.2 kpc)2 erg s−1, the scale of the corona shrinks in the radial direction, whereas the inner radius of the disc does not change considerably; however, the inner radius of the disc starts to move inward when the source exceeds the critical luminosity. We conclude that at low luminosity the increase in accretion rate only heats up the inner zone of the accretion disc without the transfer of angular momentum which occurs above a certain luminosity.

Timing analysis of EXO 2030+375 during its 2021 giant outburst observed withInsight-HXMT

ABSTRACTWe report the evolution of the X-ray pulsations of EXO 2030+375 during its 2021 outburst using the observations from Insight-HXMT. Based on the accretion torque model, we study the correlation between the spin frequency derivatives and the luminosity. Pulsations can be detected in the energy band of 1–160 keV. The pulse profile evolves significantly with luminosity during the outburst, leading to that the whole outburst can be divided into several parts with different characteristics. The evolution of the pulse profile reveals the transition between the supercritical (fan-beam dominated) and the subcritical accretion (pencil-beam dominated) mode. From the accretion torque model and the critical luminosity model, based on a distance of 7.1 kpc, the inferred magnetic fields are (0.41 − 0.74) × 1012 and (3.48 − 3.96) × 1012 G, respectively, or based on a distance of 3.6 kpc, the estimated magnetic fields are (2.4 − 4.3) × 1013 and (0.98 − 1.11) × 1012 G, respectively. Two different sets of magnetic fields both support the presence of multipole magnetic fields of the neutron star.

The unaltered pulsar: GRO J1750-27, a supercritical X-ray neutron star that does not blink an eye

When accreting X-ray pulsars (XRPs) undergo bright X-ray outbursts, their luminosity-dependent spectral and timing features can be analyzed in detail. The XRP GRO J1750-27 recently underwent one such episode, during which it was observed withNuSTARand monitored with NICER. Such a data set is rarely available, as it samples the outburst over more than 1 month at a luminosity that is always exceeding ∼5 × 1037 erg s−1. This value is larger than the typical critical luminosity value, where a radiative shock is formed above the surface of the neutron star. Our data analysis of the joint spectra returns a highly (NH ∼ (5 − 8) × 1022 cm−2) absorbed spectrum showing a Kαiron line, a soft blackbody component likely originating from the inner edge of the accretion disk, and confirms the discovery of one of the deepest cyclotron lines ever observed, at a centroid energy of ∼44 keV corresponding to a magnetic field strength of 4.7 × 1012 G. This value is independently supported by the best-fit physical model for spectral formation in accreting XRPs which, in agreement with recent findings, favors a distance of 14 kpc and also reflects a bulk-Comptonization-dominated accretion flow. Contrary to theoretical expectations and observational evidence from other similar sources, the pulse profiles as observed by NICER remain remarkably steady through the outburst rise, peak and decay. The NICER spectrum, including the iron Kαline best-fit parameters, also remain almost unchanged at all probed outburst stages, similar to the pulsed fraction behavior. We argue that all these phenomena are linked and interpret them as resulting from a saturation effect of the emission from the accretion column, which occurs in the high-luminosity regime.

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.

Comparing the super-Eddington accretion of SMC X-3 and RX J0209.6−7427 with Swift J0243.6+6124

ABSTRACT We study the giant outbursts of SMC X-3 and RX J0209.6−7427 (hereafter RX J0209) to compare their super-Eddington accretion regime with that of Swift J0243.6+6124 (hereafter Swift J0243). The high double-peak profile of SMC X-3 is found to be 0.25 phase offset from that below 2.3 × 1038 erg s−1, which is similar to Swift J0243 (happened around 0.9 × 1038 erg s−1). The profile of RX J0209 shows a similar 0.25 phase offset between high double-peak and low double-peak around 1.25 × 1038 erg s−1. The 0.25 phase offset corresponds to a 90° angle change of the emission beam and strongly supports for a transition from a fan beam to a pencil beam. Their critical luminosities imply a surface magnetic field ∼4 × 1013 and 2 × 1013 G for SMC X-3 and RX J0209, respectively, based on the recently measured cyclotron line of Swift J0243. The spin-up rate and luminosity of SMC X-3 follows a relation of $\dot{\nu }\propto L^{0.94\pm 0.03}$, while that of RX J0209 follows $\dot{\nu }\propto L^{1.00\pm 0.03}$, which are similar to Swift J0243 and consistent with the prediction of a radiation-pressure-dominated disc. These results indicate that accretion columns are indeed formed above Eddington luminosity, and the population of ultraluminous X-ray pulsars likely corresponds to X-ray pulsars of highest magnetic field.

Timing Properties of the X-Ray Accreting Pulsar 1A 0535+262 Studied with Insight-HXMT

We report results on the timing analysis of the 2020 giant outburst of 1A 0535+262, using broadband data from Insight-HXMT. The analysis of the pulse profile evolution from the subcritical-luminosity to the supercritical-luminosity regime is presented for the first time. We found that the observed pulse profile exhibits a complex dependence on both energy and luminosity. A dip structure at the energy of the cyclotron resonant scattering features is found for the first time in the pulse fraction–energy relation of 1A 0535+262, when the outburst evolves in a luminosity range from 4.8 × 1037 to 1.0 × 1038 erg s−1. The observed structure is luminosity dependent and appears around the source critical luminosity (∼6.7 × 1037 erg s−1).

Constraints on the magnetic field structure in accreting compact objects from aperiodic variability

ABSTRACTWe investigate the aperiodic variability for a relatively large sample of accreting neutron stars and intermediate polars, focusing on the properties of the characteristic break commonly observed in power spectra of accreting objects. In particular, we investigate the relation of the break frequency and the magnetic field strength, both of which are connected to the size of the magnetosphere. We find that for the majority of objects in our sample the measured break frequency values indeed agree with estimated inner radii of the accretion disc, which allows to use observed break frequencies to independently assess the magnetic field strength and structure in accreting compact objects. As a special case, we focus on Hercules X-1 which is a persistent, medium-luminosity X-ray pulsar accreting from its low-mass companion. In the literature, it has been suggested that the complex pulse profiles, the spin-up behaviour and the luminosity-correlation of the cyclotron energy seen in Her X-1 can be explained with a complex magnetic field structure of the neutron star. Here, we connect the measured break frequency to the magnetospheric radius and show that the magnetic field strength derived assuming a dipole configuration is nearly an order of magnitude smaller than the magnetic field strength corresponding to the cyclotron energy. Accordingly, this discrepancy can be explained with the magnetic field having strong multipole components. The multipolar structure would also increase the accreting area on the neutron star surface, explaining why the critical luminosity for accretion column formation is puzzlingly high in this source.

Spectral and Timing Properties of H 1743-322 in the “Faint” 2005 Normal Outburst

H 1743-322 is a well-known black hole X-ray binary (BH XRBs) that has been observed in several outbursts over the past. In this work, we have performed the spectral and timing analysis of H 1743-322 during the “faint” 2005 outburst for the first time with the RXTE/PCA data. In this outburst, the spectral and timing parameters (e.g., Tin, Γ, Rin, rms and QPOs, etc.) presented an obvious change and a q-like pattern was found in the Hardness Intensity Diagram (HID), which often named as the hysteresis effect of BH XRBs. The radius of the innermost stable circular orbit was constrained as RISCO∼3.50 Rg, which predicts that H 1743-322 is a lower-spin black hole. We further explored the correlation between timing and spectral properties. The relation of photon index Γ and X-ray flux, F3–25keV, presented a transition between negative and positive correlation when the X-ray luminosity, L3–25keV, is above and below a critical X-ray luminosity, LX,crit≃2.55×10−3 LEdd, which can be well explained by the Shakura-Sunyaev disk–corona model (SSD-corona) and advection-dominated accretion flow (ADAF). We also found the tight linear, negative correlation between photon index Γ and the total fractional rms. Since the amount of soft photons from the accretion disk seems invariable, an increase of the number of soft photons will dilute the variability from the harder photons. Therefore, the softer the X-ray spectra will result in the smaller total fractional rms. The above results suggested that the 2005 outburst of H 1743-322 was a normal outburst and H 1743-322 represented similar properties with other black hole X-ray binaries.

Accreting on the Edge: A Luminosity-dependent Cyclotron Line in the Be/X-Ray Binary 2S 1553-542 Accompanied by Accretion Regimes Transition

Abstract Accreting X-ray pulsars undergo luminous X-ray outbursts during which the luminosity-dependent spectral and timing features of the neutron star’s emission can be analyzed in detail, thus shedding light on the accretion regime at work. We took advantage of a monitoring campaign that was performed with NuSTAR, Swift/XRT, AstroSat and NICER to follow the Be/X-ray Binary 2S 1553-542 along one of its rare outbursts, and thus trace its spectral and timing evolution. We report the discovery of a luminosity-dependent cyclotron line energy for the first time in this source. The pulse profiles and pulsed fraction also show variability along the outburst, which is consistent with the interpretation that the source transitions from the subcritical to the supercritical accretion regime, separated by a critical luminosity of L crit ≈ 4 × 1037 erg s−1.

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.