X-ray Modulation Research Articles

Neutral Atmospheric Density Measurement Using Insight-HXMT Data by the Earth Occultation Technique

The Earth occultation technique has broad applications in both astronomy and atmospheric density measurements. We construct the background model during the occultation of the Crab Nebula observed by the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) at energies between 6 and 100 keV. We propose a Bayesian atmospheric density retrieval method based on the Earth occultation technique, combining Poisson and Gaussian statistics. By modeling the atmospheric attenuation of X-ray photons during the occultation, we simultaneously retrieved the neutral densities of the atmosphere at different altitude ranges. Our method considers the correlation of densities between neighboring atmospheric layers and reduces the potential systematic bias to which previous work may be subject. Previous analyses based on light-curve fitting or spectral fitting also lost some spectral or temporal information of the data. In contrast to previous work, the occultation data observed by the three telescopes on board Insight-HXMT is fully used in our analysis, further reducing the statistical error in density retrieval. We apply our method to cross-check the (semi)empirical atmospheric models, using 115 sets of occultation data of the Crab Nebula observed by Insight-HXMT. We find that the retrieved neutral density is ∼10%, ∼20%, and ∼25% less than the values of the widely used atmospheric model NRLMSISE-00, in the altitude range of 55–80 km, 80–90 km, and 90–100 km, respectively. We also show that the newly released atmospheric model NRLMSIS 2.0 is generally consistent with our density measurements.

Simulation and analysis of the secondary-particle-induced background of the follow-up x-ray telescope onboard Einstein Probe

The Einstein Probe (EP) is a small scientific satellite committed to time-domain astronomy and high-energy astrophysics. One of the main payloads in the EP is the Follow-up X-ray Telescope (FXT). To get a quantity of in-orbit data as a reference, data from the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) were adopted. The Insight-HXMT is dedicated to perform hard x-ray all-sky surveys, which has a parallel in-orbit environment with the EP. In this paper, we simulated the in-orbit background of an FXT by the Particle and Heavy-Ion Transport code System, which is the first general-purpose heavy ion transport Monte Carlo code, which has a simulated range from 0.01 meV to 1 TeV. The influence from protons in the EP orbital environment and the secondary rays caused by the shielding materials around the detector have been mainly considered. The Super Monte Carlo Simulation Program for nuclear and radiation Processes has been used to define the materials of the shielding structure. An isotropic source of protons and a complete shielding structure have been constructed in this simulation. First, the spectrum of background between 0.5 and 15 keV has been calculated. Second, we simulated the types of reactions and the fluxes of secondary particles, and all of them were calculated with the same model in the first step. Finally, we considered the effectiveness of the outermost shielding with different materials. Among the calculated spectra of background, we found two conspicuous energy responses with high counts, separately located in 7.345 keV (5 eV) and 8.045 keV (5 eV). Compared with the in-orbit data from the low energy x-ray telescope in the Insight-HXMT, the simulated results are credible. Considering the combination of the simulated types of reactions and fluxes of secondary particles, we could mostly judge that the secondary photons brought the photoelectric effects, which caused the two conspicuous responses in the spectrum of background. In addition, copper was the most suitable material for the outermost shielding in this simulation.

New method to apply the lumbar lordosis of standing radiographs to supine CT-based virtual 3D lumbar spine models

Standing radiographs play an important role in the characterization of spinal sagittal alignment, as they depict the spine under physiologic loading conditions. However, there is no commonly available method to apply the lumbar lordosis of standing radiographs to supine CT-based virtual 3D models of the lumbar spine. We aimed to develop a method for the sagittal rigid-body registration of vertebrae to standing radiographs, using the exact geometry reconstructed from CT-data. In a cohort of 50 patients with monosegmental spinal degeneration, segmentation and registration of the lumbar vertebrae and sacrum were performed by two independent investigators. Intersegmental angles and lumbar lordosis were measured both in CT scans and radiographs. Vertebrae were registered using the X-ray module of Materialise Mimics software. Postregistrational midsagittal sections were constructed of the sagittal midplane sections of the registered 3D lumbar spine geometries. Mean Hausdorff distance was measured between corresponding registered vertebral geometries. The registration process minimized the difference between the X-rays’ and postregistrational midsagittal sections’ lordoses. Intra- and inter-rater reliability was excellent based on angle and mean Hausdorff distance measurements. We propose an accessible, accurate, and reproducible method for creating patient-specific 3D geometries of the lumbar spine that accurately represent spinal sagittal alignment in the standing position.

The 100-m X-ray test facility at IHEP

The 100-m X-ray Test Facility of the Institute of High Energy Physics (IHEP) was initially proposed in 2012 for the test and calibration of the X-ray detectors of the Hard X-ray Modulation Telescope (HXMT) with the capability to support future X-ray missions. The large instrument chamber connected with a long vacuum tube can accommodate the X-ray mirror, focal plane detector and other instruments. The X-ray sources are installed at the other end of the vacuum tube with a distance of 105 m, which can provide an almost parallel X-ray beam covering 0.2sim60 keV energy band. The X-ray mirror modules of the Einstein Probe (EP) and the enhanced X-ray Timing and Polarimetry mission (eXTP) and payload of the Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) have been tested and calibrated with this facility. It has been also used to characterize the focal plane camera and aluminum filter used on the Einstein Probe. In this paper, we will introduce the overall configuration and capability of the facility, and give a brief introduction of some calibration results performed with this facility.

Spectral and Timing Analysis of the Black Hole Transient MAXI J1631–479 During its 2019 Outburst Observed with Insight-HXMT

We report spectral and timing analysis of the black hole transient MAXI J1631–479 during the hard intermediate state of its 2019 outburst from the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) observations. We find that the energy dependence of the type-C quasi-periodic oscillation (QPO) frequency evolves with time: during the initial rise of a small flare (∼MJD 58526.0-58527.1), the QPO frequency increases with increasing energy from ∼1 to ∼100 keV, and then the frequency remains constant after MJD 58527.1. We discover a possible new phenomenon of Fe line’s QPO frequency jump that has never been observed for other black hole transients: during the small flare, the QPO frequency around the Fe line energy is higher than any other energy band, with the frequency difference Δf = 0.25 ± 0.08 Hz between 5.5–7.5 keV and other energy bands. The spectral analysis shows that the evolution of QPOs is related to the equivalent width of the narrow Fe line, and its equivalent width increases during this small flare. We propose that the QPO frequency difference results from the differential precession of a vertically extended jet, and the higher QPO frequency of Fe line could be caused by the layered jet when the jet scale increases. At the same time, the evolution of QPOs is related to the accretion rate, while the energy dependence of QPOs supports the existence of deceleration in the vertically distributed jet.

The spectral-timing analysis of Cygnus X-1 with Insight-HXMT

Cygnus X-1, as the first discovered black hole binary, is a key source for understanding the mechanisms of state transitions and the scenarios of accretion in extreme gravity fields. We present a spectral-timing analysis of observations taken with the Insight–Hard X-ray Modulation Telescope (HXMT) mission, focusing on the spectral-state-dependent timing properties in the broad energy range of 1−150 keV, thus extending previous studies based on Rossi X-ray Timing Explorer (RXTE) to both lower and higher energies. Our main results are the following: (a) We successfully use a simple empirical model to fit all spectra, confirming that the reflection component is stronger in the soft state than in the hard state. (b) The evolution of the total fractional root mean square (rms) depends on the selected energy band and the spectral shape, which is a direct result of the evolution of the power spectral densities (PSDs). (c) In the hard/intermediate state, we see clear short-term variability features and a positive correlation between the central frequencies of the variability components and the soft photon index Γ1, which we also see at energies above 15 keV. In the soft state, the power spectrum is instead dominated by red noise. These behaviors can be traced to at least 90 keV. (d) Finally, the coherence and the phase-lag spectra show different behaviors, depending on the different spectral shapes.

An Insight-HXMT View of the mHz Quasi-regular Modulation Phenomenon in the Black Hole X-Ray Binary 4U 1630–47

Here we report the spectral-timing results of the black hole X-ray binary 4U 1630–47 during its 2021 outburst using observations from the Hard X-ray Modulation Telescope (Insight-HXMT). Type C quasi-periodic oscillations (QPOs) in ∼1.6–4.2 Hz and quasi-regular modulation (QRM) near 60 mHz are detected during the outburst. The mHz QRM has a fractional rms of ∼10%–16% in the 8–35 keV energy band with a Q factor (frequency/width) of ∼2–4. Benefiting from the broad energy band of Insight-HXMT, we study the energy dependence of the ∼60 mHz QRM in 1–100 keV for the first time. We find that the fractional rms of the mHz QRM increases with photon energy, while the time lags of the mHz QRM are soft and decrease with photon energy. Fast recurrence of the mHz QRM, in a timescale of less than 1 hr, has been observed during the outburst. During this period, the corresponding energy spectra moderately change when the source transitions from the QRM state to the non-QRM state. The QRM phenomenon also shows a dependence with the accretion rate. We suggest that the QRM could be caused by an unknown accretion instability aroused from the corona.

Determination of QPO properties in the presence of strong broad-band noise: a case study on the data of MAXI J1820+070

ABSTRACT Accurate calculation of the phase lags of quasi-periodic oscillations (QPOs) will provide insight into their origin. In this paper, we investigate the phase lag correction method that has been applied to calculate the intrinsic phase lags of the QPOs in MAXI J1820+070. We find that the traditional additive model between broad-band noise (BBN) and QPOs in the time domain is rejected, but the convolution model is accepted. By introducing a convolution mechanism in the time domain, the Fourier cross-spectrum analysis shows that the phase lags between QPOs components in different energy bands will have a simple linear relationship with the phase lags between the total signals, so that the intrinsic phase lags of the QPOs can be obtained by linear correction. The power density spectrum (PDS) thus requires a multiplicative model to interpret the data. We briefly discuss a physical scenario for interpreting the convolution. In this scenario, the corona acts as a low-pass filter, Green’s function containing the noise is convolved with the QPOs to form the low-frequency part of the PDS, while the high-frequency part requires an additive component. We use a multiplicative PDS model to fit the data observed by the Insight-Hard X-ray Modulation Telescope (HXMT). The overall fitting results are similar compared to the traditional additive PDS model. Neither the width nor the centroid frequency of the QPOs obtained from each of the two PDS models was significantly different, except for the rms of the QPOs. Our work thus provides a new perspective on the coupling of noise and QPOs.

Evolution of Accretion Modes between Spectral States Inferred from Spectral and Timing Analysis of Cygnus X-1 with Insight-HXMT Observations

We execute a detailed spectral-timing study of Cygnus X-1 in the low/hard, intermediate, and high/soft states with observations from the Hard X-ray Modulation Telescope. The broadband energy spectra fit well with the “truncated disk model”: the inner boundary of the accretion disk stays within ∼10 R g and moves inward as the source softens. Through studying the power density spectrum, rms, and Fourier frequency component resolved spectroscopy, we find that the X-ray variations are generated in two different regions for each state. We discover that the major contribution to the X-ray variation is from the hot corona rather than the accretion disk. We suggest a scenario with different coronal geometry for each state based on the truncated disk geometry in which the corona envelops the disk to form a sandwich geometry in the low/hard state, and then gradually moves away from the disk in a direction perpendicular to the disk until it forms a jet-like geometry in the high/soft state.

The Disk Wind in GRS 1915+105 as Seen by Insight–Hard X-Ray Modulation Telescope

We analyze three observations of GRS 1915+105 in 2017 by Insight–Hard X-ray Modulation Telescope when the source was in a spectrally soft state. We find strong absorption lines from highly ionized iron, which are due to absorption by disk wind outflowing at a velocity of ∼1000 km s−1 along our line of sight. Two of the three observations show large amplitude oscillation in their light curves and the variation pattern corresponds to state κ of GRS 1915+105. From time-averaged and flux-resolved analysis, we find that the variation in the ionization state of the disk wind follows the X-ray continuum on timescales from hundreds of seconds to months. The radial location of the disk wind is consistent with thermal driving. The mass-loss rate due to the outflowing wind is comparable to the mass accretion rate in the inner disk, which demonstrates the important role of the disk wind in the disk accretion system.

An Insight-HXMT Dedicated 33 day Observation of SGR J1935+2154. I. Burst Catalog

Magnetars are neutron stars with an extreme magnetic field and sometimes manifest as soft gamma-ray repeaters (SGRs). SGR J1935+2154 is one of the most prolific bursters and the first confirmed source of a fast radio burst (FRB; i.e., FRB 200428). Encouraged by the discovery of the first X-ray counterpart of FRBs, the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) implemented a dedicated 33-day-long Target of Opportunity observation of SGR J1935+2154 since 2020 April 28. With the HE, ME, and LE telescopes, Insight-HXMT provides a thorough monitoring of burst activity evolution of SGR J1935+2154, in a very broad energy range (1–250 keV) with high temporal resolution and high sensitivity, resulting in a unique valuable data set for detailed studies of SGR J1935+2154. In this work, we conduct a comprehensive analysis of this observation, including detailed burst search, identification, and temporal analyses. After carefully removing false triggers, we find a total of 75 bursts from SGR J1935+2154, out of which 70 are single pulsed. The maximum burst rate is about 56 bursts day−1. Both the burst duration and the waiting time between two successive bursts follow lognormal distributions, consistent with previous studies. We also find that bursts with longer duration (some are multipulsed) tend to occur during the period with relatively high burst rate. There is no correlation between the waiting time and the fluence or duration of either the former or latter burst. It also seems that there is no correlation between burst duration and hardness ratio, in contrast to some previous reports. In addition, we do not find any X-ray burst associated with any reported radio bursts except for FRB 200428.

The Accretion Flow Geometry of MAXI J1820+070 through Broadband Noise Research with Insight Hard X-ray Modulation Telescope

Here we present a detailed study of the broadband noise in the power density spectra of the black hole X-ray binary MAXI J1820+070 during the hard state of its 2018 outburst, using Hard X-ray Modulation Telescope observations. The broadband noise shows two main humps, which might separately correspond to variability from a variable disk and two Comptonization regions. We fitted the two humps with multiple Lorentzian functions and studied the energy-dependent properties of each component up to 90–150 keV and their evolution with spectral changes. The lowest-frequency component is considered as the subharmonic of the quasiperiodic oscillation component and shows a different energy dependence compared with other broadband noise components. We found that although the fractional rms of all the broadband noise components mainly decreases with the energy, their rms spectra are different in shape. Above ∼20–30 keV, the characteristic frequencies of these components increase sharply with the energy, meaning that the high-energy component is more variable on short timescales. Our results suggest that the hot inner flow in MAXI J1820+070 is likely to be inhomogeneous. We propose a geometry with a truncated accretion disk and two Comptonization regions.

Insight-HXMT Study of the Inner Accretion Disk in the Black Hole Candidate EXO 1846–031

We study the spectral evolution of the black hole candidate EXO 1846−031 during its 2019 outburst, in the 1–150 keV band, with the Hard X-ray Modulation Telescope. The continuum spectrum is well modeled with an absorbed disk-blackbody plus cutoff power law, in the hard, intermediate, and soft states. In addition, we detect an ≈6.6 keV Fe emission line in the hard intermediate state. Throughout the soft intermediate and soft states, the fitted inner disk radius remains almost constant; we suggest that it has settled at the innermost stable circular orbit (ISCO). However, in the hard and hard intermediate states, the apparent inner radius was unphysically small (smaller than the ISCO), even after accounting for the Compton scattering of some of the disk photons by the corona in the fit. We argue that this is the result of a high hardening factor, f col ≈ 2.0–2.7, in the early phases of the outburst evolution, well above the canonical value of 1.7 suitable for a steady disk. We suggest that the inner disk radius was already close to the ISCO in the low/hard state. Furthermore, we propose that this high value of the hardening factor in the relatively hard state was probably caused by the additional illuminating of the coronal irradiation onto the disk. Additionally, we estimate the spin parameter using the continuum-fitting method, over a range of plausible black hole masses and distances. We compare our results with the spin measured using the reflection-fitting method and find that the inconsistency of the two results is partly caused by different choices of f col.

Wavelet analysis of MAXI J1535–571 with Insight-HXMT

ABSTRACT In this paper, wavelet analysis is used to study the spectral-timing properties of MAXI J1535–571 observed by the Hard X-ray Modulation Telescope (Insight-HXMT). Low-frequency quasi-periodic oscillations (QPOs) are detected in nine observations. Based on wavelet analysis, the time intervals with QPOs and non-QPOs are isolated, and the corresponding spectra with QPOs and non-QPOs are analysed. We find that the spectra with QPOs (hereafter QPO spectra) are softer than those without QPOs (hereafter non-QPO spectra) in the hard intermediate state (HIMS), while in the soft intermediate state (SIMS), the QPO spectra are slightly harder. The disc temperature of the QPO regime is slightly lower during the HIMS, but becomes higher during the SIMS. The cutoff energies of QPO spectra and non-QPO spectra do not show significant differences. The flux ratio of the disc to total flux is higher for the time intervals with non-QPOs than that in the QPO regime. We propose that these differences in the spectral properties between QPO and non-QPO regimes could be explained through the scenario of Lense–Thirring precession, and the reversal of the QPO/non-QPO behaviour between the HIMS and SIMS may be associated with the appearance/disappearance of a type-B QPO, which might originate in the precession of the jet.

GRB 190530A: From Precursor, Prompt Emission to Afterglow all Originated from Synchrotron Radiation

GRB 190 530A was jointly observed by the High Energy X-ray Telescope of the Hard X-ray Modulation Telescope (Insight-HXMT/HE) and the Ground-Based Wide-Angle Camera network (GWAC-N) with the extremely large field of view. After triggered by Insight-HXMT/HE and Fermi/GBM, we observed the optical emission of GRB 190 530A, using the 30 cm telescope of GWAC (GWAC-F30) to search and locate its position. Subsequent observation of the late afterglow of GRB 190 530A was made with the 2.16 m telescope at Xinglong Observatory. In this paper, we make a detailed exploration of the origin of GRB 190 530A. In the prompt emission, a “double-tracking” pattern is presented both for the low-energy spectral index α and the peak energy E p in the Band function with Insight-HXMT/HE and Fermi/GBM data; the results of GRB 190 530A are consistent with the Amati and Yonetoku correlations; the spectral lag (τ) versus energy (E) can be estimated with . The synchrotron radiation can account for the origin of GRB 190 530A prompt emission behaviors. The α and E p of the precursor are essentially the same as that of the main prompt emission, implying that they have the same origin. For the afterglow, it can be described with the external forward shock model in ISM circumburst medium. In summary, from precursor, prompt emission to afterglow of GRB 190 530A all originated from synchrotron radiation.

Measurement of the vertical atmospheric density profile from the X-ray Earth occultation of the Crab Nebula with Insight-HXMT

Abstract. X-ray Earth occultation sounding (XEOS) is an emerging method for measuring the neutral density in the lower thermosphere. In this paper, the X-ray Earth occultation (XEO) of the Crab Nebula is investigated using the Hard X-ray Modulation Telescope (Insight-HXMT). The pointing observation data on the 30 September 2018 recorded by the low-energy X-ray telescope (LE) of Insight-HXMT are selected and analysed. The extinction light curves and spectra during the X-ray Earth occultation process are extracted. A forward model for the XEO light curve is established, and the theoretical observational signal for light curve is predicted. The atmospheric density model is built with a scale factor to the commonly used Mass Spectrometer Incoherent Scatter Radar Extended model (MSIS) density profile within a certain altitude range. A Bayesian data analysis method is developed for the XEO light curve modelling and the atmospheric density retrieval. The posterior probability distribution of the model parameters is derived through the Markov chain–Monte Carlo (MCMC) algorithm with the NRLMSISE-00 model and the NRLMSIS 2.0 model as basis functions, and the respective best-fit density profiles are retrieved. It is found that in the altitude range of 105–200 km, the retrieved density profile is 88.8 % of the density of NRLMSISE-00 and 109.7 % of the density of NRLMSIS 2.0 by fitting the light curve in the energy range of 1.0–2.5 keV based on the XEOS method. In the altitude range of 95–125 km, the retrieved density profile is 81.0 % of the density of NRLMSISE-00 and 92.3 % of the density of NRLMSIS 2.0 by fitting the light curve in the energy range of 2.5–6.0 keV based on the XEOS method. In the altitude range of 85–110 km, the retrieved density profile is 87.7 % of the density of NRLMSISE-00 and 101.4 % of the density of NRLMSIS 2.0 by fitting the light curve in the energy range of 6.0–10.0 keV based on the XEOS method. Goodness-of-fit testing is carried out for the validation of the results. The measurements of density profiles are compared to the NRLMSISE-00 and NRLMSIS 2.0 model simulations and the previous retrieval results with NASA's Rossi X-ray Timing Explorer (RXTE) satellite. For further confirmation, we also compare the measured density profile to the ones by a standard spectrum retrieval method with an iterative inversion technique. Finally, we find that the retrieved density profile from Insight-HXMT based on the NRLMSISE-00 and NRLMSIS 2.0 models is qualitatively consistent with the previous retrieved results from RXTE. The results of light curve fitting and standard energy spectrum fitting are in good agreement. This research provides a method for the evaluation of the density profiles from MSIS model predictions. This study demonstrates that the XEOS from the X-ray astronomical satellite Insight-HXMT can provide an approach for the study of the upper atmosphere. The Insight-HXMT satellite can join the family of the XEOS. The Insight-HXMT satellite with other X-ray astronomical satellites in orbit can form a space observation network for XEOS in the future.

Quasi-periodic Oscillations of the X-Ray Burst from the Magnetar SGR J1935–2154 and Associated with the Fast Radio Burst FRB 200428

The origin(s) and mechanism(s) of fast radio bursts (FRBs), which are short radio pulses from cosmological distances, have remained a major puzzle since their discovery. We report a strong quasi-periodic oscillation (QPO) of ∼40 Hz in the X-ray burst from the magnetar SGR J1935+2154 and associated with FRB 200428, significantly detected with the Hard X-ray Modulation Telescope (Insight-HXMT) and also hinted at by the Konus–Wind data. QPOs from magnetar bursts have only been rarely detected; our 3.4σ (p-value is 2.9e–4) detection of the QPO reported here reveals the strongest QPO signal observed from magnetars (except in some very rare giant flares), making this X-ray burst unique among magnetar bursts. The two X-ray spikes coinciding with the two FRB pulses are also among the peaks of the QPO. Our results suggest that at least some FRBs are related to strong oscillation processes of neutron stars. We also show that we may overestimate the significance of the QPO signal and underestimate the errors of QPO parameters if QPO exists only in a fraction of the time series of an X-ray burst that we use to calculate the Leahy-normalized periodogram.

X-Ray Fine Structure of a Limb Solar Flare Revealed by Insight-HXMT, RHESSI and Fermi

Abstract We conduct a detailed analysis of an M1.3 limb flare occurring on 2017 July 3, which have the X-ray observations recorded by multiple hard X-ray telescopes, including Hard X-ray Modulation Telescope (Insight-HXMT), Ramaty High Energy Solar Spectroscopic Imager (RHESSI), and the Fermi Gamma-ray Space Telescope (Fermi). Joint analysis has also used the extreme ultraviolet (EUV) imaging data from the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamic Observatory. The hard X-ray spectral and imaging evolution suggest a lower corona source, and the non-thermal broken power law distribution has a rather low break energy ∼15 keV. The EUV imaging shows a rather stable plasma configuration before the hard X-ray peak phase, and accompanied by a filament eruption during the hard X-ray flare peak phase. Hard X-ray image reconstruction from RHESSI data only shows one foot point source. We also determined the DEM for the peak phase by SDO/AIA data. The integrated EM beyond 10 MK at foot point onset after the peak phase, while the >10 MK source around reconnection site began to fade. The evolution of EM and hard X-ray source supports lower corona plasma heating after non-thermal energy dissipation. The combination of hard X-ray spectra and images during the limb flare provides the understanding on the interchange of non-thermal and thermal energies, and relation between lower corona heating and the upper corona instability.

Super-Eddington accretion of the first Galactic ultra-luminous X-ray pulsar Swift J0243.6+6124

ABSTRACT We present a detailed timing study of the pulse profile of Swift J0243.6+6124 with Hard X-ray Modulation Telescope (HXMT) and Fermi/GBM (Gamma-ray Burst Monitor) data during its 2017 giant outburst. The double-peak profile at luminosity above 5 × 1038 erg s−1 is found to be 0.25 phase offset from that below 1.5 × 1038erg s−1, which strongly supports for a transition from a pencil beam to a fan beam, and thus for the formation of shock dominated accretion column. During the rising stage of the high double-peak regime, the faint peak got saturated in 10–100 keV band above a luminosity of Lt ∼ 1.3 × 1039erg s−1, which is coincident with sudden spectral changes of both the main and faint peaks. They imply a sudden change of emission pattern around Lt. The spin-up rate ($\dot{\nu }$) is linearly correlated with luminosity (L) below Lt, consistent with the prediction of a radiation pressure dominated disc. The $\dot{\nu }-L$ relation flattens above Lt, indicating a less efficient transfer of angular momentum and a change of accretion disc geometry above Lt. It is likely due to irradiation of the disc by the central accretion column and indicates significant radiation feedback well before the inner disc radius reaching the spherization radius.

A Study on the X-Ray Pulse Profile and Spectrum of the Crab Pulsar Using NICER and Insight-HXMT's Observations

Abstract We analyze the energy dependence of the X-ray pulse profile and the phase-resolved spectra (PRS) of the Crab pulsar using observations from the Neutron star Interior Composition Explorer (NICER) and the Hard X-ray Modulation Telescope (Insight-HXMT). We parameterize the pulse profiles and quantify the evolution of these parameters in the broad energy band of 0.4–250 keV. A log-parabola function is used to fit the PRS in 2–250 keV, and the curvature of the spectrum, i.e., the evolution of the photon index with energy, as represented by the parameter β of the log-parabola model, also changes with phase. The relation of β and phase has two turning points slightly later than those of the pulse intensity profile, where the values of β are the lowest, suggesting that the energy-loss rate of the particles is the lowest in the corresponding regions. A three-segment broken-power-law model is also used to fit those PRS. The differences between the hard spectral index and the soft ones have a distribution similar to that of β, confirming the fitting results of the log-parabola model, while the broken energies are generally higher in the region bridging the two pulses. We find anticorrelations between the spectral indices and the curvature of the log-parabola model fitting and a similar anticorrelation between the spectral indices and broken energies of the broken-power-law model fitting, suggesting a scenario where the highest-energy particles are produced in regions where radiation energy loss is strongest.