Accretion-powered X-ray Pulsar Research Articles

Blind source separation for decomposing X-ray pulsar profiles

Accretion-powered X-ray pulsars offer a unique opportunity to study physics under extreme conditions. To fully exploit this potential, the interrelated problems of modelling radiative transport and the dynamical structure of the accretion flow must, however, be solved. This task is challenging both from a theoretical and observational point of view and is further complicated by a lack of direct correspondence between the properties of emission emerging from the neutron star and observed far away from it. In general, a mixture of emission from both poles of the neutron star viewed from different angles is indeed observed at some or even all phases of the pulse cycle. It is essential, therefore, to reconstruct the contributions of each pole to the observed flux in order to test and refine models describing the formation of the spectra and pulse profiles of X-ray pulsars. In this paper we propose a novel data-driven approach to address this problem using the pulse-to-pulse variability in the observed flux, and demonstrate its application to RXTE observations of the bright persistent X-ray pulsar Cen X-3. We then discuss the comparison of our results with previous work attempting to solve the same problem and how they can be qualitatively interpreted in the framework of a toy model describing emission from the poles of a neutron star.

An investigation of the ‘10 keV feature’ in the spectra of accretion powered X-ray pulsars with NuSTAR

ABSTRACT Some of the accreting X-ray pulsars are reported to exhibit a peculiar spectral feature at ∼10 keV, known as the ‘10 keV feature’. The feature has been characterized as either an emission line or an absorption line, and its origin is unknown. It has been found in multiple observations of the same source by different observatories, but not all the observations of any particular source consistently showed the presence of it. In this work, we have carried out a systematic investigation for the presence of the ‘10 keV feature’ using data from NuSTAR, a low background spectroscopic observatory having uninterrupted wide band coverage on either side of 10 keV. We performed a systematic spectral analysis on 58 archival NuSTAR observations of 30 bright X-ray pulsars. The 3–79 keV spectral continua of these selected sources were fitted with a model chosen on the basis of its fitting quality in 3–15 keV and model simplicity, and then inspected for the presence of the ‘10 keV feature’. Our analysis indicates the presence of such a feature in 16 out of 58 the NuSTAR observations of 11 different sources and is fitted with a Gaussian absorption model centred around 10 keV. Our analysis also suggests that such a feature could be wrongly detected if flare data is not analysed separately from persistent emission.

Changes in the distribution of circum-binary material around the HMXB GX 301-2 during a rapid spin-up episode of the neutron star

ABSTRACT Some accretion-powered X-ray pulsars with supergiant companion stars undergo occasional rapid spin-up episodes that last for weeks to a few months. We explore the changes in the accretion environment of the pulsar GX 301-2 during its latest 80 days long spin-up episode in 2019 when the spin frequency of the pulsar increased by ∼2 per cent over two orbits of the binary. By performing time-resolved spectroscopy with the MAXI/GSC spectra of the source, we estimated the equivalent hydrogen column density and equivalent width of the iron fluorescence line during the spin-up episode, and compared them with the long-term average values estimated by orbital-phase-resolved spectroscopy. The measured absorption column density during the spin-up episode is about twice that of an average orbit, while the equivalent width of the iron line is less than half of an average orbit. Though the spin-up episode started immediately after a pre-periastron flare and lasted for the two consecutive orbits of the binary, the associated enhancement in luminosity started a few days after the pre-periastron flare and lasted only during the first orbit, and some enhancement was seen again during the pre-periastron passage of the second orbit. The absorption column density and iron line equivalent width vary throughout the spin-up episode and are distinct from an average orbit. These observations indicate a significant change in the accretion and reprocessing environment in GX 301-2 during the spin-up episode and may hold important clues for the phenomenon in this source and several other sources with supergiant companions.

A Generalized Analytical Model for Thermal and Bulk Comptonization in Accretion-powered X-Ray Pulsars

We develop a new theoretical model describing the formation of the radiation spectrum in accretion-powered X-ray pulsars as a result of bulk and thermal Comptonization of photons in the accretion column. The new model extends the previous model developed by the authors in four ways: (1) we utilize a conical rather than cylindrical geometry; (2) the radiation components emitted from the column wall and the column top are computed separately; (3) the model allows for a nonzero impact velocity at the stellar surface; and (4) the velocity profile of the gas merges with Newtonian freefall far from the star. We show that these extensions allow the new model to simulate sources over a wide range of accretion rates. The model is based on a rigorous mathematical approach in which we obtain an exact series solution for the Green’s function describing the reprocessing of monochromatic seed photons. Emergent spectra are then computed by convolving the Green’s function with bremsstrahlung, cyclotron, and blackbody photon sources. The range of the new model is demonstrated via applications to the high-luminosity source Her X-1, and the low-luminosity source X Per. The new model suggests that the observed increase in spectral hardness associated with increasing luminosity in Her X-1 may be due to a decrease in the surface impact velocity, which increases the PdV work done on the radiation field by the gas.

Detection of a quasi-periodic oscillation at ∼40 mHz in Cen X-3 with Insight-HXMT

ABSTRACT We investigated the quasi-periodic oscillation (QPO) features in the accretion-powered X-ray pulsar Cen X-3 observed by Insight-HXMT. For two observations in 2020 when Cen X-3 was in an extremely soft state, the power density spectrum revealed the presence of obvious QPO features at ∼40 mHz with an averaged fractional rms amplitude of ∼9 per cent. We study the mHz QPO frequency and rms amplitude over orbital phases, and find that the QPO frequency is ∼33–39 mHz at the orbital phase of 0.1–0.4, increasing to ∼37–43 mHz in the orbital phase of 0.4–0.8, but has no strong dependence on X-ray intensity. We also carried out an energy-dependent QPO analysis, the rms amplitude of the mHz QPOs have a decreasing trend as the energy increases from 2 to 20 keV. In addition, the QPO time-lag analysis shows that the time-delay is ∼20 ms (a hard lag) in the range of ∼5–10 keV, and becomes negative [time-lag of −(20–70) ms] above ∼10 keV. The different QPO theoretical models are summarized and discussed. In the end, we suggest that these energy-dependent timing features as well as the origin of mHz QPOs in Cen X-3 may be ascribed to an instability when the accretion disc is truncated near the corotation radius.

X-ray burst ignition location on the surface of accreting X-ray pulsars: can bursts preferentially ignite at the hotspot?

ABSTRACT Hotspots on the surface of accreting neutron stars have been directly observed via pulsations in the light curves of X-ray pulsars. They are thought to occur due to magnetic channelling of the accreted fuel to the neutron star magnetic poles. Some X-ray pulsars exhibit burst oscillations during Type I thermonuclear X-ray bursts that are thought to be caused by asymmetries in the burning. In rapidly rotating neutron stars, it has been shown that the lower gravity at the equator can lead to preferential ignition of X-ray bursts at this location. These models, however, do not include the effect of accretion hotspots at the the neutron star surface. There are two accreting neutron star sources in which burst oscillations have been observed to track exactly the neutron star spin period. We analyse whether this could be due to the X-ray bursts igniting at the magnetic pole of the neutron star, because of heating in the accreted layers under the hotspot causing ignition conditions to be reached earlier. We investigate heat transport in the accreted layers using a 2D model and study the prevalence of heating down to the ignition depth of X-ray bursts for different hotspot temperatures and sizes. We perform calculations for accretion at the pole and at the equator, and infer that ignition could occur away from the equator at the magnetic pole for hotspots with temperature $T_{\mathrm{HS}}\gtrsim 1\times 10^8\, \mathrm{K}$. However, current observations have not identified such high temperatures in accretion-powered X-ray pulsars.

On the peculiar torque reversals and the X-ray luminosity history of the accretion-powered X-ray pulsar 4U 1626–67

ABSTRACT The X-ray luminosity (Lx) and the rotational properties of 4U 1626–67 have been measured at regular intervals during the last four decades. It has been recorded that the source underwent torque reversals twice. We have tried to understand whether these eccentrical sign-switches of the spin period derivative ($\dot{P}$) of 4U 1626–67 could be accounted for with the existing torque models. We have found that the observed source properties are better estimated with the distances close to the lower limit of the previously predicted distance range (5−13 kpc). Furthermore, assuming an inclined rotator, we have considered the partial accretion/ejection from the inner disc radius that leads to different Lx–$\dot{P}$ profiles than the aligned rotator cases. We have concluded that the oblique rotator assumption with the inclination angle χ ∼ (10°−30°) brings at least equally best fitting to the observed Lx and $\dot{P}$ of 4U 1626–67. More importantly, the estimated change of the mass accretion rate, which causes the change in observed Lx of 4U 1626–67 is much less than that is found in an aligned rotator case. In other words, without the need for a substantial modification of mass accretion rate from the companion star, the range of the observed Lx could be explained naturally with an inclined magnetic axis and rotation axis of the neutron star.

Observations of a GX 301–2 Apastron Flare with the X-Calibur Hard X-Ray Polarimeter Supported by NICER, the Swift XRT and BAT, and Fermi GBM

Abstract The accretion-powered X-ray pulsar GX 301−2 was observed with the balloon-borne X-Calibur hard X-ray polarimeter during late 2018 December, with contiguous observations by the Neutron star Interior Composition Explorer Mission (NICER) X-ray telescope, the Swift X-ray Telescope and Burst Alert Telescope, and the Fermi Gamma-ray Burst Monitor spanning several months. The observations detected the pulsar in a rare apastron flaring state coinciding with a significant spin up of the pulsar discovered with the Fermi Gamma-ray Burst Monitor. The X-Calibur, NICER, and Swift observations reveal a pulse profile strongly dominated by one main peak, and the NICER and Swift data show strong variation of the profile from pulse to pulse. The X-Calibur observations constrain for the first time the linear polarization of the 15–35 keV emission from a highly magnetized accreting neutron star, indicating a polarization degree of % (90% confidence limit) averaged over all pulse phases. We discuss the spin up and the X-ray spectral and polarimetric results in the context of theoretical predictions. We conclude with a discussion of the scientific potential of future observations of highly magnetized neutron stars with the more sensitive follow-up mission XL-Calibur.

The Modulating Optical Depth of the Photoelectric Absorption Edge with a Pulse Phase in Accretion-powered X-Ray Pulsars

Abstract We report the first discovery of a pulse phase modulating optical depths at the iron K-edge in accretion-powered X-ray pulsars from Suzaku observations. A significant modulating optical depth of the iron K-edge is detected for Vela X-1 and GX 1+4. Similar trends are seen in GX 301-2 and OAO 1657-415, though with poor statistical significance. The observed iron K-edge exhibits a maximum optical depth when the X-ray continuum dims, and there is no significant pulse phase variation in the ionization state of iron. The revealed changes in the optical depth with pulse phase can be explained as being due to the accreting matter captured by the magnetic field lines of the pulsar, which corotates with the neutron star spin and is responsible for photoelectric absorption. Based on the above interpretation, we propose that the accreting matter within the Alfvén radius contains iron with an ionization state of FeVI–XI with a particle density of 1017 cm−3 and has a shape flattened along the azimuthal direction, such as an accretion curtain.

Happy birthday, Reviews of Modern Physics!

Happy birthday, <i>Reviews of Modern Physics</i>!

An application of the Ghosh &amp; Lamb model to the accretion-powered X-ray pulsar X Persei

Abstract The accretion-induced pulse period changes of the Be/X-ray binary pulsar X Persei were investigated over the period of 1996 January to 2017 September. This study utilized the monitoring data acquired with the RXTE All-Sky Monitor in 1.5–12 keV and the MAXI Gas-Slit Camera in 2–20 keV. The source intensity changed by a factor of 5–6 over this period. The pulsar was spinning down for 1996–2003, and has been spinning up since 2003, as already reported. The spin-up/down rate and the 3–12 keV flux, determined every 250 d, showed a clear negative correlation, which can be successfully explained by the accretion torque model proposed by Ghosh and Lamb (1979, ApJ, 234, 296). When the mass, radius, and distance of the neutron star were allowed to vary over a range of 1.0–2.4 solar masses, 9.5–15 km, and 0.77–0.85 kpc, respectively, the magnetic field strength of B = (4–25) × 1013 G gave the best fits to the observations. In contrast, the observed results cannot be explained by the values of B ∼ 1012 G previously suggested for X Persei, as long as the mass, radius, and distance are required to take reasonable values. Assuming a distance of 0.81 ± 0.04 kpc as indicated by optical astrometry, the mass of the neutron star is estimated as M = 2.03 ± 0.17 solar masses.

A curious case of the accretion-powered X-ray pulsar GX 1+4

We present detailed spectral and timing studies using a NuSTAR observation of GX 1+4 in October 2015 during an intermediate intensity state. The measured spin period of 176.778 s is found to be one of the highest values since its discovery. In contrast to a broad sinusoidal-like pulse profile, a peculiar sharp peak is observed in profiles below ~25 keV. The profiles at higher energies are found to be significantly phase-shifted compared to the soft X-ray profiles. Broadband energy spectra of GX 1+4, obtained from NuSTAR and Swift observations, are described with various continuum models. Among these, a two component model consisting of a bremsstrahlung and a blackbody component is found to best-fit the phase-averaged and phase-resolved spectra. Physical models are also used to investigate the emission mechanism in the pulsar, which allows us to estimate the magnetic field strength to be in $\sim$(5-10)$\times$10$^{12}$ G range. Phase-resolved spectroscopy of NuSTAR observation shows a strong blackbody emission component in a narrow pulse phase range. This component is interpreted as the origin of the peculiar peak in the pulse profiles below $\le$25 keV. The size of emitting region is calculated to be $\sim$400 m. The bremsstrahlung component is found to dominate in hard X-rays and explains the nature of simple profiles at high energies.

How young the accretion-powered pulsars could be?

A question about the age of accretion-powered X-ray pulsars has recently been reopened by a discovery of the X-ray pulsar SXP 1062 in the SMC. This High Mass X-ray Binary (HMXB) contains a neutron star rotating with the period of 1062 s and is associated with a supernova remnant of the age ∼ 104 yr. An attempt to explain the origin of this young long-period X-ray pulsar within the traditional scenario of three basic states (ejector, propeller and accretor) encounters difficulties. Even if this pulsar were born as a magnetar the spin-down time during the propeller stage would exceed 104 yr. Here we explore a more circuitous way of the pulsar spin evolution in HMXBs, in which the propeller stage in the evolutionary track is avoided. We find this way to be possible if the stellar wind of the massive companion to the neutron star is magnetized. The geometry of plasma flow captured by the neutron star in this case differs from spherically symmetrical and the magnetospheric radius of the neutron star is smaller than that evaluated in the convention accretion scenarios. We show that the age of an accretion-powered pulsar in this case can be as small as ∼ 104 years without the need of invoking initial magnetic field in excess of 1013 G.

Period distribution of pulsars in the Magellanic Clouds: Propeller line versus Equilibrium period

A majority of accretion-powered X-ray pulsars in wind-fed High Mass X-ray Binaries (HMXBs) located in the Magellanic Clouds are observed to be transient X-ray sources. They are characterized by short luminous outbursts, while spending most of the time in quiescence. The quiescent states of the pulsars in the diagram “Pulsar Period vs. X-ray Luminosity” fall on a line with the slope −0.43. The same slope is expected for the propeller line which separates stars in the accretor state from stars in the propeller state. We show, however, that a line with the same slope would also be expected if rotation of the pulsars is close to equilibrium.

The Intensity Modulation of the Fluorescent Line by a Finite Light Speed Effect in Accretion-powered X-Ray Pulsars

Abstract The X-ray line diagnostic method is a powerful tool for an investigation of plasma around accretion-powered X-ray pulsars. We point out an apparent intensity modulation of emission lines, with their rotation period of neutron stars, due to the finite speed of light (we call this effect the “finite light speed effect”) if the line emission mechanism is a kind of reprocessing, such as fluorescence or recombination after ionization by X-ray irradiation from pulsars. The modulation amplitude is determined by the size of the emission region, which is in competition with the smearing effect by the light crossing time in the emission region. This is efficient if the size of the emission region is roughly comparable to that of the rotation period multiplied by the speed of light. We apply this effect to a symbiotic X-ray pulsar, GX 1+4, where a spin modulation of the intense iron line of which has been reported. The finite light speed effect can explain the observed intensity modulation if its fluorescent region is the size of ∼ 10 12 cm.

Optical pulsations from a transitional millisecond pulsar

Weakly magnetic, millisecond spinning neutron stars attain their very fast rotation through a 1E8-1E9 yr long phase during which they undergo disk-accretion of matter from a low mass companion star. They can be detected as accretion-powered millisecond X-ray pulsars if towards the end of this phase their magnetic field is still strong enough to channel the accreting matter towards the magnetic poles. When mass transfer is much reduced or ceases altogether, pulsed emission generated by particle acceleration in the magnetosphere and powered by the rotation of the neutron star is observed, preferentially in the radio and gamma-ray bands. A few transitional millisecond pulsars that swing between an accretion-powered X-ray pulsar regime and a rotationally-powered radio pulsar regime in response to variations of the mass in-flow rate have been recently identified. Here we report the detection of optical pulsations from a transitional pulsar, the first ever from a millisecond spinning neutron star. The pulsations were observed when the pulsar was surrounded by an accretion disk and originated inside the magnetosphere or within a few hundreds of kilometres from it. Energy arguments rule out reprocessing of accretion-powered X-ray emission and argue against a process related to accretion onto the pulsar polar caps; synchrotron emission of electrons in a rotation-powered pulsar magnetosphere seems more likely.

A broad-band self-consistent modelling of the X-ray spectrum of 4U 1626−67

The accretion-powered X-ray pulsar 4U 1626--67 is one of the few highly magnetized pulsars that accretes through Roche-lobe overflow from a low-mass companion. The characteristics of its broadband spectrum are similar to those of X-ray pulsars hosted in a high-mass X-ray binary systems, with a broad resonant cyclotron scattering feature (CRSF) at $\sim$37 keV. In this work, we examine the pulse-resolved and the pulse-averaged broadband spectrum using data from NuSTAR and Swift. We use the Becker & Wolff model of bulk+thermal Comptonization to infer key physical parameters of the accretion column flow and a broadband model for the disk reflected spectrum. In the softer X-ray band, we need to add a soft black-body component with $kT_{\rm bb}$ $\sim$0.5 keV, whose characteristics indicate a possible origin from the neutron star surface. Residuals suggest that the shape of the cyclotron line could be more satisfactorily fitted using a narrow core and broader wings and, at higher energies, a second harmonic could be present at $\sim$61 keV.

Comprehensive timing and X-ray spectral analysis of GX 1+4

We present analysis of RXTE--PCA observations of GX 1+4 between March 3, 2001 and January 31, 2003 together with the CGRO--BATSE X-ray flux and frequency derivative time series between 1991 and 1999. From the timing analysis of RXTE-PCA observations, we are able to phase connect pulse arrival times of the source within two different time intervals and obtain corresponding timing solutions. Using these pulse arrival times, we contribute to long term pulse frequency history of the source. We look for episodic correlations and anti-correlations between torque and X-ray luminosity using CGRO--BATSE X-ray flux and frequency derivative time series and find that correlation state of GX 1+4 seems to change on $\sim$ 100-200 days long intervals. We estimate torque noise of the source and observe flickering noise ($f^{-1}$). We achieve to measure the longest observed timescale for a noise process among accretion powered X-ray pulsars by extending the noise estimate for a time scale ranging from 31 days to 44 years. Spectral analysis of individual RXTE-PCA observations indicates a significant correlation between iron line flux and unabsorbed X-ray flux. Pulse phase resolved spectra of the source indicate a broadening of iron line complex at the bin corresponding to the pulse minimum.

A Suzaku View of Accretion-powered X-Ray Pulsar GX 1+4

Abstract We present results obtained from a Suzaku observation of the accretion-powered X-ray pulsar GX 1+4. A broadband continuum spectrum of the pulsar was found to be better described by a simple model consisting of a blackbody component and an exponential cutoff power law than the previously used compTT continuum model. Though the pulse profile had a sharp dip in soft X-rays (&lt;10 keV), phase-resolved spectroscopy confirmed that the dimming was not due to an increase in photoelectric absorption. Phase-sliced spectral analysis showed the presence of a significant spectral modulation beyond 10 keV except for the dip phase. A search for the presence of a cyclotron resonance scattering feature in the Suzaku spectra yielded a negative result. Iron K-shell (K and ) emission lines from nearly neutral iron ions (&lt;Fe iii) were clearly detected in the source spectrum. A significant emission line from almost neutral Ni atoms was detected for the first time in this source. We estimated an iron abundance of ∼80% of the solar value and an Ni/Fe abundance ratio of about two times the solar value. We searched for an iron Ly emission line and found a significant improvement in the spectral fitting by inclusion of this line. We found a clear intensity modulation of the iron line with the pulse phase with an amplitude of 7%. This finding favored an inhomogeneous fluorescent region with a radius much smaller than the size (∼3 × 1012 cm) estimated by an assumption of homogeneous matter.

The 2015 outburst of the accretion-powered pulsar IGR J00291+5934: INTEGRAL andSwiftobservations

IGR J00291+5934 is the fastest-known accretion-powered X-ray pulsar, discovered during a transient outburst in 2004. In this paper, we report on Integral and Swift observations during the 2015 outburst, which lasts for $\sim25$ d. The source has not been observed in outburst since 2008, suggesting that the long-term accretion rate has decreased by a factor of two since discovery. The averaged broad-band (0.1 - 250 keV) persistent spectrum in 2015 is well described by a thermal Comptonization model with a column density of $N_{\rm H} \approx4\times10^{21}$ cm$^{-2}$, a plasma temperature of $kT_{\rm e} \approx50$ keV, and a Thomson optical depth of $\tau_{\rm T}\approx1$. Pulsations at the known spin period of the source are detected in the Integral data up to the $\sim150$ keV energy band. We also report on the discovery of the first thermonuclear burst observed from IGR J00291+5934, which lasts around 7 min and occurs at a persistent emission level corresponding to roughly $1.6\%$ of the Eddington accretion rate. The properties of the burst suggest it is powered primarily by helium ignited at a depth of $y_{\rm ign}\approx1.5\times10^9$ g cm$^{-2}$ following the exhaustion by steady burning of the accreted hydrogen. The Swift/BAT data from the first $\sim20$ s of the burst provide indications of a photospheric radius expansion phase. Assuming this is the case, we infer a source distance of $d = 4.2 \pm 0.3$ kpc.