Star Low-mass X-ray Binaries Research Articles

On the minimum spin period of accreting pulsars

ABSTRACT The distribution of the spin frequencies of neutron stars in low-mass X-ray binaries exhibits a cut-off at 730 Hz, below the break-up frequency (mass-shedding limit) of neutron stars. The absence of submillisecond pulsars presents a problem, given that these systems are older than the spin-up time-scale. We examine models of the disc–magnetosphere interaction near torque equilibrium balanced by the torque due to gravitational wave emission. We note that field lines penetrating the disc beyond the inner radius reduce the maximum rotation frequency of the star, a result well known since the seminal work of Ghosh & Lamb. We show that the polar cap area corresponds to about half the neutron star surface area at the cut-off frequency if the inner radius is slightly smaller than the corotation radius. We then include the change in the moment of inertia of the star due to the accretion of mass and find that this effect further reduces the maximum rotation frequency of the star. Finally, we include the torque due to gravitational wave emission and calculate its contribution to the torque equilibrium. Our results suggest that all three processes are significant at the cut-off frequency, and that all of them must be considered in addressing the absence of submillisecond pulsars.

Thefalse widowlink between neutron star X-ray binaries and spider pulsars

ABSTRACTThe discovery of transitional millisecond pulsars (tMSPs) provided conclusive proof that neutron star (NS) low-mass X-ray binaries (LMXBs) comprise part of the evolutionary pathway towards binary millisecond pulsars (MSPs). Redback and black widow ‘spider’ pulsars are a subcategory of binary MSPs that ‘devour’ their companions through ablation – the process through which material is lifted from the stellar surface by a pulsar wind. In addition to reducing the companion star’s mass, ablation introduces observable characteristics like extended, energy-dependent, and asymmetric eclipse profiles in systems observed at a sufficiently high inclination. Here, we present a detailed study and comparison of the X-ray eclipses of two NS LMXBs: Swift J1858.6 − 0814 and EXO 0748 − 676. Some of the X-ray eclipse characteristics observed in these two LMXBs are similar to the radio eclipse characteristics of eclipsing redback and black widow pulsars, suggesting that they may also host ablated companion stars. X-ray irradiation or a pulsar wind could drive the ablation. We conduct orbital phase-resolved spectroscopy for both LMXBs to map the column density, ionization, and covering fraction of the material outflow. From this, we infer the presence of highly ionized and clumpy ablated material around the companion star in both systems. We term LMXBs undergoing ablation, false widows, and speculate that they may be the progenitors of redback pulsars under the assumption that ablation begins in the LMXB stage. Therefore, the false widows could provide a link between LMXBs and spider pulsars. The detection of radio pulsations during non-accreting states can support this hypothesis.

Parallel tracks of kHz QPOs: implication of the bimodal luminosity components in neutron star low-mass X-ray binaries

ABSTRACT We employ the bimodal luminosity components, i.e. the disc luminosity Ld and non-disc luminosity Lr, to interpret the parallel track phenomena in the relation between the kilohertz quasi-periodic oscillation (kHz QPO) frequency ν and X-ray luminosity LX observed in the neutron star low-mass X-ray binaries: For an individual source with a constant non-disc luminosity Lr, the increase of its disc accretion rate $\dot{M}_{\rm d}$ can arise the shrink of neutron star magnetosphere-disc radius that results in the increase of the kHz QPO frequency. Then, with the enhancements of both the kHz QPO frequency and total X-ray luminosity, LX = Ld + Lr, the source will trace out an oblique track in ν–LX relation. Furthermore, for the different sources with various constant non-disc luminosities, they trace out series of parallel tracks in ν–LX relation. Our model presents an approximate power-law relation between the upper kHz QPO frequency ν2 and LX (i.e. $\nu _2\sim L_{\rm X}^k$), where the power-law index k decreases with the ratio parameter of $\mathcal {R}\equiv L_{\rm d}/L_{\rm r}$. Moreover, the fittings of $\nu _2{\!-\!}L_{\rm X}^k$ relation with the observation data indicate a range of ∼0.1–2.7 for the k values, which is basically compatible with the model prediction. In addition, we discussed the physical factors that affect the validity of the model.

Robust Inference of Neutron-star Parameters from Thermonuclear Burst Observations

Thermonuclear (type-I) bursts arise from unstable ignition of accumulated fuel on the surface of neutron stars in low-mass X-ray binaries. Measurements of burst properties in principle enable observers to infer the properties of the host neutron star and mass donors, but a number of confounding astrophysical effects contribute to systematic uncertainties. Here we describe some commonly used approaches for determining system parameters, including composition of the burst fuel, and introduce a new suite of software tools, concord, intended to fully account for astrophysical uncertainties. The comparison of observed burst properties with the predictions of numerical models is a complementary method of constraining host properties, and the tools presented here are intended to make comprehensive model-observation comparisons straightforward. When combined with the extensive samples of burst observations accumulated by X-ray observatories, these software tools will provide a step change in the amount of information that can be inferred about typical burst sources.

MeerKAT radio observations of the neutron star low-mass X-ray binary Cen X–4 at low accretion rates

ABSTRACT Centaurus X–4 (Cen X–4) is a relatively nearby neutron star low-mass X-ray binary that showed outbursts in 1969 and 1979, but has not shown a full outburst since. Due to its proximity and sustained period of quiescence, it is a prime target to study the coupling between accretion and jet ejection in quiescent neutron star low-mass X-ray binaries. Here, we present four MeerKAT radio observations at 1.3 GHz of Cen X–4, combined with NICER and Swift X-ray monitoring. During the first and most sensitive observation, Cen X–4 was in a fully quiescent X-ray state. The three later and shorter observations targeted a brief period of faint X-ray activity in 2021 January, which has been referred to as a ‘mis-fired’ outburst. Cen X–4 is not detected in any of the four MeerKAT observations. We place these radio non-detections on the X-ray–radio luminosity diagram, improving the constraints on the correlation between the two luminosities from earlier quiescent radio studies. We confirm that Cen X–4 is radio fainter than the transitional millisecond pulsar PSR J1023+0038 at the same X-ray luminosity. We discuss the radio behaviour of accreting neutron stars at low X-ray luminosity more generally and finally comment on future observing campaigns.

Polarization properties of weakly magnetized neutron stars in low-mass X-ray binaries

ABSTRACT X-ray polarimetry missions like Imaging X-ray Polarimetry Explorer will be able to measure for the first time the polarization properties of accreting, weakly magnetized neutron stars in low-mass X-ray binaries. In this work, we present simulations of the expected X-ray polarized signal, including the coronal emission for different geometries of the corona itself, i.e. a slab above the accretion disc and a spherical shell around the neutron star. The simulations are performed with the fully relativistic Monte Carlo code monk capable of computing the X-ray polarization degree and angle for various physical input parameters of the neutron star, disc, and corona. Different coronal geometries result in significantly different X-ray polarization properties, which can therefore be used to constrain the geometry of the systems.

Accreting neutron stars: heating of the upper layers of the inner crust

ABSTRACT Neutron stars in low-mass X-ray binaries are thought to be heated up by accretion-induced exothermic nuclear reactions in the crust. The energy release and the location of the heating sources are important ingredients of the thermal evolution models. Here, we present thermodynamically consistent calculations of the energy release in three zones of the stellar crust: at the outer–inner crust interface, in the upper layers of the inner crust (up to the density ρ ≤ 2 × 1012 g cm−3), and in the underlying crustal layers. We consider three representative models of thermonuclear ashes (superburst, extreme rp, and Kepler ashes). The energy release in each zone is parametrized by the pressure at the outer–inner crust interface, Poi, which encodes all uncertainties related to the physics of the deepest inner-crust layers. Our calculations allow us to set new theoretical lower limits on the net energy release (per accreted baryon): Q ≳ 0.28 MeV for extreme rp ashes and Q ≳ 0.43–0.51 MeV for superburst and Kepler ashes. Our results can be directly incorporated into numerical codes and provide an opportunity to constrain Poi by comparing thermal evolution models of accreting neutron stars with observations.

The MAVERIC Survey: Variable Jet-accretion Coupling in Luminous Accreting Neutron Stars in Galactic Globular Clusters

Abstract Accreting neutron stars in low-mass X-ray binaries show outflows—and sometimes jets—in the general manner of accreting black holes. However, the quantitative link between the accretion flow (traced by X-rays) and outflows and/or jets (traced by radio emission) is much less well understood for neutron stars than for black holes, other than the general observation that neutron stars are fainter in the radio at a given X-ray luminosity. We use data from the deep MAVERIC radio continuum survey of Galactic globular clusters for a systematic radio and X-ray study of six luminous (L X > 1034 erg s−1) persistent neutron star X-ray binaries in our survey, as well as two other transient systems also captured by our data. We find that these neutron star X-ray binaries show an even larger range in radio luminosity than previously observed. In particular, in quiescence at L X ∼ 3 × 1034 erg s−1, the confirmed neutron star binary GRS 1747–312 in Terzan 6 sits near the upper envelope of the black hole radio/X-ray correlation, and the persistently accreting neutron star systems AC 211 (in M15) and X1850–087 (in NGC 6712) show unusual radio variability and luminous radio emission. We interpret AC 211 as an obscured “Z source” that is accreting at close to the Eddington limit, while the properties of X1850–087 are difficult to explain, and motivate future coordinated radio and X-ray observations. Overall, our results show that neutron stars do not follow a single relation between inflow and outflow, and confirm that their accretion dynamics are more complex than for black holes.

Nonequilibrium thermodynamics of accreted neutron-star crust

We show that, in order to determine the equation of state of the inner crust of an accreting neutron star, one should minimize not the Gibbs free energy, as it is generally assumed in the literature, but a different thermodynamic potential $\Psi$, which tends to the minimum at fixed pressure and neutron chemical potential. Once this potential is specified, one can calculate the heat-release distribution in the stellar crust due to nonequilibrium nuclear reactions induced by accretion of matter onto the neutron-star surface. The results are important for adequate modeling of the accreted crust and interpretation of the observations of accreting neutron stars in low-mass X-ray binaries.

Discovery of Transition from Marginally Stable Burning to Unstable Burning after a Superburst in Aql X-1

Abstract Superbursts are long duration, rare, and extremely energetic thermonuclear explosions of neutron star low-mass X-ray binaries (NS LMXBs), which are proposed to be due to unstable carbon ignition. We report the superburst properties and consequences from Aql X–1 observed by the Neutron Star Interior Composition Explorer (NICER), the Monitor of All-sky X-ray Image, Swift, and Insight Hard X-ray Modulation Telescope (Insight-HXMT) on the MJD 59130.7. We found two faint type I X-ray bursts 9.44 days after the superburst with a short recurrence time of 7.6 minutes, which is the most accurate measurement of the quenching time in all NS LMXBs with observed superbursts. We also discovered mHz quasi-periodic oscillations in the frequency range 2.7–11.3 mHz immediately after the superburst, before and after the resumption of the first type I X-ray burst from NICER, Swift, and Insight-HXMT observations. For the first time, we observed the transition from superburst, via marginally stable burning to unstable burning in NS LMXBs. We compared the quenching time and the recurrence time of type I X-ray bursts with simulations.

The MAVERIC Survey: Simultaneous Chandra and VLA observations of the transitional millisecond pulsar candidate NGC 6652B

ABSTRACT Transitional millisecond pulsars are millisecond pulsars that switch between a rotation-powered millisecond pulsar state and an accretion-powered X-ray binary state, and are thought to be an evolutionary stage between neutron star low-mass X-ray binaries and millisecond pulsars. So far, only three confirmed systems have been identified in addition to a handful of candidates. We present the results of a multiwavelength study of the low-mass X-ray binary NGC 6652B in the globular cluster NGC 6652, including simultaneous radio and X-ray observations taken by the Karl G. Jansky Very Large Array and the Chandra X-ray Observatory, and optical spectroscopy and photometry. This source is the second brightest X-ray source in NGC 6652 ($L_{\textrm {X}}\sim 1.8 \times 10^{34}{\, \mathrm{erg\, s}^{-1}}$) and is known to be variable. We observe several X-ray flares over the duration of our X-ray observations, in addition to persistent radio emission and occasional radio flares. Simultaneous radio and X-ray data show no clear evidence of anticorrelated variability. Optical spectra of NGC 6652B indicate variable, broad H α emission that transitions from double-peaked emission to absorption over a time-scale of hours. We consider a variety of possible explanations for the source behaviour, and conclude that based on the radio and X-ray luminosities, short time-scale variability and X-ray flaring, and optical spectra, NGC 6652B is best explained as a transitional millisecond pulsar candidate that displays prolonged X-ray flaring behaviour. However, this could only be confirmed with observations of a change to the rotation-powered millisecond pulsar state.

Measuring the masses and radii of neutron stars in low-mass X-ray binaries: Effects of the atmospheric composition and touchdown radius

Context. X-ray bursts (XRBs) are energetic explosive events that have been observed in low-mass X-ray binaries (LMXBs). Some Type-I XRBs exhibit photospheric radius expansion (PRE) and these PRE XRBs are used to simultaneously estimate the mass and the radius of a neutron star in LMXB. Aims. The mass and radius estimation depends on several model parameters, most of which are still uncertain. Here, we focus on the effects of the chemical composition of the photosphere, which determines the opacity during the PRE phase, and the touchdown radius, which can be larger than the neutron star radius. We investigate how these two model parameters affect the mass and radius estimation in a systematic way and whether there is any statistical trend for these two parameters as well as whether there is a possible correlation between them. Methods. We used both a Monte Carlo (MC) sampling and a Bayesian analysis to examine the effects of the photospheric composition and the touchdown radius. We applied these two methods to six LMXBs exhibiting PRE XRBs. With both methods, we solved the Eddington flux equation and the apparent angular area equation, both of which include the correction terms. For the MC sampling, we developed an iterative method in order to solve these two equations more efficiently. Results. We confirm that the effects of the photospheric composition and the touchdown radius are similar in the statistical and analytical estimation of mass and radius, even when the correction terms are considered. Furthermore, in all of the six sources, we find that a H-poor photosphere and a large touchdown radius are favored statistically regardless of the statistical method. Our Bayesian analysis also hints that touchdown can occur farther from the neutron star surface when the photosphere is more H-poor. This correlation could be qualitatively understood with the Eddington flux equation. We propose a physical explanation for this correlation between the photospheric composition and the touchdown radius. Our results show that when accounting for the uncertainties of the photospheric composition and the touchdown radius, it is most likely that the radii of the neutron stars in these six LMXBs are less than 12.5 km. This value is similar to that of the bounds placed on the neutron star radius based on the tidal deformability measured from the gravitational wave signal.

Mechanical model of a boundary layer for the parallel tracks of kilohertz quasi-periodic oscillations in accreting neutron stars

Kilohertz-scale quasi-periodic oscillations (kHz QPOs) are a distinct feature of the variability of neutron star low-mass X-ray binaries. Among all the variability modes, they are especially interesting as a probe for the innermost parts of the accretion flow, including the accretion boundary layer (BL) on the surface of the neutron star. All the existing models of kHz QPOs explain only part of their rich phenomenology. Here, we show that some of their properties can be explained by a very simple model of the BL that is spun up by accreting rapidly rotating matter from the disk and spun down by the interaction with the neutron star. In particular, if the characteristic time scales for the mass and the angular momentum transfer from the BL to the star are of the same order of magnitude, our model naturally reproduces the so-called parallel tracks effect, where the QPO frequency is correlated with luminosity at time scales of hours but becomes uncorrelated at time scales of days. The closeness of the two time scales responsible for mass and angular momentum exchange between the BL and the star is an expected outcome of the radial structure of the BL.

The radiative efficiency of neutron stars at low-level accretion

ABSTRACT When neutron star low-mass X-ray binaries (NS-LMXBs) are in the low-level accretion regime (i.e. $L_{\rm X}\lesssim 10^{36}\ \rm erg\ s^{-1}$), the accretion flow in the inner region around the NS is expected to exist in the form of the hot accretion flow, e.g. the advection-dominated accretion flow (ADAF) as that in black hole X-ray binaries. Following our previous studies in Qiao & Liu (2020a, b) on the ADAF accretion around NSs, in this paper, we investigate the radiative efficiency of NSs with an ADAF accretion in detail, showing that the radiative efficiency of NSs with an ADAF accretion is much lower than that of $\epsilon \sim {\dot{M} GM\over R_{*}}/{\dot{M} c^2}\sim 0.2$ despite the existence of the hard surface. As a result, given an X-ray luminosity LX (e.g. between 0.5 and 10 keV), $\dot{M}$ calculated by $\dot{M}=L_{\rm X}{R_{*}\over {GM}}$ is lower than the real $\dot{M}$ calculated within the framework of the ADAF accretion. The real $\dot{M}$ can be more than two orders of magnitude higher than that calculated by $\dot{M}=L_{\rm X}{R_{*}\over {GM}}$ with appropriate model parameters. Finally, we discuss that if applicable, the model of ADAF accretion around a NS can be applied to explain the observed millisecond X-ray pulsation in some NS-LMXBs (such as PSR J1023+0038, XSS J12270−4859, and IGR J17379−3747) at a lower X-ray luminosity of a few times of $10^{33}\ \rm erg\ s^{-1}$, since at this X-ray luminosity the calculated $\dot{M}$ with the model of ADAF accretion can be high enough to drive a fraction of the matter in the accretion flow to be channelled on to the surface of the NS forming the X-ray pulsation.

Resonance suppression of the r -mode instability in superfluid neutron stars: Accounting for muons and entrainment

We calculate the finite-temperature r-mode spectrum of a superfluid neutron star accounting for both muons in the core and the entrainment between neutrons and protons. We show that the standard perturbation scheme, considering the rotation rate as an expansion parameter, breaks down in this case. We develop an original perturbation scheme which circumvents this problem by treating both the perturbations due to rotation and (weak) entrainment simultaneously. Applying this scheme, we propose a simple method for calculating the superfluid r-mode eigenfrequency in the limit of vanishing rotation rate. We also calculate the r-mode spectrum at finite rotation rate for realistic microphysics input (adopting, however, the Newtonian framework and Cowling approximation when considering perturbed oscillation equations) and show that the normal r-mode exhibits resonances with superfluid r-modes at certain values of temperatures and rotation frequencies in the parameter range relevant to neutron stars in low-mass X-ray binaries (LMXBs). This turns the recently suggested phenomenological model of resonance r-mode stabilization into a quantitative theory, capable of explaining observations. A strong dependence of resonance rotation rates and temperatures on the neutron superfluidity model allows us to constrain the latter by confronting our calculations with the observations of neutron stars in LMXBs.

Effects of dynamo magnetic fields on observational properties of accreting millisecond X-ray pulsars

In this paper, we have investigated accreting millisecond X-ray pulsars, which are rapidly rotating neutron stars in low-mass X-ray binaries. These systems exhibit coherent X-ray pulsations that arise when the accretion flow is magnetically channeled to the stellar surface. Here, we have developed the fundamental equations for an accretion disk around accreting millisecond X-ray pulsars in the presence of a dynamo generated magnetic field in the inner part of the disk. We have also formulated the numerical method for the structure equations in the inner region of the disk and the highest accretion rate is enough to form the inner region of the disk, which is overpowered by radiation pressure and electron scattering. Finally, we have examined our results with the effects of dynamo magnetic fields on accreting millisecond X-ray pulsars.

Search for intermittent X-ray pulsations from neutron stars in low-mass X-ray binaries

Abstract We present the results of our extensive binary orbital motion corrected pulsation search for 13 low-mass X-ray binaries. These selected sources exhibit burst oscillations in X-rays with frequencies ranging from 45 to 1 122 Hz and have a binary orbital period varying from 2.1 to 18.9 h. We first determined episodes that contain weak pulsations around the burst oscillation frequency by searching all archival Rossi X-ray Timing Explorer data of these sources. Then, we applied Doppler corrections to these pulsation episodes to discard the smearing effect of the binary orbital motion and searched for recovered pulsations at the second stage. Here we report 75 pulsation episodes that contain weak but coherent pulsations around the burst oscillation frequency. Furthermore, we report eight new episodes that show relatively strong pulsations in the binary orbital motion corrected data.

NuSTAR observation of GRO J1744–28 at low mass accretion rate

Context. Neutron stars in low-mass X-ray binaries are important systems for studying the physics of accretion onto compact objects. The system GRO J1744–28 is particularly interesting as it usually shows clear pulsations as well as X-ray bursts. Additionally, there are claims for a magnetic field of 5 × 1011 G through the detection of a cyclotron resonant scattering feature (CRSF). Aims. We present the spectral analysis of GRO J1744–28 using ∼29 ks of NuSTAR data taken in 2017 February at a low luminosity of 3.2 × 1036 erg s−1 (3−50 keV). Our goal is to study the variability of the source spectrum with pulse phase and to search for the claimed CRSF. Methods. The continuum spectrum was modeled with an absorbed power law with exponential cutoff, and an additional iron line component. We found no obvious indications for a CRSF, and therefore performed a detailed cyclotron line search using statistical methods. We performed this search on pulse phase-averaged spectra and on phase-resolved spectra. Results. GRO J1744–28 was observed in a low-luminosity state. The previously detected Type II X-ray bursts are absent. Clear pulsations at a period of 2.141124(9) Hz are detected. The pulse profile shows an indication of a secondary peak that was not seen at higher flux. The upper limit for the strength of a CRSF in the 3−20 keV band is 0.07 keV (90% CL), lower than the strength of the line found at higher luminosity. Conclusions. The detection of pulsations shows that the source did not enter the “propeller” regime, even though the source flux of 4.15 × 10−10 erg cm−2 s−1 was almost one order of magnitude below the threshold for the propeller regime claimed in previous studies on this source. The transition into the propeller regime in GRO J1744–28 must therefore be below a luminosity of 3.2 × 1036 erg s−1 (3−50 keV), which implies a surface magnetic field ≲2.9 × 1011 G and mass accretion rate ≲1.7 × 1016 g s−1. A change of the CRSF depth as function of luminosity is not unexpected and has been observed in other sources. This result possibly implies a change in emission geometry as function of mass accretion rate to reduce the depth of the line below our detection limit.

R-mode instability of neutron stars in Low-mass X-ray binaries: effects of Fermi surface depletion and superfluidity of dense matter

Abstract The nucleon-nucleon correlation between nucleons leads to the Fermi surface depletion measured by a Z-factor in momentum distribution of dense nuclear matter. The roles of the Fermi surface depletion effect (Z-factor effect) and its quenched neutron triplet superfluidity of nuclear matter in viscosity and hence in the gravitational-wave-driven r-mode instability of neutron stars (NSs) are investigated. The bulk viscosity is reduced by both the two effects, especially the superfluid effect at low temperatures which is also able to reduce the inferred core temperature of NSs. Intriguingly, due to the neutron superfluidity, the core temperature of the NSs in known low-mass X-ray binaries (LMXBs) are found to be clearly divided into two groups: high and low temperatures which correspond to NSs with short and long recurrence times for nuclear-powered bursts respectively. Yet, a large number of NSs in these LMXBs are still located in the r-mode instability region. If the density-dependent symmetry energy is stiff enough, the occurence of direct Urca process reduces the inferred core temperature by about one order of magnitude. Accordingly, the contradiction between the predictions and observations is alleviated to some extent, but some NSs are still located inside the unstable region.

Constraining Neutron Superfluidity with R-Mode Physics.

We constrain the parameters of neutron superfluidity in the cores of neutron stars making use of the recently proposed effect of resonance stabilization of r modes. To this end, we, for the first time, calculate the finite-temperature r-mode spectra for realistic models of rotating superfluid neutron stars, accounting for both muons and neutron-proton entrainment in their interiors. We find that the ordinary (normal) r mode exhibits avoided crossings with superfluid r modes at certain stellar temperatures and spin frequencies. Near the avoided crossings, the normal r mode dissipates strongly, which leads to substantial suppression of the r-mode instability there. The extreme sensitivity of the positions of avoided crossings to the neutron superfluidity model allows us to constrain the latter by confronting the calculated spectra with observations of rapidly rotating neutron stars in low-mass x-ray binaries.