Accreting Neutron Stars Research Articles

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.

A Comprehensive X-Ray Report on AT2019wey

Abstract Here, we present MAXI, Swift, NICER, NuSTAR, and Chandra observations of the X-ray transient AT2019wey (SRGA J043520.9+552226, SRGE J043523.3+552234). From spectral and timing analyses we classify it as a Galactic low-mass X-ray binary (LMXB) with a black hole (BH) or neutron star (NS) accretor. AT2019wey stayed in the low/hard state (LHS) from 2019 December to 2020 August 21, and the hard-intermediate state (HIMS) from 2020 August 21 to 2020 November. For the first six months of the LHS, AT2019wey had a flux of ∼1 mCrab, and displayed a power-law X-ray spectrum with photon index Γ = 1.8. From 2020 June to August, it brightened to ∼20 mCrab. Spectral features characteristic of relativistic reflection became prominent. On 2020 August 21, the source left the “hard line” on the rms–intensity diagram, and transitioned from LHS to HIMS. The thermal disk component became comparable to the power-law component. A low-frequency quasi-periodic oscillation (QPO) was observed. The QPO central frequency increased as the spectrum softened. No evidence of pulsation was detected. We are not able to decisively determine the nature of the accretor (BH or NS). However, the BH option is favored by the position of this source on the Γ–L X, L radio–L X, and L opt–L X diagrams. We find the BH candidate XTE J1752−223 to be an analog of AT2019wey. Both systems display outbursts with long plateau phases in the hard states. We conclude by noting the potential of SRG in finding new members of this emerging class of low luminosity and long-duration LMXB outbursts.

Multi-wavelength Observations of AT2019wey: a New Candidate Black Hole Low-mass X-ray Binary

Abstract AT2019wey (SRGA J043520.9+552226, SRGE J043523.3+552234) is a transient first reported by the ATLAS optical survey in 2019 December. It rose to prominence upon detection, three months later, by the Spektrum-Roentgen-Gamma (SRG) mission in its first all-sky survey. X-ray observations reported in Yao et al. suggest that AT2019wey is a Galactic low-mass X-ray binary (LMXB) with a black hole (BH) or neutron star (NS) accretor. Here we present ultraviolet, optical, near-infrared, and radio observations of this object. We show that the companion is a short-period (P ≲ 16 hr) low-mass (<1 M ⊙) star. We consider AT2019wey to be a candidate BH system since its locations on the L radio–L X and L opt–L X diagrams are closer to BH binaries than NS binaries. We demonstrate that from 2020 June to August, despite the more than 10 times brightening at radio and X-ray wavelengths, the optical luminosity of AT2019wey only increased by 1.3–1.4 times. We interpret the UV/optical emission before the brightening as thermal emission from a truncated disk in a hot accretion flow and the UV/optical emission after the brightening as reprocessing of the X-ray emission in the outer accretion disk. AT2019wey demonstrates that combining current wide-field optical surveys and SRG provides a way to discover the emerging population of short-period BH LMXB systems with faint X-ray outbursts.

Plasma screening of nuclear fusion reactions in liquid layers of compact degenerate stars: a first-principle study

ABSTRACT A reliable description of nuclear fusion reactions in inner layers of white dwarfs and envelopes of neutron stars is important for realistic modelling of a wide range of observable astrophysical phenomena from accreting neutron stars to Type Ia supernovae. We study the problem of screening of the Coulomb barrier impeding the reactions by a plasma surrounding the fusing nuclei. Numerical calculations of the screening factor are performed from the first principles with the aid of quantum-mechanical path integrals in the model of a one-component plasma of atomic nuclei for temperatures and densities typical for dense liquid layers of compact degenerate stars. We do not rely on various quasi-classic approximations widely used in the literature, such as factoring out the tunnelling process, tunnelling in an average spherically symmetric mean-force potential, usage of classic free energies and pair correlation functions, linear mixing rule, and so on. In general, a good agreement with earlier results from the thermonuclear limit to Γ ∼ 100 is found. For a very strongly coupled liquid 100 ≲ Γ ≤ 175, a deviation from currently used parametrizations of the reaction rates is discovered and approximated by a simple analytic expression. The developed method of nuclear reaction rate calculations with account of plasma screening can be extended to ion mixtures and crystallized phases of stellar matter.

Radiative MHD simulations of photon bubbles in radiation-supported magnetized atmospheres of neutron stars with isotropic Thomson scattering

ABSTRACT A major uncertainty in the structure and dynamics of magnetized, radiation pressure dominated neutron star accretion columns in X-ray pulsars and pulsating ultraluminous X-ray sources is that they are thought to be subject to the photon bubble instability. We present the results of two-dimensional radiation relativistic magnetohydrodynamic simulations of a non-accreting, static atmosphere to study the development of this instability assuming isotropic Thomson scattering in the slow diffusion regime that is relevant to neutron star accretion columns. Photon bubbles generally grow faster towards shorter wavelengths, until a maximum growth rate is achieved at the radiation viscosity length-scale, which is generally quite small and requires high numerical resolution to simulate. We confirm the consistency between our simulation results and linear theory in detail, and show that the non-linear evolution inevitably leads to collapse of the atmosphere with the higher resolution simulation collapsing faster due to the presence of shorter length-scale non-linear structures. At least in static atmospheres with horizontally periodic boundary conditions, this resolution dependence may make simulations of the non-linear dynamics of photon bubble instability in neutron star accretion columns challenging. It remains to be seen whether these difficulties will persist upon inclusion of an accretion flow through the top and magnetically confined horizontal boundaries through which photons can escape. Our results here provide a foundation for such future work.

Relation of Cyclotron Resonant Energy and Luminosity in a Strongly Magnetized Neutron Star GRO J1008-57 Observed by Insight-HXMT

Abstract Cyclotron line scattering features are detected in a few tens of X-ray pulsars (XRPs) and used as direct indicators of a strong magnetic field at the surface of accreting neutron stars (NSs). In a few cases, cyclotron lines are known to be variable with the accretion luminosity of XRPs. It is accepted that the observed variations of cyclotron line scattering features are related to variations of geometry and dynamics of accretion flow above the magnetic poles of an NS. A positive correlation between the line centroid energy and luminosity is typical for subcritical XRPs, where the accretion results in hot spots at the magnetic poles. The negative correlation was proposed to be a specific feature of bright supercritical XRPs, where radiation pressure supports accretion columns above the stellar surface. The cyclotron line in the spectra of the Be-transient XRP GRO J1008-57 is detected at energies from ∼75 to 90 keV, the highest observed energy of a cyclotron line feature in XRPs. We report the peculiar relation of cyclotron line centroid energies with luminosity in GRO J1008-57 during the Type II outburst in 2017 August observed by Insight-HXMT. The cyclotron line energy was detected to be negatively correlated with the luminosity at 3.2 × 1037 erg s−1 < L < 4.2 × 1037 erg s−1 and positively correlated at L ≳ 5 × 1037 erg s−1. We speculate that the observed peculiar behavior of a cyclotron line would be due to variations of accretion channel geometry.

High-Mass X-ray binary: Classification, Formation, and Evolution

A high mass X-ray binary is a binary system consisting of an accreting neutron star or black hole and an early-type star with more than 10 solar masses. A compact star produces X-ray radiation during the accretion of material from the stellar wind or Roche lobe. High-mass X-ray binaries are ideal places to study dense stars, stellar winds, material exchange between binary stars, and the evolution of massive binary stars. In this review, the observational properties, classification, and evolution of high mass X binaries are described. According to the mass and types of X-ray resources, this review classifies the X-ray binaries and list out their features.

Spectral-temporal features of repeating and one-off fast radio bursts and axion star

The fast radio bursts ( FRBs ) are energetic radio bursts with millisecond duration only observed at radio frequencies. The generation mechanism is still mysterious. We have proposed a generation mechanism of both repeating and one-off FRBs. They arise from the axion star collision with neutron star or magnetized accretion disk of galactic black hole. Once we accept the existence of the axions, we find that the mechanism well explain previously observed spectral-temporal features. In this paper we show that it also explains recently observed phenomena such as downward drifting in the repeating FRBs, etc.. Analysis of the downward drifting based on Doppler effects has been presented in recent papers, in which a superradiance system of molecular or atom has been proposed as a source of FRBs. We apply the analysis to our mechanism and find that it well explains the relation between the downward drifting rate and the duration of the repeating FRBs. The Doppler effects lead to the fact that the duration of radio burst with higher center frequency is shorter than that of radio burst with lower center frequency in the repeating FRBs. Our generation mechanism naturally explain polarization angle swing observed in the repeating FRB180301 and one-off FRBs. We also discuss the association between the FRB200428 and magnetar SGR J1935+2154. The X ray burst observed just after the observation of the FRB could be triggered by the axion star collision with the magnetar. We also explain the consistency of our generation mechanism with observed spectral-temporal differences in the repeating and one-off FRBs, e.g. longer duration ( smaller flux density ) of repeating FRBs than duration ( flux density ) of one-off FRBs.

Deep crustal heating for realistic compositions of thermonuclear ashes

ABSTRACT The deep crustal heating, associated with exothermal nuclear reactions, is believed to be a key parameter for describing the thermal evolution of accreting neutron stars. In this paper, we present the first thermodynamically consistent calculations of the crustal heating for realistic compositions of thermonuclear ashes. In contrast to previous studies based on the traditional approach, we account for neutron hydrostatic/diffusion (nHD) equilibrium condition imposed by superfluidity of neutrons in a major part of the inner crust and rapid diffusion in the remaining part of the inner crust. We apply a simplified reaction network to model nuclear evolution of various multi-component thermonuclear burning ashes (superburst, KEPLER, and extreme rp-process ashes) in the outer crust and calculate the deep crustal heating energy release Q, parametrized by the pressure at the outer–inner crust interface, Poi. Using the general thermodynamic arguments, we set a lower limit on Q, Q ≳ 0.13−0.2 MeV per baryon (an actual value depends on the ash composition and the employed mass model).

Hidden Markov model tracking of continuous gravitational waves from a binary neutron star with wandering spin. III. Rotational phase tracking

A hidden Markov model (HMM) solved recursively by the Viterbi algorithm can be configured to search for persistent, quasimonochromatic gravitational radiation from an isolated or accreting neutron star, whose rotational frequency is unknown and wanders stochastically. Here an existing HMM analysis pipeline is generalized to track rotational phase and frequency simultaneously, by modeling the intra-step rotational evolution according to a phase-wrapped Ornstein-Uhlenbeck process, and by calculating the emission probability using a phase-sensitive version of the Bayesian matched filter known as the $\mathcal{B}$-statistic. The generalized algorithm tracks signals from isolated and binary sources with characteristic wave strain $h_0 \geq 1.3\times 10^{-26}$ in Gaussian noise with amplitude spectral density $4\times 10^{-24}\,{\rm Hz^{-1/2}}$, for a simulated observation composed of $N_T=37$ data segments, each $T_{\rm drift}=10\,{\rm days}$ long, the typical duration of a search for the low-mass X-ray binary (LMXB) Sco X$-$1 with the Laser Interferometer Gravitational Wave Observatory (LIGO). It is equally sensitive to isolated and binary sources and $\approx 1.5$ times more sensitive than the previous pipeline. Receiver operating characteristic curves and errors in the recovered parameters are presented for a range of practical $h_0$ and $N_T$ values. The generalized algorithm successfully detects every available synthetic signal in Stage I of the Sco X$-$1 Mock Data Challenge convened by the LIGO Scientific Collaboration, recovering the frequency and orbital semimajor axis with accuracies of better than $9.5\times 10^{-7}\,{\rm Hz}$ and $1.6\times 10^{-3}\,{\rm lt\,s}$ respectively. The Viterbi solver runs in $\approx 2\times 10^3$ CPU-hr for an isolated source and $\sim 10^5$ CPU-hr for a LMXB source in a typical, broadband ($0.5$-${\rm kHz}$) search.

Broadband X-ray spectral variability of the pulsing ULX NGC 1313 X-2

Context. It is thought that ultraluminous X-ray sources (ULXs) are mainly powered by super-Eddington accreting neutron stars or black holes as shown by the recent discovery of X-ray pulsations and relativistic winds. Aims. This work presents a follow-up study of the spectral evolution over two decades of the pulsing ULX NGC 1313 X-2 in order to understand the structure of the accretion disc. The primary objective is to determine the shape and nature of the dominant spectral components by investigating their variability with the changes in the source luminosity. Methods. We performed a spectral analysis over the canonical 0.3–10.0 keV energy band of all the high signal-to-noise XMM-Newton observations (96% of the available data), and we tested a number of different spectral models, which should approximate super-Eddington accretion discs. The baseline model consists of two thermal blackbody components with different temperatures plus an exponential cutoff powerlaw. Results. The baseline model provides a good description of the X-ray spectra. In particular, the hotter and brighter (LX ∼ 6–9 × 1039 erg s−1) thermal component describes the emission from the super-Eddington inner disc and the cutoff powerlaw describes the contribution from the accretion column of the neutron star. Instead, the cooler component describes the emission from the outer region of the disc close to the spherisation radius and the wind. The luminosity-temperature relation for the cool component follows a negative trend, which is not consistent with L ∝ T4, as is expected from a sub-Eddington thin disc of Shakura-Sunayev. This is not consistent with L ∝ T2 either, as is expected for an advection-dominated disc. However, this would rather agree with a wind-dominated X-ray emitting region. Instead, the (Lx, Tdisk) relation for the hotter component is somewhere in between the first two theoretical scenarios. Conclusions. Our findings agree with the super-Eddington scenario and provide further detail on the disc structure. The source spectral evolution is qualitatively similar to that seen in NGC 1313 X-1 and Holmberg IX X-1, indicating a common structure and evolution among archetypal ULXs.

Ultracompact X-ray binaries with He star companions

ABSTRACT Ultracompact X-ray binaries (UCXBs) are low-mass X-ray binaries with hydrogen-deficient mass donors and ultrashort orbital periods. They have been suggested to be the potential Laser Interferometer Space Antenna (LISA) sources in the low-frequency region. Several channels for the formation of UCXBs have been proposed so far. In this paper, we carried out a systematic study on the He star donor channel, in which a neutron star (NS) accretes matter from a He main-sequence (MS) star through Roche lobe overflow, where the mass transfer is driven by the gravitational wave radiation. First, we followed the long-term evolution of the NS+He MS binaries by employing the stellar evolution code Modules for Experiments in Stellar Astrophysics (mesa ), and thereby obtained the initial parameter spaces for the production of UCXBs. We then used these results to perform a detailed binary population synthesis approach to obtain the Galactic rates of UCXBs through this channel. We estimate the Galactic rates of UCXBs appearing as LISA sources to be ${\sim} 3.1\!-\!11.9\, \rm Myr^{-1}$ through this channel, and the number of such UCXB-LISA sources in the Galaxy can reach about 1–26 calibrated by observations. This work indicates that the He star donor channel may contribute significantly to the Galactic UCXB formation rate. We found that the evolutionary tracks of UCXBs through this channel can account for the location of the five transient sources with relatively long orbital periods quite well. We also found that such UCXBs can be identified by their locations in the mass-transfer rate versus the orbital period diagram.

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.

XMM-Newton campaign on the ultraluminous X-ray source NGC 247 ULX-1: outflows

ABSTRACT Most ultraluminous X-ray sources (ULXs) are believed to be powered by super-Eddington accreting neutron stars and, perhaps, black holes. Above the Eddington rate the disc is expected to thicken and to launch powerful winds through radiation pressure. Winds have been recently discovered in several ULXs. However, it is yet unclear whether the thickening of the disc or the wind variability causes the switch between the classical soft and supersoft states observed in some ULXs. In order to understand such phenomenology and the overall super-Eddington mechanism, we undertook a large (800 ks) observing campaign with XMM-Newton to study NGC 247 ULX-1, which shifts between a supersoft and classical soft ULX state. The new observations show unambiguous evidence of a wind in the form of emission and absorption lines from highly ionized ionic species, with the latter indicating a mildly relativistic outflow (−0.17c) in line with the detections in other ULXs. Strong dipping activity is observed in the light curve and primarily during the brightest observations, which is typical among soft ULXs, and indicates a close relationship between the accretion rate and the appearance of the dips. The latter is likely due to a thickening of the disc scale height and the wind as shown by a progressively increasing blueshift in the spectral lines.

Quark matter contribution to the heat capacity of magnetized neutron stars

In this paper, we find the heat capacity of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and use it to explore the feasibility of this phase for a neutron star interior. MDCDW is a spatially inhomogeneous phase of quark matter known to be favored at intermediate densities over the chirally symmetric phase and the color-flavor-locked superconducting phase. By comparing our result to the lower limit of the core heat capacity established from observations of transiently accreting neutron stars, we show that the heat capacity of MDCDW quark matter is well above that lower limit and hence cannot be ruled out. This result adds to a wealth of complementary investigations, all of which has served to strengthen the viability of a neutron star interior made of MDCDW quark matter. For completeness, we review the contributions to the heat capacity of the main neutron star ingredients at low, high, and intermediate densities, with and without the presence of a magnetic field.

Heating in Magnetar Crusts from Electron Captures

The persistent thermal luminosity of magnetars and their outbursts suggest the existence of some internal heat sources located in their outer crust. The compression of matter accompanying the decay of the magnetic field may trigger exothermic electron captures and, possibly, pycnonuclear fusions of light elements that may have been accreted onto the surface from the fallback of supernova debris, from a disk or from the interstellar medium. This scenario bears some resemblance to deep crustal heating in accreting neutron stars, although the matter composition and the thermodynamic conditions are very different. The maximum possible amount of heat that can be released by each reaction and their locations are determined analytically taking into account the Landau–Rabi quantization of electron motion. Numerical results are also presented using experimental, as well as theoretical nuclear data. Whereas the heat deposited is mainly determined by atomic masses, the locations of the sources are found to be very sensitive to the magnetic field strength, thus providing a new way of probing the internal magnetic field of magnetars. Most sources are found to be concentrated at densities 1010–1011 g cm−3 with heat power W∞∼1035–1036 erg/s, as found empirically by comparing cooling simulations with observed thermal luminosity. The change of magnetic field required to trigger the reactions is shown to be consistent with the age of known magnetars. This suggests that electron captures and pycnonuclear fusion reactions may be a viable heating mechanism in magnetars. The present results provide consistent microscopic inputs for neutron star cooling simulations, based on the same model as that underlying the Brussels-Montreal unified equations of state.

The formulation of vector potential evolution equation on rapidly rotating and accreting neutron star in the frame of Zero Angular Momentum Observers (ZAMO)

The equation for the dynamics of the magnetic field can explain the decrease in the magnetic field due to accretion. Maxwell’s relativistic equations formulate these equations. The formulation of the solution to the Maxwell equation is said to be correct if it is by the Schwarzschild space-time case by formulating the vector potential evolution equation. Maxwell’s second relativistic equation, the covariance tensor of the electromagnetic field, and the vector potential are used to obtain the equation for the evolution of the vector potential. All equations are calculated in the Zero Angular Momentum Observers (ZAMO) framework. The purpose of this research is to formulate the vector potential evolution equation for each component in a rapidly rotating and accreting neutron star. The results obtained have covariant terms with the slow rotating neutron star. However, the equation for a rapidly rotating neutron star has a more complex description. There are terms that cannot be simplified, such as in slowly rotating neutron stars.

Expanded Atmospheres and Winds in Type I X-Ray Bursts from Accreting Neutron Stars

Abstract We calculate steady-state models of radiation-driven super-Eddington winds and static expanded envelopes of neutron stars caused by high luminosities in type I X-ray bursts. We use flux-limited diffusion to model the transition from optically thick to optically thin, and include effects of general relativity, allowing us to study the photospheric radius close to the star as the hydrostatic atmosphere evolves into a wind. We find that the photospheric radius evolves monotonically from static envelopes (r ph ≲ 50–70 km) to winds (r ph ≈ 100–1000 km). Photospheric radii of less than 100 km, as observed in most photospheric radius expansion bursts, can be explained by static envelopes, but only in a narrow range of luminosity. In most bursts, we would expect the luminosity to increase further, leading to a wind with photospheric radius ≳100 km. In the contraction phase, the expanded envelope solutions show that the photosphere is still ≈1 km above the surface when the effective temperature is only 3% away from its maximum value. This is a possible systematic uncertainty when interpreting the measured Eddington fluxes from bursts at touchdown. We also discuss the applicability of steady-state models to describe the dynamics of bursts. In particular, we show that the sub- to super-Eddington transition during the burst rise is rapid enough that static models are not appropriate. Finally, we analyze the strength of spectral shifts in our models. Expected shifts at the photosphere are dominated by gravitational redshift, and are therefore predicted to be less than a few percent.

Role of microscopic temperature-dependent binding energies in the decay of Si*32 formed in the O20+C12 reaction

The investigation of fusion reactions involving light neutron-rich exotic nuclei is of paramount significance to understand nucleosynthesis in astrophysical scenarios. It is also estimated as a possible heat source to ignite $^{12}\mathrm{C}+^{12}\mathrm{C}$ reaction and production of x-ray superbursts from accreting neutron star. Recently, the fusion of neutron-rich $^{20}\mathrm{O}$ with $^{12}\mathrm{C}$ target has been studied with measurement of fusion cross-section $({\ensuremath{\sigma}}_{\text{fus}})$. Bass model under predicts the ${\ensuremath{\sigma}}_{\text{fus}}$ and time-dependent Hartree-Fock model also fails to explain the experimental data. To explicate the same, the investigation of $^{20}\mathrm{O}+^{12}\mathrm{C}$ reaction at near barrier energies has been made within quantum mechanical fragmentation-based dynamical cluster-decay model (DCM). Within DCM, the fragmentation potential comprises temperature-dependent Coulomb, nuclear and centrifugal potentials, along with temperature-dependent binding energies (T.B.E.) calculated within the macroscopic approach of Davidson mass formula. Recently, we have explored the temperature-dependence of different nuclear properties and nuclear symmetry energy within microscopic relativistic mean-field (RMF) theory [M. Kaur et al., Nucl. Phys. A 1000, 121871 (2020)]. In the present work, we inculcate the microscopic T.B.E. from RMF theory within DCM and investigate the structure of fragmentation potential for $^{32}\mathrm{Si}^{*}$ formed in $^{20}\mathrm{O}+^{12}\mathrm{C}$ reaction, comparatively for macroscopic (mac) and microscopic (mic) T.B.E. obtained from Davidson mass formula and RMF theory, respectively. The structure and magnitude of fragmentation potential are found to change drastically/notably along with a change in energetically favored/minimized fragments for both choices of T.B.E. The $\ensuremath{\alpha}$ particles $(^{4}\mathrm{He}$, $^{5}\mathrm{He})$ are favored at lower angular momenta in fragmentation profile for mic T.B.E. case only, which is in the agreement with predictions of statistical model results. This change in the nuclear structure embodied via fragmentation potential energy carries its imprints in the preformation probability ${P}_{0}$ of different fragments and affects the contribution of individual light-charged particle (LCP) channel in the ${\ensuremath{\sigma}}_{\text{fus}}$. A comparison of the relative cross-section of different LCP channels toward ${\ensuremath{\sigma}}_{\text{fus}}$ is quite different for both cases of T.B.E. The cross-section of $^{2}\mathrm{H}$ and $^{4}\mathrm{He}$ LCP channels is relatively enhanced for mic T.B.E. compared to mac T.B.E. Among different LCP channels, the $^{5}\mathrm{He}$ channel is the major contributor in ${\ensuremath{\sigma}}_{\text{fus}}$, which is in line with the results of the statistical EVAPOR model. The DCM-calculated ${\ensuremath{\sigma}}_{\text{fus}}$ is in agreement with the experimental data.

Magnetic angle evolution in accreting neutron stars

ABSTRACT The rotation of a magnetized accreting neutron star (NS) in a binary system is described by its spin period and two angles: spin inclination α with respect to the orbital momentum and magnetic angle χ between the spin and the magnetic moment. Magnetospheric accretion spins the NS up and adjusts its rotation axis, decreasing α to nearly perfect alignment. Its effect upon the magnetic angle is more subtle and relatively unstudied. In this work, we model the magnetic angle evolution of a rigid spherical accreting NS. We find that the torque spinning the NS up may affect the magnetic angle while both α and χ significantly deviate from zero, and the spin-up torque varies with the phase of the spin period. As the rotation axis of the NS is being aligned with the spin-up torque, the magnetic axis becomes misaligned with the rotation axis. Under favourable conditions, magnetic angle may increase by Δχ ∼ 15°−20°. This orthogonalization may be an important factor in the evolution of millisecond pulsars, as it partially compensates the χ decrease potentially caused by pulsar torques. If the direction of the spin-up torque changes randomly with time, as in wind-fed high-mass X-ray binaries, both the rotation axis of the NS and its magnetic axis become involved in a non-linear random-walk evolution. The ultimate attractor of this process is a bimodal distribution in χ peaking at χ = 0° and χ = 90°.