Neutron Star Spin Research Articles

Long-term evolution of spin and other properties of neutron star low-mass X-ray binaries: implications for millisecond X-ray pulsars

ABSTRACT A neutron star (NS) accreting matter from a companion star in a low-mass X-ray binary (LMXB) system can spin up to become a millisecond pulsar (MSP). Properties of many such MSP systems are known, which is excellent for probing fundamental aspects of NS physics when modelled using the theoretical computation of NS LMXB evolution. Here, we systematically compute the long-term evolution of NS, binary, and companion parameters for NS LMXBs using the stellar evolution code mesa. We consider the baryonic to gravitational mass conversion to calculate the NS mass evolution and show its cruciality for the realistic computation of some parameters. With computations using many combinations of parameter values, we find the general nature of the complex NS spin frequency ($\nu$) evolution, which depends on various parameters, including accretion rate, fractional mass-loss from the system, and companion star magnetic braking. Further, we utilize our results to precisely match some main observed parameters, such as $\nu$, orbital period ($P_{\rm orb}$), etc., of four accreting millisecond X-ray pulsars (AMXPs). By providing the $\nu$, $P_{\rm orb}$, and the companion mass spaces for NS LMXB evolution, we indicate the distribution and plausible evolution of a few other AMXPs. We also discuss the current challenges in explaining the parameters of AMXP sources with brown dwarf companions and indicate the importance of modelling the transient accretion in LMXBs as a possible solution.

Dynamical tides during the inspiral of rapidly spinning neutron stars: Solutions beyond mode resonance

Dynamical tides during the inspiral of rapidly spinning neutron stars: Solutions beyond mode resonance

Applying the starquake model to study the formation of elastic mountains on spinning neutron stars

ABSTRACT When a neutron star is spun-up or spun-down, the changing strains in its solid elastic crust can give rise to sudden fractures known as starquakes. Early interest in starquakes focused on their possible connection to pulsar glitches. While modern glitch models rely on pinned superfluid vorticity rather than crustal fracture, starquakes may nevertheless play a role in the glitch mechanism. Recently, there has been interest in the issue of starquakes resulting in non-axisymmetric shape changes, potentially linking the quake phenomenon to the building of neutron star mountains, which would then produce continuous gravitational waves. Motivated by this issue, we present a simple model that extends the energy minimization-based calculations, originally developed to model axisymmetric glitches, to also include non-axisymmetric shape changes. We show that the creation of a mountain in a quake necessarily requires a change in the axisymmetric shape too. We apply our model to the specific problem of the spin-up of an initially non-rotating star, and estimate the maximum mountain that can be built in such a process, subject only to the constraints of energy and angular momentum conservation.

Inferring Small Neutron Star Spins with Neutron Star–Black Hole Mergers

The precise measurement of neutron star (NS) spins can provide important insight into the formation and evolution of compact binaries containing NSs. While traditional methods of NS spin measurement rely on pulsar observations, gravitational-wave detections offer a complementary avenue. However, determining component spins with gravitational waves is hindered by the small dimensionless spins of the NSs and the degeneracy in the mass and spin parameters. This degeneracy can be addressed by the inclusion of higher-order modes in the waveform, which are important for systems with unequal masses. This study shows the suitability of NS–black hole mergers, which are naturally mass-asymmetric, for precise NS spin measurements. We explore the effects of the black hole masses and spins, higher-mode content, inclination angles, and detector sensitivity on the measurement of NS spin. We find that networks with next-generation observatories like the Cosmic Explorer and the Einstein Telescope can distinguish NS dimensionless spin of 0.04 (0.1) from zero at 1σ confidence for events within ∼350 (∼1000) Mpc. Networks with A+ and A♯ detectors achieve similar distinction within ∼30 (∼70) Mpc and ∼50 (∼110) Mpc, respectively.

The Curious Case of Twin Fast Radio Bursts: Evidence for Neutron Star Origin?

Fast radio bursts (FRBs) are brilliant short-duration flashes of radio emission originating at cosmological distances. The vast diversity in the properties of currently known FRBs and the fleeting nature of these events make it difficult to understand their progenitors and emission mechanism(s). Here we report high time resolution polarization properties of FRB 20210912A, a highly energetic event detected by the Australian Square Kilometre Array Pathfinder (ASKAP) in the Commensal Real-time ASKAP Fast Transients survey, which show intraburst position angle (PA) variation similar to Galactic pulsars and unusual variation of Faraday rotation measure (RM) across its two sub-bursts. The observed intraburst PA variation and apparent RM variation pattern in FRB 20210912A may be explained by a rapidly spinning neutron star origin, with rest-frame spin periods of ∼1.1 ms. This rotation timescale is comparable to the shortest known rotation period of a pulsar and close to the shortest possible rotation period of a neutron star. Curiously, FRB 20210912A exhibits a remarkable resemblance to the previously reported FRB 20181112A, including similar rest-frame emission timescales and polarization profiles. These observations suggest that these two FRBs may have similar origins.

Quasi-periodic oscillations in rotating and deformed space–times

ABSTRACT Quasi-periodic oscillation (QPOs) analysis is important for understanding the dynamical behaviour of many astrophysical objects during transient events such as gamma-ray bursts, solar flares, magnetar flares, and fast radio bursts. In this paper, we analyse QPO data in low-mass X-ray binary (LMXB) systems, using the Lense-Thirring, Kerr, and approximate Zipoy-Voorhees metrics. We demonstrate that the inclusion of spin and quadrupole parameters modifies the well-established results for the fundamental frequencies in the Schwarzschild space–time. We interpret the QPO data within the framework of the standard relativistic precession model, allowing us to infer the values of the mass, spin, and quadrupole parameters of neutron stars in LMXBs. We explore recent QPO data sets from eight distinct LMXBs, assess their optimal parameters, and compare our findings with results in the existing literature. Finally, we discuss the astrophysical implications of our findings.

Discovery of a strong rotation of the X-ray polarization angle in the galactic burster GX 13+1

Weakly magnetized neutron stars in X-ray binaries show a complex phenomenology with several spectral components that can be associated with the accretion disk, the boundary, and/or a spreading layer, a corona, and a wind. Spectroscopic information alone, however, is not enough to distinguish these components. The analysis of the timing data revealed that most of the variability, and in particular, kilohertz quasi-period oscillations, are associated with the high-energy component that corresponds to the boundary and/or spreading layer. Additional information about the nature of the spectral components, and in particular, about the geometry of the emission region, can be provided by X-ray polarimetry. One of the objects of the class, a bright, persistent, and rather peculiar galactic Type I X-ray burster was observed with the Imaging X-ray Polarimetry Explorer (IXPE) and the X-ray Multi-Mirror Mission Newton ( Using the data, we obtained the best-fit values for the continuum spectral parameters and detected strong absorption lines associated with the accretion disk wind. IXPE data showed the source to be significantly polarized in the 2--8 keV energy band, with an overall polarization degree (PD) of $1.4<!PCT!> at a polarization angle (PA) of $-2 (errors at the 68<!PCT!> confidence level). During the two-day long observation, we detected rotation of the PA by about 70 with the corresponding changes in the PD from 2<!PCT!> to nondetectable and then up to 5<!PCT!>. These variations in polarization properties are not accompanied by visible spectral state changes of the source. The energy-resolved polarimetric analysis showed a significant change in polarization, from being strongly dependent on energy at the beginning of the observation to being almost constant with energy in the later parts of the observation. As a possible interpretation, we suggest a constant polarization component, strong wind scattering, or a different polarization of the two main spectral components with an individually peculiar behavior. The rotation of the PA suggests a misalignment of the neutron star spin from the orbital axis.

Fermionic quantum turbulence: Pushing the limits of high-performance computing.

Ultracold atoms provide a platform for analog quantum computer capable of simulating the quantum turbulence that underlies puzzling phenomena like pulsar glitches in rapidly spinning neutron stars. Unlike other platforms like liquid helium, ultracold atoms have a viable theoretical framework for dynamics, but simulations push the edge of current classical computers. We present the largest simulations of fermionic quantum turbulence to date and explain the computing technology needed, especially improvements in the Eigenvalue soLvers for Petaflop Applications library that enable us to diagonalize matrices of record size (millions by millions). We quantify how dissipation and thermalization proceed in fermionic quantum turbulence by using the internal structure of vortices as a new probe of the local effective temperature. All simulation data and source codes are made available to facilitate rapid scientific progress in the field of ultracold Fermi gases.

The polarization of the boundary layer around weakly magnetized neutron stars in X-ray binaries

Context. X-ray binaries hosting a compact object have been among the main targets of the Imaging X-ray Polarimetry Explorer (IXPE) since its launch, due to their high brightness in the 2–8 keV energy band. The spectropolarimetric analysis performed so far has proved to be of great importance in providing constraints on the accretion geometry of these systems. However, the data statistics is not enough to unambiguously disentangle the contribution of the single components to the net observed polarimetric signal. Aims. In this work, we aim to present a model for computing the polarization degree and polarization angle of the boundary layer around weakly magnetized neutron stars in low-mass X-ray binaries in the soft state. The main motivation is to provide strong theoretical support to data interpretation of observations performed by IXPE or future satellites for X-ray polarimetry. Methods. The results were obtained by modeling the boundary layer as an equatorial belt around the compact object and locally approximating it as a plane-parallel scattering atmosphere, for which the associated radiative transfer equation for polarized radiation in the Thomson limit was solved. The polarimetric quantities were then transformed from the comoving frame to the observer frame using the numerical methods formerly developed for X-ray pulsars. Results. For typical values of the optical depth and electron temperature of the boundary layer of these systems in a soft state, the polarization degree was less then 0.5%, while the polarization angle was rotated by ≲5° with respect to the neutron star spin axis due to special and general relativistic effects for fast rotation, the amount progressively decreasing for lower spin frequencies. The derived quantities can be used to remove degeneracy when multicomponent spectropolarimetry is performed.

Long-term Study of the First Galactic Ultraluminous X-Ray Source Swift J0243.6+6124 Using NICER

We present the results obtained from detailed X-ray timing and spectral studies of X-ray pulsar Swift J0243.6+6124 during its giant and normal X-ray outbursts between 2017 and 2023 observed by the Neutron star Interior Composition Explorer (NICER). We focused on a timing analysis of the normal outbursts. A distinct break is found in the power density spectra of the source. The corresponding break frequency and slopes of the power laws around the break vary with luminosity, indicating a change in the accretion dynamics with the mass accretion rate. Interestingly, we detected quasiperiodic oscillations within a specific luminosity range, providing further insights into the underlying physical processes. We also studied the neutron star spin period evolution and a luminosity variation in the pulse profile during the recent 2023 outburst. The spectral analysis was conducted comprehensively for the giant and all other normal outbursts. We identified a double transition at luminosities of ≈7.5 × 1037 and 2.1 × 1038 erg s−1 in the evolution of continuum parameters like the photon index and cutoff energy with luminosity. This indicates three distinct accretion modes experienced by the source, mainly during the giant X-ray outburst. A soft blackbody component with a temperature of 0.08–0.7 keV is also detected in the spectra. The observed temperature undergoes a discontinuous transition when the pulsar evolves from a sub- to super-Eddington state. Notably, in addition to an evolving 6–7 keV iron line complex, a 1 keV emission line was observed during the super-Eddington state of the source, implying X-ray reflection from the accretion disk or outflow material.

Glitching pulsars as gravitational wave sources

Spinning neutron stars, when observed as pulsars, are seen to undergo occasional spin-up events known as glitches. Despite several decades of study, the physical mechanisms responsible for glitches are still not well understood, but probably involve an interplay between the star’s outer elastic crust, and the superfluid and superconducting core that lies within. Glitches will be accompanied by some level of gravitational wave emission. In this article, we review proposed models that link gravitational wave emission to glitches, exploring both short duration burst-like emission, and longer-lived signals. We illustrate how detections (and in some cases, non-detections) of gravitational signals probe both the glitch mechanism, and, by extension, the behaviour of matter at high densities.

The dynamical tides of spinning Newtonian stars

ABSTRACT We carefully develop the framework required to model the dynamical tidal response of a spinning neutron star in an inspiralling binary system, in the context of Newtonian gravity, making sure to include all relevant details and connections to the existing literature. The tidal perturbation is decomposed in terms of the normal oscillation modes, used to derive an expression for the effective Love number which is valid for any rotation rate. In contrast to previous work on the problem, our analysis highlights subtle issues relating to the orthogonality condition required for the mode-sum representation of the dynamical tide and shows how the prograde and retrograde modes combine to provide the overall tidal response. Utilizing a slow-rotation expansion, we show that the dynamical tide (the effective Love number) is corrected at first order in rotation, whereas in the case of the static tide (the static Love number) the rotational corrections do not enter until second order.

VLA monitoring of LS V +44 17 reveals scatter in the X-ray–radio correlation of Be/X-ray binaries

ABSTRACT LS V +44 17 is a persistent Be/X-ray binary (BeXRB) that displayed a bright, double-peaked period of X-ray activity in late 2022/early 2023. We present a radio monitoring campaign of this outburst using the Very Large Array. Radio emission was detected, but only during the second, X-ray brightest, peak, where the radio emission followed the rise and decay of the X-ray outburst. LS V +44 17 is therefore the third neutron star BeXRB with a radio counterpart. Similar to the other two systems (Swift J0243.6+6124 and 1A 0535+262), its X-ray and radio luminosity are correlated: we measure a power-law slope $\beta = 1.25^{+0.64}_{-0.30}$ and a radio luminosity of LR = (1.6 ± 0.2) × 1026 erg s−1 at a 0.5–10 keV X-ray luminosity of 2 × 1036 erg s−1 (i.e. $\sim 1~{{\ \rm per\ cent}}$LEdd). This correlation index is slightly steeper than measured for the other two sources, while its radio luminosity is higher. We discuss the origin of the radio emission, specifically in the context of jet launching. The enhanced radio brightness compared to the other two BeXRBs is the first evidence of scatter in the giant BeXRB outburst X-ray–radio correlation, similar to the scatter observed in subclasses of low-mass X-ray binaries. While a universal explanation for such scatter is not known, we explore several options: we conclude that the three sources do not follow proposed scalings between jet power and neutron star spin or magnetic field, and instead briefly explore the effects that ambient stellar wind density may have on BeXRB jet luminosity.

Probing the Solar Interior with Lensed Gravitational Waves from Known Pulsars

When gravitational waves (GWs) from a spinning neutron star arrive from behind the Sun, they are subjected to gravitational lensing that imprints a frequency-dependent modulation on the waveform. This modulation traces the projected solar density and gravitational potential along the path as the Sun passes in front of the neutron star. We calculate how accurately the solar density profile can be extracted from the lensed GWs using a Fisher analysis. For this purpose, we selected three promising candidates (the highly spinning pulsars J1022+1001, J1730−2304, and J1745−23) from the pulsar catalog of the Australia Telescope National Facility. The lensing signature can be measured with 3σ confidence when the signal-to-noise ratio (S/N) of the GW detection reaches 100 (f/300 Hz)−1 over a 1 yr observation period (where f is the GW frequency). The solar density profile can be plotted as a function of radius when the S/N improves to ≳104.

Banks of templates for directed and all-sky narrow-band searches of continuous gravitational waves from spinning neutron stars with several spindowns

We construct efficient banks of templates suitable for searches of continuous gravitational waves from isolated spinning neutron stars. We assume that the search algorithm is based on the time-domain maximum-likelihood -statistic and we consider narrow-band searches with several spindown parameters included. Our template banks are suitable for both all-sky and directed searches and they enable the usage of the fast Fourier transform in the computation of the -statistic as well as, in the case of all-sky searches, efficient resampling of data to barycentric time.

Spin Equilibrium of Rapidly Spinning Neutron Stars via Transient Accretion

The concept of spin equilibrium due to an interaction between the stellar magnetosphere and a thin, Keplerian accretion disk, and a well-known formula of the corresponding equilibrium spin frequency, provide a key understanding of spin evolution and the distribution of rapidly spinning neutron stars, viz., millisecond pulsars. However, this concept and formula are for stable accretion, but the mass transfer to most accreting millisecond pulsars is transient and the accretion rate evolves by orders of magnitude during an outburst. In this short and focussed review, we briefly discuss a relatively new concept of the spin equilibrium condition and a new formula for the equilibrium spin frequency for transiently accreting millisecond pulsars. We also review a new method to estimate this equilibrium spin frequency for observed transiently accreting millisecond pulsars, even when a pulsar has not yet attained the spin equilibrium. These will be crucial to probe the spin evolution and distribution of millisecond pulsars, and should also be applicable to all magnetic stars transiently accreting via a thin, Keplerian accretion disk.

Fallback onto kicked neutron stars and its effect on spin-kick alignment

ABSTRACT Fallback in core-collapse supernova explosions is potentially of significant importance for the birth spins of neutron stars and black holes. It has recently been pointed out that the angular momentum imparted onto a compact remnant by fallback material is subtly intertwined with its kick because fallback onto a moving neutron star or black hole will preferentially come for a conical region around its direction of travel. We show that contrary to earlier expectations such one-sided fallback accretion onto a neutron star will tend to produce spin-kick misalignment. Since the baroclinic driving term in the vorticity equation is perpendicular to the nearly radial pressure gradient, convective eddies in the progenitor as well as Rayleigh–Taylor plumes growing during the explosion primarily carry angular momentum perpendicular to the radial direction. Fallback material from the accretion volume of a moving neutron star therefore carries substantial angular momentum perpendicular to the kick velocity. We estimate the seed angular momentum fluctuations from convective motions in core-collapse supernova progenitors and argue that accreted fallback material will almost invariably be accreted with the maximum permissible specific angular momentum for reaching the Alfvén radius. This imposes a limit of ${\sim }10^{-2}\, \mathrm{M}_\odot$ of fallback accretion for fast-spinning young neutron stars with periods of ${\sim }20\, \mathrm{ms}$ and less for longer birth spin periods.

Impact of neutron star spin on Poynting–Robertson drag during a type I X-ray burst

ABSTRACT External irradiation of a neutron star (NS) accretion disc induces Poynting–Robertson (PR) drag, removing angular momentum and increasing the mass accretion rate. Recent simulations show PR drag significantly enhancing the mass accretion rate during Type I X-ray bursts, which could explain X-ray spectral features such as an increase in the persistent emission and a soft excess. However, prograde spin of the NS is expected to weaken PR drag, challenging its importance during bursts. Here, we study the effect of spin on PR drag during X-ray bursts. We run four simulations, with two assuming a non-spinning NS and two using a spin parameter of a* = 0.2, corresponding to a rotation frequency of 500 Hz. For each scenario, we simulate the disc evolution subject to an X-ray burst and compare it to the evolution found with no burst. PR drag drains the inner disc region during a burst, moving the inner disc radius outwards by ≈1.6 km in the a* = 0 and by ≈2.2 km in the a* = 0.2 simulation. The burst enhances the mass accretion rate across the innermost stable circular orbit ≈7.9 times when the NS is not spinning and ≈11.2 times when it is spinning. The explanation for this seemingly contradictory result is that the disc is closer to the NS when a* = 0.2, and the resulting stronger irradiating flux offsets the weakening effect of spin on the PR drag. Hence, PR drag remains a viable explanation for the increased persistent emission and soft excess observed during X-ray bursts in spinning NS systems.

Energy-resolved pulse profiles of accreting pulsars: Diagnostic tools for spectral features

Aims. We introduce a method for extracting spectral information from energy-resolved light curves folded at the neutron star spin period (known as pulse profiles) in accreting X-ray binaries. Spectra of these sources are sometimes characterized by features superimposed on a smooth continuum, such as iron emission lines and cyclotron resonant scattering features. We address here the question on how to derive quantitative constraints on such features from energy-dependent changes in the pulse profiles. Methods. We developed a robust method for determining in each energy-selected bin the value of the pulsed fraction using the fast Fourier transform opportunely truncated at the number of harmonics needed to satisfactorily describe the actual profile. We determined the uncertainty on this value by sampling through Monte Carlo simulations a total of 1000 faked profiles. We rebinned the energy-resolved pulse profiles to have a constant minimum signal-to-noise ratio throughout the whole energy band. Finally we characterize the dependence of the energy-resolved pulsed fraction using a phenomenological polynomial model and search for features corresponding to spectral signatures of iron emission or cyclotron lines using Gaussian line profiles. Results. We apply our method to a representative sample of NuSTAR observations of well-known accreting X-ray pulsars. We show that, with this method, it is possible to characterize the pulsed fraction spectra, and to constrain the position and widths of such features with a precision comparable with the spectral results. We also explore how harmonic decomposition, correlation, and lag spectra might be used as additional probes for detection and characterization of such features.

Accretion Spin-up and a Strong Magnetic Field in the Slow-spinning Be X-Ray Binary MAXI J0655-013

We present Monitor of All-sky X-ray Image (MAXI) and Nuclear Spectroscopic Telescope Array (NuSTAR) observations of the Be X-ray binary, MAXI J0655−013, in outburst. NuSTAR observed the source once early in the outburst, when spectral analysis yields a bolometric (0.1–100 keV), unabsorbed source luminosity of L bol = 5.6 × 1036 erg s−1, and a second time 54 days later, by which time the luminosity had dropped to L bol = 4 × 1034 erg s−1 after first undergoing a dramatic increase. Timing analysis of the NuSTAR data reveals a neutron star spin period of 1129.09 ± 0.04 s during the first observation, which decreased to 1085 ± 1 s by the time of the second observation, indicating spin-up due to accretion throughout the outburst. Furthermore, during the first NuSTAR observation, we observed quasi-periodic oscillations (QPOs) with centroid frequency ν 0 = 89 ± 1 mHz, which exhibited a second harmonic feature. By combining the MAXI and NuSTAR data with pulse period measurements reported by Fermi/GBM, we are able to show that apparent flaring behavior in the MAXI light curve is an artifact introduced by uneven sampling of the pulse profile, which has a large pulsed fraction. Finally, we estimate the magnetic field strength at the neutron star surface via three independent methods, invoking a tentative cyclotron resonance scattering feature at 44 keV, QPO production at the inner edge of the accretion disk, and spin-up via interaction of the neutron star magnetic field with accreting material. Each of these result in a significantly different value. We discuss the strengths and weaknesses of each method and infer that MAXI J0655−013 is likely to have a high surface magnetic field strength, B s > 1013 G.