X-ray Bursts Research Articles

Similarity to earthquakes again: periodic radio pulses of the magnetar SGR 1935+2154 are accompanied by aftershocks like fast radio bursts

ABSTRACT It was recently discovered that the time correlations of repeating fast radio bursts (FRBs) are similar to earthquake aftershocks. Motivated by the association between FRBs and magnetars, here we report correlation function analyses in the time-energy space for the 563 periodic radio pulses and the 579 X-ray short bursts from the magnetar SGR 1935+2154, which is known to have generated FRBs. Although radio pulses are concentrated near the fixed phase of the rotational cycle, we find that when multiple pulses occur within a single cycle, their correlation properties (aftershock production probability, aftershock rate decaying in power of time, and more) are similar to those of extragalactic FRBs and earthquakes. A possible interpretation is that the radio pulses are produced by rupture of the neutron star crust, and the first pulse within one cycle is triggered by external force periodically exerted on the crust. The periodic external force may be from the interaction of the magnetosphere with material ejected in an outburst. For X-ray bursts, we found no significant correlation signal, though correlation on the same time-scale as radio pulses may be hidden due to the long event duration. The aftershock similarity between the periodic radio pulsation and FRBs is surprising, given that the two are energetically very different, and therefore the energy sources would be different. This suggests that the essence of FRB-like phenomena is starquakes, regardless of the energy source, and it is important to search for FRB-like bursts from neutron stars with various properties or environments.

Simulating Lateral H/He Flame Propagation in Type I X-ray Bursts

X-ray bursts are the thermonuclear runaway of a mixed H/He layer on the surface of a neutron star. Observations suggest that the burning begins locally and spreads across the surface of the star as a flame. Recent multidimensional work has looked in detail at pure He flames spreading across a neutron star. Here we report on progress in multidimensional modeling of mixed H/He flames and discuss the challenges.

Concise Spectrotemporal Studies of Magnetar SGR J1935+2154 Bursts

SGR J1935+2154 has truly been the most prolific magnetar over the last decade: it has been entering into burst active episodes once every 1–2 yr since its discovery in 2014, it emitted the first Galactic fast radio burst associated with an X-ray burst in 2020, and it has emitted hundreds of energetic short bursts. Here, we present the time-resolved spectral analysis of 51 bright bursts from SGR J1935+2154. Unlike conventional time-resolved X-ray spectroscopic studies in the literature, we follow a two-step approach to probe true spectral evolution. For each burst, we first extract spectral information from overlapping time segments, fit them with three continuum models, and employ a machine-learning-based clustering algorithm to identify time segments that provide the largest spectral variations during each burst. We then extract spectra from those nonoverlapping (clustered) time segments and fit them again with the three models: the cutoff power-law model, the sum of two blackbody functions, and the model considering the emission of a modified blackbody undergoing resonant cyclotron scattering, which is applied systematically at this scale for the first time. Our novel technique allowed us to establish the genuine spectral evolution of magnetar bursts. We discuss the implications of our results and compare their collective behavior with the average burst properties of other magnetars.

A catalogue of low-mass X-ray binaries in the Galaxy: From the INTEGRAL to the Gaia era

Context. Low-mass X-ray binaries (LMXBs) are high-energy sources that require multi-wavelength follow-up campaigns to be fully characterised. New transients associated with LMXBs are regularly discovered, and previously known systems are often revisited by astronomers to constrain their intrinsic parameters. All of this information compiled into a catalogue may build a useful tool for subsequent studies on LMXBs and their population. Aims. We aim to provide an update on past LMXB catalogues dating back 16 yr and propose to the community a database on Galactic LMXBs with the most complete, manually curated set of parameters and their original references. On top of a fixed version accessible through Vizier, we propose hosting the catalogue independently on our GitHub collaboration, side-by-side with our previous catalogue on high-mass X-ray binaries. The database will be regularly updated based on new publications and community inputs. Methods. We built a working base by cross-matching previous LMXB catalogues and supplementing them with lists of hard X-ray sources detected over the past 20 yr. We compiled information from Simbad on LMXBs as a starting point for a thorough, manual search in the literature to retrieve important parameters that characterize LMXBs. We retrieved newly detected LMXBs and candidates directly from literature searches. Counterparts to these LMXBs are compiled from hard X-ray to infrared and radio domains. Every piece of information presented on the LMXBs is curated and backed by accurate references. Results. We present a catalogue of 339 Galactic LMXBs listing their coordinates, companion star spectral type, systemic radial velocity, component masses and compact object nature, the presence of type I X-ray bursts, as well as orbital data. Coordinates and identifiers of counterparts at various wavelengths are given, including 140 LMXBs detected in Gaia DR3.

Episodic Energy Release during the Main and Post-impulsive Phases of a Solar Flare

When and where the magnetic field energy is released and converted in eruptive solar flares remains an outstanding topic in solar physics. To shed light on this question, here we report multiwavelength observations of a C9.4-class eruptive limb flare that occurred on 2017 August 20. The flare, accompanied by a magnetic flux rope eruption and a white light coronal mass ejection, features three post-impulsive X-ray and microwave bursts immediately following its main impulsive phase. For each burst, both microwave and X-ray imaging suggest that the nonthermal electrons are located in the above-the-loop-top region. Interestingly, contrary to many other flares, the peak flux of the three post-impulsive microwave and X-ray bursts shows an increase for later bursts. Spectral analysis reveals that the sources have a hardening spectral index, suggesting a more efficient electron acceleration into the later post-impulsive bursts. We observe a positive correlation between the acceleration of the magnetic flux rope and the nonthermal energy release during the post-impulsive bursts in the same event. Intriguingly, different from some other eruptive events, this correlation does not hold for the main impulse phase of this event, which we interpret as energy release due to the tether-cutting reconnection before the primary flux rope acceleration occurs. In addition, using footpoint brightenings at conjugate flare ribbons, a weakening reconnection guide field is inferred, which may also contribute to the hardening of the nonthermal electrons during the post-impulsive phase.

Thermonuclear explosions on neutron stars reveal the speed of their jets.

Relativistic jets are observed from accreting and cataclysmic transients throughout the Universe, and have a profound impact on their surroundings1,2. Despite their importance, their launch mechanism is not known. For accreting neutron stars, the speed of their compact jets can reveal whether the jets are powered by magnetic fields anchored in the accretion flow3 or in the star itself4,5, but so far no such measurements exist. These objects can show bright explosions on their surface due to unstable thermonuclear burning of recently accreted material, called type-I X-ray bursts6, during which the mass-accretion rate increases7-9. Here, we report on bright flares in the jet emission for a few minutes after each X-ray burst, attributed to the increased accretion rate. With these flares, we measure the speed of a neutron star compact jet to be , much slower than those from black holes at similar luminosities. This discovery provides a powerful new tool in which we can determine the role that individual system properties have on the jet speed, revealing the dominant jet launching mechanism.

The double-peaked type I X-ray bursts with different mass accretion rate and fuel composition

ABSTRACT Using the mesa (Modules for Experiments in Stellar Astrophysics) code, we have carried out a detailed survey of the available parameter space for the double-peaked type I X-ray bursts. We find that the double-peaked structure appears at mass accretion rate $\dot{M}$ in the range of $\sim (4-8)\times 10^{-10}\, {\rm M}_{\odot }\,{\rm yr}^{-1}$ when metallicity Z = 0.01, while in the range of $\sim (4-8)\times 10^{-9}\, {\rm M}_{\odot }\,\rm {yr}^{-1}$ when Z = 0.05. Calculations of the metallicity impact suggest that the double peaks will disappear when Z ≲ 0.005 for $\dot{M}=5\times 10^{-10}\, {\rm M}_{\odot }\,\rm {yr}^{-1}$ and Z ≲ 0.04 for $\dot{M}=5\times 10^{-9}\, {\rm M}_{\odot }\,\rm {yr}^{-1}$. Besides, the impacts of base heating Qb, as well as nuclear reaction waiting points: $^{22}\rm {Mg}$, $^{26}\rm {Si}$, $^{30}\rm {S}$, $^{34}\rm {Ar}$, 56Ni, $^{60}\rm Zn$, $^{64}\rm {Ge}$, $^{68}\rm {Se}$, and $^{72}\rm {Kr}$ have been explored. The luminosity of the two peaks decreases as Qb increases. 68Se(p, γ)69Br is the most sensitive reaction, the double peaks disappear assuming that 56Ni(p, γ)57Cu, and 64Ge(p, γ)65As reaction rates have been underestimated by a factor of 100 and the 22Mg(α, p)25Al reaction rate has been overestimated by a factor of 100, which indicates that 22Mg, 56Ni, 64Ge, and 68Se are possibly the most important nuclear waiting points impedance in the thermonuclear reaction flow to explain the double-peaked bursts. Comparisons to the double-peaked bursts from 4U 1636−53 and 4U 1730−22 suggest that the nuclear origins of double-peaked type I X-ray bursts are difficult to explain the observed larger peak times ($t_{\rm p,1}\gtrsim 4\, {\rm s}$, $t_{\rm p,2}\gtrsim 8\, {\rm s}$) and smaller peak ratio (r1, 2 ≲ 0.5). The composition of ashes from double-peaked bursts is very different from the single-peaked bursts especially for the heavier p-nuclei.

NICER views moderate, strong, and extreme photospheric expansion bursts from the ultracompact X-ray binary 4U 1820–30

Type I X-ray bursts in the ultracompact X-ray binary 4U 1820–30 are powered by the unstable thermonuclear burning of hydrogen-deficient material. We report the detection of 15 type I X-ray bursts from 4U 1820–30 observed by NICER between 2017 and 2023. All these bursts occurred in the low state for the persistent flux in the range of 2.5–8 × 10−9 erg s−1 cm−2 in 0.1–250 keV. The burst spectra during the tail can be nicely explained by blackbody model. However, for the first ~5 s after the burst onset, the time-resolved spectra showed strong deviations from the blackbody model. The significant improvement of the fit can be obtained by taking into account of the enhanced persistent emission due to the Poynting–Robterson drag, the extra emission modeled by another blackbody component, or by the reflection from the surrounding accretion disk. The reflection model provides a self-consistent and physically motivated explanation. We find that the accretion disk density changed with 0.5 s delay in response to the burst radiation, which indicates the distortion of the accretion disk during X-ray bursts. From the time-resolved spectroscopy, all bursts showed the characteristic of photospheric radius expansion (PRE). We find one superexpansion burst with the extreme photospheric radius rph > 103 km and blackbody temperature of ~0.2 keV, 13 strong PRE bursts for rph > 102 km, and one moderate PRE burst for rph ~ 55 km.

Spectral and type I X-ray burst studies of 4U 1702−429 using AstroSat observations

ABSTRACT 4U 1702−429, an atoll-type neutron star low-mass X-ray binary, was observed twice by the AstroSat/Soft X-ray Telescope (SXT) and Large Area X-ray Proportional Counters (LAXPC-20) on 2018 April 27 and 2019 August 8. Persistent emission spectra of the source were well fitted with the model combination - constant × tbabs (thcomp × diskbb+powerlaw). The parameters obtained from the spectral analysis revealed the source to be in a hard spectral state during the observations. Time-resolved spectral analyses were performed on the three type I X-ray bursts detected from the source. Burst analysis showed that the source underwent a photospheric radius expansion. Consequently, the radius of the neutron star and distance to the source (with isotropic and anisotropic burst emission) were obtained as 12.65$\substack{+0.90\\-0.86}$ km and 6.92$\substack{+0.16\\-0.09}$ and 8.43$\substack{+0.20\\-0.10}$ kpc, respectively.

Rapid spin changes around a magnetar fast radio burst.

Magnetars are neutron stars with extremely high magnetic fields (≳1014 gauss) that exhibit various X-ray phenomena such as sporadic subsecond bursts, long-term persistent flux enhancements and variable rotation-period derivative1,2. In 2020, a fast radio burst (FRB), akin to cosmological millisecond-duration radio bursts, was detected from the Galactic magnetar SGR 1935+2154 (refs. 3-5), confirming the long-suspected association between some FRBs and magnetars. However, the mechanism for FRB generation in magnetars remains unclear. Here we report the X-ray observation of two glitches in SGR 1935+2154 within a time interval of approximately nine hours, bracketing an FRB that occurred on 14 October 20226,7. Each glitch involved a significant increase in the magnetar's spin frequency, being among the largest abrupt changes in neutron-star rotation8-10 observed so far. Between the glitches, the magnetar exhibited a rapid spin-down phase, accompanied by an increase and subsequent decline in its persistent X-ray emission and burst rate. We postulate that a strong, ephemeral, magnetospheric wind11 provides the torque that rapidly slows the star's rotation. The trigger for the first glitch couples the star's crust to its magnetosphere, enhances the various X-ray signals and spawns the wind that alters magnetospheric conditions that might produce the FRB.

Insight-HXMT observations of thermonuclear X-ray bursts in 4U 1636−53

ABSTRACT We conducted an analysis of 45 bursts observed from 4U 1636−53. To investigate the mechanism behind the light-curve profiles and the impact of thermonuclear X-ray bursts on the accretion environment in accreting neutron star low-mass X-ray binaries. This analysis employed both light-curve and time-resolved spectroscopy methodologies, with data collected by the Insight-Hard X-ray Modulation Telescope instrument. We found that 30 bursts exhibited similar light-curve profiles and were predominantly in the hard state, and two photospheric radius expansion (PRE) bursts were in the soft state. The light curves of most bursts did not follow a single exponential decay but displayed a dual-exponential behaviour. The initial exponent had a duration of approximately 6 s. We utilized both the standard method and the ‘fa’ method to fit the burst spectra. The majority of the ‘fa’ values exceeded 1, indicating an enhancement of the persistent emission during the burst. Under the two Comptonization components assumption, we suggest that the scattering of burst photons by the inner corona may mainly contribute to the persistent emission enhancement. We also observed an inverse correlation between the maximum fa and the persistent emission flux in the non-PRE burst. This anticorrelation suggests that when the accretion rate is lower, there is a greater enhancement of persistent emission during the burst peak. The prediction based on Poynting–Robertson drag (P–R drag) aligns with this observed anticorrelation.

Low-energy Explosions in a Gravitational Field: Implications for Sub-energetic Supernovae and Fast X-Ray Transients

Observations and theory suggest that core-collapse supernovae can span a range of explosion energies, and when sub-energetic the shockwave initiating the explosion can decelerate to speeds comparable to the escape speed of the progenitor. In these cases, gravity will complicate the explosion hydrodynamics and conceivably cause the shock to stall at large radii within the progenitor star. To understand these unique properties of weak explosions, we develop a perturbative approach for modeling the propagation of an initially strong shock into a time-steady, infalling medium in the gravitational field of a compact object. This method writes the shock position and the post-shock velocity, density, and pressure as series solutions in the (time-dependent) ratio of the freefall speed to the shock speed, and predicts that the shock stalls within the progenitor if the explosion energy is below a critical value. We show that our model agrees very well with hydrodynamic simulations, and accurately predicts (for example) the time-dependent shock position and velocity and the radius at which the shock stalls. Our results have implications for black hole formation and the newly detected class of fast X-ray transients (FXTs). In particular, we propose that a “phantom shock breakout”—where the outer edge of the star falls through a stalled shock—can yield a burst of X-rays without a subsequent optical/UV signature, similar to FXTs. This model predicts the rise time of the X-ray burst, t d, and the mean photon energy, kT, are anticorrelated, approximately as T∝td−5/8 .

The self-organized criticality behaviours of two new parameters in SGR J1935+2154

ABSTRACT The minimum variation time-scale (MVT) and spectral lag of hundreds of X-ray bursts (XRBs) from soft gamma-ray repeater (SGR) J1935+2154 were analysed in detail for the first time in our recent work, which are important probes for studying the physical mechanism and radiation region. In this work, we investigate their differential and cumulative distributions carefully and find that they follow power-law models. Besides, the distributions of fluctuations in both parameters follow the Tsallis q-Gaussian distributions and the q values are consistent for different scale intervals. Therefore, these results indicate that both parameters are scale-invariant, which provides new parameters for the study of self-organized criticality systems. Interestingly, we find that the q values for MVT and spectral lag are similar with duration and fluence, respectively.

Flux and estimated spectra from a low-intensity laser-driven X-ray source

Abstract Laser-driven X-rays as probes for high-energy-density physics spans an extremely large parameter space with laser intensities varying by 8 orders of magnitude. We have built and characterized a soft X-ray source driven by a modest intensity laser of 4 × 1013 W/cm2. Emitted X-rays were measured by diamond radiation detectors and a filtered soft X-ray camera. A material-dependence study on Al, Ti, stainless steel alloy 304, Fe, Cu and Sn targets indicated 5-μm-thick Cu foils produced the highest X-ray yield. X-ray emission in the laser direction and emission in the reverse direction depend strongly on the foil material and the thickness due to the opacity and hydrodynamic disassembly time. The time-varying X-ray signals are used to measure the material thinning rate and is found to be ∼1.5 μm/ns for the materials tested implying thermal temperature around 0.6 eV. The X-ray spectra from Cu targets peaks at ∼2 keV with no emission >4 keV and was estimated using images with eight different foil filters. One-dimensional hydrodynamic and spectral calculations using HELIOS-CR provide qualitative agreement with experimental results. Modest intensity lasers can be an excellent source for nanosecond bursts of soft X-rays.

Spin Evolution of the Magnetar SGR J1935+2154

Fast radio bursts (FRBs) are short pulses observed in radio frequencies usually originating from cosmological distances. The discovery of FRB 200428 and its X-ray counterpart from the Galactic magnetar SGR J1935+2154 suggests that at least some FRBs can be generated by magnetars. However, the majority of X-ray bursts from magnetars are not associated with radio emission. The fact that only in rare cases can an FRB be generated raises the question regarding the special triggering mechanism of FRBs. Here we report long time spin evolution of SGR J1935+2154 until the end of 2022. According to ν and , the spin evolution of SGR J1935+2154 could be divided into two stages. The first stage evolves relatively steady evolution until 2020 April 27. After the burst activity in 2020, the spin of SGR J1935+2154 shows strong variations, especially for . After the burst activity in 2022 October, a new spin-down glitch with Δν/ν = (–7.2 ± 0.6) × 10−6 is detected around MJD 59876, which is the second event in SGR J1935+2154. At the end, spin frequency and pulse profile do not show variations around the time of FRB 200428 and radio bursts 221014 and 221021, which supply strong clues to constrain the trigger mechanism of FRBs or radio bursts.

Mapping Observations of Peptide-like Molecules around Sagittarius B2

Peptide-like molecules, which have a close connection with the origin of life, have been detected in the Universe. Mapping observations of HCONH2 and CH3CONH2, two of the simplest peptide-like molecules, are performed toward the Sagittarius B2 (Sgr B2) complex with the IRAM 30 m telescope. Seven transitions of HCONH2 and five transitions of CH3CONH2 are used in the analysis. The spatial distributions of the excitation temperature and column density of HCONH2 in the molecular envelope of Sgr B2 are obtained by rotation diagrams. Assuming the same excitation temperature of HCONH2, the column densities of CH3CONH2 are also calculated. The results show that the excitation temperature ranges from 6 to 46 K in the molecular envelope of Sgr B2. The abundance ratios between HCONH2 and CH3CONH2 are calculated to explore the relationship between them, as are those between HCONH2 and HNCO. The abundance ratio of CH3CONH2/HCONH2 varies from 10% to 20%, while that of HCONH2/HNCO ranges from 1.5% to 10%. CH3CONH2 is enhanced with respect to HCONH2 in the northwest region of Sgr B2. One transition of H13CONH2 is detected toward 12 positions of Sgr B2, from which a 12C/13C ratio of 28.7 is obtained. A time-dependent chemical model with a short-duration X-ray burst is used to explain the observed abundances of HCONH2 and CH3CONH2, with the best-fitting result at T dust = 53–56 K. More chemical reactions are required to be included in the model since the modeled abundance is lower than the observed one at the observed T dust.

Individual and averaged power density spectra of X-ray bursts from SGR J1935+2154: quasi-periodic oscillation search and slopes

ABSTRACT The study of quasi-periodic oscillations (QPOs) and power density spectra (PDSs) continuum properties can help shed light on the still elusive emission physics of magnetars and as a window into the interiors of neutron stars using asteroseismology. In this work, we employ a PDS method to search for the QPOs in the hundreds of X-ray bursts from SGR J1935+2154 observed by Insight-HXMT, GECAM, and Fermi/GBM from 2014 July to 2022 January. Although no definitive QPO signal (significance >3 σ) is detected in individual bursts or the averaged periodogram of the bursts grouped by duration, we identify several bursts exhibiting features at ∼40 Hz, attributed to the the proximity intervals between adjacent pulses and consistent with that reported in the X-ray burst associated with FRB 200428. We investigate the PDS continuum properties and find that the distribution of the PDS slope in the simple power-law model peaks at ∼2.5, which is consistent with other magnetars but higher than 5/3 commonly seen in gamma-ray bursts. Besides, the distribution of the break frequency in the broken power-law model peaks at ∼60 Hz. Finally, we report that the power-law index of PDS has an anti-correlation and power-law dependence on the burst duration as well as the minimum variation time-scale.

A Fully Explicit Integrator for Modeling Astrophysical Reactive Flows

Simulating complex astrophysical reacting flows is computationally expensive—reactions are stiff and typically require implicit integration methods. The reaction update is often the most expensive part of a simulation, which motivates the exploration of more economical methods. In this research note, we investigate how the explicit Runge–Kutta–Chebyshev (RKC) method performs compared to an implicit method when applied to astrophysical reactive flows. These integrators are applied to simulations of X-ray bursts arising from unstable thermonuclear burning of accreted fuel on the surface of neutron stars. We show that the RKC method performs with similar accuracy to our traditional implicit integrator, but is more computationally efficient when run on CPUs.

Effects of solar activity and geographic latitude on genetic homeostasis of human somatic cells

BACKGROUND: Associations between genetic stability of human somatic cells and solar activity across latitudes have been studied. A human buccal epithelium micronucleus test was selected as a method for evaluating genetic homeostasis.
 AIM: To assess effects of solar activity on the genetic stability of human somatic cells using the micronucleus test in buccal epithelium in relation to the geographical location of subjects.
 METHODS: Men aged 18 to 21 years with no harmful habits and taking no medication comprised the sample. Studies were conducted simultaneously in four cities of the Russian Federation: Sevastopol, Voronezh, Tomsk, and Khanty-Mansiysk. The effect of three types of solar flares, whose classification is based on changes in the amplitude of the thermal X-ray burst, was studied. Material for the cytogenetic study was collected on days 3, 7, and 10 after the solar flare. The human buccal epithelium micronucleus test was selected as a method to evaluate genetic homeostasis. At least 1,000 cells were examined on each preparation, among which the number of cells with micronuclei, perinuclear vacuoles, notches, “broken egg” and “tongue” type protrusions, karyorexis, karyolisis, and karyopyknosis was determined. In total, 495 thousand buccal epithelial cells were analyzed. Statistical processing of the data was performed using “Stadia” and “Statistica” software packages. Effecs of solar andlatitude on genetic homeostasis of somatic cells was performed using multivariate analysis of variance and two-factor analysis of variance with fixed effects.
 RESULTS: Solar activity affected the stability of the human genetic apparatus by increasing the influence of the city pollution and its geographical location on the number of cells with nucleus abnormalities. We also observed a combined effect of solar flare and season on the number of cells with nucleus aberrations. More nuclear anomalies were registered in the winter. We did not detect any difference in the number of cells with nucleus anomalies on the 3rd, the 7th, the 10th, and the 17th days after the flare suggesting no associations between solar activity and the number of cells with nuclear abnormalities.
 CONCLUSION: The highest number of cells with nucleus abnormalities is observed in Sevastopol reflecting with the greatest level of anthropogenic pollution of this city compared to the other locations. Solar activity increases the influence of the city pollution and its geographical location on the number of cells with nucleus abnormalities. The results obtained can be used in conducting a micronucleus test of human buccal epithelium and in planning measures to assess the genotoxicity of the environment.

Constraints on Neutron Star Structure from the Clocked X-Ray Burster 1RXS J180408.9−342058

Type I X-ray bursts are rapid-brightening transient phenomena on the surfaces of accreting neutron stars (NSs). Some X-ray bursts, called clocked bursters, exhibit regular behavior with similar light-curve profiles in their burst sequences. The periodic nature of clocked bursters has the advantage of constraining X-ray binary parameters and physics inside the NS. In the present study, we compute numerical models, based on different equations of state and NS masses, which are compared with the observations of a recently identified clocked burster, 1RXS J180408.9−342058. We find that the relation between the accretion rate and the recurrence time is highly sensitive to the NS mass and radius. We determine, in particular, that 1RXS J180408.9−342058 appears to possess a mass less than 1.7M ⊙ and favors a stiffer nuclear equation of state (with an NS radius ≳12.7 km). Consequently, the observations of this new clocked burster may provide additional constraints for probing the structure of NSs.