Neutron Star Surface Research Articles

Crab pulsar: IXPE observations reveal unified polarization properties in the optical and soft X-ray bands

We present a phase-dependent analysis of the polarized emission from the Crab pulsar based on three sets of observations by the Imaging X-ray Polarimetry Explorer (IXPE). We found that a phenomenological model involving a simple linear transformation of the Stokes parameters adequately describes the IXPE data. This model enabled us to establish a connection between the polarization properties of the Crab pulsar in the optical and soft X-ray bands for the first time, which suggests a common underlying emission mechanism in these bands that likely is synchrotron radiation. In particular, the phase-dependent polarization degree in X-rays for the pure pulsar emission shows similar features, but is reduced by a factor ≈(0.46 − 0.56) compared to the optical band (when we accounted for the contribution of the knot in the optical), which implies an energy-dependent polarized emission. Using this model, we also studied the polarization angle swing in the X-rays and identified a potentially variable phase shift at the interpulse relative to the optical band, alongside a phase shift that is marginally consistent with zero and persists at the main pulse. While the origin of this variability is unknown and presents a new challenge for the theoretical interpretation, our findings suggest that the emission mechanism for the main pulse is likely located far from the neutron star surface, perhaps near to or beyond the light cylinder, and that it does not operate in the inner magnetosphere, where vacuum birefringence is expected to be at work. Ignoring the phase shifts would result in identical phase-dependent polarization angles between the optical and X-ray bands for the pure pulsar emission.

Evolution of the Accretion Disk and Corona during the Outburst of the Neutron Star Transient MAXI J1807+132

Low-mass X-ray binaries with a neutron star as the primary object show a complex array of phenomenology during outbursts. The observed variability in X-ray emission primarily arises from changes in the innermost regions of the accretion disk, neutron star surface, and corona. In this work, we present the results of a comprehensive X-ray spectral and timing analysis of the neutron star transient MAXI J1807+132 during its 2023 outburst using data from the NICER observatory. The outburst is marked by a very rapid rise in the count rate by about a factor of 20 in a day. The source undergoes full state transitions and displays the hysteresis effect in the hardness and rms intensity diagrams. Spectral analysis with a three-component model is consistent with disk truncation during the hard states and reaching the last stable orbit during the intermediate and soft states. We discuss the different values of the last stable radius in the context of the possible distance of the source and magnetic field strength. The characteristic frequencies throughout the hard and intermediate states are found to be strongly correlated with the inner radius of the disk. Together with the spectral and fast variability properties, we attempt to trace the evolution of the size of the corona along the outburst. Following the main outburst, the source undergoes a high-amplitude reflare, wherein it shows a complex behavior with relatively high variability (10%), but low hardness.

Modeling Competing Line-broadening Mechanisms in Neutron Star Atmospheres: Interference between Motional Stark and Ion Broadening

Neutron star surfaces have extremely high magnetic fields. In the atmosphere, the broadening of spectral lines will be substantial from the dense plasma as well as from the magnetic field. One broadening mechanism of note is due to the motional Stark effect (MSE)—an additional electric field that arises from the motion of the atom in the magnetic field. However, approximate formulae are often used to construct atmosphere models, and the MSE is assumed to be the dominant line-broadening mechanism even in ions. Detailed pressure-broadening models in these extreme magnetic fields are now currently being developed. In these more detailed models, it was suggested that the MSE may not be as large as previously predicted. If correct, this hypothesis implies that neutron star line widths might be dominated by pressure broadening rather than by motional Stark broadening. We find that, in the absence of plasma perturbations, for typical magnetic fields (B = 1012 G), mid-Z elements, such as oxygen, have motional Stark widths of order 1 eV for transitions between dipole-allowed transitions from the ground state, though higher temperatures and transitions to higher-energy states are expected to have more broadening. The MSE also breaks down selection rules, giving rise to forbidden transitions, which have much larger widths. When plasma perturbations are included, we find that the plasma perturbation and motional Stark processes are not independent and, as a result, the spectral lines become narrow in a nontrivial way and display harmonics of the ion cyclotron frequency.

Pulsed and Polarized X‐Ray Emission From Neutron Star Surfaces

ABSTRACTThe intense magnetic fields of neutron stars naturally lead to strong anisotropy and polarization of radiation emanating from their surfaces, both being sensitive to the hot spot position on the surface. Accordingly, pulse phase‐resolved intensities and polarizations depend on the angle between the magnetic and spin axes and the observer's viewing direction. In this paper, results are presented from a Monte Carlo simulation of neutron star atmospheres that uses a complex electric field vector formalism to treat polarized radiative transfer due to magnetic Thomson scattering. General relativistic influences on the propagation of light from the stellar surface to a distant observer are taken into account. The paper outlines a range of theoretical predictions for pulse profiles at different X‐ray energies, focusing on magnetars and also neutron stars of lower magnetization. By comparing these models with observed intensity and polarization pulse profiles for the magnetar 1RXS J1708‐40, and the light curve for the pulsar PSR J0821‐4300, constraints on the stellar geometry angles and the size of putative polar cap hot spots are obtained.

Radiative back-reaction on charged particle motion in the dipole magnetosphere of neutron stars

The motion of charged particles under the Lorentz force in the magnetosphere of neutron stars, represented by a dipole field in the Schwarzschild spacetime, can be determined by an effective potential, whose local extrema govern circular orbits both in and off the equatorial plane, which coincides with the symmetry plane of the dipole field. In this work, we provide a detailed description of the properties of these “conservative” circular orbits and, using the approximation represented by the Landau-Lifshitz equation, examine the role of the radiative back-reaction force that influences the motion of charged particles following both the in and off equatorial circular orbits, as well as the chaotic orbits confined to belts centered around the circular orbits. To provide clear insight into these dynamics, we compare particle motion with and without the back-reaction force. We demonstrate that, in the case of an attractive Lorentz force, the back-reaction leads to the charged particles falling onto the neutron star's surface in all scenarios considered. For the repulsive Lorentz force, in combination with the back-reaction force, we observe a widening of stable equatorial circular orbits; the off-equatorial orbits shift toward the equatorial plane and subsequently widen if they are sufficiently close to the plane. Otherwise, the off-equatorial orbits evolve toward the neutron star surface. The critical latitude, which separates orbital widening from falling onto the surface, is determined numerically as a function of the electromagnetic interaction's intensity.

Exploring Waveform Variations among Neutron Star Ray-tracing Codes for Complex Emission Geometries

Pulse profile modeling (PPM), the technique used to infer mass, radius, and geometric parameters for rotation-powered millisecond pulsars using data from the Neutron Star Interior Composition Explorer (NICER), relies on relativistic ray-tracing of thermal X-ray photons from hot spots on the neutron star surface to the observer. To verify our ray-tracing codes we have in the past conducted cross tests for simple hot spot geometries, focusing primarily on the implementation of the spacetime model. In this paper, we present verification for test problems that explore the more complex hot spot geometries that are now being employed in the NICER PPM analyses. We conclude that the accuracy of our computed waveforms is in general sufficiently high for analyses of current NICER data sets. We have however identified some extreme configurations where extra care may be needed.

Broadband X-ray spectral and timing properties of the accreting millisecond X-ray pulsar IGR J17498−2921 during the 2023 outburst

We report on the broadband spectral and timing properties of the accreting millisecond X-ray pulsar IGR J17498−2921 during its April 2023 outburst. We used data from NICER (1–10 keV), NuSTAR (3–79 keV), Insight-HXMT (2–150 keV), and INTEGRAL (30–150 keV). We detected significant 401 Hz pulsations across the 0.5–150 keV band. The pulse fraction increases from ∼2% at 1 keV to ∼13% at 66 keV. We detected five type-I X-ray bursts, including three photospheric radius expansion bursts, with a rise time of ∼2 s and an exponential decay time of ∼5 s. The recurrence time is ∼9.1 h, which can be explained by unstable thermonuclear burning of hydrogen-deficient material on the neutron star surface. The quasi-simultaneous 1–150 keV broadband spectra from NICER, NuSTAR and INTEGRAL can be aptly fitted by an absorbed reflection model, relxillCp, and a Gaussian line of instrumental origin. The Comptonized emission from the hot corona is characterized by a photon index Γ of ∼1.8 and an electron temperature kTe of ∼40 keV. We obtained a low inclination angle i ∼ 34°. The accretion disk shows properties of strong ionization, log(ξ/erg cm s−1)∼4.5, over-solar abundance, AFe ∼ 7.7, and high density, log(ne/cm−3)∼19.5. However, a lower disk density with normal abundance and ionization could also be possible. Based on the inner disk radius of Rin = 1.67RISCO and the long-term spin-down rate of −3.1(2)×10−15 Hz s−1, we were able to constrain the magnetic field of IGR J17498−2921 to the range of (0.9 − 2.4)×108 G.

Pulsar Nulling and Vacuum Radio Emission from Axion Clouds.

Nonrelativistic axions can be efficiently produced in the polar caps of pulsars, resulting in the formation of a dense cloud of gravitationally bound axions. Here, we investigate the interplay between such an axion cloud and the electrodynamics in the pulsar magnetosphere, focusing specifically on the dynamics in the polar caps, where the impact of the axion cloud is expected to be most pronounced. For sufficiently light axions m_{a}≲10^{-7} eV, we show that the axion cloud can occasionally screen the local electric field responsible for particle acceleration and pair production, inducing a periodic nulling of the pulsar's intrinsic radio emission. At larger axion masses, the small-scale fluctuations in the axion field tend to suppress the backreaction of the axion on the electrodynamics; however, we point out that the incoherent oscillations of the axion in short-lived regions of vacuum near the neutron star surface can produce a narrow radio line, which provides a complementary source of radio emission to the plasma-resonant emission processes identified in previous work. While this Letter focuses on the leading order correction to pair production in the magnetosphere, we speculate that there can exist dramatic deviations in the electrodynamics of these systems when the axion backreaction becomes nonlinear.

A More Precise Measurement of the Radius of PSR J0740+6620 Using Updated NICER Data

PSR J0740+6620 is the neutron star with the highest precisely determined mass, inferred from radio observations to be 2.08 ± 0.07 M ⊙. Measurements of its radius therefore hold promise to constrain the properties of the cold, catalyzed, high-density matter in neutron star cores. Previously, Miller et al. and Riley et al. reported measurements of the radius of PSR J0740+6620 based on Neutron Star Interior Composition Explorer (NICER) observations accumulated through 2020 April 17, and an exploratory analysis utilizing NICER background estimates and a data set accumulated through 2021 December 28 was presented in Salmi et al. Here we report an updated radius measurement, derived by fitting models of X-ray emission from the neutron star surface to NICER data accumulated through 2022 April 21, totaling ∼1.1 Ms additional exposure compared to the data set analyzed in Miller et al. and Riley et al., and to data from XMM-Newton observations. We find that the equatorial circumferential radius of PSR J0740+6620 is 12.92−1.13+2.09 km (68% credibility), a fractional uncertainty ∼83% the width of that reported in Miller et al., in line with statistical expectations given the additional data. If we were to require the radius to be less than 16 km, as was done in Salmi et al., then our 68% credible region would become R=12.76−1.02+1.49 km, which is close to the headline result of Salmi et al. Our updated measurements, along with other laboratory and astrophysical constraints, imply a slightly softer equation of state than that inferred from our previous measurements.

Neutron Star Kicks plus Rockets as a Mechanism for Forming Wide Low-eccentricity Neutron Star Binaries

Recent neutron star surface observations corroborate a long-standing theory that neutron stars may be accelerated over extended periods after their birth. We analyze how these prolonged rocket-like accelerations, combined with rapid birth kicks, impact binary orbits. We find that even a small contribution of rocket kicks combined with instantaneous natal kicks can allow binaries to reach period–eccentricity combinations unattainable in standard binary evolution models. We propose these kick + rocket combinations as a new channel to form wide low-eccentricity neutron star binaries such as Gaia NS1, as well as inducing stellar mergers months to years after a supernova to cause peculiar high-energy transients.

3D code for MAgneto-Thermal evolution in Isolated Neutron Stars, MATINS: thermal evolution and light curves

ABSTRACT The thermal evolution of isolated neutron stars is a key element in unravelling their internal structure and composition and establishing evolutionary connections among different observational subclasses. Previous studies have predominantly focused on one-dimensional or axisymmetric two-dimensional models. In this study, we present the thermal evolution component of the novel three-dimensional magnetothermal code MATINS (MAgneto-Thermal evolution of Isolated Neutron Star). MATINS employs a finite volume scheme and integrates a realistic background structure, along with state-of-the-art microphysical calculations for the conductivities, neutrino emissivities, heat capacity, and superfluid gap models. This paper outlines the methodology employed to solve the thermal evolution equations in MATINS, along with the microphysical implementation that is essential for the thermal component. We test the accuracy of the code and present simulations with non-evolving magnetic fields of different configurations (all with electrical currents confined to the crust and a magnetic field that does not thread the core), to produce temperature maps of the neutron star surface. Additionally, for a specific magnetic field configuration, we show one fully coupled evolution of magnetic field and temperature. Subsequently, we use a ray-tracing code to link the neutron star surface temperature maps obtained by MATINS with the phase-resolved spectra and pulsed profiles that would be detected by distant observers. This study, together with our previous article focused on the magnetic formalism, presents in detail the most advanced evolutionary code for isolated neutron stars, with the aim of comparison with their timing properties, thermal luminosities and the associated X-ray light curves.

Neutron dynamics in ultra-strong electromagnetic fields: an example model

Abstract This work is concerned with the relativistic quantum dynamics of a self-interacting neutron in the presence of an external ultra-strong electromagnetic (EM) field in a cylindrical inertial frame. We first regard the Dirac–Pauli (DP) Lagrangian to study the planar dynamics of a neutron polarized along the z-axis subjected to a confining external static EM field composed of a homogeneous magnetic field in the z-direction and a linear radial electric field in the polar plane. The corresponding discrete Landau energy levels are found. As a nonlinear (NL) example model, we introduce a 1-flavor Nambu Jona–Lasinio (NJL) mass term into the DP Lagrangian. The continuous ground-state Landau levels are determined. We readily obtain modified Maxwell’s equations associated with these levels. We consider a simple application of the model related to the dynamics of neutrons in the presence of strong-QED fields inside the surface of aligned neutron stars. We briefly comment on possible classical solitonic solutions of the model.

On the lack of X-ray pulsation in most neutron star low-mass X-ray binaries

ABSTRACT We have investigated whether the lack of X-ray pulsations from most neutron star (NS) low-mass X-ray binaries (LMXBs) could be due to the extension of their inner disc to the NS surface. To estimate the inner disc radii, we have employed the model, recently proposed to account for the torque reversals of LMXBs. In this model, the inner disc radius depends on the spin period as well as the dipole moment and the mass inflow rate of the disc. Our model results indicate that most LMXBs have mass accretion rates above the minimum critical rates required for the inner disc to reach down to the NS surface and thereby quench the pulsed X-ray emission. For most sources X-ray pulsations are allowed when the period decreases below a certain critical value. For the same parameters, the model is also consistent with the observed X-ray luminosity ranges of the individual accreting millisecond X-ray pulsars (AMXPs). The paucity of AMXPs compared to the majority population of non-pulsing LMXBs is explained, as well as the fact that AMXPs are transient sources.

On the origin of the quasi-periodic micro-pulses observed in the radio-frequency emission of some neutron stars

ABSTRACT The linear relationship between pulsar micro-pulse widths and rotation period is consistent with the existence of a physical length L on the neutron-star surface and seen on the observer arc of transit across the polar cap. Within the ion–proton model it is the width of the minimum area of surface that can support the critical growth rate of the unstable two-beam Langmuir mode that is the source of the radio emission.

Insight–HXMT observations of thermonuclear X-ray bursts from 4U 1608–52 in the low/hard state: the energy-dependent hard X-ray deficit and cooling saturation of the corona

ABSTRACT During thermonuclear bursts, it is suspected that cooling of the corona by the burst emission may be the cause of hard X-ray deficits. Although such a deficit has been observed in nine sources, it has not been observed from 4U 1608–52, a nearby prolific burster. Therefore, the authenticity and universality of the hard X-ray deficit may be in question. To investigate this suspicion, Insight–HXMT performed cadence observations during the low/hard state of 4U 1608–52 in 2022 September and detected 10 thermonuclear X-ray bursts. Two of these bursts show a double-peaked structure in the soft X-ray band, which could be caused by the high temperature of the burst emission and a marginal photospheric radius expansion (PRE) around the burst peak time. This is indicated by their peak fluxes being up to the Eddington limit and having a large colour factor at the peak of the bursts. A hard X-ray deficit is observed at a significant level during bursts at > 30 keV. Furthermore, the fraction of this deficit shows saturation at 50 per cent for the first eight bursts. This saturation may indicate that the corona is layered and only part of the corona is cooled by the bursts: for example, the part close to the neutron star surface is cooled while the rest remains intact during bursts. This result provides a clue to the geometry of the corona. For example, a possible scenario is that the corona has two forms: a quasi-spheric corona between the neutron star and the disc and a disc corona on both surfaces of the disc.

New insight into the hard X-ray emission influenced by the type I bursts observed by Insight-HXMT during the outburst of 4U 1636–536

Context. Thermonuclear bursts, also known as type I X-ray bursts, result from unstable nuclear burning of H/He accreted to the surface of neutron stars, lasting from tens to hundreds of seconds. Thermonuclear bursts have an important impact on accretion environments around the neutron stars, such as their disks and coronas, and are therefore a subject of extensive research. Thermonuclear bursts can be used as probes to gain a deeper understanding of the properties of their disks and coronas. Aims. By analyzing the data from Insight-HXMT and NICER, we can determine the evolution of the significance of the hard shortage in 4U 1636–536 with its spectral state, as well as the evolution of the fraction of deficit with energy. Additionally, we investigate the possible geometry and evolution of the corona in 4U 1636–536 by combining our findings with the results of spectral analysis. Methods. We extracted the light curves from the Insight-HXMT low-energy, medium-energy, and high-energy data and subtracted their pre-burst emission, which allowed us to estimate the significance of the hard shortages during the bursts. By fitting the spectra, the correlation between the persistent spectral parameters and the significance of the hard shortages could be established. The bursts were then grouped according to the spectral state in which they occurred, and the significance of the hard shortages was estimated. These in turn helped to investigate the evolution of the fraction of deficit with energy. Results. We find that during the soft state the significance of possible hard X-ray shortage in bursts is almost zero. However, in the hard state, some bursts exhibit significant shortages (> 3σ), while others do not. We attempt to establish a correlation between the significance of the hard X-ray shortage and the spectral parameters, but the data quality and the limited number of bursts prevent us from finding a strong correlation. For bursts with insignificant shortages in the soft state, the fraction of the deficit remains small. However, in the hard state the fraction of deficit for all bursts increases with energy, regardless of the significance of the shortage of individual bursts. For bursts during the hard state, we investigated the evolution of the fraction of deficit during the bursts by stacking the peaks and decays of the bursts, and find that as the flux of the bursts decreases, the energy corresponding to the maximum of the fraction of deficit becomes progressively higher. Conclusions. We explore the possible geometry and evolution of the corona suggested by the evolution of the fraction of deficit, which is obtained from the spectral and temporal analysis.

A Quantum Mechanical Treatment of Electron Broadening in Strong Magnetic Fields. II. Large Enhancements due to Exchange Interactions

We present a quantum treatment of atom–electron collisions in magnetic fields, demonstrating the significant importance of including the effect of exchange that arises from two interacting electrons. We find strange behaviors that are not encountered in collisions without a magnetic field. In high magnetic fields, exchange can lead to orders of magnitude enhancements of collision cross sections. Additionally, the elastic collision cross sections that involve the ground state become comparable to those involving excited states, and states with large orbits have the largest contribution to the collisions. We anticipate significant changes to spectral line broadening in neutron star surfaces and atmospheres.

A Transition Discovered in the Subcritical Regime of 1A 0535+262

We present NICER observations of the accreting X-ray pulsar 1A 0535+262 during its faint state (≲6 × 1036 erg s−1), observed in several type I and type II outbursts. We discovered a transition of temporal and spectral properties around the luminosity L t = 3.3 × 1035 erg s−1, below which spectra are relatively soft and the pulse profiles have only a narrow peak. The spectra are harder and a secondary hump gradually appears in the pulse profiles when L ≳ L t. We discuss possible physical mechanisms for this transition, including different Comptonization seed photons, the disappearance of gas shocks on the neutron star surface, and the combination of plasma and vacuum polarization effects.

Probing the accretion geometry of the atoll source 4U 1702−429 in different spectral states with NICER, NuSTAR, and AstroSat

ABSTRACT We perform a comprehensive spectral study of a carefully selected sample (total exposure ∼50.5 ks) of NICER observations of the atoll neutron star low-mass X-ray binary 4U 1702−429. Our sample encompasses nearly all classical spectral states found within the NICER data set. We require two thermal emission components, originating from the accretion disc and the boundary layer, to describe the soft state spectra in the energy band 0.3–10.0 keV. In contrast, in our model, only the disc component directly contributes to the intermediate/hard state. Additionally, we use a thermally Comptonized component (or a power law with pegged normalization) to represent the hard coronal emission in the soft and intermediate/hard state spectra. The boundary layer emerges as the principal source providing soft seed photons for Comptonization across all spectral states. In contrast to a previously held assertion regarding this source, our analyses reveal a decrease in the inner disc temperature coupled with the retreat of the inner disc from the neutron star surface as the source evolves from the soft to the intermediate/hard state. The reflection features are either absent or weak (∼3σ–4σ) in all these observations. Further investigation using broad-band NuSTAR (3.0–50.0 keV) and AstroSat spectra (1.3–25.0 keV) shows a slightly stronger iron emission line (∼5.8σ) in the NuSTAR spectra. However, this feature is not significantly detected in the AstroSat observation. The AstroSat data suggest a highly ionized disc, explaining the absence of reflection features. In the case of NuSTAR, a truncated disc is likely responsible for the weak reflection features.

Dynamics of baryon ejection in magnetar giant flares: implications for radio afterglows, r-process nucleosynthesis, and fast radio bursts

ABSTRACT We explore the impact of a magnetar giant flare (GF) on the neutron star (NS) crust, and the associated baryon mass ejection. We consider that sudden magnetic energy dissipation creates a thin high-pressure shell above a portion of the NS surface, which drives a relativistic shockwave into the crust, heating a fraction of these layers sufficiently to become unbound along directions unconfined by the magnetic field. We explore this process using spherically symmetric relativistic hydrodynamical simulations. For an initial shell pressure PGF we find the total unbound ejecta mass roughly obeys the relation $M_{\rm {ej}}\sim 4\!-\!9\times 10^{24}\, \rm {g}\, (P_{\rm GF}/10^{30}\, \rm {erg}\, \rm {cm}^{-3})^{1.43}$. For $P_{\rm {GF}}\sim 10^{30}\!-\!10^{31}\, \rm {erg}\, \rm {cm}^{-3}$ corresponding to the dissipation of a magnetic field of strength $\sim 10^{15.5}\!-\!10^{16}\, \rm {G}$, we find $M_{\rm {ej}}\sim 10^{25}\!-\!10^{26}\, \rm {g}$ with asymptotic velocities vej/c ∼ 0.3–0.6 compatible with the ejecta properties inferred from the afterglow of the 2004 December GF from SGR 1806-20. Because the flare excavates crustal material to a depth characterized by an electron fraction Ye ≈ 0.40–0.46, and is ejected with high entropy and rapid expansion time-scale, the conditions are met for heavy element r-process nucleosynthesis via the alpha-rich freeze-out mechanism. Given an energetic GF rate of roughly once per century in the Milky Way, we find that magnetar GFs could be an appreciable heavy r-process source that tracks star formation. We predict that GFs are accompanied by short ∼minutes long, luminous $\sim 10^{39}\, \rm {erg}\, \rm {s}^{-1}$ optical transients powered by r-process decay (nova brevis), akin to scaled-down kilonovae. Our findings also have implications for the synchrotron nebulae surrounding some repeating fast radio burst sources.