We report on two new quiescent {\it XMM-Newton} observations (in addition to the earlier {\it Swift}/XRT and {\it XMM-Newton} coverage) of the cooling neutron star crust in the low-mass X-ray binary 1RXS J180408.9$-$342058. Its crust was heated during the $\sim$4.5 month accretion outburst of the source. From our quiescent observations, fitting the spectra with a neutron star atmosphere model, we found that the crust had cooled from $\sim$ 100 eV to $\sim$73 eV from $\sim$8 days to $\sim$479 days after the end of its outburst. However, during the most recent observation, taken $\sim$860 days after the end of the outburst, we found that the crust appeared not to have cooled further. This suggested that the crust had returned to thermal equilibrium with the neutron star core. We model the quiescent thermal evolution with the theoretical crustal cooling code NSCool and find that the source requires a shallow heat source, in addition to the standard deep crustal heating processes, contributing $\sim$0.9 MeV per accreted nucleon during outburst to explain its observed temperature decay. Our high quality {\it XMM-Newton} data required an additional hard component to adequately fit the spectra. This slightly complicates our interpretation of the quiescent data of 1RXS J180408.9$-$342058. The origin of this component is not fully understood.
A region of toroidally oriented quantized flux lines must exist in the proton superconductor in the core of the neutron star. This region will be a site of vortex pinning and creep. Entrainment of the neutron superfluid with the crustal lattice leads to a requirement of superfluid moment of inertia associated with vortex creep in excess of the available crustal moment of inertia. This will effect constraints on the equation of state. The toroidal flux region provides the moment of inertia necessary to complement the crust superfluid with postglitch relaxation behavior fitting the observations.
We discuss the origin of strong crustal magnetic field in one of central compact objects (CCOs) --- a neutron star PSR J1852+0040 in the supernova remnant Kes 79. Taking into account its relatively long present day spin period we conclude that the field could not be generated via a dynamo mechanism. If this neutron star indeed is a magnetar with field submerged during a strong fall-back episode, then it argues against the dynamo field origin in magnetars. Otherwise, Kes 79 is not a close relative of normal magnetars. A discovery of an anti-magnetar with a millisecond period and strong crustal …
The neutron star crustal EoS and transition point properties are computed within a unified meta-modeling approach. A Bayesian approach is employed including two types of filters: bulk nuclear properties are controlled from low density effective field theory (EFT) predictions as well as the present knowledge from nuclear experiments, while the surface energy is adjusted on experimental nuclear masses. Considering these constraints, a quantitative prediction of crustal properties can be reached with controlled confidence intervals and increased precision with respect to previous calculations: {$…
Large pulsar frequency glitches are generally interpreted as sudden transfers of angular momentum between the neutron superfluid permeating the inner crust and the rest of the star. Despite the absence of viscous drag, the neutron superfluid is strongly coupled to the crust due to non-dissipative entrainment effects. These effects are shown to severely limit the maximum amount of angular momentum that can possibly be transferred during glitches. In particular, it is found that the glitches observed in the Vela pulsar require an additional reservoir of angular momentum.
Using a theoretical model, we track the thermal evolution of a cooling neutron star crust after an accretion induced heating period with the goal of constraining the crustal parameters. We present for the first time a crust cooling model $-\text{ } NSCool\text{ } -$ that takes into account detailed variability during the full outburst based on the observed light curve. We apply our model to KS 1731-260. The source was in outburst for $\sim$12 years during which it was observed to undergo variations on both long (years) and short (days-weeks) timescales. Our results show that KS 1731-260 does n…
A quasi-statistical equilibrium model is constructed to simulate the multicomponent composition of the crust of an accreting neutron star. The ashes of rp-process nucleosynthesis are driven by accretion through a series of electron captures, neutron emissions, and pycnonuclear fusions up to densities near the transition between the neutron star crust and core. A liquid droplet model which includes nuclear shell effects is used to provide nuclear masses far from stability. Reaction pathways are determined consistently with the nuclear mass model. The nuclear symmetry energy is an important unce…
We present a new mechanism for deep crustal heating in accreting neutron stars. Charged pions ($π^+$) are produced in nuclear collisions on the neutron star surface during active accretion and upon decay they provide a flux of neutrinos into the neutron star crust. For massive and/or compact neutron stars, neutrinos deposit $\approx 1\textrm{--} 2 \, \mathrm{MeV}$ of heat per accreted nucleon into the inner crust. The strength of neutrino heating is comparable to the previously known sources of deep crustal heating, such as from pycnonuclear fusion reactions, and is relevant for studies of coo…
In this work, we have studied oscillations in the crust of a neutron star which magnetic field has both dipolar and toroidal components, the former extends from the stellar interior to the outer space and the later is confined inside the star radius. Our study is based on the solutions we have got for perturbations in the star fluid, confined to the crust thickness. Our results are compared to the frequencies observed in the Soft Gamma Repeaters signals.
The elastic crust of a neutron star fractures repeatedly as it spins down electromagnetically. An idealised, macroscopic model of inhomogeneous crustal failure is presented based on a cellular automaton with nearest-neighbour tectonic interactions involving strain redistribution and thermal dissipation. Predictions are made of the size and waiting-time distributions of failure events, as well as the rate of failure as the star spins down. The last failure event typically occurs when the star spins down to approximately 1% of its birth frequency with implications for rotational glitch activity.…
We use the effective relativistic mean-field (E-RMF) model to study the crustal properties of the neutron star. The unified equations of state (EoS) are constructed using recently developed E-RMF parameter sets, such as FSUGarnet, IOPB-I, and G3. The outer crust composition is determined using the atomic mass evaluation 2020 data [Chinese Physics C {\bf 45}, 030002 (2021)] along with the available Hartree-Fock-Bogoliubov mass models [Phys. Rev. C {\bf 88}, 024308 (2013)] for neutron-rich nuclei. The structure of the inner crust is estimated by performing the compressible liquid drop model calc…
We consider how superfluidity of dripped neutrons in the crust of a neutron star affects the frequencies of the crust's fundamental torsional oscillations. A nonnegligible superfluid part of dripped neutrons, which do not comove with nuclei, act to reduce the enthalpy density and thus enhance the oscillation frequencies. By assuming that the quasi-periodic oscillations observed in giant flares of soft gamma repeaters arise from the fundamental torsional oscillations and that the mass and radius of the neutron star is in the range of 1.4 < M/M_SUN < 1.8 and 10 km < R < 14 km, we constrain the d…
In order to assess the ability of purely crust-driven glitch models to match the observed glitch activity in the Vela pulsar, we conduct a systematic analysis of the dependence of the fractional moment of inertia of the inner crustal neutrons on the stiffness of the nuclear symmetry energy at saturation density $L$. We take into account both crustal entrainment and the fact that only a fraction $Y_{\rm g}$ of the core neutrons may couple to the crust on the glitch-rise timescale. We use a set of consistently-generated crust and core compositions and equations-of-state which are fit to results …
High resolution, pulse to pulse observation of the 2016 Vela glitch and its relaxation provided an opportunity to probe the neutron star internal structure and dynamics with unprecedented detail. We use the observations of this glitch to infer superfluid characteristics in the framework of the vortex creep model. The glitch rise time constraint of 12.6 seconds put stringent limits on the angular momentum exchange between the crustal superfluid and the observed crust. Together with the observed excess acceleration in the rotation rate as compared to the post-glitch equilibrium value this discri…
Following an extremely interesting idea \cite{R1}, published long ago, the work function at the outer crust region of a strongly magnetized neutron star is obtained using relativistic version of Thomas-Fermi type model. In the present scenario, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges. An approximate estimate of the electron density in the magnetosphere due to field emission and photo emission current, from the polar cap region are obtained.
Central compact objects are young neutron stars emitting thermal X-rays with bolometric luminosities $L_X$ in the range $10^{32}$-$10^{34}$ erg/s. Gourgouliatos, Hollerbach and Igoshev recently suggested that peculiar emission properties of central compact objects can be explained by tangled magnetic field configurations formed in a stochastic dynamo during the proto-neutron star stage. In this case the magnetic field consists of multiple small-scale components with negligible contribution of global dipolar field. We study numerically three-dimensional magneto-thermal evolution of tangled crus…
Under normal conditions in a neutron-star crust, ions are locked in place in the crustal lattice and only electrons are mobile, and magnetic-field evolution is thus directly related to the electron velocity. The evolution, however, builds magnetic stresses that can become sufficiently large for the crust to exceed its elastic limit, and to flow plastically. We consider the nature of this plastic flow and the back-reaction on the crustal magnetic field evolution. We formulate a plane-parallel model for the local failure, showing that surface motions are inevitable once the crust yields, in the …
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 …
With the inclusion of the isovector scalar channel in the meson-nucleon couplings, taking DD-ME$δ$ as an effective interaction, the moments of inertia of neutron stars possessing various stellar masses are studied within the density dependent relativistic mean field (RMF) theory. The isovector scalar channel contributes to the softening of the neutron-star matter equation of state (EOS) and therefore the reduction of the maximum mass and radius of neutron stars. Smaller values of the total moment of inertia $I$ and the crustal moment of inertia $Δ{I}$ are then obtained in DD-ME$δ$ via numerica…
Isolated neutron stars (NSs) show a bewildering variety of astrophysical manifestations, presumably shaped by the magnetic field strength and topology at birth. Here, using state-of-the art calculations of the coupled magnetic and thermal evolution of NSs, we compute the thermal spectra and pulse profiles expected for a variety of initial magnetic field configurations. In particular, we contrast models with purely poloidal magnetic fields to models dominated by a strong internal toroidal component. We find that, while the former displays double peaked profiles and very low pulsed fractions, in…
In the late inspiral phase, gravitational waves from binary neutron star mergers carry the imprint of the equation of state due to the tidally deformed structure of the components. If the stars contain solid crusts, then their shear modulus can affect the deformability of the star and, thereby, modify the emitted signal. Here, we investigate the effect of realistic equations of state (EOSs) of the crustal matter, with a realistic model for the shear modulus of the stellar crust in a fully general relativistic framework. This allows us to systematically study the deviations that are expected fr…
A precondition for the radio emission of pulsars is the existence of strong, small-scale magnetic field structures (`magnetic spots') in the polar cap region. Their creation can proceed via crustal Hall drift out of two qualitatively and quantitatively different initial magnetic field configurations: a field confined completely to the crust and another which penetrates the whole star. The aim of this study is to explore whether these magnetic structures in the crust can deform the star sufficiently to make it an observable source of gravitational waves. We model the evolution of these field co…
We calculate crustal properties of neutron stars, namely, mass ($M_{\rm crust}$), radius ($R_{\rm crust}$) and fraction of moment of inertia ($ΔI/I$) from parametrizations of hadronic relativistic mean-field (RMF) model consistent with symmetric and asymmetric nuclear matter constraints, as well as some stellar boundaries. We verify which one are also in agreement with restrictions of $ΔI/I \geqslant 1.4\%$ and $ΔI/I \geqslant 7\%$ related to the glitching mechanism observed in pulsars, such as the Vela one. The latter constraint explains the glitches phenomenon when entrainment effects are ta…
It is assumed that accreting neutron stars (NSs) in LMXBs are heated due to the compression of the existing crust by the accreted matter which gives rise to nuclear reactions in the crust. It has been shown that most of the energy is released deep in the crust by pycnonuclear reactions involving low-Z elements. We discuss if NSs in very-faint X-ray transients (VFXTs; those which have peak X-ray luminosities < 1E36 erg/s) can be used to test this model. Unfortunately we cannot conclusively answer this because of the large uncertainties in our estimates of the accretion rate history of those VFX…
The amplification of magnetic fields plays an important role in explaining numerous astrophysical phenomena associated with binary neutron-star mergers, such as mass ejection and the powering of short gamma-ray bursts. Magnetic fields in isolated neutron stars are often assumed to be confined to a small region near the stellar surface, while they are normally taken to fill the whole stars in the numerical modelling. By performing high-resolution, global, and high-order general-relativistic magnetohydrodynamic simulations we investigate the impact of a purely crustal magnetic field and contrast…
With various sets of the parameters that characterize the equation of state (EOS) of nuclear matter, we systematically examine the thickness of a neutron star crust and of the pasta phases contained therein. Then, with respect to the thickness of the phase of spherical nuclei, the thickness of the cylindrical phase, and the crust thickness, we successfully derive fitting formulas that express the ratio of each thickness to the star's radius as a function of the star's compactness, the incompressibility of symmetric nuclear matter, and the density dependence of the symmetry energy. In particula…
Estimation of neutron star mass and radius of FRB 20240114A by identification of crustal oscillations
Kochi University（高知大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；University of Tübingen（蒂宾根大学）；University of Maryland, College Park（马里兰大学帕克分校）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）
Transient neutron star (NS) LMXBs undergo episodes of accretion, alternated with quiescent periods. During an accretion outburst, the NS heats up due to exothermic accretion-induced processes taking place in the crust. Besides the long-known deep crustal heating of nuclear origin, a likely non-nuclear source of heat, dubbed 'shallow heating', is present at lower densities. Most of the accretion-induced heat slowly diffuses into the core on a timescale of years. Over many outburst cycles, a state of equilibrium is reached when the core temperature is high enough that the heating and cooling (ph…
I construct a model of the inner crust of neutron stars using interactions from chiral effective field theory (EFT) in order to calculate its equation of state (EOS), shear properties, and the spectrum of crustal shear modes. I systematically study uncertainties associated with the nuclear physics input, the crust composition, and neutron entrainment, and estimate their impact on crustal shear properties and the shear-mode spectrum. I find that the uncertainties originate mainly in two sources: The neutron-matter EOS and neutron entrainment. I compare the spectrum of crustal shear modes to obs…
Crustal torsional oscillations depend on not only crust properties but also the stellar mass and radius. Thus, one could extract stellar information by identifying the observed frequencies of stellar oscillations with the crustal torsional oscillations. Owing to the confinement of torsional oscillations inside the crust region of neutron stars, we successfully derive an empirical formula for the fundamental crustal torsional oscillations as a function of the stellar mass, radius, the so-called slope parameter of the nuclear symmetry energy, and the angular index of oscillations, with which one…
This study investigates elastic deformation driven by the Hall drift in a magnetized neutron-star crust. Although the dynamic equilibrium initially holds without elastic displacement, the magnetic-field evolution changes the Lorentz force over a secular timescale, which inevitably causes the elastic deformation to settle in a new force balance. Accordingly, elastic energy is accumulated, and the crust is eventually fractured beyond a particular threshold. We assume that the magnetic field is axially symmetric, and we explicitly calculate the breakup time, maximum elastic energy stored in the c…
Besides their intrinsic nuclear-structure value, nuclear mass models are essential for astrophysical applications, such as r-process nucleosynthesis and neutron-star structure. To overcome the intrinsic limitations of existing "state-of-the-art" mass models, we propose a refinement based on a Bayesian Neural Network (BNN) formalism. A novel BNN approach is implemented with the goal of optimizing mass residuals between theory and experiment. A significant improvement (of about 40%) in the mass predictions of existing models is obtained after BNN refinement. Moreover, these improved results are …
The monitoring of quiescent emission from neutron star transients with accretion outbursts long enough to significantly heat the neutron star crust has opened a new vista onto the physics of dense matter. In this paper we construct models of the thermal relaxation of the neutron star crust following the end of a protracted accretion outburst. We confirm the finding of Shternin et al., that the thermal conductivity of the neutron star crust is high, consistent with a low impurity parameter. We describe the basic physics that sets the broken power-law form of the cooling lightcurve. The initial …
We systematically examine torsional shear oscillations of neutron star crusts by newly taking into account the possible presence of the phase of cylindrical nuclei. In this study, we neglect an effect of magnetic fields, under which the shear oscillations can be damped by the magnetic interaction. First, by identifying the low frequency quasi-periodic oscillations (QPOs) observed in the soft-gamma repeaters (SGRs) as the fundamental torsional oscillations, we constrain the slope parameter of the nuclear symmetry energy, $L$, for reasonable values of the star's mass $M$ and radius $R$. Meanwhil…
The accretion of matter onto the surface of a neutron star in a low-mass X-ray binary triggers X-ray bursts, whose ashes are buried and further processed thus altering the composition and the properties of the stellar crust. In this second paper of a series, the impact of accretion on the equation of state and on the global properties of neutron stars is studied in the framework of the nuclear energy-density functional theory. Considering ashes made of $^{56}$Fe, we calculated the equations of state using the same Brussels-Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21, as…
We study the properties of pasta structures and their influence on the neutron star observables employing the effective relativistic mean-field (E-RMF) model. The compressible liquid drop model is used to incorporate the finite size effects, considering the possibility of nonspherical structures in the inner crust. The unified equation of states are constructed for several E-RMF parameters to study various properties such as pasta mass and thickness in the neutron star's crust. The majority of the pasta properties are sensitive to the symmetry energy in the subsaturation density region. Using …
The shear modulus of neutron star matter is one of the important properties for determining torsional oscillations in neutron stars. We take into account the effects of finite sizes of spherical nuclei on the shear modulus and examine the frequencies of crustal torsional oscillations. The shear modulus decreases owing to the finite-size effect, which in turn decreases the frequencies of torsional oscillations. In particular, the finite-size effect becomes more crucial for oscillations with a larger azimuthal quantum number and for neutron star models with a weaker density dependence of nuclear…
Observations of soft X-ray transients in quiescence suggest the existence of heat sources in the crust of accreting neutron stars. Heat is thought to be released by electroweak and nuclear processes triggered by the burying of ashes of X-ray bursts. The heating is studied using a fully quantum approach taking consistently into account nuclear shell effects. We have followed the evolution of ashes made of $^{56}$Fe employing the nuclear energy-density functional theory. Both the outer and inner crusts are described using the same functional, thus ensuring a unified and thermodynamically consist…
Pulsars are highly magnetized rotating neutron stars with a very stable rotation speed. Irrespective of their stable rotation rate, many pulsars have been observed with the sudden jump in the rotation rate, which is known as pulsar glitch. The glitch phenomena are considered to be an exhibit of superfluidity of neutron matter inside the neutron star's crustal region. The magnitude of such rapid change in rotation rate relative to their stable rotation frequency can quantify the moment of inertia of the crustal region to the total moment of inertia of the star called as the fractional moment of…
Neutron stars harbour extremely strong magnetic fields within their solid outer crust. The topology of this field strongly influences the surface temperature distribution, and hence the star's observational properties. In this work, we present the first realistic simulations of the coupled crustal magneto-thermal evolution of isolated neutron stars in three dimensions with account for neutrino emission, obtained with the pseudo-spectral code Parody. We investigate both the secular evolution, especially in connection with the onset of instabilities during the Hall phase, and the short-term evol…
We study long-term thermal evolution of neutron stars in soft X-ray transients (SXTs), taking the deep crustal heating into account consistently with the changes of the composition of the crust. We collect observational estimates of average accretion rates and thermal luminosities of such neutron stars and compare the theory with observations. We perform simulations of thermal evolution of accreting neutron stars, considering the gradual replacement of the original nonaccreted crust by the reprocessed accreted matter, the neutrino and photon energy losses, and the deep crustal heating due to n…
Detailed structures of the Vela pulsar (PSR B0833-45, with a period of $89.33$ milliseconds) are predicted by adopting a recently-constructed unified treatment of all parts of neutron stars: the outer crust, the inner crust and the core based on modern microscopic Brueckner-Hartree-Fock calculations. To take the pulsar mass ranging from $1.0M_{\odot}$ to $2.0M_{\odot}$, we calculate the central density, the core/crust radii, the core/crust mass, the core/crustal thickness, the moment of inertia, and the crustal moment of inertia. Among them, the crustal moment of inertia could be effectively c…
The dissipation of intense crustal electric currents produces high Joule heating rates in cooling neutron stars. Here it is shown that Joule heating can counterbalance fast cooling, making it difficult to infer the presence of hyperons (which accelerate cooling) from measurements of the observed thermal luminosity $L_γ$. Models with and without hyperon cores match $L_γ$ of young magnetars (with poloidal-dipolar field $B_{\textrm{dip}} \gtrsim 10^{14}$ G at the polar surface and $L_γ \gtrsim 10^{34}$ erg s$^{-1}$ at $t \lesssim 10^5$ yr) as well as mature, moderately magnetized stars (with $B_{…
Superbursts are rare and energetic thermonuclear carbon flashes observed to occur on accreting neutron stars. We create the first multi-zone models of series of superbursts using a stellar evolution code. We self-consistently build up the fuel layer at different rates, spanning the entire range of observed mass accretion rates for superbursters. For all models light curves are presented. They generally exhibit a shock breakout, a precursor burst due to shock heating, and a two-component power-law decay. Shock heating alone is sufficient for a bright precursor, that follows the shock breakout o…
Spectral Evidence of Heavy Nuclei from the Neutron Star Crust in Magnetar Bursts
Central China Normal University（华中师范大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
The spin-down of a neutron star, e.g. due to magneto-dipole losses, results in compression of the stellar matter and induces nuclear reactions at phase transitions between different nuclear species in the crust. We show that this mechanism is effective in heating recycled pulsars, in which the previous accretion process has already been compressing the crust, so it is not in nuclear equilibrium. We calculate the corresponding emissivity and confront it with available observations, showing that it might account for the likely thermal ultraviolet emission of PSR J0437-4715.
Crustal cooling of accretion-heated neutron stars provides insight into the stellar interior of neutron stars. The neutron star X-ray transient, KS~1731$-$260, was in outburst for 12.5 years before returning to quiescence in 2001. We have monitored the cooling of this source since then through {\it Chandra} and {\it XMM-Newton} observations. Here, we present a 150 ks {\it Chandra} observation of KS~1731$-$260 taken in August 2015, about 14.5 years into quiescence, and 6 years after the previous observation. We find that the neutron star surface temperature is consistent with the previous obser…
The remarkable null pulse coincident with the 2016 glitch in Vela rotation indicates a dynamical event involving the crust and the magnetosphere of the neutron star. We propose that a crustal quake associated with the glitch strongly disturbed the Vela magnetosphere and thus interrupted its radio emission. We present the first global numerical simulations of a neutron starquake. Our code resolves the elasto-dynamics of the entire crust and follows the evolution of Alfvén waves excited in the magnetosphere. We observe Rayleigh surface waves propagating away from the epicenter of the quake, arou…
Magnetars, isolated neutron stars with magnetic field strengths typically $\gtrsim10^{14}$~G, exhibit distinctive months-long outburst epochs during which strong evolution of soft X-ray pulse profiles, along with nonthermal magnetospheric emission components, is often observed. Using near-daily NICER observations of the magnetar SGR 1830-0645 during the first 37 days of a recent outburst decay, a pulse peak migration in phase is clearly observed, transforming the pulse shape from an initially triple-peaked to a single-peaked profile. Such peak merging has not been seen before for a magnetar. O…
