Neutron Star Crust Research Articles

Inner crust of a neutron star at the point of crystallization in a multicomponent approach

Context. The possible presence of amorphous and heterogeneous phases in the inner crust of a neutron star is expected to reduce the electrical conductivity of the crust, potentially with significant consequences on the magneto-thermal evolution of the star. In cooling simulations, the disorder is quantified by an impurity parameter, which is often taken as a free parameter. Aims. We aim to give a quantitative prediction of the impurity parameter as a function of the density in the crust, performing microscopic calculations including up-to-date microphysics of the crust. Methods. A multicomponent approach was developed at a finite temperature using a compressible liquid-drop description of the ions with an improved energy functional based on recent microscopic nuclear models and optimized on extended Thomas-Fermi calculations. Thermodynamic consistency was ensured by adding a rearrangement term, and deviations from the linear mixing rule were included in the liquid phase. Results. The impurity parameter is consistently calculated at the crystallization temperature as determined in the one-component plasma approximation for the different functionals. Our calculations show that at the crystallization temperature, the composition of the inner crust is dominated by nuclei with charge number around Z ≈ 40, while the range of the Z distribution varies from about 20 near the neutron drip to about 40 closer to the crust-core transition. This reflects on the behavior of the impurity parameter that monotonically increases with density reaching up to around 40 in the deeper regions of the inner crust. Conclusions. Our study shows that the contribution of impurities is non-negligible, thus potentially having an impact on the transport properties in the neutron-star crust. The obtained values of the impurity parameter represent a lower limit; larger values are expected in the presence of nonspherical geometries and/or fast cooling dynamics.

Experimental constraints on shallow heating in accreting neutron-star crusts

The observed thermal relaxation of transiently accreting neutron stars during quiescence periods in low-mass X-ray binaries suggests the existence of unknown heat sources in the shallow layers of neutron-star crust. Making use of existing experimental nuclear data, we estimate the maximum possible amount of heat that can be deposited in the outer crust of an accreting neutron star due to electron captures and pycnonuclear fusion reactions triggered by the burial of X-ray burst ashes.

Adding crust to BPS Skyrme neutron stars

The Skyrme model and its generalisations provide a conceptually appealing field-theory basis for the description of nuclear matter and, after its coupling to gravity, also of neutron stars. In particular, a specific Skyrme submodel, the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrme model, allows both for an exact field-theoretic and a mean-field treatment of neutron stars, as a consequence of its perfect fluid property. A pure BPS Skyrme model description of neutron stars, however, only describes the neutron star core, by construction. Here we consider different possibilities to extrapolate a BPS Skyrme neutron star at high baryon density to a description valid at lower densities. In the exact field-theoretic case, a simple effective description of the neutron star crust can be used, because the exact BPS Skyrme neutron star solutions formally extend to sufficiently low densities. In the mean-field case, on the other hand, the BPS Skyrme neutron star solutions always remain above the nuclear saturation density and, therefore, must be joined to a different nuclear physics equation of state already for the outer core. We study the resulting neutron stars in both cases, facilitating an even more complete comparison between Skyrmionic neutron stars and neutron stars obtained from other approaches, as well as with observations.

Structure and composition of the inner crust of neutron stars from Gogny interactions

The detailed knowledge of the inner crust properties of neutron stars might be important to explain different phenomena such as pulsar glitches or the possibility of an {\it r-process} site in neutron star mergers. It has been shown in the literature that quantal effects like shell correction or pairing may play a relevant role to determine the composition of the inner crust of the neutron star. In this paper we construct the equation of state of the inner crust using the finite-range Gogny interactions, where the mean field and the pairing field are calculated with same interaction. We have used the semiclassical Variational Wigner-Kirkwood method along with shell and pairing corrections calculated with the Strutinsky integral method and the BCS approximation, respectively. Our results are compared with those of some popular models from the literature. We report a unified equation of state of the inner crust and core computed with the D1M* Gogny force, which was specifically fabricated for astrophysical calculations.

Analytical determination of the structure of the outer crust of a cold nonaccreted neutron star: Extension to strongly quantizing magnetic fields

The iterative method recently proposed for determining the internal constitution of the outer crust of a nonaccreted neutron star is extended to magnetars by taking into account the Landau-Rabi quantization of electron motion induced by the presence of a very high magnetic field. It is shown that in the strongly quantizing regime, the method can be efficiently implemented using new analytical solutions for the transitions between adjacent crustal layers. Detailed numerical computations are performed to assess the performance and precision of the method.

Magnetic Field Evolution in the Crust of Neutron Stars: Crust Failure and Plastic Flow

AbstractThe evolution of the magnetic field in neutron star crusts because of the Hall effect has received significant attention over the last two decades, which is strongly justified because of the dominance of this effect in highly magnetised neutron stars. However, the applicability of the Hall effect is based on the assumption that the crust does not fail and sustains its rigidity. This assumption can be violated for substantially strong magnetic fields. If this is the case, the evolution of the magnetic field is described by a different set of equations, which include the effects of a non-rigid crust. In this talk, after a brief review of the main characteristic of the Hall evolution, I will discuss the impact a plastic flow of the crust has on the magnetic field, studying axisymmetric models. Moreover, the way the crust fails impacts the overall evolution, with major differences appearing if the failure is local, intermediate or global. Quite remarkably, crustal failure and plasticity do not annul the Hall effect, and under certain circumstances they may even lead to a more dramatic evolution. I will discuss the impact of these effects in the context of neutron star timing behaviour, with special focus on timing noise, outbursts and glitches.

Unexpected late-time temperature increase observed in the two neutron star crust-cooling sources XTE J1701−462 and EXO 0748−676

Transient low-mass X-ray binaries (LMXBs) that host neutron stars (NSs) provide excellent laboratories for probing the dense matter physics present in NS crusts. During accretion outbursts in LMXBs, exothermic reactions may heat the NS crust, disrupting the crust-core equilibrium. When the outburst ceases, the crust cools to restore thermal equilibrium with the core. Monitoring this cooling evolution allows us to probe the dense matter physics in the crust. Properties of the deeper crustal layers can be probed at later times after the end of the outburst. We report on the unexpected late-time temperature evolution (≳2000 days after the end of their outbursts) of two NSs in LMXBs, XTE J1701−462 and EXO 0748−676. Although both these sources exhibited very different outbursts (in terms of duration and the average accretion rate), they exhibit an unusually steep decay of ∼7 eV in the observed effective temperature (occurring in a time span of ∼700 days) around ∼2000 days after the end of their outbursts. Furthermore, they both showed an even more unexpected rise of ∼3 eV in temperature (over a time period of ∼500–2000 days) after this steep decay. This rise was significant at the 2.4σ and 8.5σ level for XTE J1701−462 and EXO 0748−676, respectively. The physical explanation for such behaviour is unknown and cannot be straightforwardly be explained within the cooling hypothesis. In addition, this observed evolution cannot be well explained by low-level accretion either without invoking many assumptions. We investigate the potential pathways in the theoretical heating and cooling models that could reproduce this unusual behaviour, which so far has been observed in two crust-cooling sources. Such a temperature increase has not been observed in the other NS crust-cooling sources at similarly late times, although it cannot be excluded that this might be a result of the inadequate sampling obtained at such late times.

Recurrent low-level luminosity behaviour after a giant outburst in the Be/X-ray transient 4U 0115+63

In 2017, the Be/X-ray transient 4U 0115+63 exhibited a new type II outburst that was two times fainter than its 2015 giant outburst (in the Swift/BAT count rates). Despite this difference between the two bright events, the source displayed similar X-ray behaviour after these periods. Once the outbursts ceased, the source did not transit towards quiescence directly, but was detected about a factor of 10 above its known quiescent level. It eventually decayed back to quiescence over timescales of months. In this paper, we present the results of our Swift monitoring campaign, and an XMM-Newton observation of 4U 0115+63 during the decay of the 2017 type II outburst and its subsequent low-luminosity behaviour. We discuss the possible origin of the decaying source emission at this low-level luminosity, which has now been shown as a recurrent phenomenon, in the framework of the two proposed scenarios to explain this faint state: cooling from an accretion-heated neutron star crust or continuous low-level accretion. In addition, we compare the outcome of our study with the results we obtained from the 2015/2016 monitoring campaign on this source.

Thermodynamically Consistent Equation of State for an Accreted Neutron Star Crust.

We study the equation of state (EOS) of an accreting neutron star crust. Usually, such an EOS is obtained by assuming (implicitly) that the free (unbound) neutrons and nuclei in the inner crust move together. We argue that this assumption violates the condition μ_{n}^{∞}=const, required for hydrostatic (and diffusion) equilibrium of unbound neutrons (μ_{n}^{∞} is the redshifted neutron chemical potential). We construct a new EOS respecting this condition, working in the compressible liquid-drop approximation. We demonstrate that it is close to the catalyzed EOS in most of the inner crust, being very different from EOSs of accreted crust discussed in the literature. In particular, the pressure at the outer-inner crust interface does not coincide with the neutron drip pressure, usually calculated in the literature, and is determined by hydrostatic (and diffusion) equilibrium conditions within the star. We also find an instability at the bottom of the fully accreted crust that transforms nuclei into homogeneous nuclear matter. It guarantees that the structure of the fully accreted crust remains self-similar during accretion.

Nuclear mass measurements map the structure of atomic nuclei and accreting neutron stars

We present mass excesses (ME) of neutron-rich isotopes of Ar through Fe, obtained via TOF-$B\rho$ mass spectrometry at the National Superconducting Cyclotron Laboratory. Our new results have significantly reduced systematic uncertainties relative to a prior analysis, enabling the first determination of ME for $^{58,59}{\rm Ti}$, $^{62}{\rm V}$, $^{65}{\rm Cr}$, $^{67,68}{\rm Mn}$, and $^{69,70}{\rm Fe}$. Our results show the $N=34$ subshell weaken at Sc and vanish at Ti, along with the absence of an $N=40$ subshell at Mn. This leads to a cooler accreted neutron star crust, highlighting the connection between the structure of nuclei and neutron stars.

Estimation of Electrical Conductivity and Magnetization Parameter of Neutron Star Crusts and Applied to the High-Braking-Index Pulsar PSR J1640-4631

Young pulsars are thought to be highly magnetized neutron stars (NSs). The crustal magnetic field of a NS usually decays at different timescales in the forms of Hall drift and Ohmic dissipation. The magnetization parameter ω B τ is defined as the ratio of the Ohmic timescale τ O h m to the Hall drift timescale τ H a l l . During the first several million years, the inner temperature of the newly born neutron star cools from T = 10 9 K to T = 1.0 × 10 8 K, and the crustal conductivity increases by three orders of magnitude. In this work, we adopt a unified equations of state for cold non-accreting neutron stars with the Hartree–Fock–Bogoliubov method, developed by Pearson et al. (2018), and choose two fiducial dipole magnetic fields of B = 1.0 × 10 13 G and B = 1.0 × 10 14 G, four different temperatures, T, and two different impurity concentration parameters, Q, and then calculate the conductivity of the inner crust of NSs and give a general expression of magnetization parameter for young pulsars: ω B τ ≃ ( 1 − 50 ) B 0 / ( 10 13 G) by using numerical simulations. It was found when B ≤ 10 15 G, due to the quantum effects, the conductivity increases slightly with the increase in the magnetic field, the enhanced magnetic field has a small effect on the matter in the low-density regions of the crust, and almost has no influence the matter in the high-density regions. Then, we apply the general expression of the magnetization parameter to the high braking-index pulsar PSR J1640-4631. By combining the observed arrival time parameters of PSR J1640-4631 with the magnetic induction equation, we estimated the initial rotation period P 0 , the initial dipole magnetic field B 0 , the Ohm dissipation timescale τ O h m and Hall drift timescale τ H a l l . We model the magnetic field evolution and the braking-index evolution of the pulsar and compare the results with its observations. It is expected that the results of this paper can be applied to more young pulsars.

A mixing interpolation method to mimic pasta phases in compact star matter

We present a new method to interpolate between two matter phases that allows for a description of mixed phases and can be used, e.g., for mimicking transitions between pasta structures occurring in the crust as well as in the inner core of compact stars. This interpolation method is based on assuming switch functions that are used to define a mixture of subphases while fulfilling constraints of thermodynamic stability. The width of the transition depends on a free parameter, the pressure increment relative to the critical pressure of a Maxwell construction. As an example we present a trigonometric function ansatz for the switch function together with a pressure increment during the transition. We note that the resulting mixed phase equation of state bears similarities with the appearance of substitutional compounds in neutron star crusts and with the sequence of transitions between different pasta phases in the hadron-to-quark matter transition. We apply this method to the case of a hadron-to-quark matter transition and test the robustness of the compact star mass twin phenomenon against the appearance of pasta phases modelled in this way.

Coordinate-space solver for finite-temperature Hartree-Fock-Bogoliubov calculations using the shifted Krylov method

In order to study structure of proto-neutron stars and those in subsequent cooling stages, it is of great interest to calculate inhomogeneous hot and cold nuclear matter in a variety of phases. The finite-temperature Hartree-Fock-Bogoliubov (FT-HFB) theory is a primary choice for this purpose, however, its numerical calculation for superfluid (superconducting) many-fermion systems in three dimensions requires enormous computational costs. To study a variety of phases in the crust of hot and cold neutron stars, we propose an efficient method to perform the FT-HFB calculation with the three-dimensional (3D) coordinate-space representation. Recently, an efficient method based on the contour integral of Green's function with the shifted conjugate-orthogonal conjugate-gradient method has been proposed [Phys. Rev. C 95, 044302 (2017)]. We extend the method to the finite temperature, using the shifted conjugate-orthogonal conjugate-residual method. We benchmark the 3D coordinate-space solver of the FT-HFB calculation for hot isolated nuclei and fcc phase in the inner crust of neutron stars at finite temperature. The computational performance of the present method is demonstrated. Different critical temperatures of the quadrupole and the octupole deformations are confirmed for $^{146}$Ba. The robustness of the shape coexistence feature in $^{184}$Hg is examined. For the neutron-star crust, the deformed neutron-rich Se nuclei embedded in the sea of superfluid low-density neutrons appear in the fcc phase at the nucleon density of 0.045 fm$^{-3}$ and the temperature of $k_B T=200$ keV. The efficiency of the developed solver is demonstrated for nuclei and inhomogeneous nuclear matter at finite temperature. It may provide a standard tool for nuclear physics, especially for the structure of the hot and cold neutron-star matters.

Magnetic-field evolution with large-scale velocity circulation in a neutron-star crust

ABSTRACT We examine the effects of plastic flow that appear in a neutron-star crust when a magnetic stress exceeds the threshold. The dynamics involved are described using the Navier–Stokes equation comprising the viscous-flow term, and the velocity fields for the global circulation are determined using quasi-stationary approximation. We simulate the magnetic-field evolution by taking into consideration the Hall drift, Ohmic dissipation, and fluid motion induced by the Lorentz force. The decrease in the magnetic energy is enhanced, as the energy converts to the bulk motion energy and heat. It is found that the bulk velocity induced by the Lorentz force has a significant influence in the low-viscosity and strong-magnetic-field regimes. This effect is crucial near magnetar surfaces.

Precursor flares of short gamma-ray bursts from crust yielding due to tidal resonances in coalescing binaries of rotating, magnetized neutron stars

As evidenced by the coincident detections of GW170817 and GRB 170817A, short gamma-ray bursts are likely associated with neutron star-neutron star merger events. Although rare, some bursts display episodes of early emission, with precursor flares being observed up to $\sim 10$ seconds prior to the main burst. As the stars inspiral due to gravitational wave emission, the exertion of mutual tidal forces leads to the excitation of stellar oscillation modes, which may come into resonance with the orbital motion. Mode amplitudes increase substantially during a period of resonance as tidal energy is deposited into the star. The neutron star crust experiences shear stress due to the oscillations and, if the resonant amplitudes are large enough, may become over-strained. This over-straining can lead to fractures or quakes which release energy, thereby fueling precursor activity prior to the merger. Using some simple Maclaurin spheroid models, we investigate the influence of magnetic fields and rapid rotation on tidally-forced $f$- and $r$- modes, and connect the associated eigenfrequencies with the orbital frequencies corresponding to precursor events seen in, for example, GRB 090510.

Analytical determination of the structure of the outer crust of a cold nonaccreted neutron star

A very fast iterative method is presented to calculate the internal constitution of the outer crust of a cold nonaccreted neutron star, making use of very accurate analytical formulas for the transition pressures between adjacent crustal layers and their density. In addition to the composition of the different crustal layers, their depth and their baryonic mass content can be simultaneously estimated using an approximate solution of Einstein's general relativistic equations. The overall computing time is drastically reduced compared to the traditional approach, thus opening the door to large-scale statistical studies and sensitivity analyses.

The effect of diffusive nuclear burning in neutron star envelopes on cooling in accreting systems

ABSTRACT Valuable information about the neutron star (NS) interior can be obtained by comparing observations of thermal radiation from a cooling NS crust with theoretical models. Nuclear burning of lighter elements that diffuse to deeper layers of the envelope can alter the relation between surface and interior temperatures and can change the chemical composition over time. We calculate new temperature relations and consider two effects of diffusive nuclear burning (DNB) for H–C envelopes. First, we consider the effect of a changing envelope composition and find that hydrogen is consumed on short time-scales and our temperature evolution simulations correspond to those of a hydrogen-poor envelope within ∼100 d. The transition from a hydrogen-rich to a hydrogen-poor envelope is potentially observable in accreting NS systems as an additional initial decline in surface temperature at early times after the outburst. Second, we find that DNB can produce a non-negligible heat flux, such that the total luminosity can be dominated by DNB in the envelope rather than heat from the deep interior. However, without continual accretion, heating by DNB in H–C envelopes is only relevant for <1–80 d after the end of an accretion outburst, as the amount of light elements is rapidly depleted. Comparison to crust cooling data shows that DNB does not remove the need for an additional shallow heating source. We conclude that solving the time-dependent equations of the burning region in the envelope self-consistently in thermal evolution models instead of using static temperature relations would be valuable in future cooling studies.

Warming nuclear pasta with dark matter: kinetic and annihilation heating of neutron star crusts

Neutron stars serve as excellent next-generation thermal detectors of dark matter, heated by the scattering and annihilation of dark matter accelerated to relativistic speeds in their deep gravitational wells. However, the dynamics of neutron star cores are uncertain, making it difficult at present to unequivocally compute dark matter scattering in this region. On the other hand, the physics of an outer layer of the neutron star, the crust, is more robustly understood. We show that dark matter scattering solely with the low-density crust still kinetically heats neutron stars to infrared temperatures detectable by forthcoming telescopes. We find that for both spin-independent and spin-dependent scattering on nucleons, the crust-only cross section sensitivity is 10−43 − 10−41 cm2 for dark matter masses of 100 MeV − 1 PeV, with the best sensitivity arising from dark matter scattering with a crust constituent called nuclear pasta (including gnocchi, spaghetti, and lasagna phases). For dark matter masses from 10 eV to 1 MeV, the sensitivity is 10−39 − 10−34 cm2, arising from exciting collective phonon modes in a neutron superfluid in the inner crust. Furthermore, for any s-wave or p-wave annihilating dark matter, we show that dark matter will efficiently annihilate by thermalizing just with the neutron star crust, regardless of whether the dark matter ever scatters with the neutron star core. This implies efficient annihilation in neutron stars for any electroweakly interacting dark matter with inelastic mass splittings of up to 200 MeV, including Higgsinos. We conclude that neutron star crusts play a key role in dark matter scattering and annihilation in neutron stars.

Asymmetric accretion and thermal ‘mountains’ in magnetized neutron star crusts

ABSTRACT Accreting neutron stars (NSs) are one of the main targets for continuous gravitational wave searches, as asymmetric accretion may lead to quadrupolar deformations, or ‘mountains’, on the crust of the star, which source gravitational wave (GW) emission at twice the rotation frequency. The GW torque may also impact on the spin evolution of the star, possibly dictating the currently observed spin periods of NSs in low-mass X-ray binaries and leading to the increased spin-down rate observed during accretion in PSR J1023+0038. Previous studies have shown that deformed reaction layers in the crust of the NS lead to thermal and compositional gradients that can lead to GW emission. However, there are no realistic constraints on the level of asymmetry that is expected. In this paper, we consider a natural source of asymmetry, namely the magnetic field, and calculate the density and pressure perturbations that are expected in the crust of accreting NSs. In general, we find that only the outermost reaction layers of the NS are strongly perturbed. The mass quadrupole that we estimate is generally small and cannot explain the increase of spin-down rate of PSR J1023+0038. However, if strong shallow heating sources are present at low densities in the crust, as cooling observations suggest, these layers will be strongly perturbed and the resulting quadrupole could explain the observed spin-down of PSR J1023+0038, and lead to observable GW signals from systems with higher accretion rates.

Structure of multicomponent Coulomb crystals.

Coulomb plasmas crystallize in a number of physical systems, such as dusty plasmas, neutron star crusts, and white dwarf cores. The crystal structure of the one-component and binary plasma has received significant attention in the literature, though the less studied multicomponent plasma may be most relevant for many physical systems which contain a large range of particle charges. We report on molecular dynamics simulations of multicomponent plasmas near the melting temperature with mixtures taken to be realistic x-ray burst ash compositions. We quantify the structure of the crystal with the bond order parameters and radial distribution function. Consistent with past work, low charge particles form interstitial defects and we argue that they are in a quasiliquid state within the lattice. The lattice shows screening effects which preserves long-range order despite the large variance in particle charges, which may impact transport properties relevant to astrophysics.