Crust-core Interface Research Articles

Effects of Β-sitosterol oleogel on fat uptake reduction, physicochemical properties, oxidative stability, and sensory characteristics of fried surimi fish balls

Surimi, a minced fish meat, is available in various forms, including deep-fried surimi. However, deep-fried surimi tends to absorb high amounts of oil during frying, potentially contributing to obesity and cardiovascular diseases. Additionally, its high fat content renders it susceptible to lipid oxidation during storage, which can degrade its quality over time. Therefore, reducing oil absorption and subsequent oxidation is crucial for enhancing the quality of deep-fried surimi. In this study, we prepared oleogels with varying concentrations of β-sitosterol and investigated their effects on fat uptake, physicochemical attributes, oxidative stability, and sensory properties of frozen (−18 °C) fried surimi fish balls over a period of 30 days. Images that were obtained by scanning electron microscope demonstrated that surimi fish balls with 0.2 % β-sitosterol oleogel had a more compact and smoother crust-core interface than other groups. The addition of 0.2 % β-sitosterol oleogel led to the lowest fat absorption (8.63 %), decreased lipid oxidation (3.65 mg MDA/kg), reduced porosity, higher moisture content (57.72 %), elevated pH and color values, as well as increased bulk density compared to the control (p ≤ 0.05). Although atherogenicity and thrombogenesis indices increased, they remained below recommended levels. Importantly, this treatment did not adversely affect the product's texture and sensory properties. Given the increasing demand for healthier food products, it is recommended that the food industry incorporate 0.2 % β-sitosterol oleogel into the production of low-fat fried surimi. This approach can effectively mitigate lipid oxidation while maintaining product quality and sensory attributes. The study offers a valuable contribution to the food industry by addressing the challenges associated with deep-fried surimi and aligns with the growing consumer preference for healthier food choices.

Probing phase transitions in neutron stars via the crust-core interfacial mode

Gravitational waves emitted from the binary neutron star (BNS) systems can carry information about the dense matter phase in these compact stars. The crust-core interfacial mode is an oscillation mode in a neutron star, and it depends mostly on the equation of state of the matter in the crust-core transition region. This mode can be resonantly excited by the tidal field of an inspiraling-in BNS system, thereby affecting the emitted gravitational waves and hence could be used to probe the equation of state in the crust-core transition region. In this work, we investigate, in detail, how the first-order phase transition inside the neutron star, if it exists, affects the properties of the crust-core interfacial mode using a Newtonian fluid perturbation theory on a general relativistic background solution of the stellar structure. Two possible types of phase transitions are considered: (1) the phase transitions happen in the fluid core but near the crust-core interface, which results in density discontinuities, and (2) the strong interaction phase transitions in the dense core (as in the conventional hybrid star case). We study how these phase transitions affect the properties of the neutron star oscillation mode excited at the interface, where there exists a shear modulus discontinuity (interfacial mode). In particular, the former phase transition has a minor effect on the mass-radius relation, and the adiabatic tidal deformability, but has the potential to significantly affect the interfacial mode frequency and thereby could be probed using gravitational waves. For the BNS systems, we discuss the possible observational signatures of these phase transitions in the gravitational waveforms and their detectability. Our work enriches the exploration of the physical properties of the crust-core interfacial mode and provides a promising method for probing the phase transition using the seismology of a compact star.

Crust-core interface and bulk neutron star properties

The nuclear symmetry energy plays an important role in the description of the properties of finite nuclei as well as neutron stars. Especially, for low values of baryon density, the accurate description of the crust-core interface strongly depends on the symmetry energy. Usually, the well known parabolic approximation is employed for the definition of the symmetry energy without avoiding some drawbacks. In the present paper, a class of nuclear models, suitable for the description of the inner and outer core of neutron stars, is applied in studying the effect of higher orders of the expansion of the energy on the location of the crust-core transition. The thermodynamical and dynamical methods are used for the determination of the transition density ${n}_{\mathrm{t}}$ and pressure ${P}_{\mathrm{t}}$. The corresponding energy density functional is applied for the study of some relevant properties of both nonrotating and slowly rotating neutron stars. We found that the larger the value of the slope parameter $L$, the slower the convergence of the expansion. In addition, a universal relation is presented between ${n}_{\mathrm{t}}$ and $L$, by employing the full expression and dynamical approach. The crustal moment of inertia is very sensitive to the location of the transition while the effects are moderated concerning the critical angular velocity of the $r$-mode instability and minimum mass configuration. The effect on the tidal deformability is less but not negligible. In any case, the use of the parabolic approximation leads to the overestimation of ${n}_{\mathrm{t}}$ and ${P}_{\mathrm{t}}$ and, consequently, on inaccurate predictions. Moreover, in some cases, even the matching process at the interface may affect considerably the predictions, introducing errors of the same order with the one due to the employed method.

Equation of state effects on the core-crust interface of slow rotating neutron stars

We systematically study the symmetry energy effects of the transition density ntand the transition pressure Ptaround the crust-core interface of a neutron star in the framework of the dynamical and the thermodynamical method respectively. We employ both the parabolic approximation and the full expansion, for the definition of the symmetry energy. We use various theoretical nuclear models. Firstly we derive and present an approximation for the transition pressure Ptand crustal mass Mcrust. Secondly, we explore the effects of the Equation of State (EoS) on a few astrophysical applications which are sensitive to the values of n­tand Pt. We found that the above quantities are sensitive mainly on the applied approximation for the symmetry energy (confirming previous results). Furthermore, an additional sensitivity also exists, depending on the used method (dynamical or thermodynamical). The above findings lead us to claim that the determination of the n­tand Ptmust be reliable and accurate before they are used to constrain relevant neutron star properties.

Effects of the equation of state on the core-crust interface of slowly rotating neutron stars

We systematically study the symmetry energy effects of the transition density $n_{\rm t}$ and the transition pressure $P_{\rm t}$ around the crust-core interface of a neutron star in the framework of the dynamical and the thermodynamical method respectively. We employ both the parabolic approximation and the full expansion, for the definition of the symmetry energy. We use various theoretical nuclear models, which are suitable for reproducing the bulk properties of nuclear matter at low densities, close to saturation density as well as the maximum observational neutron star mass. Firstly we derive and present an approximation for the transition pressure $P_{\rm t}$ and crustal mass $M_{\rm crust}$. Secondly, we explore the effects of the Equation of State (EoS) on a few astrophysical applications which are sensitive to the values of $n_{\rm t}$ and $P_{\rm t}$ including neutron star oscillation frequencies, thermal relaxation of the crust, crustal fraction of the moment of inertia and the r-mode instability window of a rotating neutron star. We found that the above quantities are sensitive mainly on the applied approximation for the symmetry energy (confirming previous results). Furthermore, an additional sensitivity also exists, depending on the used method (dynamical or thermodynamical). The above findings lead us to claim that the determination of the $n_{\rm t}$ and $P_{\rm t}$ must be reliable and accurate before they are used to constrain relevant neutron star properties.

Gravitational waves from isolated neutron stars: Mass dependence of r -mode instability

In this work we study the r-mode instability windows and the gravitational wave signatures of neutron stars in the slow rotation approximation using the equation of state obtained from the density dependent M3Y effective interaction. We consider the neutron star matter to be $\beta$-equilibrated neutron-proton-electron matter at the core with a rigid crust. The fiducial gravitational and viscous timescales, the critical frequencies and the time evolutions of the frequencies and the rates of frequency change are calculated for a range of neutron star masses. We show that the young and hot rotating neutron stars lie in the r-mode instability region. We also emphasize that if the dominant dissipative mechanism of the r-mode is the shear viscosity along the boundary layer of the crust-core interface, then the neutron stars with low $L$ value lie in the r-mode instability region and hence emit gravitational radiation.

Some Theoretical Aspects of Magnetars

Magnetars have been observationally determined to have surface magnetic fields of order of 10 14 – 10 15 G, and the implied internal field strength may be even larger. We discuss the effect of strong field on the dense matter expected to be inside neutron stars. We describe the microphysics, phenomenology, and astrophysical implications of strong field induced unpairing effect that may occur in magnetars, if the local magnetic field in the core of a magnetar exceeds a critical value. The density dependence of the pairing of proton condensate implies that the critical value required for the unpairing effect to occur is maximal at the crust–core interface and decreases towards the center of the star. As a consequence, magnetar cores with homogeneous constant fields will be partially superconducting for “medium-field” magnetars, whereas “strong-field” magnetars will be void of superconductivity. We also discuss its effect on some observational phenomena which depend on the nature and composition of matter inside neutron stars.

Quasi-periodic oscillations in superfluid, relativistic magnetars with nuclear pasta phases

We study the torsional magneto-elastic oscillations of relativistic superfluid magnetars and explore the effects of a phase transition in the crust-core interface (nuclear pasta) which results in a weaker elastic response. Exploring various models with different extension of nuclear pasta phases, we find that the differences in the oscillation spectrum present in purely elastic modes (weak magnetic field), are smeared out with increasing strength of the magnetic field. For magnetar conditions, the main characteristic and features of models without nuclear pasta are preserved. We find in general two classes of magneto-elastic oscillations which exhibit a different oscillation pattern. For B_p < 4 x 10^{14} G, the spectrum is characterised by the turning points and edges of the continuum which are confined into the star's core, and have no constant phase. Increasing the magnetic field, we find, in addition, several magneto-elastic oscillations which reach the surface and have an angular structure similar to crustal modes. These global magneto-elastic oscillations show a constant phase and become dominant when B_p > 5 x 10^{14} G. We do not find any evidence of fundamental pure crustal modes in the low frequency range (below 200 Hz) for B_p >= 10^{14} G.

Rapid rotational crust-core relaxation in magnetars

If a magnetar interior $B$-field exceeds $10^{15}$~G, it will unpair the proton superconductor in the stellar core by inducing diamagnetic currents that destroy the Cooper pair coherence. Then, the $P$-wave neutron superfluid in these non-superconducting regions will couple to the stellar plasma by scattering of protons off the quasiparticles that are confined in the cores of neutron vortices by the strong (nuclear) force. The dynamical timescales associated with this interaction span from several minutes at the crust-core interface to a few seconds in the deep core. We show that (a) the rapid crust-core coupling is incompatible with oscillation models of magnetars that completely decouple the core superfluid from the crust and (b) magnetar precession is damped by the coupling of normal fluids to the superfluid core and, if observed, needs to be forced or continuously excited by seismic activity.

Magnetar superconductivity versus magnetism: Neutrino cooling processes

We describe the microphysics, phenomenology, and astrophysical implication of a $B$-field induced unpairing effect that may occur in magnetars, if the local $B$ field in the core of a magnetar exceeds a critical value ${H}_{c2}$. Using the Ginzburg-Landau theory of superconductivity, we derive the ${H}_{c2}$ field for proton condensate taking into the correction $(\ensuremath{\le}30%)$ which arises from its coupling to the background neutron condensate. The density dependence of pairing of proton condensate implies that ${H}_{c2}$ is maximal at the crust-core interface and decreases towards the center of the star. As a consequence, magnetar cores with homogenous constant fields will be partially superconducting for ``medium-field'' magnetars $({10}^{15}\ensuremath{\le}B\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{G})$ whereas ``strong-field'' magnetars $(B&gt;5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{G})$ will be void of superconductivity. The neutrino emissivity of a magnetar's core changes in a twofold manner: (i) the $B$-field assisted direct Urca process is enhanced by orders of magnitude, because of the unpairing effect in regions where $B\ensuremath{\ge}{H}_{c2}$; (ii) the Cooper-pair breaking processes on protons vanish in these regions and the overall emissivity by the pair-breaking processes is reduced by a factor of only a few.

Large-amplitude solitons in gravitationally balanced quantum plasmas

Using the quantum fluid model for self-gravitating quantum plasmas with the Bernoulli pseudopotential method and taking into account the relativistic degeneracy effect, it is shown that gravity-induced large-amplitude density rarefaction solitons can exist in gravitationally balanced quantum plasmas. These nonlinear solitons are generated due to the force imbalance between the gravity and the quantum fluid pressure via local density perturbations, similar to that on shallow waters. It is found that both the fluid mass-density and the atomic-number of the constituent ions have significant effect on the amplitude and width of these solitonic profiles. Existence of a large-scale gravity-induced solitonic activities on neutron-star surface, for instance, can be a possible explanation for the recently proposed resonant shattering mechanism [D. Tsang et al., Phys. Rev. Lett. 108, 011102 (2012)] causing the intense short gamma ray burst phenomenon, in which release of ≃1046–1047 ergs would be possible from the surface. The resonant shattering of the crust in a neutron star has been previously attributed to the crust-core interface mode and the tidal surface tensions. We believe that current model can be a more natural explanation for the energy liberation by solitonic activities on the neutron star surfaces, without a requirement for external mergers like other neutron stars or black holes for the crustal shatter.

Pulsar glitches: The crust may be enough

Pulsar glitches-the sudden spin-up in the rotational frequency of a neutron star-suggest the existence of an angular-momentum reservoir confined to the inner crust of the neutron star. Large and regular glitches observed in the Vela pulsar have originally constrained the fraction of the stellar moment of inertia that must reside in the solid crust to about 1.4%. However, crustal entrainment-which until very recently has been ignored-suggests that in order to account for the Vela glitches, the fraction of the moment of inertia residing in the crust must increase to about 7%. This indicates that the required angular momentum reservoir may exceed that which is available in the crust. We explore the possibility that uncertainties in the equation of state provide enough flexibility for the construction of models that predict a large crustal thickness and consequently a large crustal moment of inertia. Given that analytic results suggest that the crustal moment of inertia is sensitive to the transition pressure at the crust-core interface, we tune the parameters of the model to maximize the transition pressure, while still providing an excellent description of nuclear observables. In this manner we are able to obtain fractional moments of inertia as large as 7% for neutron stars with masses below 1.6 solar masses. In particular, we find that if the neutron-skin thickness of 208Pb falls within the (0.20-0.26) fm range, large enough transition pressures can be generated to explain the large Vela glitches without invoking an additional angular-momentum reservoir beyond that confined to the solid crust. Our results suggest that the crust may be enough.

Constraints on the symmetry energy from neutron star observations

The modeling of many neutron star observables incorporates the microphysics of both the stellar crust and core, which is tied intimately to the properties of the nuclear matter equation of state (EoS). We explore the predictions of such models over the range of experimentally constrained nuclear matter parameters, focusing on the slope of the symmetry energy at nuclear saturation density L. We use a consistent model of the composition and EoS of neutron star crust and core matter to model the binding energy of pulsar B of the double pulsar system J0737-3039, the frequencies of torsional oscillations of the neutron star crust and the instability region for r-modes in the neutron star core damped by electron-electron viscosity at the crust-core interface. By confronting these models with observations, we illustrate the potential of astrophysical observables to offer constraints on poorly known nuclear matter parameters complementary to terrestrial experiments, and demonstrate that our models consistently predict L < 70 MeV.

Resonant Shattering of Neutron Star Crusts

The resonant excitation of neutron star (NS) modes by tides is investigated as a source of short gamma-ray burst (SGRB) precursors. We find that the driving of a crust-core interface mode can lead to shattering of the NS crust, liberating ∼10{46}-10{47} erg of energy seconds before the merger of a NS-NS or NS-black-hole binary. Such properties are consistent with Swift/BAT detections of SGRB precursors, and we use the timing of the observed precursors to place weak constraints on the crust equation of state. We describe how a larger sample of precursor detections could be used alongside coincident gravitational wave detections of the inspiral by Advanced LIGO class detectors to probe the NS structure. These two types of observations nicely complement one another, since the former constrains the equation of state and structure near the crust-core boundary, while the latter is more sensitive to the core equation of state.

Direct Urca process in a neutron star mantle

We show that the direct Urca process of neutrino emission is allowed in two possible phases of nonspherical nuclei (inverse cylinders and inverse spheres) in the mantle of a neutron star near the crust-core interface. The process is open because neutrons and protons move in a periodic potential created by inhomogeneous nuclear structures. In this way the nucleons acquire large quasimomenta needed to satisfy momentum-conservation in the neutrino reaction. The appropriate neutrino emissivity in a nonsuperfluid matter is about 2--3 orders of magnitude higher than the emissivity of the modified Urca process in the stellar core. The process may noticeably accelerate the cooling of low-mass neutron stars.

R-modes in accreting neutron stars with magnetoviscous boundary layers

We explore the dynamics of the r-modes in accreting neutron stars in two ways. First, we explore how dissipation in the magneto-viscous boundary layer (MVBL) at the crust-core interface governs the damping of r-mode perturbations in the fluid interior. Two models are considered: one assuming an ordinary-fluid interior, the other taking the core to consist of superfluid neutrons, type II superconducting protons, and normal electrons. We show, within our approximations, that no solution to the magnetohydrodynamic equations exists in the superfluid model when both the neutron and proton vortices are pinned. However, if just one species of vortex is pinned, we can find solutions. When the neutron vortices are pinned and the proton vortices are unpinned there is much more dissipation than in the ordinary-fluid model, unless the pinning is weak. When the proton vortices are pinned and the neutron vortices are unpinned the dissipation is comparable or slightly less than that for the ordinary-fluid model, even when the pinning is strong. We also find in the superfluid model that relatively weak radial magnetic fields ~ 10^9 G (10^8 K / T)^2 greatly affect the MVBL, though the effects of mutual friction tend to counteract the magnetic effects. Second, we evolve our two models in time, accounting for accretion, and explore how the magnetic field strength, the r-mode saturation amplitude, and the accretion rate affect the cyclic evolution of these stars. If the r-modes control the spin cycles of accreting neutron stars we find that magnetic fields can affect the clustering of the spin frequencies of low mass x-ray binaries (LMXBs) and the fraction of these that are currently emitting gravitational waves.

Magnetic effects on the viscous boundary layer damping of ther-modes in neutron stars

This paper explores the effects that magnetic fields have on the viscous boundary layers (VBLs) that can form in neutron stars at the crust-core interface, and it investigates the VBL damping of the gravitational-radiation driven r-mode instability. Approximate solutions to the magnetohydrodynamic equations valid in the VBL are found for ordinary-fluid neutron stars. It is shown that magnetic fields above ${10}^{9}{(10}^{10} \mathrm{K}/T)\mathrm{G}$ significantly change the structure of the VBL, and that magnetic fields decrease the VBL damping time. Furthermore, VBL damping completely suppresses the r-mode instability for $B\ensuremath{\gtrsim}{10}^{12} \mathrm{G}$ (independent of the temperature). These bounds refer to the strength of the radial component of the equilibrium field at the location of the core radius. Magnetic effects on the VBL vanish wherever the radial component of the equilibrium field vanishes. Thus, magnetic fields will profoundly affect the VBL damping of the r-mode instability in hot young pulsars (that are cool enough to have formed a solid crust). One can speculate that magnetic fields can affect the VBL damping of this instability in low-mass x-ray binary systems and other cold old pulsars (if they have sufficiently large internal fields).

The evolution of the core and surface magnetic fields in isolated neutron stars

We apply the model of flux expulsion from the superfluid and superconductive core of a neutron star, developed by Konenkov & Geppert, both to neutron star models based on different equations of state and to different initial magnetic field structures. Initially, when the core and the surface magnetic field are of the same order of magnitude, the rate of flux expulsion from the core is almost independent of the equation of state, and the evolution of the surface field decouples from the core field evolution with increasing stiffness. When the surface field is initially much stronger than the core field, the magnetic and rotational evolution resembles that of a neutron star with a purely crustal field configuration; the only difference is the occurrence of a residual field. In the case of an initially submerged field, significant differences from the standard evolution only occur during the early period of the life of a neutron star, until the field has been re-diffused to the surface. The reminder of the episode of submergence is a correlation of the residual field strength with the submergence depth of the initial field. We discuss the effect of the re-diffusion of the magnetic field on the difference between the real and the active age of young pulsars and on their braking indices. Finally, we estimate the shear stresses built up by the moving fluxoids at the crust–core interface and show that these stresses may cause crust cracking, preferentially in neutron stars with a soft equation of state.