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Neutron stars are the densest objects in the Universe. They have a microscopically homogeneous core and heterogeneous crust. In particular, there may be a specific layer inside neutron stars, the mantle, which consists of substantially non-spherical nuclei immersed in a background of relativistic degenerate electrons and quasi-free neutrons. In this paper, we reconsider the transverse shear modulus for cylindrical phases of the mantle within the framework of the compressible liquid drop model. We demonstrate that transverse shearing affects the shape of nuclear clusters: their cross-section becomes elliptical. This effect reduces the respective elastic constant. Using a simple model, we perform all derivations analytically and obtain the expression for the transverse shear modulus, which can be useful for astrophysical applications.

Nuclear pasta phases in the neutron stars mantle can affect the mechanical and transport properties of superdense matter, thus playing an important role in the dynamics and evolution of neutron stars. In this paper, we compare results obtained by the Extended Thomas–Fermi (ETF) method with the compressible liquid drop model (CLDM), based on the thermodynamically consistent description of the surface properties calculated for the two-phase plane interface and the same energy-density functional (for numerical illustration, we applied the Skyrme-type functional SLy4). Our ETF calculations found that pasta phases in cylindrical form cover a significant crustal region (both normal and inverse phases, aka spaghetti and bucatini are presented). Meanwhile, within the applied CLDM framework, which includes the thermodynamically required effect of neutron adsorption on the cluster’s surface but neglects curvature corrections, only the spaghetti phase was found to be energetically favorable in the small density range prior to crust–core transition. On the other hand, the recent CLDM of Dinh Thi et al., 2021, which, on the contrary, accounts for curvature term but neglects neutron adsorption, predicts pasta phase onset in better agreement with the ETF. This fact highlights the importance of the curvature effects and allows counting on the potential validity of the CLDMs as a convenient, transparent and accurate tool for investigation of the pasta-phase properties.

Observed temperatures of transiently accreting neutron stars in the quiescent state are generally believed to be supported by deep crustal heating, associated with non-equilibrium exothermic reactions in the crust. Traditionally, these reactions are studied by considering nuclear evolution governed by compression of the accreted matter. Here we show that this approach has a basic weakness, that is that in some regions of the inner crust the conservative forces, applied for matter components (nuclei and neutrons), are not in mechanical equilibrium. In principle the force balance can be restored by dissipative forces, however the required diffusion fluxes are of the same order as total baryon flux at Eddington accretion. We argue that redistribution of neutrons in the inner crust should be involved in realistic model of accreted crust., Comment: Accepted for publication in MNRAS:Letters, 6 pages, 1 figure

The strength of neutron star crust is crucial for modelling magnetar flares, pulsar glitches and gravitational wave emission. We aim to shed some light on this problem by analysing uniaxial stretch deformation (elongation and contraction) of perfect body-centered cubic Coulomb crystals, paying special attention to the inherent anisotropy of this process. Our analysis is based on the semi-analytical approach of Baiko and Kozhberov (2017), which, for any uniform deformation, allows one to calculate, in fully non-linear regime, critical deformation parameters beyond which the lattice loses its dynamic stability. We determine critical strain, pressure anisotropy and deformation energy for any stretch direction with respect to the crystallographic axes. These quantities are shown to be strongly anisotropic: they vary by a factor of almost 10 depending on the orientation of the deformation axis. For polycrystalline crust, we argue that the maximum strain for the stretch deformation sustainable elastically is 0.04. It is lower than the breaking strain of 0.1 obtained in molecular dynamic simulations of a shear deformation by Horowitz and Kadau (2009). The maximum pressure anisotropy of polycrystalline matter is estimated to be in the range from 0.005 to 0.014 $nZ^2e^2/a$, where $n$ is the ion number density, $Ze$ is the ion charge, and $a$ is the ion-sphere radius. We discuss possible mechanisms of plastic motion and formation of large crystallites in neutron star crust as well as analyse energy release associated with breaking of such crystallites in the context of magnetic field evolution and magnetar flaring activity., Comment: 7 pages, 6 figures, accepted to MNRAS

To put new constraints on the r-mode instability window, we analyse the formation of millisecond pulsars (MSPs) within the recycling scenario, making use of three sets of observations: (a) X-ray observations of neutron stars (NSs) in low-mass X-ray binaries; (b) timing of millisecond pulsars; and (c) X-ray and UV observations of MSPs. As shown in previous works, r-mode dissipation by shear viscosity is not sufficient to explain observational set (a), and enhanced r-mode dissipation at the red-shifted internal temperatures $T^\infty\sim 10^8$ K is required to stabilize the observed NSs. Here, we argue that models with enhanced bulk viscosity can hardly lead to a self-consistent explanation of observational set (a) due to strong neutrino emission, which is typical for these models (unrealistically powerful energy source is required to keep NSs at the observed temperatures). We also demonstrate that the observational set (b), combined with the theory of internal heating and NS cooling, provides evidence of enhanced r-mode dissipation at low temperatures, $T^\infty\sim 2\times 10^7$ K. Observational set (c) allows us to set an upper limit on the internal temperatures of MSPs, $T^\infty, 15 pages, 5 figures, accepted for publication in MNRAS

I suggest a novel approach for deriving evolution equations for rapidly rotating relativistic stars affected by radiation-driven Chandrasekhar-Friedman-Schutz (CFS) instability. This approach is based on the multipolar expansion of gravitational wave emission and appeals to the global physical properties of the star (energy, angular momentum, and thermal state), but not to canonical energy and angular momentum, which is traditional. It leads to simple derivation of the CFS instability criterion for normal modes and the evolution equations for a star, affected by this instability. The approach also gives a precise form to simple explanation of the CFS instability: it occurs when two conditions met: (a) gravitational wave emission removes angular momentum from the rotating star (thus releasing the rotation energy) and (b) gravitational waves carry less energy, than the released amount of the rotation energy. Results are illustrated by r-mode instability in slowly rotating Newtonian stars. In resulting evolution equations emission of gravitational waves directly affects the spin frequency, being in line with the arguments by Levin & Ushomirsky (2001), but in contrast to widely accepted equations by Lindblom et al. (1998); Ho & Lai (2000), there effective spin frequency decrease is coupled with dissipation of unstable mode. This problem, initially stressed by Levin & Ushomirsky (2001), is shown to be superficial, and arises as a result of definition of the effective spin frequency by Lindblom et al. (1998); Ho & Lai (2000). Namely, it is shown, that if this definition is taken into account properly, the evolution equations coincide with obtained here in the leading order in mode amplitude. I also argue that the next-to-leading order terms in evolution equations (which differ for Owen et al. 1998 and Ho & Lai 2000) require clarification and thus it would be more self-consistent to omit them., 7 pages, accepted for publication in PASA (special issue on the Neutron Stars, related to the NewCompStar conference 2017 in Warsaw)

We discuss magnetic field enhancement by unstable r-modes (driven by the gravitational radiation reaction force) in rotating stars. In the absence of a magnetic field, gravitational radiation exponentially increases the r-mode amplitude $\alpha$, and accelerates differential rotation (secular motion of fluid elements). For a magnetized star, differential rotation enhances the magnetic field energy. Rezzolla et al. (2000--2001) argued that if the magnetic energy grows faster than the gravitational radiation reaction force pumps energy into the r-modes, then the r-mode instability is suppressed. Chugunov (2015) demonstrated that without gravitational radiation, differential rotation can be treated as a degree of freedom decoupled from the r-modes and controlled by the back reaction of the magnetic field. In particular, the magnetic field windup does not damp r-modes. Here we discuss the effect of the back reaction of the magnetic field on differential rotation of unstable r-modes, and show that it limits the generated magnetic field and the magnetic energy growth rate preventing suppression of the r-mode instability by magnetic windup at low saturation amplitudes, $\alpha \ll 1$, predicted by current models., Comment: 5 pages; Contribution to the proceedings of the Physics of Neutron Stars - 2017 (Saint Petersburg, July 10-14, 2017), associated with a talk by A.I. Chugunov

How long do neutron star mountains last? The durability of elastically deformed crust is important for neutron star physics including pulsar glitches, emission of gravitational waves from static mountains, and flares from star quakes. The durability is defined by the strength properties of the Yukawa crystals of ions, which make up the crust. In this paper we extend our previous results [Mon. Not. R. Astron. Soc. 407, L54 (2010)] and accurately describe the dependence of the durability on crust composition (which can be reduced to the dependence on the screening length λ of the Yukawa potential). We perform several molecular dynamics simulations of crust breaking and describe their results with a phenomenological model based on the kinetic theory of strength. We provide an analytical expression for the durability of neutron star crust matter for different densities, temperatures, stresses, and compositions. This expression can also be applied to estimate durability of Yukawa crystals in other systems, such as dusty plasmas in the laboratory (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

It is shown that the Coulomb energy U of fully ionized ionic mixture can be written as a sum over partial contributions of ion species j: U = T ΣjNju (Γj, yj) (generalized linear mixing rule). In contrast to the traditional linear mixing rule ULM = T ΣjNjuOCP(Γj), applicable for strong coupling, the partial contribution function u depends not only on Γj, but on an additional parameter yj = (rD/rDOCP)2 also. Here rD and rDOCP are Debye radiuses in the mixture and in the one component plasma at coupling parameter Γj, correspondingly. The parameter yj does not depend on a specific composition of the mixture, but on the Debye radius rD only, making function u (Γj, yj) universal. The generalized linear mixing rule can be applied at any coupling parameter, if ionic mixture is not crystallized. It reproduces results of the Debye-Huckel theory at weak coupling and traditional linear mixing rule at strong coupling. It can be easily applied to the complicated mixtures, composed of a large number of ion species. Since yj is temperature independent, the Coulomb contribution to Helmholtz free energy of the mixture can also be presented in a form of generalized linear mixing rule (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The electrical conductivity of the neutron star crust at low temperatures is calculated by taking into account the mixing of the electron wave functions due to the interaction with the crystal lattice of atomic nuclei. We show that the previously existed model of exponential reduction of the electron-ion scattering rate can lead to an overestimation of the electrical conductivity by several orders of magnitude. We propose a simple interpolation formula for use in applications that joins the previously known results of calculating the electrical conductivity at high temperatures with the low-temperature asymptotics found here.

For the first time, non-radial oscillations of superfluid non-rotating stars are self-consistently studied at finite stellar temperatures. We apply a realistic equation of state and realistic density-dependent model of critical temperature of neutron and proton superfluidity. In particular, we discuss three-layer configurations of a star with no neutron superfluidity at the centre and in the outer region of the core but with a superfluid intermediate region. We show that oscillation spectra contain a set of modes whose frequencies can be very sensitive to temperature variations. Fast temporal evolution of the pulsation spectrum in the course of neutron star cooling is also analysed.

The breaking stress (the maximum of the stress–strain curve) of neutron star crust is important for neutron star physics including pulsar glitches, emission of gravitational waves from static mountains and flares from star quakes. We perform many molecular dynamic simulations of the breaking stress at different coupling parameters (inverse temperatures) and strain rates. We describe our results with the Zhurkov model of strength. We apply this model to estimate the breaking stress for time-scales ∼1 s–1 yr, which are most important for applications, but much longer than can be directly simulated. At these time-scales, the breaking stress depends strongly on the temperature. For coupling parameter Γ≲ 200 matter breaks at very small stress, if it is applied for a few years. This viscoelastic creep can limit the lifetime of mountains on neutron stars. We also suggest an alternative model of time-scale-independent breaking stress, which can be used to estimate an upper limit on the breaking stress.

We analyse the thermal conductivity of ions (equivalent to the conductivity of phonons in crystalline matter) in a neutron star envelope. We calculate the ion/phonon thermal conductivity in a crystal of atomic nuclei using variational formalism and performing momentum space integration by Monte Carlo method. We take into account phonon‐phonon and phonon‐electron scattering mechanisms and show that phonon‐electron scattering dominates at not too low densities. We extract the ion thermal conductivity in ion liquid or gas from literature. Numerical values of the ion/phonon conductivity are approximated by analytical expressions, valid for T 10 5 K and 10 5 gc m −3 ρ 10 14 gc m −3 . Typical magnetic fields B ∼ 10 12 Gi n neutron star envelopes do not affect this conductivity although they strongly reduce the electron thermal conductivity across the magnetic field. The ion thermal conductivity remains much smaller than the electron conductivity along the magnetic field. However, in the outer neutron star envelope it can be larger than the electron conductivity across the field, which is important for heat transport across magnetic field lines in cooling neutron stars. The ion conductivity can greatly reduce the anisotropy of heat conduction in outer envelopes of magnetized neutron

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l the fundamental mode (without radial nodes) has a frequency ~300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies >=20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (have approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.

We calculate the electron shear viscosity (determined by Coulomb electron collisions) for a dense matter in a wide range of parameters typical for white dwarf cores and neutron star crusts. In the density range from ~10^3 g cm^-3 to 10^7-10^10 g cm^-3 we consider the matter composed of widely abundant astrophysical elements, from H to Fe. For higher densities, 10^10-10^14 g cm^-3, we employ the ground-state nuclear composition, taking into account finite sizes of atomic nuclei and the distribution of proton charge over the nucleus. Numerical values of the viscosity are approximated by an analytic expression convenient for applications. Using the approximation of plane-parallel layer we study eigenfrequencies, eigenmodes and viscous damping times of oscillations of high multipolarity, l~500-1000, localized in the outer crust of a neutron star. For instance, at l~500 oscillations have frequencies f >= 40 kHz and are localized not deeper than ~300 m from the surface. When the crust temperature decreases from 10^9 K to 10^7 K, the dissipation time of these oscillations (with a few radial nodes) decreases from ~1 year to 10-15 days., 23 pages, 13 figures

A compact cross section data base is obtained for almost 5000 nonresonance nuclear reactions involving stable and unstable Be, B, C, N, O, F, Ne, Na, Mg, and Si isotopes. The calculations are performed using the San Paulo potential and the barrier penetration formalism. The calculated cross sections are approximated by simple analytical formulas. The results are necessary for simulating nuclear burning in neutron stars.

Results are presented from experimental studies of runaway electrons in the ohmic heating regime in the Globus-M tokamak. The periodical hard X-ray bursts observed with the help of two hard X-ray spectrometers with high time resolution are attributed to MHD oscillations in the plasma core and at the periphery.

The pair distribution function g(r) ≡ g(x, y, z) and the radial pair distribution function g(r) of ions in body-centred-cubic and face-centred-cubic Coulomb crystals are calculated within the harmonic-lattice (HL) approximation in a wide temperature range, from the high-temperature classical limit (T wp, wp being the ion plasma frequency) to the low-temperature quantum limit (T wp). In the classical limit, g(r) is also calculated by the Monte Carlo (MC) method. MC and HL results are demonstrated to be in good agreement. With decreasing T, the correlation peaks of g(r) and g(r) become narrower. At T wp they become temperature independent (determined by zero-point ion vibrations).

The pair distribution function g( r ) of ions in body-centered-cubic and face-centered-cubic Coulomb crystals is calculated using the harmonic-lattice (HL) approximation in a wide temperature range, from the high-temperature classical regime ( T⪢ℏω p , ω p is the ion plasma frequency) to the low-temperature quantum regime (T⪡ℏωp). The radial pair distribution function g(r) is calculated by averaging g( r ) over orientations of r . In the classical limit, g(r) is also obtained from extensive Monte Carlo (MC) simulations. MC and HL results are shown to be in good agreement. With decreasing temperature T, the correlation peaks of g( r ) and g(r) become narrower and finally freeze at T⪡ℏωp being solely determined by zero-point ion vibrations.

1. The method of measuring acoustic properties may be used not only for studying structure, but also for determining the phase content of titanium alloys. 2. The damping factor for ultrasonic vibrations and propagation rate for longitudinal ultrasonic waves in titanium alloys are governed by the degree of stability for β-phase as well as for α″ and ω-phases.