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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.

Thermal emission of neutron stars in soft X-ray transients (SXTs) in a quiescent state is believed to be powered by the heat deposited in the stellar crust due to nuclear reactions during accretion (deep crustal heating paradigm). Confronting observations of SXTs with simulations helps to verify theoretical models of the dense matter in the neutron stars. Usually, such simulations were carried out assuming that the free neutrons and nuclei in the inner crust move together. A recently proposed thermodynamically consistent approach allows for independent motion of the free neutrons. We simulate the thermal evolution of the SXTs within the thermodynamically consistent approach and compare the results with the traditional approach and with observations. For the latter, we consider a collection of quasi-equilibrium thermal luminosities of the SXTs in quiescence and the observed neutron star crust cooling in SXT MXB 1659$-$29. We test different models of the equation of state and baryon superfluidity and take into account additional heat sources in the shallow layers of neutron-star crust (the shallow heating). We find that the observed quasi-stationary thermal luminosities of the SXTs can be equally well fitted using the traditional and thermodynamically consistent models, provided that the shallow heat diffusion into the core is taken into account. The observed crust cooling in MXB 1659$-$29 can also be fitted in the frames of both models, but the choice of the model affects the derived parameters responsible for the thermal conductivity in the crust and for the shallow heating., Comment: 11 pages, 13 figures, 2 tables, accepted by MNRAS. In v2, beside minor text improvements, caption and headers of the tables are corrected and a few observational points in figures are updated; in v.3, a few typos in the reference list are fixed

Using path-integral Monte Carlo (PIMC) simulations, we have calculated energy of a crystal composed of atomic nuclei and uniform incompressible electron background in the temperature and density range, covering fully ionized layers of compact stellar objects, white dwarfs and neutron stars, including the high-density regime, where ion quantization is important. We have approximated the results by convenient analytic formulae, which allowed us to integrate and differentiate the energy with respect to temperature and density to obtain various thermodynamic functions such as Helmholtz free energy, specific heat, pressure, entropy etc. In particular, we have demonstrated, that the total crystal specific heat can exceed the well-known harmonic lattice contribution by a factor of 1.5 due to anharmonic effects. By combining our results with the PIMC thermodynamics of a quantum Coulomb liquid, updated in the present work, we were able to determine density dependences of such melting parameters as the Coulomb coupling strength at melting, latent heat, and a specific heat jump. Our results are necessary for realistic modelling of thermal evolution of compact degenerate stars., Comment: 17 pages, 17 figures, 4 tables, accepted to MNRAS

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.

Neutron stars are the densest objects in the Universe. In this paper we consider so-called inner crust - the layer, where neutron-excess nuclei are immersed into degenerate gas of electrons and sea of quasi-free neutrons. It was generally believed that spherical nuclei become unstable with respect to quadrupole deformations at high densities and here we consider this instability. Within perturbative approach we show that spherical nuclei with equilibrium number density are, in fact, stable with respect to infinitesimal quadrupole deformation. This is due to background of degenerate electrons and associated electrostatic potential which maintain stability of spherical nuclei. However, if the number of atomic nuclei per unit volume is much less than the equilibrium value, instability can arise. To avoid confusion we stress that our results are limited to infinitesimal deformations and do not guaranty strict thermodynamic stability of spherical nuclei. In particular, they does not exclude that substantially non-spherical nuclei (so-called pasta phase) represent thermodynamic equilibrium state of the densest layers of neutron star crust. Rather our results points that spherical nuclei can be metastable even if they are not energetically favourable and the timescale of transformation of spherical nuclei to the pasta phases should be estimated subsequently., 10 pages, 2 figures

Neutron stars in low-mass X-ray binaries are thought to be heated up by accretion-induced exothermic nuclear reactions in the crust. The energy release and the location of the heating sources are important ingredients of the thermal evolution models. Here we present thermodynamically consistent calculations of the energy release in three zones of the stellar crust: at the outer-inner crust interface, in the upper layers of the inner crust (up to the density $\rho \leq 2\times 10^{12}$ g cm$^{-3}$), and in the underlying crustal layers. We consider three representative models of thermonuclear ashes (Superburst, Extreme rp, and Kepler ashes). The energy release in each zone is parametrized by the pressure at the outer-inner crust interface, which encodes all uncertainties related to the physics of the deepest inner-crust layers. Our calculations allow us, in particular, to set new lower limits on the net energy release (per accreted baryon): $Q\gtrsim0.28$ MeV for Extreme rp ashes and Q~0.43-0.51 MeV for Superburst and Kepler ashes., Comment: 5 pages, 1 figure; submitted to MNRAS:Letters

The elasticity of neutron star crust is important for adequate interpretation of observations. To describe elastic properties one should rely on theoretical models. The most widely used is Coulomb crystal model (system of point-like charges on neutralizing uniform background), in some works it is corrected for electron screening. These models neglect finite size of nuclei. This approximation is well justified except for the innermost crustal layers, where nuclei size becomes comparable with the inter-nuclear spacing. Still, even in those dense layers it seems reasonable to apply the Coulomb crystal result, if one assumes that nuclei are spherically symmetric: Coulomb interaction between them should be the same as interaction between point-like charges. This argument is indeed correct, however, as we point here, shear of crustal lattice generates (microscopic) quadrupole electrostatic potential in a vicinity of lattice cites, which induces deformation on the nuclei. We analyze this problem analytically within compressible liquid drop model, using ionic spheroid model (which is generalization of well known ion sphere model). In particular, for ground state crust composition the effective shear modulus is reduced for a factor of $1-u^{5/3}/(2+3\,u-4\,u^{1/3})$, where u is the filling factor (ratio of the nuclei volume to the volume of the cell). This result is universal and does not depend on the applied nucleon interaction model. For the innermost layers of inner crust u~0.2 leading to reduction of the shear modulus by ~25%, which can be important for correct interpretation of quasi-periodic oscillations in the tails of magnetar flares., Comment: 7 pages, submitted to MNRAS on Sept. 8

We show that, in order to determine the equation of state of the inner crust of an accreting neutron star, one should minimize not the Gibbs free energy, as it is generally assumed in the literature, but a different thermodynamic potential $\Psi$, which tends to the minimum at fixed pressure and neutron chemical potential. Once this potential is specified, one can calculate the heat-release distribution in the stellar crust due to nonequilibrium nuclear reactions induced by accretion of matter onto the neutron-star surface. The results are important for adequate modeling of the accreted crust and interpretation of the observations of accreting neutron stars in low-mass X-ray binaries., Comment: 6 pages, accepted for publication in Phys. Rev. D (Letters)

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 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 apply a simplified reaction network to model nuclear evolution of various multi-component thermonuclear burning ashes (superburst, KEPLER, and extreme rp-process ashes) in the outer crust and calculate the deep crustal heating energy release Q, parametrized by the pressure at the outer-inner crust interface, P_{oi}. Using the general thermodynamic arguments, we set a lower limit on Q, Q>0.13-0.2 MeV per baryon (an actual value depends on the ash composition and the employed mass model)., 12 pages, 8 figures. Updated to AME2020. Accepted for publication in MNRAS

Observed thermal emission from accreting neutron stars (NSs) in a quiescent state is believed to be powered by nonequilibrium nuclear reactions that heat the stellar crust (deep crustal heating paradigm). We derive a simple universal formula for the heating efficiency, assuming that an NS has a fully accreted crust. We further show that, within the recently proposed thermodynamically consistent approach to the accreted crust, the heat release can be parametrized by the only one parameter -- the pressure $P_{\rm oi}$ at the outer-inner crust interface (as we argue, this pressure should not necessarily coincide with the neutron-drip pressure). We discuss possible values of $P_{\rm oi}$ for a selection of nuclear models that account for shell effects, and determine the net heat release and its distribution in the crust as a function of $P_{\rm oi}$. We conclude that the heat release should be reduced by a factor of few in comparison to previous works., 5 pages, 1 figure, 1 table + 5 pages supplemental material

I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modeled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress-strain tensor has additional symmetry: contraction $B_{ijil}=0$. It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to $-2/15$ of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus: $\sum_Z 0.12\, n_Z Z^{5/3}e^2 /a_\mathrm{e}$. Here summation is taken over ion species, $n_Z$ is number density of ions with charge $Ze$. Finally $a_\mathrm{e}=(4 \pi n_\mathrm{e}/3)^{-1/3}$ is electron sphere radius. Quasineutrality condition $n_\mathrm{e}=\sum_Z Z n_Z$ is assumed., Comment: 5 pages, accepted for publication in MNRAS:Letters

Dewitt et al. (1973) derived a useful relation between the plasma screening factor for a reaction of two fusing ions and their chemical potentials, based on the plasma pair distribution functions. We show that their result can be derived in a simpler, more straightforward way, by applying the principle of detailed balance, which also enables us to generalize the relation to reactions involving $N$ fusing ions. In order to demonstrate the usefulness of applying the principle of detailed balance, we calculate the screening factor for the $pep$ reaction, $p+e+p\rightarrow ^{2}$D $+\nu_{e}$. For the plasma conditions near the centre of the Sun, the reaction is suppressed by roughly the same amount by which the reaction $p+p\rightarrow ^{2}$D $+$ $e^{+}+\nu_{e}$ is enhanced. This effect may be measured in the near future., Comment: 4 pages, no figures. Minor revisions following referee report

Neutron stars can appear as sources of different nature. In this paper we address the observability of a hypothetical class of neutron stars—HOt and Fast Non-Accreting Rotators, HOFNARs. These objects are heated due to the r-mode instability. With surface temperatures ∼106 K they are expected to be thermal soft X-ray emitters. We perform a population synthesis modeling of HOFNARs to predict the number of potentially detectable sources in the eROSITA all-sky survey. For surface temperatures ∼106 K we obtain ∼500 sources above the detection limit 0.01 cts s−1 and ∼100 easier identifiable sources with >0.1 cts s−1. Temperatures ≳1.2 × 106 K start to be in contradiction with non-detection of HOFNARs by ROSAT. Only for T ≲ 5 × 105 K numbers predicted for eROSITA turn out to be so low that identification does not look possible. We conclude that eROSITA has good chances to discover HOFNARs, if they exist. Non-detection will put very stringent limits on the properties of this type of neutron stars.

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

Neutron stars are superdense compact astrophysical objects. The central region of the neuron star (the core) consists of locally homogeneous nuclear matter, while in the outer region (the crust) nucleons are clustered. In the outer crust these nuclear clusters represent neutron-rich atomic nuclei and all nucleons are bound within them. Whereas in the inner crust some neutrons are unbound, but nuclear clusters still keeps generally spherical shape. Here we consider the region between the crust and the core of the star, so-called mantle, where non-spherical nuclear clusters may exist. We apply compressible liquid drop model to calculate the energy density for several shape types of nuclear clusters. It allows us to identify the most energetically favorable configuration as function of baryon number density. Employing four Skyrme-type forces (SLy4 and BSk24, BSk25, BSk26), which are widely used in the neutron star physics, we faced with strong model dependence of the ground state composition. In particular, in agreement with previous works within liquid drop model, mantle is absent for SLy4 (nuclear spheres directly transit into homogeneous nuclear matter; exotic nuclear shapes do not appear).

We combined Chandra ACIS observations of the globular cluster 47 Tucanae (hereafter, 47 Tuc) from 2000, 2002, and 2014-15 to create a deeper X-ray source list, and study some of the faint radio millisecond pulsars (MSPs) present in this cluster. We have detected 370 X-ray sources within the half-mass radius (2$'$.79) of the cluster, 81 of which are newly identified, by including new data and using improved source detection techniques. The majority of the newly identified sources are in the crowded core region, indicating cluster membership. We associate five of the new X-ray sources with chromospherically active BY Dra or W UMa variables identified by Albrow et al. (2001). We present alternative positions derived from two methods, centroiding and image reconstruction, for faint, crowded sources. We are able to extract X-ray spectra of the recently discovered MSPs 47 Tuc aa, 47 Tuc ab, the newly timed MSP 47 Tuc Z, and the newly resolved MSPs 47 Tuc S and 47 Tuc F. Generally, they are well fit by black body or neutron star atmosphere models, with temperatures, luminosities and emitting radii similar to those of other known MSPs in 47 Tuc, though 47 Tuc aa and 47 Tuc ab reach lower X-ray luminosities. We limit X-ray emission from the full surface of the rapidly spinning (542 Hz) MSP 47 Tuc aa, and use this limit to put an upper bound for amplitude of r-mode oscillations in this pulsar as $\alpha, Comment: 17 pages, 11 figures, 6 tables, Accepted for publication in MNRAS

We study equation of state (EOS) of an accreting neutron star crust. Usually, such EOS is obtained assuming (implicitly) that the free (unbound) neutrons and nuclei in the inner crust move together. We argue, that this assumption violates the condition $\mu_n^\infty={\rm const}$, required for hydrostatic (and diffusion) equilibrium of unbound neutrons ($\mu^\infty_n$ 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 part 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 fully accreted crust that transforms nuclei into homogeneous nuclear matter. It guarantees that the structure of fully accreted crust remains self-similar during accretion., Comment: 11 pages, 5 figures, submitted to PRL on 2019-11-26

Transiently accreting neutron stars in low mass X-ray binaries are generally believed to be heated up by nuclear reactions in accreted matter during hydrostatic compression. Detailed modeling of these reactions is required for the correct interpretation of observations. In this paper, we construct a simplified reaction network, which can be easily implemented and depends mainly on atomic mass tables as nuclear physics input. We show that it reproduces results of the detailed network by Lau et al. (2018) very well, if one applies the same mass model. However, the composition and the heating power are shown to be sensitive to the mass table used and treatment of mass tables boundary, if one applies several of them in one simulation. In particular, the impurity parameter $Q_\mathrm{imp}$ at density $\rho=2\times 10^{12}$ g cm$^{-3}$ can differ for a factor of few, and even increase with density increase. The profile of integrated heat realize shown to be well confined between results by Fantina et al. (2018) and Lau et al. (2018)., Comment: Accepted for publication in MNRAS, 10 pages, 8 figures

To study the runaway electron (RE) dynamics during plasma discharge and develop scenarios for disruption mitigation, a hard X-ray (HXR) spectrometric system has been developed and commissioned at the ASDEX Upgrade tokamak (AUG). The diagnostic system consists of two high-performance spectrometers based on LaBr3(Ce) scintillation detectors supplied with advanced electronics and analysis algorithms. These spectrometers view the AUG tokamak chamber quasi-radially at the equatorial plane. The measurements were carried out in the RE beam generation regimes by injecting argon into a deuterium plasma. In the interaction of a developed RE beam with a heavy gas target, powerful bremsstrahlung flux is induced, reaching energy close to 20 MeV. The electron energy distributions were reconstructed from the measured HXR spectra by deconvolution methods. The experimentally obtained maximum RE energies at different discharge stages were compared with relativistic test particle simulations that include the effect of toroidal electric field, plasma collisional drag force, synchrotron deceleration force. It was observed that the electrons attain their maximum energies within 50-100 ms after the gas injection. It gradually decreases due to the drop in loop voltage, energy loss due to synchrotron radiation emission and collisions dissipation of energy with the background plasma. HXR measurements at the discharge with multiple deuterium pellet injections allowed observing the effects of plasma cooling and argon ion recombination after the pellet injections. Argon density in AUG plasma after massive gas injection was estimated using HXR measurements.

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

Plasma screening can enhance the thermonuclear reaction rates significantly. The most pronounced effect takes place in the white dwarf cores and neutron star envelopes; there the enhancement factor can reach as tenths orders of magnitude. Here thermodynamically consistent description of this effect, which does not violate of the detailed balance principle, is discussed.

Neutron star crust consists of highly neutron excess nuclei, which are inaccessible for laboratory experiments. In the deepest region of the crust (so-called inner crust, located after the neutron drip) atomic nuclei are immersed into the sea of degenerate unbound neutrons. Study of the crust structure and equation of state in such conditions relies on the theoretical nuclear mass models. In particular, it is convenient to use the compressible liquid drop model, which contains the surface tension term. A thermodynamically consistent description must take into account adsorption of neutrons on the nucleus surface (neutron skin) and dependence of surface tension on matter properties in two-phase equilibrium. We calculate the surface tension of nuclear matter by the extended Thomas-Fermi approach. For this aim, we parametrize the number density profile of the two-phase system by Fermi-Dirac type functions, totally containing 5 parameters, and minimize the thermodynamic potential Ω to obtain equilibrium configuration. We use Skyrme-type nuclear interactions SLy4 and BSk24, fulfilling experimental data of atomic nuclei, observational constraints on the maximal neutron star mass and theoretical calculations of high-density nuclear matter. The results are presented as a function of neutron chemical potential, which is useful for compressible liquid drop models in the inner crust of a neutron star.

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 nuclear reactions in the accreted crust. We test and compare results for different modern theoretical models. We update a compilation of the observational estimates of the thermal luminosities in quiescence and average accretion rates in the SXTs and compare the observational estimates with the theoretical results. Long-term thermal evolution of transiently accreting neutron stars is nonmonotonic. The quasi-equilibrium temperature in quiescence reaches a minimum and then increases toward the final steady state. The quasi-equilibrium thermal luminosity of a neutron star in an SXT can be substantially lower at the minimum than in the final state. This enlarges the range of possibilities for theoretical interpretation of observations of such neutron stars. The updates of the theory and observations leave unchanged the previous conclusions that the direct Urca process operates in relatively cold neutron stars and that an accreted heat-blanketing envelope is likely present in relatively hot neutron stars in the SXTs in quiescence. The results of the comparison of theory with observations favor suppression of the triplet pairing type of nucleon superfluidity in the neutron-star matter., 16 pages, 2 tables, 14 figures. In v4, Eq.(18) is corrected (results are not affected)

With a spin frequency of 707 Hz, PSR J0952-0607 is the second fastest spinning pulsar known. It was discovered in radio by LOFAR in 2017 at an estimated distance of either 0.97 or 1.74 kpc and has a low-mass companion with a 6.42 hr orbital period. We report discovery of the X-ray counterpart of PSR J0952-0607 using XMM-Newton. The X-ray spectra can be well-fit by a single power law model (Gamma = 2.5) or by a thermal plus power law model (kTeff = 40 eV and Gamma = 1.4). We do not detect evidence of variability, such as that due to orbital modulation from pulsar wind and companion star interaction. Because of its fast spin rate, PSR J0952-0607 is a crucial source for understanding the r-mode instability, which can be an effective mechanism for producing gravitational waves. Using the high end of our measured surface temperature, we infer a neutron star core temperature of ~10^7 K, which places PSR J0952-0607 within the window for the r-mode to be unstable unless an effect such as superfluid mutual friction damps the fluid oscillation. The measured luminosity limits the dimensionless r-mode amplitude to be less than ~1x10^-9., Comment: 10 pages, 4 figures; accepted for publication in ApJ; minor edits and addition of references and GW search discussion

I consider differential rotation, associated with radiation-driven Chandrasekhar-Friedman-Schutz (CFS) instability and its possible observational evidences. I focus on the evolution of the apparent spin frequency, which is typically associated with the motion of a specific point on the stellar surface (e.g., polar cap). I start from long-term evolution (on the timescale when instability significantly changes the spin frequency). For this case, I reduce evolution equations to one differential equation and demonstrate that it can be directly derived from energy conservation law. This equation governs evolution rate through sequence of thermally equilibrium states and provides linear coupling for the cooling power and rotation energy losses via gravitational wave emission. In particular, it shows that differential rotation do not affect long-term spin-down. On the contrary, on the short timescales, differential rotation can significantly modify the apparent spin-down, if one examines a strongly unstable star with very small initial amplitude of unstable mode. This statement is confirmed by consideration of Newtonian non-magnetized perfect fluid and dissipative stellar models as well as magnetized stellar model. For example, despite that widely applied evolution equations predict effective spin to be constant in absence of dissipation, the CFS-unstable star should be observed as spinning-down. However, effects of differential rotation on apparent spin-down are negligible for realistic models of neutron star recycling, unless: (1) the neutron star is not magnetized, and (2) r-mode amplitude is modulated faster than the shear viscosity dissipation timescale, being large enough that spin-down can be measured on modulation timescale., 14 pages, 1 figure, accepted for publication in MNRAS

Rezzolla et al. [ApJ 531 (2000), L139; Phys. Rev. D 64 (2001), 104013; Phys. Rev. D 64 (2001), 104014] draw attention to the second order secular drift associated with r-modes and claimed that it should lead to magnetic field enhancement and suppression of r-mode instability in magnetized neutron stars. We critically revise these results. We present a particular second order r-mode solution with vanishing secular drift, thus refuting a widely believed statement that secular drift is an unavoidable feature of r-modes. This non-drifting solution is not affected by magnetic field $B$, if $B\ll B_{\mathrm{crit}}\approx 10^{17}\,(\nu/600\,\mathrm{Hz})$ G ($\nu$ is a spin frequency) and does not lead to secular evolution of magnetic field. For general second order r-mode solution the drift does not necessarily vanish, but the solution can be presented as a superposition of two solutions: one describes evolution of differential rotation in nonoscillating star (which describes secular drift; for nonmagnetized star it is arbitrary stationary rotation stratified on cylinders; for magnetized star differential rotation evolves on the Alfv\'{e}n timescale and may lead to magnetic energy enhancement), and another one is non-drifting r-mode solution mentioned above. This representation allows us to conclude that enhancement of magnetic field energy is limited by initial energy of differential rotation, which is much less (for a factor $\propto \alpha^2$, where $\alpha$ is mode amplitude) than the total energy of r-mode. Hence, magnetic field enhancement by drift cannot suppress r-mode instability. Results can be generalized for any oscillation mode in any medium, if this mode has non-drifting solution for $B=0$., Comment: 8 pages, accepted for publication in MNRAS

I suggest a novel type of nuclear reactions in accreting neutron stars - neutron transfer, which is quantum tunneling of weakly bounded neutron from one nucleus to another. I estimate the rate of this process for fixed nuclei separation and then average the result over realistic distribution of nuclei to get the rate value for astrophysical conditions. The neutron transfer can modify reaction chains in accreting neutron stars, thus affecting their heating and cooling. In particular, it can suppress cooling by URCA pairs of nuclei, which is supposed to be crucial for the hottest neutron stars., Comment: 6 pages, 1 figure; accepted for publication in MNRAS:Letters

At second order in perturbation theory, the unstable r-mode of a rotating star includes growing differential rotation whose form and growth rate are determined by gravitational-radiation reaction. With no magnetic field, the angular velocity of a fluid element grows exponentially until the mode reaches its nonlinear saturation amplitude and remains nonzero after saturation. With a background magnetic field, the differential rotation winds up and amplifies the field, and previous work where large mode amplitudes were considered suggests that the amplification may damp out the instability. A background magnetic field, however, turns the saturated time-independent perturbations corresponding to adding differential rotation into perturbations whose characteristic frequencies are of order the Alfv\'en frequency. As found in previous studies, we argue that magnetic- field growth is sharply limited by the saturation amplitude of an unstable mode. In contrast to previous work, however, we show that if the amplitude is small, i.e., of order 10^(-4), then the limit on the magnetic-field growth is stringent enough to prevent the loss of energy to the magnetic field from damping or significantly altering an unstable r-mode in nascent neutron stars with normal interiors and in cold stars whose interiors are type II superconductors. We show this result first for a toy model, and we then obtain an analogous upper limit on magnetic field growth using a more realistic model of a rotating neutron star. Our analysis depends on the assumption that there are no marginally unstable perturbations, and this may not hold when differential rotation leads to a magnetorotational instability., Comment: This is essentially the published version

Correct interpretation of X-ray observations of transiently accreting neutron stars requires modeling of nuclear-physical processes in these objects. We consider a chain of nuclear reactions that drives the crust composition in an accreting neutron star and heats up the star. We constructed multicomponent approach with the kinetics of nuclear reactions described in simplified stepwise manner. The redistribution of nucleons between nuclei by emission and capture of neutrons is shown to significantly affect the nuclear reaction chains and the composition of the inner crust. In particular, even if the outer crust has one-component composition, the appearance of free neutrons in the inner crust leads to branching of reaction chains and formation of the multicomponent composition. We apply the compressible liquid drop nuclear model, which includes effects of free neutrons on nuclear energies. It allows us to calculate the composition, the heating profile and the equation of state of matter up to densities \rho ~ 2 \times 10^{13} g cm^{-3}., Comment: 5 pages, 3 figures, published in proceedings of the International Conference PhysicA.Spb/2019, St. Petersburg, October 22-24, 2019

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.