IGR J17480-2446 is a low-mass x-ray binary, harboring an exceptional accreting pulsar (a neutron star) with an unusual spin frequency of 11 Hz and a very slow postoutburst crust cooling. The former may imply that it is observed at an early stage of recycling, while the latter was shown to indicate the presence in the outer crust of a low thermal conductivity layer, possibly made of glass. Here we argue that the glass layer formation is a natural result of accretion induced failure of pristine cold crystalline crust. This allows us to determine the mass of the accreted material as ΔM≈2.4×10^{-6}M_{⊙}, confirming a very early accretion stage for this neutron star. An analysis of the spin and thermal state reveals a peculiar set of neutron star birth properties which is commonly associated with "recycled" neutron stars, i.e., those that have been experiencing prolonged periods of accretion from a companion. We speculate that such birth properties may represent the outcome of neutron star formation in an electron-capture supernova.

Near-equilibrium bottom-up crystallization of fully-ionized neutron star crusts or white dwarf cores is considered. We argue that this process is similar to liquid-phase epitaxial (i.e. preserving order of previous layers) crystal growth or crystal pulling from melt in Earth laboratories whereby lateral positions of newly crystallizing ions are anchored by already solidified layers. Their vertical positions are set by charge neutrality. Consequently, interplane spacing of a growing crystal either gradually increases, tracing $n_\mathrm{e}$ decrease, as the crystallization front moves away from the stellar center, or decreases, tracing decrease of $\langle Z \rangle$, when the crystallization front crosses a boundary between layers of different compositions. This results in a formation of stretched Coulomb crystals, in contrast to the standard assumption of cubic crystal formation, which is based on energetics arguments but does not take into account growth kinetics. Overstretched crystals break, which limits the vertical sizes of growing crystallites. We study breaking shear strain and effective shear modulus of stretched matter and discuss possibility of macrocrystallite formation. The latter has interesting astrophysical implications, for instance, appearance of weak crustal layers, whose strength may increase by a few orders of magnitude upon breaking and refreezing at a late-time event. We also analyze interaction of adjacent Coulomb crystals, having different ion compositions, and estimate the strength of such interfaces.

Crystallization of dense matter in neutron star crusts and white dwarf cores may be similar to epitaxial crystal growth in terrestrial laboratories. However in stellar crystals, the spacing between horizontal planes has to gradually increase with the outward movement of the crystallization front, tracing decrease of the electron density. This process produces Coulomb crystals with stretched rather than cubic elementary cells. We extend the analysis of the elastic and breaking properties of such crystals to the face-centered (fc) lattice. Shear deformations orthogonal to the stretch direction have been studied for 22 crystallographic shear planes. A common property for all these planes is a reduction and eventual nulling of the breaking shear strain with deviation from the unstretched configuration. The effective shear moduli for deformations orthogonal to the stretch direction have been calculated. It is possible that the epitaxial crystallization in compact stars results in a formation of large-scale crystallites or, at least, in growth of the whole crystallization front perpendicular to particular crystallographic planes. For fc structure growth orthogonal to the $\{111\}$ planes, we expect that, at any density, $\sim 5\%$ ($\sim 0.5\%$) of crystallite height is occupied by layers one (two) orders of magnitude weaker than the bulk of the crystallite. This may be important for realistic modeling of crustquakes on neutron stars.

Thermal evolution of the central region of a $0.9 \, M_\odot$ C/O white dwarf at the initial stage of the ion mixture crystallization is studied by numerically solving the heat equation on a fine spatial and temporal grid and by including a detailed treatment of the latent heat release. Formation of two spherical shells is observed. The outer one surrounds a region where crystallization has begun. The inner one bounds a fully solidified core which has exhausted its latent heat. The region between the shells is partially liquid and partially solid. It gradually emits the latent heat of crystallization and also it releases light elements (carbon) in the process of element redistribution, accompanying the mixture solidification. Assuming that all released light elements cross the outer shell, we have estimated their flux induced by the mixture crystallization. The resulting flux is not divergent and is much smaller than an estimate derived from the growth rate of the fully crystallized core.

Based on the linear mixing approach, we calculate the latent heat for crystallizing fully-ionized $^{12}$C/$^{16}$O and $^{16}$O/$^{20}$Ne mixtures in white dwarf (WD) cores for two different parametrizations of the corrections to the linear-mixing energies and with account of ion quantum effects. We report noticeable composition-dependent deviations of the excess entropy in both directions from the standard value of 0.77 per ion. Within the same framework, we evaluate the excess entropy and released or absorbed heat accompanying the exsolution process in solidified WD layers. The inclusion of this effect is shown to be important for reliable interpretation of WD cooling data. We also analyze the latent heat of crystallizing eutectic $^{12}$C/$^{22}$Ne mixture, where we find a qualitative dependence of both the phase diagram and the latent heat behaviour on ion quantum effects. This may be important for the model with $^{22}$Ne distillation in cooling C/O/$^{22}$Ne WD proposed as a solution for the ultramassive WD multi-Gyr cooling anomaly. Astrophysical implications of our findings for crystallizing WD are discussed.

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.

Phase diagrams of fully ionized binary ionic mixtures are considered within the framework of the linear mixing formalism taking into account recent advances in understanding quantum one-component plasma thermodynamics. We have followed a transformation of azeotropic phase diagrams into peritectic and eutectic types with increase of the charge ratio. For solid ^12C/^16O and ^16O/^20Ne mixtures, we have found extensive miscibility gaps. Their appearance seems to be a robust feature of the theory. The gaps evolve naturally into two-solid regions of eutectic phase diagrams at higher Z_2/Z_1. They do not depend on thermodynamic fit extensions beyond their applicability limits. The gaps are sensitive to binary mixture composition and physics, being strongly different for C/O and O/Ne mixtures and for the three variants of corrections to linear-mixing solid-state energies available in the literature. When matter cools to its miscibility gap temperature, the exsolution process takes place. It results in a separation of heavier and lighter solid solutions. This may represent a significant reservoir of gravitational energy and should be included in future white dwarf (WD) cooling simulations. Ion quantum effects mostly resulted in moderate modifications, however, for certain Z_2/Z_1, these effects can produce qualitative restructuring of the phase diagram. This may be important for the model with ^22Ne distillation in cooling C/O/Ne WD proposed as a solution for the ultramassive WD cooling anomaly.

ABSTRACT A reliable description of nuclear fusion reactions in inner layers of white dwarfs and envelopes of neutron stars is important for realistic modelling of a wide range of observable astrophysical phenomena from accreting neutron stars to Type Ia supernovae. We study the problem of screening of the Coulomb barrier impeding the reactions by a plasma surrounding the fusing nuclei. Numerical calculations of the screening factor are performed from the first principles with the aid of quantum-mechanical path integrals in the model of a one-component plasma of atomic nuclei for temperatures and densities typical for dense liquid layers of compact degenerate stars. We do not rely on various quasi-classic approximations widely used in the literature, such as factoring out the tunnelling process, tunnelling in an average spherically symmetric mean-force potential, usage of classic free energies and pair correlation functions, linear mixing rule, and so on. In general, a good agreement with earlier results from the thermonuclear limit to Γ ∼ 100 is found. For a very strongly coupled liquid 100 ≲ Γ ≤ 175, a deviation from currently used parametrizations of the reaction rates is discovered and approximated by a simple analytic expression. The developed method of nuclear reaction rate calculations with account of plasma screening can be extended to ion mixtures and crystallized phases of stellar matter.

ABSTRACT Using the Metropolis method to compute path integrals, the energy of a quantum strongly coupled Coulomb liquid (1 ≤ Γ ≤ 175), composed of distinguishable atomic nuclei and a uniform incompressible electron background, is calculated from first principles. The range of temperatures and densities considered represents fully ionized layers of white dwarfs and neutron stars. In particular, the results allow one to determine reliably the heat capacity of ions in dense fluid stellar matter, which is a crucial ingredient for modelling the thermal evolution of compact degenerate stars.

We present an accurate analytic approximation for the energy of a quantum one-component Coulomb liquid of ions in a uniform electron background that has been recently calculated from first principles. The approximation enables us to develop in an analytic form a complete thermodynamic description of quantum ions in a practically important range of mass densities at temperatures above crystallization. We show that ionic quantum effects in liquid cores of white dwarfs (WDs) affect heat capacity, cooling, thermal compressibility, pulsation frequencies, and radii of sufficiently cold WDs, especially with relatively massive helium and carbon cores.

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.

We have studied phonon modes of a body-centered cubic (bcc) Coulomb crystal of ions in the presence of a uniform magnetic field B taking into account the polarizability of the electron background (electron screening) described by the Thomas-Fermi formalism. For k≫κTF (k and κTF are the phonon wavevector and Thomas-Fermi wavenumber, respectively), electron polarizability is not important. At k≪κTF, the electron response results in a pronounced effect. One of the three available modes is acoustic. For orthogonal propagation (k⊥B), its frequency Ω is independent of B and κTF. For k∥B, Ω∝1/κTF and is independent of B. Another mode is quadratic. Its frequency is ∝1/(BκTF) for orthogonal propagation and ∝1/B and independent of κTF for the parallel case. The third mode is optic with Ω≈ωB (ωB is the ion cyclotron frequency). A general expression is derived for the dynamic matrix of a Coulomb crystal with a polarizable background and more than one ion in the primitive cell. It is employed for a study of a magnetized hexagonal close-packed Coulomb crystal. We have also presented an analysis of phonon polarization vectors in a magnetized bcc crystal with or without screening. The results obtained can be used for realistic calculations of electron-phonon scattering rates and electron thermal and electrical conductivities in neutron star crusts.

Although crystallized neutron star crust is responsible for many fascinating observational phenomena, its actual microscopic structure in tremendous gravitational and magnetic fields is not understood. Here we show that in a non-uniform magnetic field, three-dimensional ionic Coulomb crystals comprising the crust may stretch or shrink while their electrostatic pressure becomes anisotropic. The pressure depends non-linearly on the magnitude of the stretch, so that a continuous magnetic field evolution may result in an abrupt crystal elongation or contraction. This may provide a trigger for magnetar activity. A phonon mode instability is revealed, which sets the limits of magnetic field variation beyond which the crystal is destroyed. These limits sometimes correspond to surprisingly large deformations. It is not known what happens to crust matter subject to a pressure anisotropy exceeding these limits. We hypothesize that the ion system then possesses a long-range order only in one or two dimensions, that is becomes a liquid crystal.

A brief overview of the history of atmospheric Cherenkov gamma-ray telescopes is given. Topical problems of modern astrophysics and fundamental physics to be solved with these instruments are listed. The ALEGRO project of a low-threshold gamma-ray observatory is characterized in detail. The aim of this project is to examine cosmic gamma-ray sources (especially the rapidly variable gamma-ray sources, gamma-ray transients) with high statistics of detected photons in the energy range of 5–50 GeV.

We study electrical and thermal conductivities of degenerate electrons emitting and absorbing phonons in a strongly magnetized crystalline neutron star crust. We take into account modification of the phonon spectrum of a Coulomb solid of ions caused by a strong magnetic field. Boltzmann transport equation is solved using a generalized variational method. The ensuing three-dimensional integrals over the transferred momenta are evaluated by two different numerical techniques, the Monte-Carlo method and a regular integration over the first Brillouin zone. The results of the two numerical approaches are shown to be in a good agreement. An appreciable growth of electrical and thermal resistivities is reported at quantum and intermediate temperatures $T \lesssim 0.1 T_{\rm p}$ ($T_{\rm p}$ is the ion plasma temperature) in a wide range of chemical compositions and mass densities of matter even for moderately magnetized crystals $\omega_{\rm B} \sim \omega_{\rm p}$ ($\omega_{\rm B}$ and $\omega_{\rm p}$ are the ion cyclotron and plasma frequencies). This effect is due to an appearance of a soft ($\omega \propto k^2$) phonon mode in the magnetized ion Coulomb crystal, which turns out to be easier to excite than acoustic phonons characteristic of the field-free case. These results are important for modelling magneto-thermal evolution of neutron stars.

The concept of a new-generation terrestrial Cherenkov gamma observatory is proposed on the basis of the results of numerical modeling and research and development work. The key parameters of this observatory are estimated. Its primary objective should be the observation of cosmic gamma-ray sources in the 5–50 GeV energy range. Neither ground-based Cherenkov gamma observatories nor orbital gamma telescopes are presently able to perform such observations efficiently.

One-component Coulomb crystals of ions with hexagonal close-packed (hcp) lattice likely form in the crust of strongly-magnetized neutron stars (magnetars). In this work we present a detailed study of vibration modes and thermodynamic properties of such crystals in a wide range of temperatures at zero magnetic field. In contrast to typically considered lattices, the phonon spectrum of the system exhibits a peculiar crossing of the acoustic modes near the Brillouin zone center in certain directions of the wavevector. It is demonstrated that in the field-free regime the Helmholtz free energy of the hcp Coulomb crystal is always higher than those of the Coulomb crystals with body-centered cubic and face-centered cubic lattices. The results of our numerical calculations are fitted by simple analytic expressions.

We calculate electrostatic, spectral, and thermal properties of two-component Coulomb crystals of ions and determine the limits of applicability of the linear mixing theory to such systems.