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We study heat diffusion after an energy release in a deep spherical layer of the outer neutron star crust (10^7 < ��< 4 x 10^{11} g/cm^3). We demonstrate that this layer possesses specific heat-accumulating properties, absorbing heat and directing it mostly inside the star. It can absorb up to about 10^{43}-10^{44} erg due to its high heat capacity, until its temperature exceeds T ~ 3 x 10^9 K and triggers a rapid neutrino cooling. A warm layer with T ~ 10^8 - 3 x 10^9 K can serve as a good heat reservoir, which is thermally decoupled from the inner crust and the stellar core for a few months. We present a toy model to explore the heat diffusion within the heat-accumulating layer, and we test this model using numerical simulations. We formulate some generic features of the heat propagation which can be useful, for instance, for the interpretation of superbursts in accreting neutron stars. We present a self-similar analysis of late afterglow after such superbursts, which can be helpful to estimate properties of bursting stars., 17 pages, 9 figures, MNRAS, accepted, a few typos and bib references corrected

We study a simple model describing thermal radiation spectra from magnetized neutron stars. The model assumes that a star is nearly spherical and isothermal inside and possesses dipole magnetic fields ($B \lesssim 10^{14}$ G) near the surface, which make the surface temperature distribution non--uniform. We assume further that any surface element emits a blackbody (BB) spectrum with a local effective temperature. We show that such thermal spectra (including phase--resolved) are accurately approximated by simple equivalent two--BB (2BB) models. We introduce and study phase--space maps of 2BB parameters and show that these maps can be useful for interpreting neutron star observations, in which 2BB spectral fits have been done., Comment: 10 pages, 8 figures, MNRAS, accepted

Near the surface of any neutron star there is a thin heat blanketing envelope that produces substantial thermal insulation of warm neutron star interiors and that relates the internal temperature of the star to its effective surface temperature. Physical processes in the blanketing envelopes are reasonably clear but the chemical composition is not. The latter circumstance complicates inferring physical parameters of matter in the stellar interiors from observations of the thermal surface radiation of the stars and urges one to elaborate the models of blanketing envelopes. We outline physical properties of these envelopes, particularly, the equation of state, thermal conduction, ion diffusion and others. Various models of heat blankets are reviewed, such as composed of separate layers of different elements, or containing diffusive binary ion mixtures in or out of diffusion equilibrium. The effects of strong magnetic fields in the envelopes are outlined as well as the effects of high temperatures which induce strong neutrino emission in the envelopes themselves. Finally, we discuss how the properties of the heat blankets affect thermal evolution of neutron stars and the ability to infer important information on internal structure of neutron stars from observations., Comment: 82 pages, 26 figures, accepted for publication in Physics Reports

We study breaking stress of deformed Coulomb crystals in a neutron star crust, taking into account electron plasma screening of ion-ion interaction; calculated breaking stress is fitted as a function of electron screening parameter. We apply the results for analyzing torsional oscillation modes in the crust of a non-magnetic star. We present exact analytic expression for the fundamental frequencies of such oscillations and show that the frequencies of all torsional oscillations are insensitive to the presence of the outer neutron star crust. The results can be useful in theoretical modeling of processes involving deformed Coulomb crystals in the crust of neutron stars, such as magnetic field evolution, torsional crustal or thermo-elastic quasi-periodic oscillations of flaring soft gamma-ray repeaters, pulsar glitches. The applicability of the results to soft gamma-ray repeaters is discussed., 11 pages, 6 figures, Accepted by MNRAS

Ages and thermal luminosities of neutron stars, inferred from observations, can be interpreted with the aid of the neutron star cooling theory to gain information on the properties of superdense matter in neutron-star interiors. We present a survey of estimated ages, surface temperatures and thermal luminosities of middle-aged neutron stars with relatively weak or moderately strong magnetic fields, which can be useful for these purposes. The catalogue includes results selected from the literature, supplemented with new results of spectral analysis of a few cooling neutron stars. The data are compared with the theory. We show that overall agreement of theoretical cooling curves with observations improves substantially for models where neutron superfluidity in stellar core is weak., Comment: 23 pages, 3 figures, 2 tables, accepted by MNRAS. In v.2, acknowledgements are supplemented

We study the bulk viscosity in two (anti-spaghetti and Swiss cheese) phases of non- spherical nuclei in the mantle of an oscillating neutron star near the boundary with the stellar core. The bulk viscosity is produced by non-equilibrium Urca neutrino emis- sion processes. In the mantle, the direct Urca process may be open (Gusakov et al., 2004) if neutrons and protons move in a periodic potential created by a lattice of non- spherical nuclei (which allows the nucleons to have large quasi-momenta and satisfy direct Urca momentum-conservation). This bulk viscosity can dominate over that due to the modified Urca process in the outer stellar core and over the shear viscosity. The bulk viscosity depends strongly on temperature, oscillation frequency and nucleon superfluidity. The enhanced bulk viscosity in the mantle can control propagation and damping of neutron star oscillations., Comment: 7 pages, 1 figure, MNRAS, accepted

We present an accurate analytic approximation for the energy of a quantum one-component Coulomb liquid of ions in a uniform electron background which has been recently calculated from first principles (Baiko 2019). 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., 19 pages, 6 figures; submitted 5 weeks ago

We study the effects of heat blanketing envelopes of neutron stars on their cooling. To this aim, we perform cooling simulations using newly constructed models of the envelopes composed of binary ion mixtures (H--He, He--C, C--Fe) varying the mass of lighter ions (H, He or C) in the envelope. The results are compared with those calculated using the standard models of the envelopes which contain the layers of lighter (accreted) elements (H, He and C) on top of the Fe layer, varying the mass of accreted elements. The main effect is that the chemical composition of the envelopes influences their thermal conductivity and, hence, thermal insulation of the star. For illustration, we apply these results to estimate the internal temperature of the Vela pulsar and to study the cooling of neutron stars of ages of 0.1 - 1 Myr at the photon cooling stage. The uncertainties of the cooling models associated with our poor knowledge of chemical composition of the heat insulating envelopes strongly complicate theoretical reconstruction of the internal structure of cooling neutron stars from observations of their thermal surface emission., 8 pages, 4 figures, MNRAS, accepted

We construct new models of outer heat blanketing envelopes of neutron stars composed of binary ion mixtures (H - He, He - C, C - Fe) in and out of diffusive equilibrium. To this aim, we generalize our previous work on diffusion of ions in isothermal gaseous or Coulomb liquid plasmas to handle non-isothermal systems. We calculate the relations between the effective surface temperature Ts and the temperature Tb at the bottom of heat blanketing envelopes (at a density rhob= 1e8 -- 1e10 g/cc) for diffusively equilibrated and non-equilibrated distributions of ion species at different masses DeltaM of lighter ions in the envelope. Our principal result is that the Ts - Tb relations are fairly insensitive to detailed distribution of ion fractions over the envelope (diffusively equilibrated or not) and depend almost solely on DeltaM. The obtained relations are approximated by analytic expressions which are convenient for modeling the evolution of neutron stars., Comment: 12 pages, 7 figures, MNRAS, published

Neutron stars contain superdense matter in their interiors. Characteristic densities in their cores are several times higher than the standard density of nuclear matter. This matter is so dense that it would be natural to assume that frequent particle collisions produce immediate equilibration. However, because of the slowness of some reactions, the equilibration with respect to them can be greatly delayed. Then one should deal with non-equilibrium stars which contain extra energy to be released. Deviations from equilibrium can affect neutrino emission of neutron stars, warm up their interiors and influence their thermal evolution. The effects of equilibration can be important for pulsating, rotating, accreting neutron stars, as well as for merging binary neutron stars.

We study thermal relaxation in a neutron star after internal heating events (outbursts) in the crust. We consider thin and thick spherically symmetric heaters, superfluid and non-superfluid crusts, stars with open and forbidden direct Urca processes in their cores. In particular, we analyze long-term thermal relaxation after deep crustal heating produced by nuclear transformations in fully or partly accreted crusts of transiently accreting neutron stars. This long-term relaxation has a typical relaxation time and an overall finite duration time for the crust to thermally equilibrate with the core. Neutron superfluidity in the inner crust greatly affects the relaxation if the heater is located in the inner crust. It shortens and unifies the time of emergence of thermal wave from the heater to the surface. This is important for the interpretation of observed outbursts of magnetars and transiently accreting neutron stars in quasi-persistent low-mass X-ray binaries., 15 pages, 10 figures, Astrophysics and Space Science, published

Thermal evolution of neutron stars is known to depend on the properties of superdense matter in neutron star cores. We suggest a statistical analysis of isolated cooling middle-aged neutron stars and old transiently accreting quasi-stationary neutron stars warmed up by deep crustal heating in low-mass X-ray binaries. The method is based on simulations of the evolution of stars of different masses and on averaging the results over respective mass distributions. This gives theoretical distributions of isolated neutron stars in the surface temperature--age plane and of accreting stars in the photon thermal luminosity--mean mass accretion rate plane to be compared with observations. This approach permits to explore not only superdense matter but also the mass distributions of isolated and accreting neutron stars. We show that the observations of these stars can be reasonably well explained by assuming the presence of the powerful direct Urca process of neutrino emission in the inner cores of massive stars, introducing a slight broadening of the direct Urca threshold (for instance, by proton superfluidity), and by tuning mass distributions of isolated and accreted neutron stars., Comment: 13 pages, 20 figures

We derive analytic approximations for the neutrino luminosities and the heat capacities of neutron stars with isothernal nucleon cores as functions of the mass and radius of stars. The neutrino luminosities are approximated for the three basic neutrino emission mechanisms, and the heat capacities for the five basic combinations of the partial heat capacities. The approximations are valid for for a wide class of equations of state of dense nucleonmatter. The results significantly simplify the theoretical interpretation of observations of cooling neutron stars as well as of quasistationary thermal states of neutron stars in X-ray transients. For illustration, we present an analysis of the neutrino cooling functions of nine isolated neutron stars taking into account the effects of their magnetic fields and of the presence of light elements in their heat blanketing envelopes. These results allow one to investigate the superfluid properties of neutron star cores., 15 pages, 9 figures, 5 tables

We discuss the effect of the chemical composition of heat blanketing envelopes of neutron stars (NSs) on the interpretation of the observations of these stars. First we analyze the diffusive fluxes of ions in non-isothermal and non-ideal Coulomb plasmas. Then we outline models of diffusively-equilibrated heat blanketing envelopes composed of binary ionic mixtures and finally we study their effect on the cooling of isolated NSs.

The conference This was the 11th gathering on neutron star physics in Saint Petersburg since 1988. The 2017 Conference was organized by the Theoretical Astrophysics Department of the Ioffe Institute and the Relativistic Astrophysics Department of the Sternberg Astronomical Institute. It commemorated the semicentenary of the discovery of pulsars. During these 50 years, the field of astrophysics of neutron stars has become a broad field covering all ranges of physical scales, from microscales characteristic of strong interactions to macroscales of neutron star sizes strongly affected by General Relativity. All branches of contemporary physics are involved in the research of astrophysical phenomena related to neutron stars, and observations throughout the entire range of electromagnetic spectra have been used to constrain fundamental physical theories. Towards the end of the 20th century, electromagnetic observations were joined by direct neutrino detections from a newly born neutron star (Supernova 1987a) and, between the end of the Conference and the publication of this volume, a long-awaited gravitational wave signal from a binary neutron star merger was detected for the first time, thus promoting neutron stars to the first class of astrophysical sources observed in the electromagnetic band, neutrinos, and gravitational waves. With many more detections of binary neutron star mergers to come, the next decade of the neutron star research is expected to be developing under great influence of the gravitational wave astronomy. In addition, the launch of telescopes of the next generation (proposed, planned and already operating) will shed light on many of the current mysteries, but surely it will also unveil new ones, making the near future even more stimulating than the previous five decades. List of Acknowledgments, Organizing committees, Invited speakers, Conference photo are available in this PDF

We describe the cooling theory for isolated neutron stars that are several tens of years old. Their cooling differs greatly from the cooling of older stars that has been well studied in the literature. It is sensitive to the physics of the inner stellar crust and even to the thermal conductivity of the stellar core, which is never important at later cooling stages. The absence of observational evidence for the formation of a neutron star during the explosion of Supernova 1987A is consistent with the fact that the star was actually born there. It may still be hidden in the dense center of the supernova remnant. If, however, the star is not hidden, then it should have a low thermal luminosity (below ∼1034 erg s−1) and a short internal thermal relaxation time (shorter than 13 yr). This requires that the star undergo intense neutrino cooling (e.g., via the direct Urca process) and have a thin crust with strong superfluidity of free neutrons and/or an anomalously high thermal conductivity.

We simulate the cooling of the neutron star in the X-ray transient KS 1731-260 after the source returned to quiescence in 2001 from a long (>~ 12.5 yr) outburst state. We show that the cooling can be explained assuming that the crust underwent deep heating during the outburst stage. In our best theoretical scenario the neutron star has no enhanced neutrino emission in the core, and its crust is thin, superfluid, and has the normal thermal conductivity. The thermal afterburst crust-core relaxation in the star may be not over., 5 pages, 2 figures, accepted by MNRAS. In v.2, two references added and typos corrected

We model thermal evolution of magnetars with a phenomenological heat source in a spherical internal layer and compare the results with observations of persistent thermal radiation from magnetars. We show that the heat source should be located in the outer magnetar’s crust, at densities ρ≲5×1011 g cm−3, and the heating rate should be ∼1020 erg cm−3 s−1. Heating deeper layers is extremely inefficient because the thermal energy is mainly radiated away by neutrinos and does not warm up the surface to the magnetar’s level. This deep heating requires too much energy; it is inconsistent with the energy budget of neutron stars.

The central compact object in the supernova remnant HESS J1731-347 appears to be the hottest observed isolated cooling neutron star. The cooling theory of neutron stars enables one to explain observations of this star by assuming the presence of strong proton superfluidity in the stellar core and the existence of the surface heat blanketing envelope which almost fully consists of carbon. The cooling model of this star is elaborated to take proper account of the neutrino emission due to neutron-neutron collisions which is not suppressed by proton superfluidity. Using the results of spectral fits of observed thermal spectra for the distance of 3.2 kpc and the cooling theory for the neutron star of age 27 kyr, new constraints on the stellar mass and radius are obtained which are more stringent than those derived from the spectral fits alone., 9 pages, 5 figures, MNRAS, accepted

We apply our recently suggested statistical approach to thermal evolution of isolated neutron stars and accreting quasistationary neutron stars in X-ray transients for constraining the position and relative broadening alpha of the direct Urca threshold of powerful neutrino emission in neutron star cores. We show that most likely explanation of observations corresponds to alpha = 0.08 - 0.10 and to the neutron star mass, at which the direct Urca process is open, M_D = (1.6 - 1.8) M_sun., 10 pages, 10 figures

We present a simple model for electron transport in a possible layer of exotic nuclear clusters (in the so called nuclear pasta layer) between the crust and liquid core of a strongly magnetized neutron star. The electron transport there can be strongly anisotropic and gyrotropic. The anisotropy is produced by different electron effective collision frequencies along and across local symmetry axis in domains of exotic ordered nuclear clusters and by complicated effects of the magnetic field. We also calculate averaged kinetic coefficients in case local domains are freely oriented. Possible applications of the obtained results and open problems are outlined., Comment: 11 pages 5 figures, MNRAS, accepted

We study the pycnonuclear burning of 34 Ne in the inner crust of an accreting neutron star. We show that the associated energy production rate can be calculated analytically for any arbitrary temporal variability of the mass accretion rate. We argue that the theoretical time-scale for 34 Ne burning is currently very uncertain and ranges from a fraction of a millisecond to a few years. The fastest allowable burning may change the composition of the accreted crust while the slowest burning leads to a time-independent nuclear energy generation rate for a variable accretion. The results are important for constructing self-consistent models of the accreted crust and deep crustal heating in neutron stars which enter soft X-ray transients.

We study thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in a spherical internal layer. We explore the location of this layer as well as the heating rate that could explain high observable thermal luminosities of magnetars and would be consistent with the energy budget of neutron stars. We conclude that the heat source should be located in an outer magnetar's crust, at densities rho < 5e11 g/cm^3, and should have the heat intensity of the order of 1e20 erg/s/cm^3. Otherwise the heat energy is mainly emitted by neutrinos and cannot warm up the surface.

We study the cooling of superfluid neutron stars whose cores consist of nucleon matter with the Akmal-Pandharipande-Ravenhall equation of state. This equation of state opens the powerful direct Urca process of neutrino emission in the interior of most massive neutron stars. Extending our previous studies (Gusakov et al. 2004a, Kaminker et al. 2005), we employ phenomenological density-dependent critical temperatures T_{cp}(\rho) of strong singlet-state proton pairing (with the maximum T_{cp}^{max} \sim 7e9 K in the outer stellar core) and T_{cnt}(\rho) of moderate triplet-state neutron pairing (with the maximum T_{cnt}^{max} \sim 6e8 K in the inner core). Choosing properly the position of T_{cnt}^{max} we can obtain a representative class of massive neutron stars whose cooling is intermediate between the cooling enhanced by the neutrino emission due to Cooper pairing of neutrons in the absence of the direct Urca process and the very fast cooling provided by the direct Urca process non-suppressed by superfluidity., Comment: 9 pages, 6 figures; accepted for publication in MNRAS

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

We discuss pycnonuclear burning of highly exotic atomic nuclei in deep crusts of neutron stars, at densities up to 1e13 g/cc. As an application, we consider pycnonuclear burning of matter accreted on a neutron star in a soft X-ray transient (SXT, a compact binary containing a neutron star and a low-mass companion). The energy released in this burning, while the matter sinks into the stellar crust under the weight of newly accreted material, is sufficient to warm up the star and initiate neutrino emission in its core. The surface thermal radiation of the star in quiescent states becomes dependent of poorly known equation of state (EOS) of supranuclear matter in the stellar core, which gives a method to explore this EOS. Four qualitatively different model EOSs are tested against observations of SXTs. They imply different levels of the enhancement of neutrino emission in massive neutron stars by (1) the direct Urca process in nucleon/hyperon matter; (2) pion condensates; (3) kaon condensates; (4) Cooper pairing of neutrons in nucleon matter with the forbidden direct Urca process. A low level of the thermal quiescent emission of two SXTs, SAX J1808.4-3658 and Cen X-4, contradicts model (4). Observations of SXTs test the same physics of dense matter as observations of thermal radiation from cooling isolated neutron stars, but the data on SXTs are currently more conclusive., Comment: 4 pages, 3 figures, style file included. Proc. of ENAM-2004, Callaway Gardens, Sept. 2004; Europ. Phys. J. A, 2005, in press

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.

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., 7 pages, 3 figures, submitted to A&A

We calculate the thermal structure and quiescent thermal luminosity of accreting neutron stars (warmed by deep crustal heating in accreted matter) in soft X-ray transients (SXTs). We consider neutron stars with nucleon and hyperon cores and with accreted envelopes. It is assumed that an envelope has an outer helium layer (of variable depth) and deeper layers of heavier elements, either with iron or with much heavier nuclei (of atomic weight A > 100) on the top (Haensel & Zdunik 1990, 2003, astro-ph/0305220). The relation between the internal and surface stellar temperatures is obtained and fitted. The quiescent luminosity of the hottest (low-mass) and coldest (high-mass) neutron stars is calculated, together with the ranges of its possible variations due to variable thickness of the helium layer. The results are compared with observations of SXTs, particularly, containing the coldest (SAX J1808.4-3658) and the hottest (Aql X-1) neutron stars. The observations of SAX J1808.4-3658 in a quiescent state on March 24, 2001 (Campana et al. 2002, astro-ph/0206376) can be explained only if this SXT contains a massive neutron star with a nucleon/hyperon core; a hyperon core with a not too low fraction of electrons is preferable. Future observations may discriminate between the various models of hyperon/nucleon dense matter. The thermal emission of SAX J1808.4-3658 is also sensitive to the models of plasma ionization in the outermost surface layers and can serve for testing such models., 12 pages, 5 figures, 4 tables, LaTeX2e with aa.cls v.5.3 (included). Accepted by A&A

The cooling theory of isolated neutron stars is reviewed. The main cooling regulators are discussed, first of all, operation of direct Urca process (or similar processes in exotic phases of dense matter) and superfluidity in stellar interiors. The prospects to constrain gross parameters of supranuclear matter in neutron-star interiors by confronting cooling theory with observations of isolated neutron stars are outlined. A related problem of thermal states of transiently accreting neutron stars with deep crustal heating of accreted matter is discussed in application to soft X-ray transients., 10 pages, 3 figures, Proceedings of the 34th COSPAR Scientific Assembly (Adv. Sp. Res., accepted)

We study thermal states of transiently accreting neutron stars (with mean accretion rates $\dot{M} \sim 10^{-14}-10^{-9}$ M$_\odot$ yr$^{-1}$) determined by the deep crustal heating of accreted matter sinking into stellar interiors. We formalize a direct correspondence of this problem to the problem of cooling neutron stars. Using a simple toy model we analyze the most important factors which affect the thermal states of accreting stars: a strong superfluidity in the cores of low-mass stars and a fast neutrino emission (in nucleon, pion-condensed, kaon-condensed, or quark phases of dense matter) in the cores of high-mass stars. We briefly compare the results with the observations of soft X-ray transients in quiescence. If the upper limit on the quiescent thermal luminosity of the neutron star in SAX J1808.4-3658 (Campana et al. 2002) is associated with the deep crustal heating, it favors the model of nucleon neutron-star cores with switched-on direct Urca process., Comment: 7 pages, 2 figures, revised after the referee remarks, to appear in A&A

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.

The adiabatic index Gamma_1 for perturbations of dense matter is studied under various physical conditions which can prevail in neutron star cores. The dependence of Gamma_1 on the composition of matter (in particular, on the presence of hyperons), on the stellar pulsation amplitude, and on the baryon superfluidity is analyzed. Timescales of damping of stellar pulsations are estimated at different compositions, temperatures, and pulsation amplitudes. Damping of pulsations by bulk viscosity in the neutron-star cores can prevent the stars to pulsate with relative amplitudes > (1-15)% (depending on the composition of matter)., 5 pages, 2 figures, accepted for publication in A&A

Cooling of neutron stars (NSs) with the cores composed of neutrons, protons, and electrons is simulated assuming $^1$S$_0$ pairing of neutrons in the NS crust, and also $^1$S$_0$ pairing of protons and weak $^3$P$_2$ pairing of neutrons in the NS core, and using realistic density profiles of the superfluid critical temperatures $T_{\rm c}(\rho)$. The theoretical cooling models of isolated middle-aged NSs can be divided into three main types. (I) {\it Low-mass}, {\it slowly cooling} NSs where the direct Urca process of neutrino emission is either forbidden or almost fully suppressed by the proton superfluidity. (II) {\it Medium-mass} NSs which show {\it moderate} cooling via the direct Urca process suppressed by the proton superfluidity. (III) {\it Massive} NSs which show {\it fast} cooling via the direct Urca process weakly suppressed by superfluidity. Confronting the theory with observations we treat RX J0822--43, PSR 1055--52 and RX J1856--3754 as slowly cooling NSs. To explain these sufficiently warm sources we need a density profile $T_{\rm c}(\rho)$ in the crust with a rather high and flat maximum and sharp wings. We treat 1E 1207--52, RX J0002+62, PSR 0656+14, Vela, and Geminga as moderately cooling NSs. We can determine their masses for a given model of proton superfluidity, $T_{\rm cp}(\rho)$, and the equation of state in the NS core. No rapidly cooling NS has been observed so far., Comment: 12 pages, 10 figures, Astron. Astrophys., submitted

We study thermal radiation of a warm neutron star with a variable shell-like heater located in its crust. The heater and the star are taken to be initially in a stationary state. Then the heat power is increased or decreased for some period of time producing a peak or a dip of the thermal surface emission; afterwards the stationary state is restored. Only a small fraction of the generated heat is thermally emitted through the surface. Time variation of the surface luminosity is weakened and distorted with respect to the variation of the generated heat power; the former variation can be observable only under special conditions —neutron stars are “hiding” their internal temperature variations. These results can be useful for the interpretation of the observations of neutron stars with variable thermal surface emission, particularly, magnetars and transiently accreting neutron stars in low-mass X-ray binaries.

Based on the formalism by Kaminker et al. (Astron. Astrophys. 343 (1999) 1009) we derive an analytic approximation for neutrino-pair bremsstrahlung emissivity due to scattering of electrons by atomic nuclei in the neutron star crust of any realistic composition. The emissivity is expressed through generalized Coulomb logarithm which we fit by introducing an effective potential of electron-nucleus scattering. In addition, we study the conditions at which the neutrino bremsstrahlung in the crust is affected by strong magnetic fields. The results can be applied for modelling of many phenomena in neutron stars, such as thermal relaxation in young isolated neutron stars and in accreting neutron stars with overheated crust in soft X-ray transients., 6 pages, 3 figures, EPL, accepted

We calculate interdiffusion coefficients in a two-component, weakly or strongly coupled ion plasma (gas or liquid, composed of two ion species immersed into a neutralizing electron background). We use an effective potential method proposed recently by Baalrud and Daligaut [PRL, 110, 235001, (2013)]. It allows us to extend the standard Chapman-Enskog procedure of calculating the interdiffusion coefficients to the case of strong Coulomb coupling. We compute binary diffusion coefficients for several ionic mixtures and fit them by convenient expressions in terms of the generalized Coulomb logarithm. These fits cover a wide range of plasma parameters spanning from weak to strong Coulomb couplings. They can be used to simulate diffusion of ions in ordinary stars as well as in white dwarfs and neutron stars., Comment: 10 pages, 4 figures, Phys. Rev. E (accepted)

We analyze enhancement of thermonuclear fusion reactions due to strong plasma screening in dense matter using a simple electron drop model. The model assumes fusion in a potential that is screened by an effective electron cloud around colliding nuclei (extended Salpeter ion-sphere model). We calculate the mean field screened Coulomb potentials for atomic nuclei with equal and nonequal charges, appropriate astrophysical S factors, and enhancement factors of reaction rates. As a byproduct, we study analytic behavior of the screening potential at small separations between the reactants. In this model, astrophysical S factors depend not only on nuclear physics but on plasma screening as well. The enhancement factors are in good agreement with calculations by other methods. This allows us to formulate the combined, pure analytic model of strong plasma screening in thermonuclear reactions. The results can be useful for simulating nuclear burning in white dwarfs and neutron stars., Comment: 15 pages, 8 figures

We consider models of cooling neutron stars with nucleon cores which possess moderately strong triplet-state superfluidity of neutrons. When the internal temperature drops below the maximum of the critical temperature over the core, $T_{\rm C}$, this superfluidity sets in. It produces a neutrino outburst due to Cooper pairing of neutrons which greatly accelerates the cooling. We show that the cooling of the star with internal temperature $T$ within $0.6\,T_{\rm C} \lesssim T \leq T_{\rm C}$ is described by analytic self-similar relations. A measurement of the effective surface temperature of the star and its decline, supplemented by assumptions on star's mass, radius and composition of heat-blanketing envelope, allows one to construct a family of cooling models parametrized by the value of $T_{\rm C}$. Each model reconstructs cooling history of the star including its neutrino emission level before neutron superfluidity onset and the intensity of Cooper pairing neutrinos. The results are applied to interpret the observations of the neutron star in the Cassiopeia A supernova remnant., Comment: 10 pages, 14 figures, 2 tables; published in MNRAS. In version 2, typos and references corrected

The thermal structure of neutron stars with magnetized envelopes is studied using modern physics input. The relation between the internal (T_i) and local surface temperatures is calculated and fitted by analytic expressions for magnetic field strengths B from 0 to 10^{16} G and arbitrary inclination of the field lines to the surface. The luminosity of a neutron star with dipole magnetic field is calculated and fitted as a function of B, T_i, stellar mass and radius. In addition, we simulate cooling of neutron stars with magnetized envelopes. In particular, we analyse ultramagnetized envelopes of magnetars and also the effects of the magnetic field of the Vela pulsar on the determination of critical temperatures of neutron and proton superfluids in its core., Comment: 14 pages, 1 table, 11 figures, LaTeX2e using aa.cls (included) and epsf.sty. Accepted by A&A. Proof-stage version: minor text corrections and one correction of an in-line formula

We study the bulk viscosity in neutron star cores due to modied Urca processes involving nucleons, electrons and muons and analyze its reduction by singlet-state or triplet-state superfluidity of nucleons. In com- bination with the results of our previous paper on the bulk viscosity due to direct Urca processes, a realistic description of the bulk viscosity in superfluid neutron star cores is obtained. Switching o direct Urca processes with decreasing density in a nonsuperfluid matter lowers the bulk viscosity by 3{5 orders of magnitude. The presence of muons opens additional source of bulk viscosity due to muon Urca processes and lowers the threshold density of the electron direct Urca process. The superfluidity may strongly reduce the bulk viscosity and aect thus damping of neutron star vibrations.

Matter of subnuclear density in the inner crusts of neutron stars consists of neutron-rich atomic nuclei immersed in strongly degenerate relativistic gas of electrons and strongly nonideal liquid of neutrons. We give a brief account of thermodynamic and kinetic properties of this matter which are greatly affected by Coulomb and nuclear interactions (a companion paper on the outer envelopes is astro-ph/0012316) and show how they can be studied from observations of thermal radiation of young (age < 100 yr) neutron stars (for a discussion of the latter possibility, see astro-ph/0012306).