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.
Long-lived magnetic fields are known to exist in upper main-sequence stars, white dwarfs, and neutron stars. In order to explore possible equilibrium configurations of the magnetic field inside these ...stars, we have performed 3D-magnetohydrodynamic simulations of the evolution of initially random magnetic fields in stably stratified and barotropic stars with an ideal-gas equation of state using the {\sc Pencil Code}, a high-order finite-difference code for compressible hydrodynamic flows in the presence of magnetic fields. In barotropic (isentropic) stars, we confirm previous results in the sense that all initial magnetic fields we tried decay away, unable to reach a stable equilibrium. In the case of stably stratified stars (with radially increasing specific entropy), initially random magnetic fields appear to always evolve to a stable equilibrium. However, the nature of this equilibrium depends on the dissipation mechanisms considered. If magnetic diffusivity (or hyperdiffusivity) is included, the final state is more axially symmetric and dominated by large wavelengths than the initial state, whereas this is not the case if only viscosity (or hyperviscosity) is present. In real stars, the main mechanism allowing them to relax to an equilibrium is likely to be phase mixing, which we argue is more closely mimicked by viscosity. Therefore, we conclude that, depending on its formation mechanism, the equilibrium magnetic field in these stars could in principle be very asymmetric.
We calculate the relativistic entrainment matrix Y{sub ik} at zero temperature for a nucleon-hyperon mixture composed of neutrons, protons, and {lambda} and {sigma}{sup -} hyperons, as well as ...electrons and muons. This matrix is analogous to the entrainment matrix (also termed mass-density matrix or Andreev-Bashkin matrix) of nonrelativistic theory. It is an important ingredient for modeling the pulsations of massive neutron stars with superfluid nucleon-hyperon cores. The calculation is done in the frame of the relativistic Landau Fermi-liquid theory generalized to the case of superfluid mixtures; the matrix Y{sub ik} is expressed through the Landau parameters of nucleon-hyperon matter. The results are illustrated with a particular example of the {sigma}-{omega}-{rho} mean-field model with scalar self-interactions. Using this model, we calculate the matrix Y{sub ik} and the Landau parameters. We also analyze the stability of the ground state of nucleon-hyperon matter with respect to small perturbations.
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.
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).
We calculate the finite-temperature r-mode spectrum of a superfluid neutron star accounting for both muons in the core and the entrainment between neutrons and protons. We show that the standard ...perturbation scheme, considering the rotation rate as an expansion parameter, breaks down in this case. We develop an original perturbation scheme which circumvents this problem by treating both the perturbations due to rotation and (weak) entrainment simultaneously. Applying this scheme, we propose a simple method for calculating the superfluid r-mode eigenfrequency in the limit of vanishing rotation rate. We also calculate the r-mode spectrum at finite rotation rate for realistic microphysics input (adopting, however, the Newtonian framework and Cowling approximation when considering perturbed oscillation equations) and show that the normal r-mode exhibits resonances with superfluid r-modes at certain values of temperatures and rotation frequencies in the parameter range relevant to neutron stars in low-mass X-ray binaries (LMXBs). This turns the recently suggested phenomenological model of resonance r-mode stabilization into a quantitative theory, capable of explaining observations. A strong dependence of resonance rotation rates and temperatures on the neutron superfluidity model allows us to constrain the latter by confronting our calculations with the observations of neutron stars in LMXBs.
The relativistic analogue of the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) hydrodynamics is derived making use of the phenomenological method similar to that used by Bekarevich and Khalatnikov 1 in ...their derivation of HVBK-hydrodynamics. The resulting equations describe a finite-temperature superfluid liquid with the distributed vorticity. The main dissipative effects, including mutual friction, are taken into account. The proposed hydrodynamics is needed for reliable modeling of the dynamical properties of superfluid neutron stars.
The self-consistent approach to the magnetic field evolution in neutron star cores, developed recently, is generalised to the case of superfluid and superconducting neutron stars. Applying this ...approach to the cold matter of neutron star cores composed of neutrons, protons, electrons, and muons we find that, similarly to the case of normal matter, an arbitrary configuration of the magnetic field may result in generation of macroscopic particle velocities, strongly exceeding their diffusive (relative) velocities. This effect substantially accelerates evolution of the magnetic field in the stellar core. An hierarchy of timescales of such evolution at different stages of neutron star life is proposed and discussed. It is argued that the magnetic field in the core cannot be considered as frozen or vanishing and that its temporal evolution should affect the observational properties of neutron stars.
We constrain the parameters of neutron superfluidity in the cores of neutron
stars making use of the recently proposed effect of resonance stabilization of
$r$-modes. To this end, we, for the first ...time, calculate the
finite-temperature $r$-mode spectra for realistic models of rotating superfluid
neutron stars, accounting for both muons and neutron-proton entrainment in
their interiors. We find that the ordinary (normal) $r$-mode exhibits avoided
crossings with superfluid $r$-modes at certain stellar temperatures and spin
frequencies. Near the avoided crossings, the normal $r$-mode dissipates
strongly, which leads to substantial suppression of the $r$-mode instability
there. The extreme sensitivity of the positions of avoided crossings to the
neutron superfluidity model allows us to constrain the latter by confronting
the calculated spectra with observations of rapidly rotating neutron stars in
low-mass X-ray binaries.
We formulate hydrodynamic equations for nonsuperfluid multicomponent magnetized charged relativistic mixtures, taking into account chemical reactions as well as viscosity, diffusion, thermodiffusion, ...and thermal conductivity effects. The resulting equations have a rather simple form and can be readily applied, e.g., for studying magnetothermal evolution of neutron stars. We also establish a link between our formalism and the results known in the literature, and express the phenomenological diffusion coefficients through momentum transfer rates which are calculated from microscopic theory.
