We calculate the important quantity of superfluid hydrodynamics, the relativistic entrainment matrix for a nucleon-hyperon mixture at arbitrary temperature. In the nonrelativistic limit this matrix is also termed the Andreev-Bashkin or mass-density matrix. Our results can be useful for modeling the pulsations of massive neutron stars with superfluid nucleon-hyperon cores and for studies of the kinetic properties of superfluid baryon matter.
We calculate the relativistic entrainment matrix Y_ik at zero temperature for nucleon-hyperon mixture composed of neutrons, protons, Lambda and Sigma^- hyperons, as well as of electrons and muons. This matrix is analogous to the entrainment matrix (also termed mass-density matrix or Andreev-Bashkin matrix) of non-relativistic theory. It is an important ingredient for modelling 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 matri…
I show that the usual model of the rotational response of a neutron star, which predicts rotation-induced neutronic vortices and no rotation-induced protonic vortices, does not hold (i) beyond a certain threshold of entrainment interaction strength nor (ii) in case of nonzero $Σ^-$ hyperon gap. I demonstrate that in both these cases the rotational response involves creation of phase windings in electrically charged condensate. Lattices of bound states of vortices which are caused these effects can (for a range of parameters) strongly reduce the interaction between rotation-induced vortices wit…
Observations of massive ($M \approx 2.0~M_\odot$) neutron stars (NSs), PSRs J1614-2230 and J0348+0432, rule out most of the models of nucleon-hyperon matter employed in NS simulations. Here we construct three possible models of nucleon-hyperon matter consistent with the existence of $2~M_\odot$ pulsars as well as with semi-empirical nuclear matter parameters at saturation, and semi-empirical hypernuclear data. Our aim is to calculate for these models all the parameters necessary for modelling dynamics of hyperon stars (such as equation of state, adiabatic indices, thermodynamic derivatives, re…
We consider sound waves in superfluid nucleon-hyperon matter of massive neutron-star cores. We calculate and analyze the speeds of sound modes and their damping times due to the shear viscosity and non-equilibrium weak processes of particle transformations. For that, we employ the dissipative relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated recently [M.E. Gusakov and E.M. Kantor, Phys. Rev. D78, 083006 (2008)]. We demonstrate that the damping times of sound modes calculated using this hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other b…
In this article we present an analytical two-component model for pulsar rotational dynamics. Under the assumption of axial symmetry, implemented by a paraxial array of straight vortices that thread the entire neutron superfluid, we are able to project exactly the 3D hydrodynamical problem to a 1D cylindrical one. In the presence of density dependent entrainment the superfluid rotation is non-columnar: we circumvent this by using an auxiliary dynamical variable directly related to the areal density of vortices. The main result is a system of differential equations that take consistently into ac…
We present a numerical model for uniformly rotating superfluid neutron stars, for the first time with realistic microphysics including entrainment, in a fully general relativistic framework. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a non-dissipative interaction which in case of a non-vanishing relative velocity between the fluids, causes the fluid momenta being not aligned with…
We analyse the oscillations of general relativistic superfluid hyperon stars, following the approach suggested by Gusakov & Kantor and Gusakov et al. and generalizing it to the nucleon-hyperon matter. We show that the equations governing the oscillations can be split into two weakly coupled systems with the coupling parameters $s_{\rm e}$, $s_{\rm μ}$, and $s_{\rm str}$. The approximation $s_{\rm e} = s_{\rm μ} = s_{\rm str} = 0$ (decoupling approximation) allows one to drastically simplify the calculations of stellar oscillation spectra. An efficiency of the presented scheme is illustrated by…
A simple description of superfluid hydrodynamics in the inner crust of a neutron star is given. Particular attention is paid to the effect of the lattice of nuclei on the properties of the superfluid neutrons, and the effects of entrainment, the fact that some fraction of the neutrons are locked to the motion of the protons in nuclei.
In order to establish whether the unstable r-modes in a rotating neutron star provide a detectable source of gravitational waves, we need to understand the details of the many dissipative processes that tend to counteract the instability. It has been established that the bulk viscosity due to exotic particles, like hyperons, may be particularly important in this respect. However, the effects of hyperon superfluidity have so far not been fully accounted for. While the associated suppression of the reaction rates that give rise to the bulk viscosity has been estimated, superfluid aspects of the …
We calculate the finite-temperature r-mode spectrum of a slowly rotating superfluid Newtonian neutron star neglecting the entrainment between neutron and proton liquid components (i.e., neglecting the off-diagonal element of the entrainment matrix). We show that for `minimal' NS core composition (neutrons, protons, and electrons) only two $m=2$ r-modes exist --- normal mode, which is similar to ordinary r-mode in a nonsuperfluid star, and a superfluid temperature-dependent mode. Accounting for muons in the core dramatically modifies the oscillation spectrum, resulting in an infinite set of sup…
We construct equilibrium configurations of magnetized, two-fluid neutron stars using an iterative numerical method. Working in Newtonian framework we assume that the neutron star has two regions: the core, which is modelled as a two-component fluid consisting of type-II superconducting protons and superfluid neutrons, and the crust, a region composed of normal matter. Taking a new step towards more complete equilibrium models, we include the effect of entrainment, which implies that a magnetic force acts on neutrons, too. We consider purely poloidal field cases and present improvements to an e…
We calculate the spectrum of inertial oscillation modes in a slowly rotating superfluid neutron star, including, for the first time, both the effects of finite temperatures and entrainment between superfluid neutrons and protons. We work in the Newtonian limit and assume minimal core composition (neutrons, protons and electrons). We also developed an approximate method that allows one to calculate the superfluid r-mode analytically. Finally, we derive and analyze dispersion relations for inertial modes in the superfluid NS matter in the short wavelength limit.
Pulsar glitches are traditionally viewed as a manifestation of vortex dynamics associated with a neutron superfluid reservoir confined to the inner crust of the star. In this Letter we show that the non-dissipative entrainment coupling between the neutron superfluid and the nuclear lattice leads to a less mobile crust superfluid, effectively reducing the moment of inertia associated with the angular momentum reservoir. Combining the latest observational data for prolific glitching pulsars with theoretical results for the crust entrainment we find that the required superfluid reservoir exceeds …
We study the effects of an elastic crust on the oscillation spectrum of superfluid neutron stars. Within the two fluid formalism, we consider Newtonian stellar models that include the relevant constituents of a mature neutron stars. The core is formed by a mixture of superfluid neutrons and a conglomerate of charged particles, while the inner crust is described by a lattice of nuclei permeated by superfluid neutrons. We linearise the Poisson and the conservation equations of nonrotating superfluid stars and study the effects of elasticity, entrainment and composition stratification on the shea…
Building on a recently improved understanding of the problem of heat flow in general relativity, we develop a hydrodynamical model for coupled finite temperature superfluids. The formalism is designed with the dynamics of the outer core of a mature neutron star (where superfluid neutrons are coupled to a conglomerate of protons and electrons) in mind, but the main ingredients are relevant for a range of analogous problems. The entrainment between material fluid components (the condensates) and the entropy (the thermal excitations) plays a central role in the development. We compare and contras…
We study the effects of finite stellar temperatures on the oscillations of superfluid neutron stars. The importance of these effects is illustrated with a simple example of a radially pulsating general relativistic star. Two main effects are taken into account: (i) temperature dependence of the entrainment matrix and (ii) the variation of the size of superfluid region with temperature. Four models are considered, which include either one or both of these two effects. Pulsation spectra are calculated for these models, and asymptotes for eigenfrequencies at temperatures close to critical tempera…
We study two-fluid systems with nonzero fluid velocities and compute their sound modes, which indicate various instabilities. For the case of two zero-temperature superfluids we employ a microscopic field-theoretical model of two coupled bosonic fields, including an entrainment coupling and a non-entrainment coupling. We analyse the onset of the various instabilities systematically and point out that the dynamical two-stream instability can only occur beyond Landau's critical velocity, i.e., in an already energetically unstable regime. A qualitative difference is found for the case of two norm…
