Pinning of superfluid vortices to magnetic flux tubes in the outer core of a neutron star supports a velocity difference of $\sim 10^5$ \cms\ between the neutron superfluid and the proton-electron fluid as the star spins down. Under the Magnus force that arises on the vortex array, vortices undergo {\em vortex creep} through thermal activation or quantum tunneling. We examine the hydrodynamic stability of this situation. Vortex creep introduces two low-frequency modes, one of which is unstable above a critical wavenumber for any non-zero flow velocity of the neutron superfluid with respect to the charged fluid. For typical pinning parameters of the outer core, the superfluid flow is unstable over wavelengths $λ\lap 10$ m and over timescales of $\sim (λ/{1 m})^{1/2}$ yr down to $\sim 1$ d. The vortex lattice could degenerate into a tangle, and the superfluid flow would become turbulent. We suggest that superfluid turbulence could be responsible for the red timing noise seen in many neutron stars, and find a predicted spectrum that is generally consistent with observations.
Pinning of superfluid vortices to the nuclear lattice of the inner crust of a neutron star supports a velocity difference between the superfluid and the solid as the star spins down. Under the Magnus force that arises on the vortex lattice, vortices undergo {\em vortex creep} through thermal activation or quantum tunneling. We examine the hydrodynamic stability of this situation. Vortex creep introduces two low-frequency modes, one of which is unstable above a critical wavenumber for any non-zero flow velocity of the superfluid with respect to the solid. For typical pinning parameters of the i…
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 investigate dynamical coupling timescales of a neutron star's superfluid core, taking into account the interactions of quantized neutron vortices with quantized flux lines of the proton superconductor in addition to the previously considered scattering of the charged components against the spontaneous magnetization of the neutron vortex line. We compare the cases where vortex motion is constrained in different ways by the array of magnetic flux tubes associated with superconducting protons. This includes absolute pinning to and creep across a uniform array of flux lines. The effect of a tor…
Mature neutron stars are cold enough to contain a number of superfluid and superconducting components. These systems are distinguished by the presence of additional dynamical degrees of freedom associated with superfluidity. In order to consider models with mixtures of condensates we need to develop a multifluid description that accounts for the presence of rotational neutron vortices and magnetic proton fluxtubes. We also need to model the forces that impede the motion of vortices and fluxtubes, and understand how these forces act on the condensates. This paper concerns the development of suc…
According to recent results of Ho & Heinke (2009) and Heinke & Ho (2010), the Cassiopeia A supernova remnant contains a young neutron star which has carbon atmosphere and shows noticeable decline of the effective surface temperature. We report a new (November 2010) Chandra observation which confirms the previously reported decline rate. The decline is naturally explained if neutrons have recently become superfluid (in triplet-state) in the NS core, producing a splash of neutrino emission due to Cooper pair formation (CPF) process that currently accelerates the cooling. This scenario puts strin…
Experimental and numerical evidence is reviewed for the existence of a Stewartson layer in spherical Couette flow at small Ekman and Rossby numbers ($\Ek \lsim 10^{-3}$, $\Ro \lsim 10^{-2}$), the relevant hydrodynamic regime in the superfluid outer core of a neutron star. Numerical simulations of a superfluid Stewartson layer are presented for the first time, showing how the layer is disrupted by nonaxisymmetric instabilities. The unstable ranges of $\Ek$ and $\Ro$ are compared with estimates of these quantities in radio pulsars that exhibit glitches. It is found that glitching pulsars lie on …
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.
We analyze how recent computations of the shear viscosity $η$ in the core of superfluid neutron stars affect the r-mode instability window. We first analyze the contribution of superfluid phonons to the viscosity, both in their hydrodynamical and ballistic regime. We also consider the recent computation of $η$ arising from the collisions of electrons with electrons and protons by Shternin and Yakovlev, and discuss how the interactions among superfluid phonons and electrons might contribute to the shear viscosity. For assessing the r-mode instability window we compare the shear viscosity due to…
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…
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.
The inner crust of mature neutron stars, where an elastic lattice of neutron-rich nuclei coexists with a neutron superfluid, impacts on a range of astrophysical phenomena. The presence of the superfluid is key to our understanding of pulsar glitches, and is expected to affect the thermal conductivity and hence the evolution of the surface temperature. The coupling between crust and superfluid must also be accounted for in studies of neutron star dynamics, discussions of global oscillations and associated instabilities. In this paper we develop Lagrangian perturbation theory for this problem, p…
Superfluid hydrodynamics affects the spin-evolution of mature neutron stars, and may be key to explaining timing irregularities such as pulsar glitches. However, most models for this phenomenon exclude the global instability required to trigger the event. In this paper we discuss a mechanism that may fill this gap. We establish that small scale inertial r-modes become unstable in a superfluid neutron star that exhibits a rotational lag, expected to build up due to vortex pinning as the star spins down. Somewhat counterintuitively, this instability arises due to the (under normal circumstances …
We show that equations governing pulsations of superfluid neutron stars can be splitted into two sets of weakly coupled equations, one describing the superfluid modes and another one -- the normal modes. The coupling parameter s is small, |s| ~ 0.01-0.05, for realistic equations of state. Already an approximation s=0 is sufficient to calculate the pulsation spectrum within the accuracy of a few percents. Our results indicate, in particular, that emission of gravitational waves from superfluid pulsation modes is suppressed in comparison to that from normal modes. The proposed approach allows to…
The linear response of a superfluid neutron liquid onto external vector field is studied for the case of $^{3}P_{2}-\,^{3}F_{2}$ pairing. The consideration is limited to the case when the wave-length of the perturbation is large as compared to the coherence length in the superfluid matter and the transferred energy is small in comparison with the gap amplitude. The obtained results are used to analyse the collisionless phonon-like excitations of the condensate of superfluid neutrons. In particular, we analyze the case of neutron condensation into the state with $m_{j}=0$ which is conventionall…
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 show that suppression of the baryon energy gaps, caused by the relative motion of superfluid and normal liquid components, can substantially influence dynamical properties and evolution of neutron stars. This effect has been previously ignored in the neutron-star literature.
In a simple model it is demonstrated that the neutron star surface temperature evolution is sensitive to the phase state of the triplet superfluid condensate. A multicomponent triplet pairing of superfluid neutrons in the core of a neutron star with participation of several magnetic quantum numbers leads to neutrino energy losses exceeding the losses from the unicomponent pairing. A phase transition of the neutron condensate into the multicomponent state triggers more rapid cooling of superfluid core in neutron stars. This makes it possible to simulate an anomalously rapid cooling of neutron s…
The supernova remnant Cassiopeia A contains the youngest known neutron star which is also the first one for which real time cooling has ever been observed. In order to explain the rapid cooling of this neutron star, we first present the fundamental properties of neutron stars that control their thermal evolution with emphasis on the neutrino emission processes and neutron/proton superfluidity/superconductivity. Equipped with these results, we present a scenario in which the observed cooling of the neutron star in Cassiopeia A is interpreted as being due to the recent onset of neutron superflui…
For the first time nonradial oscillations of superfluid nonrotating 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 superfluid intermediate region. We show, that oscillation spectra contain a set of modes whose frequencies can be very sensitive to temperature variations. Fast temporal evol…
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 t…
We demonstrate a possibility of existence of a peculiar temperature-dependent composition $g$-modes in superfluid neutron stars. We calculate the Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ frequency for these modes, as well as their eigenfrequencies. The latter turn out to be rather large, up to $\sim 500$ Hz for a chosen model of a neutron star. This result indicates, in particular, that use of the barotropic equation of state may be not a good approximation for calculation of inertial modes even in most rapidly rotating superfluid neutron stars.
We present recent work on using astronomical observations of neutron stars to reveal unique insights into nuclear matter that cannot be obtained from laboratories on Earth. First, we discuss our measurement of the rapid cooling of the youngest neutron star in the Galaxy; this provides the first direct evidence for superfluidity and superconductivity in the supra-nuclear core of neutron stars. We show that observations of thermonuclear X-ray bursts on neutron stars can be used to constrain properties of neutron superfluidity and neutrino emission. We describe the implications of rapid neutron s…
Neutron stars accreting matter from low-mass binary companions are observed to undergo bursts of X-rays due to the thermonuclear explosion of material on the neutron star surface. We use recent results on superfluid and superconducting properties to show that the core temperature in these neutron stars may not be uniquely determined for a range of observed accretion rates. The degeneracy in inferred core temperatures could contribute to explaining the difference between neutron stars which have very short recurrence times between multiple bursts and those which have long recurrence times betwe…
We study the shear and bulk viscosity coefficients as well as the thermal conductivity as arising from the collisions among phonons in superfluid neutron stars. We use effective field theory techniques to extract the allowed phonon collisional processes, written as a function of the equation of state and the gap of the system. The shear viscosity due to phonon scattering is compared to calculations of that coming from electron collisions. We also comment on the possible consequences for r-mode damping in superfluid neutron stars. Moreover, we find that phonon collisions give the leading contri…
The linear response of a neutron spin-triplet superfluid onto external weak axial-vector field is studied for the case of $^{3}P_{2}$ pairing with a projection of the total angular momentum $m_{j}=0$. The problem is considered in the BCS approximation discarding Fermi-liquid effects. The anomalous axial-vector vertices of neutron quasiparticles possess singularities at some frequencies which specify existence of undamped spin-density waves in the Cooper condensate. The spin waves are of a low excitation energy and are kinematically able to decay into neutrino pairs through neutral weak current…
We compute the contribution of phonons to the thermal conductivity in the core of superfluid neutron stars. We use effective field theory techniques to extract the phonon scattering rates, written as a function of the equation of state of the system. We also calculate the phonon dispersion law beyond linear order, which depends on the gap of superfluid neutron matter. With all these ingredients, we solve the Boltzmann equation numerically using a variational approach. We find that the thermal conductivity $κ$ is dominated by combined small and large angle binary collisions. As in the color-fla…
We present a quantitative analysis of superfluidity and superconductivity in dense matter from observations of isolated neutron stars in the context of the minimal cooling model. Our new approach produces the best fit neutron triplet superfluid critical temperature, the best fit proton singlet superconducting critical temperature, and their associated statistical uncertainties. We find that the neutron triplet critical temperature is likely $2.09^{+4.37}_{-1.41} \times 10^{8}$ K and that the proton singlet critical temperature is $7.59^{+2.48}_{-5.81} \times 10^{9}$ K. However, we also show th…
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…
Force on proton vortices in superfluid and superconducting matter of neutron stars is calculated at vanishing stellar temperature. Both longitudinal (dissipative) and transverse (Lorentz-type) components of the force are derived in a coherent way and compared in detail with the corresponding expressions available in the literature. This allows us to resolve a controversy about the form of the Lorentz-type force component acting on proton vortices. The calculated force is a key ingredient in magnetohydrodynamics of superconducting neutron stars and is important for modeling the evolution of ste…
We study non-radial oscillations of neutron stars with superfluid baryons, in a general relativistic framework, including finite temperature effects. Using a perturbative approach, we derive the equations describing stellar oscillations, which we solve by numerical integration, employing different models of nucleon superfluidity, and determining frequencies and gravitational damping times of the quasi-normal modes. As expected by previous results, we find two classes of modes, associated to superfluid and non-superfluid degrees of freedom, respectively. We study the temperature dependence of t…
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…
The eigen mode of spin oscillations with $ω\simeq \sqrt{58/35}Δ$ is predicted to exist besides already known spin waves with $ω\simeqΔ/\sqrt{5}$ in the triplet superfluid neutron condensate in the inner core of neutron stars. The new mode is kinematically able to decay into neutrino pairs through neutral weak currents. The problem is considered in BCS approximation for the case of $^{3}P_{2}-^{3}F_{2}$ pairing with a projection of the total angular momentum $m_{j}=0$ which is conventionally considered as preferable one at supernuclear densities.
We analyze damping of oscillations of general relativistic superfluid neutron stars. To this aim we extend the method of decoupling of superfluid and normal oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R) (2011)]. All calculations are made self-consistently within the finite temperature superfluid hydrodynamics. The general analytic formulas are derived for damping times due to the shear and bulk viscosities. These formulas describe both normal and superfluid neutron stars and are valid for oscillation modes of arbitrary multipolarity. We show that: (i) use of the ordi…
We formulate a low energy effective theory describing phases of matter that are both solid and superfluid. These systems simultaneously break translational symmetry and the phase symmetry associated with particle number. The symmetries restrict the combinations of terms that can appear in the effective action and the lowest order terms featuring equal number of derivatives and Goldstone fields are completely specified by the thermodynamic free energy, or equivalently by the long-wavelength limit of static correlation functions in the ground state. We show that the underlying interaction betwee…
We study transport properties of a strongly interacting superfluid mixture of two Fermi-liquids. A typical example of such matter is the neutron-proton liquid in the cores of neutron stars. To describe the mixture, we employ the Landau theory of Fermi-liquids, generalized to allow for the effects of superfluidity. We formulate the kinetic equation and analyze linear response of the system to vector (e.g., electromagnetic) perturbation. In particular, we calculate the transverse and longitudinal polarization functions for both liquid components. We demonstrate, that they can be expressed throug…
