Superfluid Dynamics in Neutron Star Crusts

Measurement of the superfluid fraction of a supersolid by Josephson effect

A new class of superfluids and superconductors with spatially periodic modulation of the superfluid density is arising1-12. It might be related to the supersolid phase of matter, in which the spontaneous breaking of gauge and translational symmetries leads to a spatially modulated macroscopic wavefunction13-16. This relation was recognized only in some cases1,2,5-9 and there is the need for a universal property quantifying the differences between supersolids and ordinary matter, such as the superfluid fraction, which measures the reduction in superfluid stiffness resulting from the spatial modulation16-18. The superfluid fraction was introduced long ago16, but it has not yet been assessed experimentally. Here we demonstrate an innovative method to measure the superfluid fraction based on the Josephson effect, a ubiquitous phenomenon associated with the presence of a physical barrier between two superfluids or superconductors19, which might also be expected for supersolids20, owing to the spatial modulation. We demonstrate that individual cells of a supersolid can sustain Josephson oscillations and we show that, from the current-phase dynamics, we can derive directly the superfluid fraction. Our study of a cold-atom dipolar supersolid7 reveals a relatively large sub-unity superfluid fraction that makes realistic the study of previously unknown phenomena such as partially quantized vortices and supercurrents16-18. Our results open a new direction of research that may unify the description of all supersolid-like systems.

A hybrid GNA instability

A semi-analytic admixed model formalism to study the stability effects of the inner crust regions against the local collective perturbations in non-rotating neutron stars is proposed. It consists of the viscoelastic heavy neutron-rich nuclei, superfluid neutrons, and degenerate quantum electrons. A normal spherical mode analysis yields a generalized linear dispersion relation multiparametrically mimicking the inner crust features of neutron stars. A hybrid gravito-nucleo-acoustic (GNA) instability mode is found to be excited. It is demonstrated that the electron density and the inner crust curvature act as its accelerating and antidispersive agents. In contrast, the heavy neutron-rich nucleus and neutron densities act as decelerating factors. The heavy nucleus density, electron density, and geometric curvature act as its destabilizers. It is only the neutron density that acts as the GNA stabilizing agent. The heavy neutron-rich nucleus and neutron densities are found to act as dispersive broadening factors to it. The high-[Formula: see text] regions are the more unstable spectral windows indicating that the GNA mode plays a dominant role in the inner crust zone towards the local stability. Its fair reliability is indicated in light of the recent astronomic observed scenarios. It could be useful to explore acoustic mode signatures in non-rotating neutron stars and similar other compact astroobjects.

A Superfluid Perspective on Neutron Star Dynamics

As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometre or so is expected to freeze to form an elastic crust of increasingly neutron-rich nuclei, coexisting with a superfluid neutron component, while the star’s fluid core contains a mixed superfluid/superconductor. The dynamics of the star depend heavily on the parameters associated with the different phases. The presence of superfluidity brings new degrees of freedom—in essence we are dealing with a complex multi-fluid system—and additional features: bulk rotation is supported by a dense array of quantised vortices, which introduce dissipation via mutual friction, and the motion of the superfluid is affected by the so-called entrainment effect. This brief survey provides an introduction to—along with a commentary on our current understanding of—these dynamical aspects, paying particular attention to the role of entrainment, and outlines the impact of superfluidity on neutron-star seismology.

Thermodynamically Consistent Equation of State for an Accreted Neutron Star Crust

We study the equation of state (EOS) of an accreting neutron star crust. Usually, such an EOS is obtained by assuming (implicitly) that the free (unbound) neutrons and nuclei in the inner crust move together. We argue that this assumption violates the condition μ_{n}^{∞}=const, required for hydrostatic (and diffusion) equilibrium of unbound neutrons (μ_{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 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 the fully accreted crust that transforms nuclei into homogeneous nuclear matter. It guarantees that the structure of the fully accreted crust remains self-similar during accretion.

Probing the equation of state of nuclear matter via neutron star asteroseismology

We general-relativistically calculate the frequency of fundamental torsional oscillations of neutron star crusts, where we focus on the crystalline properties obtained from macroscopic nuclear models in a way that is dependent on the equation of state of nuclear matter. We find that the calculated frequency is sensitive to the density dependence of the symmetry energy, but almost independent of the incompressibility of symmetric nuclear matter. By identifying the lowest-frequency quasiperiodic oscillation in giant flares observed from soft gamma-ray repeaters as the fundamental torsional mode and allowing for the dependence of the calculated frequency on stellar models, we provide a lower limit of the density derivative of the symmetry energy as L≃50  MeV.