arXiv subjects

G. L. Comer

Publications and source records attributed to G. L. Comer.

At least 37 records · Page 2Linked to original sources

arXiv2009

Relativistic Two-stream Instability

We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This instability requires a relative flow -- either across an interface or when two or more fluids interpenetrate -- and can be triggered, for example, when one-dimensional plane-waves appear to be left-moving with respect to one fluid, but right-moving with respect to another. The dispersion relation of the two-fluid system is studied for different two-fluid equations of state: (i) the "free" (where there is no direct coupling between the fluid densities), (ii) coupled, and (iii) entrained (where the fluid momenta are linear combinations of the velocities) cases are considered in a frame-independent fashion (eg. no restriction to the rest-frame of either fluid). As a by-product of our analysis we determine the necessary conditions for a two-fluid system to be causal and absolutely stable and establish a new constraint on the entrainment.

gr-qc↗

arXiv2007

Oscillations of General Relativistic Multi-fluid/Multi-layer Compact Stars

We develop the formalism for determining the quasinormal modes of general relativistic multi-fluid compact stars in such a way that the impact of superfluid gap data can be assessed. Our results represent the first attempt to study true multi-layer dynamics, an important step towards considering realistic superfluid/superconducting compact stars. We combine a relativistic model for entrainment with model equations of state that explicity incorporate the symmetry energy. Our analysis emphasises the many different parameters that are required for this kind of modelling, and the fact that standard tabulated equations of state are grossly incomplete in this respect. To make progress, future equations of state need to provide the energy density as a function of the various nucleon number densities, the temperature (i.e. entropy), and the entrainment among the various components.

gr-qc↗

arXiv2007

Waves and instabilities in dissipative rotating superfluid neutron stars

We discuss wave propagation in rotating superfluid neutron star cores, taking into account the vortex mediated mutual friction force. For models where the two fluids co-rotate in the unperturbed state, our analysis clarifies the role of chemical coupling and entrainment for sound and inertial waves. We also investigate the mutual friction damping, providing results that demonstrate the well-known fact that sound waves propagating along a vortex array are undamped. We show that the same is not true for inertial waves, which are damped by the mutual friction regardless of the propagation direction. We then include the vortex tension, which arises due to local vortex curvature. Focussing on purely transverse inertial waves, we derive the small correction that the tension induces in the wave frequency. Finally, we allow for a relative linear flow in the background (along the rotation axis). In this case we show how the mutual friction coupling may induce a dynamical instability in the inertial waves. We discuss the critical flow required for the instability to be present, its physical interpretation and the possible relevance it may have for neutron star physics.

astro-ph↗

arXiv2007

Superfluid neutron star turbulence

We analyse the implications of superfluid turbulence for neutron star physics. We begin by extending our previous results for the mutual friction force for a straight vortex array to account for the self-induced flow which arises when the vortices are curved. We then discuss Vinen's phenomenological model for isotropic turbulence, and derive the associated (Gorter-Mellink) form for the mutual friction. We compare this derivation to a more recent analysis of Schwarz, which sheds light on various involved issues. Having discussed isotropic turbulence, we argue that this case is unlikely to be relevant for neutron stars. Instead we expect a rotating neutron star to exhibit polarised turbulence, where relative flow drives the turbulence and rotation counteracts it. Based on recent results for superfluid Helium, we construct a phenomenological model that should have the key features of such a polarised turbulent system.

astro-ph↗

arXiv2006

Relativistic Fluid Dynamics: Physics for Many Different Scales

The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process, an understanding of bulk features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as ``small'' as heavy ions in collisions, and as large as the universe itself, with ``intermediate'' sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multiple) fluid model. We focus on the variational principle approach championed by Brandon Carter and his collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the ``standard'' text-book derivation of the equations of motion from the divergence of the stress-energy tensor, in that one explicitly obtains the relativistic Euler equation as an ``integrability'' condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory.

gr-qc↗

arXiv2005

Mutual Friction in Superfluid Neutron Stars

We discuss vortex-mediated mutual friction in the two-fluid model for superfluid neutron star cores. Our discussion is based on the general formalism developed by Carter and collaborators, which makes due distinction between transport velocity and momentum for each fluid. This is essential for an implementation of the so-called entrainment effect, whereby the flow of one fluid imparts momentum in the other and vice versa. The mutual friction follows by balancing the Magnus force that acts on the quantised neutron vortices with a resistive force due to the scattering of electrons off of the magnetic field with which each vortex core is endowed. We derive the form of the macroscopic mutual friction force which is relevant for a model based on smooth-averaging over a collection of vortices. We discuss the coefficients that enter the expression for this force, and the timescale on which the two interpenetrating fluids in a neutron star core are coupled. This discussion confirms that our new formulation accords well with previous work in this area.

astro-ph↗

arXiv2005

A Flux-Conservative Formalism for Convective and Dissipative Multi-Fluid Systems, with Application to Newtonian Superfluid Neutron Stars

We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of mass, energy, and linear and angular momentum conservation to specify the equations of motion. Also used extensively are insights gleaned from a convective variational action principle, key being the distinction between each velocity and its canonically conjugate momentum. Dissipation is incorporated to second order in the ``thermodynamic forces'' via the approach pioneered by Onsager. An immediate goal of the investigation is to understand better the number, and form, of independent dissipation terms required for a consistent set of equations of motion in the multi-fluid context. A significant, but seemingly innocuous detail, is that one must be careful to isolate ``forces'' that can be written as total gradients, otherwise errors can be made in relating the net internal force to the net externally applied force. Our long-range aim is to provide a formalism that can be used to model dynamical multi-fluid systems both perturbatively and via fully nonlinear 3D numerical evolutions. To elucidate the formalism we consider the standard model for a heat-conducting, superfluid neutron star, which is believed to be dominated by superfluid neutrons, superconducting protons, and a highly degenerate, ultra-relativistic gas of normal fluid electrons. We determine that in this case there are, in principle, 19 dissipation coefficients in the final set of equations.

physics.flu-dyn↗

arXiv2005

3+1 Approach to the Long Wavelength Iteration Scheme

Large-scale inhomogeneities and anisotropies are modeled using the Long Wavelength Iteration Scheme. In this scheme solutions are obtained as expansions in spatial gradients, which are taken to be small. It is shown that the choice of foliation for spacetime can make the iteration scheme more effective in two respects: (i) the shift vector can be chosen so as to dilute the effect of anisotropy on the late-time value of the extrinsic curvature of the spacelike hypersurfaces of the foliation; and (ii) pure gauge solutions present in a similar calculation using the synchronous gauge vanish when the spacelike hypersurfaces have extrinsic curvature with constant trace. We furthermore verify the main conclusion of the synchronous gauge calculation which is large-scale inhomogeneity decays if the matter--considered to be that of a perfect-fluid with a barotropic equation of state--violates the strong-energy condition. Finally, we obtain the solution for the lapse function and discuss its late-time behaviour. It is found that the lapse function is well-behaved when the matter violates the strong energy condition.

hep-th↗

arXiv2005

Superfluid Analog of the Davies-Unruh Effect

We produce an analog of the Davies-Unruh effect for superfluid helium four. There are two temperatures which result--one is associated with ordinary, or first, sound and the other with second sound.

gr-qc↗

arXiv2005

How viscous is a superfluid neutron star core?

We discuss the effects of superfluidity on the shear viscosity in a neutron star core. Our study combines existing theoretical results for the viscosity coefficients with data for the various superfluid energy gaps into a consistent description. In particular, we provide a simple model for the electron viscosity which is relevant both when the protons form a normal fluid and when they become superconducting. This model explains in a clear way why proton superconductivity leads to a significant strengthening of the shear viscosity. We present our results in a form which permits the use of data for any given modern equation of state (our final formulas are explicitly dependent on the proton fraction). We discuss a simple description of the relevant superfluid pairing gaps, and construct a number of models (spanning the range of current uncertainty) which are then used to discuss the superfluid suppression of shear viscosity. We conclude by a discussion of a number of challenges that must be met if we are to make further progress in this area of research.

astro-ph↗

arXiv2005

Relativistic numerical models for stationary superfluid Neutron Stars

We have developed a theoretical model and a numerical code for stationary rotating superfluid neutron stars in full general relativity. The underlying two-fluid model is based on Carter's covariant multi-fluid hydrodynamic formalism. The two fluids, representing the superfluid neutrons on one hand, and the protons and electrons on the other, are restricted to uniform rotation around a common axis, but are allowed to have different rotation rates. We have performed extensive tests of the numerical code, including quantitative comparisons to previous approximative results for these models. The results presented here are the first ``exact'' calculations of such models in the sense that no approximations (other than that inherent in a discretized numerical treatment) are used. Using this code we reconfirm the existence of prolate-oblate shaped configurations. We studied the dependency of the Kepler rotation limit and of the mass-density relation on the relative rotation rate. We further demonstrate how one can simulate a (albeit fluid) neutron-star ``crust'' by letting one fluid extend further outwards than the other, which results in interesting cases where the Kepler limit is actually determined by the outermost but slower fluid.

gr-qc↗

arXiv2004

Lagrangian perturbation theory of nonrelativistic rotating superfluid stars

We develop a Lagrangian perturbation framework for rotating non-relativistic superfluid neutron stars. This leads to the first generalization of classic work on the stability properties of rotating stars to models which account for the presence of potentially weakly coupled superfluid components. Our analysis is based on the standard two-fluid model expected to be relevant for the conditions that prevail in the outer core of mature neutron stars. We discuss the implications of our results for dynamical and secular instabilities of a simple neutron star model in which the two fluids are allowed to assume different (uniform) rotation rates.

astro-ph↗

arXiv2004

Slowly Rotating General Relativistic Superfluid Neutron Stars with Relativistic Entrainment

Neutron stars that are cold enough should have two or more superfluids/supercondutors in their inner crusts and cores. The implication of superfluidity/superconductivity for equilibrium and dynamical neutron star states is that each individual particle species that forms a condensate must have its own, independent number density current and equation of motion that determines that current. An important consequence of the quasiparticle nature of each condensate is the so-called entrainment effect, i.e. the momentum of a condensate is a linear combination of its own current and those of the other condensates. We present here the first fully relativistic modelling of slowly rotating superfluid neutron stars with entrainment that is accurate to the second-order in the rotation rates. The stars consist of superfluid neutrons, superconducting protons, and a highly degenerate, relativistic gas of electrons. We use a relativistic $σ$ - $ω$ mean field model for the equation of state of the matter and the entrainment. We determine the effect of a relative rotation between the neutrons and protons on a star's total mass, shape, and Kepler, mass-shedding limit.

gr-qc↗

arXiv2003

Inertial modes of non-stratified superfluid neutron stars

We present results concerning adiabatic inertial-mode oscillations of non-stratified superfluid neutron stars in Newtonian gravity, using the anelastic and slow-rotation approximations. We consider a simple two-fluid model of a superfluid neutron star, where one fluid consists of the superfluid neutrons and the second fluid contains all the comoving constituents (protons, electrons). The two fluids are assumed to be ``free'' in the sense that vortex-mediated forces like mutual friction or pinning are absent, but they can be coupled by the equation of state, in particular by entrainment. The stationary background consists of the two fluids rotating uniformly around the same axis with potentially different rotation rates. We study the special cases of co-rotating backgrounds, vanishing entrainment, and the purely toroidal r-modes, analytically. We calculate numerically the eigenfunctions and frequencies of inertial modes in the general case of non co-rotating backgrounds, and study their dependence on the relative rotation rate and entrainment. In these non-stratified models we find avoided crossings only between associated mode-pairs, eg. an ``ordinary'' mode and its ``superfluid'' counterpart, while other mode-frequencies generally cross as the background parameters are varied. We confirm (for the first time in a mode calculation) the onset of a ``two-stream instability'' at a critical relative background rotation rate, and study some of the properties of this instability for the inertial modes.

astro-ph↗

arXiv2002

A Relativistic Mean Field Model for Entrainment in General Relativistic Superfluid Neutron Stars

General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic $σ- ω$ mean field model for the nucleons and their interactions. In this context there are two notions of ``relativistic'': relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro's number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly-rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.

gr-qc↗

arXiv2002

Stationary structure of relativistic superfluid neutron stars

We describe recent progress in the numerical study of the structure of rapidly rotating superfluid neutron star models in full general relativity. The superfluid neutron star is described by a model of two interpenetrating and interacting fluids, one representing the superfluid neutrons and the second consisting of the remaining charged particles (protons, electrons, muons). We consider general stationary configurations where the two fluids can have different rotation rates around a common rotation axis. The previously discovered existence of configurations with one fluid in a prolate shape is confirmed.

gr-qc↗

arXiv2002

The superfluid two-stream instability and pulsar glitches

This paper provides the first study of a new dynamical instability in superfluids. This instability is similar to the two-stream instability known to operate in plasmas. It is analogous to the Kelvin-Helmholtz instability, but has the distinguishing feature that the two fluids are interpenetrating. The instability sets in once the relative flow between the two components of the system reaches a critical level. Our analysis is based on the two-fluid equations that have been used to model the dynamics of the outer core of a neutron star, where superfluid neutrons are expected to coexist with superconducting protons and relativistic electrons. These equations are analogous to the standard Landau model for superfluid Helium. We study this instability for two different model problems. First we analyze a local dispersion relation for waves in a system where one fluid is at rest while the other flows at a constant rate. This provides a proof of principle of the existence of the two-stream instability for superfluids. Our second model problem concerns two rotating fluids confined within an infinitesimally thin spherical shell. The aim of this model is to assess whether the two-stream instability may be relevant (perhaps as a trigger mechanism) for pulsar glitches. Our results for this problem show that the entrainment effect could provide a sufficiently strong coupling for the instability to set in at a relative flow small enough to be astrophysically plausible.

astro-ph↗

arXiv2002

Are pulsar glitches triggered by a superfluid two-stream instability?

Mature neutron stars are expected to have several superfluid components. Strong evidence for this is provided by the glitches that have been observed in dozens of pulsars. The underlying idea behind most glitch models is that, as the neutron star crust spins down due to the emission of electromagnetic radiation, the superfluid component lags behind until a critical point is reached and angular momentum is transferred from the superfluid to the crust, leading to the spin-up associated with the glitch. In this Letter we describe a superfluid analogue of the two-stream instability that is well known in plasma physics, and provide evidence that this instability is likely to be relevant for neutron stars. This is a new physical mechanism which may play a key role in explaining the glitch mechanism and which could also prove to be relevant in laboratory experiments on superfluid Helium.

astro-ph↗