Superfluid instability of r-modes in "differentially rotating" neutron stars

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 dissipative) vortex-mediated mutual friction. We explore the nature of the superfluid instability for a simple incompressible model, allowing for entrainment coupling between the two fluid components. Our results recover a previously discussed dynamical instability in systems where the two components are strongly coupled. In addition, we demonstrate for the first time that the system is secularly unstable (with a growth time that scales with the mutual friction) throughout much of parameter space. Interestingly, large scale r-modes are also affected by this new aspect of the instability. We analyse the damping effect of shear viscosity, which should be particularly efficient at small scales, arguing that it will not be sufficient to completely suppress the instability in astrophysical systems.Comment: RevTex, 11 figure

Advective collisions

Small particles advected in a fluid can collide (and therefore aggregate) due to the stretching or shearing of fluid elements. This effect is usually discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1, 16-30, (1956)]. We show that in complex or random flows the Saffman-Turner theory for the collision rate describes only an initial transient (which we evaluate exactly). We obtain precise expressions for the steady-state collision rate for flows with small Kubo number, including the influence of fractal clustering on the collision rate for compressible flows. For incompressible turbulent flows, where the Kubo number is of order unity, the Saffman-Turner theory is an upper bound.Comment: 4 pages, 1 figur

The dynamics of dissipative multi-fluid neutron star cores

We present a Newtonian multi-fluid formalism for superfluid neutron star cores, focussing on the additional dissipative terms that arise when one takes into account the individual dynamical degrees of freedom associated with the coupled "fluids". The problem is of direct astrophysical interest as the nature of the dissipative terms can have significant impact on the damping of the various oscillation modes of the star and the associated gravitational-wave signatures. A particularly interesting application concerns the gravitational-wave driven instability of f- and r-modes. We apply the developed formalism to two specific three-fluid systems: (i) a hyperon core in which both Lambda and Sigma^- hyperons are present, and (ii) a core of deconfined quarks in the colour-flavour-locked phase in which a population of neutral K^0 kaons is present. The formalism is, however, general and can be applied to other problems in neutron-star dynamics (such as the effect of thermal excitations close to the superfluid transition temperature) as well as laboratory multi-fluid systems.Comment: RevTex, no figure

Non-adiabatic holonomic quantum computation

We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $\Lambda$ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.Comment: Some changes, journal reference adde

R-mode oscillations and rocket effect in rotating superfluid neutron stars. I. Formalism

We derive the hydrodynamical equations of r-mode oscillations in neutron stars in presence of a novel damping mechanism related to particle number changing processes. The change in the number densities of the various species leads to new dissipative terms in the equations which are responsible of the {\it rocket effect}. We employ a two-fluid model, with one fluid consisting of the charged components, while the second fluid consists of superfluid neutrons. We consider two different kind of r-mode oscillations, one associated with comoving displacements, and the second one associated with countermoving, out of phase, displacements.Comment: 10 page

The Cosmological Time Function

Let $(M,g)$ be a time oriented Lorentzian manifold and $d$ the Lorentzian distance on $M$. The function $\tau(q):=\sup_{p< q} d(p,q)$ is the cosmological time function of $M$, where as usual $p< q$ means that $p$ is in the causal past of $q$. This function is called regular iff $\tau(q) < \infty$ for all $q$ and also $\tau \to 0$ along every past inextendible causal curve. If the cosmological time function $\tau$ of a space time $(M,g)$ is regular it has several pleasant consequences: (1) It forces $(M,g)$ to be globally hyperbolic, (2) every point of $(M,g)$ can be connected to the initial singularity by a rest curve (i.e., a timelike geodesic ray that maximizes the distance to the singularity), (3) the function $\tau$ is a time function in the usual sense, in particular (4) $\tau$ is continuous, in fact locally Lipschitz and the second derivatives of $\tau$ exist almost everywhere.Comment: 19 pages, AEI preprint, latex2e with amsmath and amsth

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.Comment: 15 pages, 2 eps-figure

Gravitational-wave astronomy: the high-frequency window

This contribution is divided in two parts. The first part provides a text-book level introduction to gravitational radiation. The key concepts required for a discussion of gravitational-wave physics are introduced. In particular, the quadrupole formula is applied to the anticipated ``bread-and-butter'' source for detectors like LIGO, GEO600, EGO and TAMA300: inspiralling compact binaries. The second part provides a brief review of high frequency gravitational waves. In the frequency range above (say) 100Hz, gravitational collapse, rotational instabilities and oscillations of the remnant compact objects are potentially important sources of gravitational waves. Significant and unique information concerning the various stages of collapse, the evolution of protoneutron stars and the details of the supranuclear equation of state of such objects can be drawn from careful study of the gravitational-wave signal. As the amount of exciting physics one may be able to study via the detections of gravitational waves from these sources is truly inspiring, there is strong motivation for the development of future generations of ground based detectors sensitive in the range from hundreds of Hz to several kHz.Comment: 21 pages, 5 figures, Lectures presented at the 2nd Aegean Summer School on the Early Universe, Syros, Greece, September 200

Quark-Gluon-Plasma Formation at SPS Energies?

By colliding ultrarelativistic ions, one achieves presently energy densities close to the critical value, concerning the formation of a quark-gluon-plasma. This indicates the importance of fluctuations and the necessity to go beyond the investigation of average events. Therefore, we introduce a percolation approach to model the final stage ($\tau > 1$ fm/c) of ion-ion collisions, the initial stage being treated by well-established methods, based on strings and Pomerons. The percolation approach amounts to finding high density domains, and treating them as quark-matter droplets. In this way, we have a {\bf realistic, microscopic, and Monte--Carlo based model which allows for the formation of quark matter.} We find that even at SPS energies large quark-matter droplets are formed -- at a low rate though. In other words: large quark-matter droplets are formed due to geometrical fluctuation, but not in the average event.Comment: 7 Pages, HD-TVP-94-6 (1 uuencoded figure