A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics

We present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients in the construction are i) the use of a lower dimensional matter space for each fluid component, and ii) an extended functional dependence for the associated volume forms. In an effort to make the concepts clear, the formalism is developed in steps with the model example of matter coupled to heat considered at each level. Thus we discuss a model for heat flow, derive the relativistic Navier-Stokes equations and discuss why the individual dissipative stress tensors need not be spacetime symmetric. We argue that the new formalism, which notably does not involve an expansion away from an assumed equilibrium state, provides a conceptual breakthrough in this area of research and provide an ambitious list of directions in which one may want to extend it in the future. This involves an exciting set of problems, relating to both applications and foundational issues.Comment: 21 pages RevTex, 3 pdf figures, matches the published version. arXiv admin note: text overlap with arXiv:1107.1005 by other author

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

The nonlinear development of the relativistic two-stream instability

The two-stream instability has been mooted as an explanation for a range of astrophysical applications from GRBs and pulsar glitches to cosmology. Using the first nonlinear numerical simulations of relativistic multi-species hydrodynamics we show that the onset and initial growth of the instability is very well described by linear perturbation theory. In the later stages the linear and nonlinear description match only qualitatively, and the instability does not saturate even in the nonlinear case by purely ideal hydrodynamic effects.Comment: 15 pages, 9 figure

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

Buoyancy and g-modes in young superfluid neutron stars

We consider the local dynamics of a realistic neutron star core, including composition gradients, superfluidity and thermal effects. The main focus is on the gravity g-modes, which are supported by composition stratification and thermal gradients. We derive the equations that govern this problem in full detail, paying particular attention to the input that needs to be provided through the equation of state and distinguishing between normal and superfluid regions. The analysis highlights a number of key issues that should be kept in mind whenever equation of state data is compiled from nuclear physics for use in neutron star calculations. We provide explicit results for a particular stellar model and a specific nucleonic equation of state, making use of cooling simulations to show how the local wave spectrum evolves as the star ages. Our results show that the composition gradient is effectively dominated by the muons whenever they are present. When the star cools below the superfluid transition, the support for g-modes at lower densities (where there are no muons) is entirely thermal. We confirm the recent suggestion that the g-modes in this region may be unstable, but our results indicate that this instability will be weak and would only be present for a brief period of the star's life. Our analysis accounts for the presence of thermal excitations encoded in entrainment between the entropy and the superfluid component. Finally, we discuss the complete spectrum, including the normal sound waves and, in superfluid regions, the second sound.Comment: 29 pages, 9 figures, submitted to MNRA

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

Seismology of adolescent neutron stars: Accounting for thermal effects and crust elasticity

We study the oscillations of relativistic stars, incorporating key physics associated with internal composition, thermal gradients and crust elasticity. Our aim is to develop a formalism which is able to account for the state-of-the-art understanding of the complex physics associated with these systems. As a first step, we build models using a modern equation of state including composition gradients and density discontinuities associated with internal phase-transitions (like the crust-core transition and the point where muons first appear in the core). In order to understand the nature of the oscillation spectrum, we carry out cooling simulations to provide realistic snapshots of the temperature distribution in the interior as the star evolves through adolescence. The associated thermal pressure is incorporated in the perturbation analysis, and we discuss the presence of $g$-modes arising as a result of thermal effects. We also consider interface modes due to phase-transitions and the gradual formation of the star's crust and the emergence of a set of shear modes.Comment: 27 pages, 14 figure

Implications of an r-mode in XTE J1751-305: Mass, radius and spin evolution

Recently Strohmayer and Mahmoodifar presented evidence for a coherent oscillation in the X-ray light curve of the accreting millisecond pulsar XTE J1751-305, using data taken by RXTE during the 2002 outburst of this source. They noted that a possible explanation includes the excitation of a non-radial oscillation mode of the neutron star, either in the form of a g-mode or an r-mode. The r-mode interpretation has connections with proposed spin-evolution scenarios for systems such as XTE J1751-305. Here we examine in detail this interesting possible interpretation. Using the ratio of the observed oscillation frequency to the star's spin frequency, we derive an approximate neutron star mass-radius relation which yields reasonable values for the mass over the range of expected stellar radius (as constrained by observations of radius-expansion burst sources). However, we argue that the large mode amplitude suggested by the Strohmayer and Mahmoodifar analysis would inevitably lead to a large spin-down of the star, inconsistent with its observed spin evolution, regardless of whether the r-mode itself is in a stable or unstable regime. We therefore conclude that the r-mode interpretation of the observed oscillation is not consistent with our current understanding of neutron star dynamics and must be considered unlikely. Finally we note that, subject to the availability of a sufficiently accurate timing model, a direct gravitational-wave search may be able to confirm or reject an r-mode interpretation unambiguously, should such an event, with a similar inferred mode amplitude, recur during the Advanced detector era.Comment: 8 pages, 3 figures; submitted to MNRA

The dynamics of neutron star crusts: Lagrangian perturbation theory for a relativistic superfluid-elastic system

The inner crust of a mature neutron star is composed of an elastic lattice of neutron-rich nuclei penetrated by free neutrons. These neutrons can flow relative to the crust once the star cools below the superfluid transition temperature. In order to model the dynamics of this system, which is relevant for a range of problems from pulsar glitches to magnetar seismology and continuous gravitational-wave emission from rotating deformed neutron stars, we need to understand general relativistic Lagrangian perturbation theory for elastic matter coupled to a superfluid component. This paper develops the relevant formalism to the level required for astrophysical applications.Comment: 31 pages, double spacing, minor typos fixe