R-Modes in Superfluid Neutron Stars

The analogs of r-modes in superfluid neutron stars are studied here. These modes, which are governed primarily by the Coriolis force, are identical to their ordinary-fluid counterparts at the lowest order in the small angular-velocity expansion used here. The equations that determine the next order terms are derived and solved numerically for fairly realistic superfluid neutron-star models. The damping of these modes by superfluid ``mutual friction'' (which vanishes at the lowest order in this expansion) is found to have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a ``typical'' superfluid neutron-star model. This time-scale is far too long to allow mutual friction to suppress the recently discovered gravitational radiation driven instability in the r-modes. However, the strength of the mutual friction damping depends very sensitively on the details of the neutron-star core superfluid. A small fraction of the presently acceptable range of superfluid models have characteristic mutual friction damping times that are short enough (i.e. shorter than about 5 s) to suppress the gravitational radiation driven instability completely.Comment: 15 pages, 8 figure

The r-modes in accreting neutron stars with magneto-viscous boundary layers

We explore the dynamics of the r-modes in accreting neutron stars in two ways. First, we explore how dissipation in the magneto-viscous boundary layer (MVBL) at the crust-core interface governs the damping of r-mode perturbations in the fluid interior. Two models are considered: one assuming an ordinary-fluid interior, the other taking the core to consist of superfluid neutrons, type II superconducting protons, and normal electrons. We show, within our approximations, that no solution to the magnetohydrodynamic equations exists in the superfluid model when both the neutron and proton vortices are pinned. However, if just one species of vortex is pinned, we can find solutions. When the neutron vortices are pinned and the proton vortices are unpinned there is much more dissipation than in the ordinary-fluid model, unless the pinning is weak. When the proton vortices are pinned and the neutron vortices are unpinned the dissipation is comparable or slightly less than that for the ordinary-fluid model, even when the pinning is strong. We also find in the superfluid model that relatively weak radial magnetic fields ~ 10^9 G (10^8 K / T)^2 greatly affect the MVBL, though the effects of mutual friction tend to counteract the magnetic effects. Second, we evolve our two models in time, accounting for accretion, and explore how the magnetic field strength, the r-mode saturation amplitude, and the accretion rate affect the cyclic evolution of these stars. If the r-modes control the spin cycles of accreting neutron stars we find that magnetic fields can affect the clustering of the spin frequencies of low mass x-ray binaries (LMXBs) and the fraction of these that are currently emitting gravitational waves.Comment: 19 pages, 8 eps figures, RevTeX; corrected minor typos and added a referenc

Stability of the r-modes in white dwarf stars

Stability of the r-modes in rapidly rotating white dwarf stars is investigated. Improved estimates of the growth times of the gravitational-radiation driven instability in the r-modes of the observed DQ Her objects are found to be longer (probably considerably longer) than 6x10^9y. This rules out the possibility that the r-modes in these objects are emitting gravitational radiation at levels that could be detectable by LISA. More generally it is shown that the r-mode instability can only be excited in a very small subset of very hot (T>10^6K), rather massive (M>0.9M_sun) and very rapidly rotating (P_min<P<1.2P_min) white dwarf stars. Further, the growth times of this instability are so long that these conditions must persist for a very long time (t>10^9y) to allow the amplitude to grow to a dynamically significant level. This makes it extremely unlikely that the r-mode instability plays a significant role in any real white dwarf stars.Comment: 5 Pages, 5 Figures, revte

The metaphysics of Machian frame-dragging

The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding

Numerical evolutions of nonlinear r-modes in neutron stars

Nonlinear evolution of the gravitational radiation (GR) driven instability in the r-modes of neutron stars is studied by full numerical 3D hydrodynamical simulations. The growth of the r-mode instability is found to be limited by the formation of shocks and breaking waves when the dimensionless amplitude of the mode grows to about three in value. This maximum mode amplitude is shown by numerical tests to be rather insensitive to the strength of the GR driving force. Upper limits on the strengths of possible nonlinear mode--mode coupling are inferred. Previously unpublished details of the numerical techniques used are presented, and the results of numerous calibration runs are discussed.Comment: RevTeX 4, 17 pages, 26 figures. Slightly revised. To be published in PRD (April 2002

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Common Cerambycid Pheromone components as attractants for Longhorn Beetles (Cerambycidae) breeding in ephemeral oak substrates in Northern Europe

Longhorn beetles are ecologically important insects in forest ecosystems as decomposers of woody substrates, microhabitat engineers, and as components of forest food webs. These species can be greatly affected both positively and negatively by modern forestry management practices, and should be monitored accordingly. Through headspace sampling, coupled gas chromatography-electroantennography, gas chromatography-mass spectrometry, and field bioassays, we identified two compounds, 2-methyl-1-butanol and 3-hydroxy-2-hexanone, that constitute aggregation-sex pheromone attractants of three cerambycid species which breed primarily in different types of fresh, recently dead oak wood in Northern Europe: Pyrrhidium sanguineum (L.), Phymatodes alni ssp. alni (L.), and Phymatodes testaceus (L.) (Cerambycinae: Callidiini). Analyses of headspace volatiles collected from live insects indicated that the male-produced aggregation-sex pheromone of P. sanguineum is a 1–15:100 blend of (R)-2-methyl-1-butanol and (R)-3-hydroxy-2-hexanone, whereas the corresponding ratios for P. alni were 70–110:100. In field bioassays, adult P. sanguineum and P. alni were significantly attracted to multiple blends with varying ratios of the two compounds. When tested individually, the compounds were minimally attractive. In contrast, adult P. testaceus exhibited nonspecific attraction to both of the individual compounds and to different blends, despite the hydroxyketone not being part of its pheromone, which consists of (R)-2-methyl-1-butanol alone. Overall, our results suggest that a blend of 50:100 of racemic 2-methyl-1-butanol and 3-hydroxy-2-hexanone is appropriate for parallel, cost-efficient pheromone-based monitoring of all three species. In particular, these species could serve as useful indicators of how modern forestry practices affect a whole guild of saproxylic insects that require ephemeral deadwood substrates for successful breeding

On the Causality and Stability of the Relativistic Diffusion Equation

This paper examines the mathematical properties of the relativistic diffusion equation. The peculiar solution which Hiscock and Lindblom identified as an instability is shown to emerge from an ill-posed initial value problem. These do not meet the mathematical conditions required for realistic physical problems and can not serve as an argument against the relativistic hydrodynamics of Landau and Lifshitz.Comment: 6 page

Dynamic modelling of nitrous oxide emissions from three Swedish sludge liquor treatment systems

The objective of this paper is to model the dynamics and validate the results of nitrous oxide (N2O) emissions from three Swedish nitrifying/denitrifying, nitritation and anammox systems treating real anaerobic digester sludge liquor. The Activated Sludge Model No. 1 is extended to describe N2O production by both heterotrophic and autotrophic denitrification. In addition, mass transfer equations are implemented to characterize the dynamics of N2O in the water and the gas phases. The biochemical model is simulated and validated for two hydraulic patterns: (1) a sequencing batch reactor; and (2) a moving-bed biofilm reactor. Results show that the calibrated model is partly capable of reproducing the behaviour of N2O as well as the nitritation/nitrification/denitrification dynamics. However, the results emphasize that additional work is required before N2O emissions from sludge liquor treatment plants can be generally predicted with high certainty by simulations. Continued efforts should focus on determining the switching conditions for different N2O formation pathways and, if full-scale data are used, more detailed modelling of the measurement devices might improve the conclusions that can be drawn.</jats:p