Differential rotation of nonlinear r-modes

Differential rotation of r-modes is investigated within the nonlinear theory up to second order in the mode amplitude in the case of a slowly-rotating, Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes. This solution includes a piece induced by first-order quantities and another one which is a pure second-order effect. Since the latter is stratified on cylinders, it cannot cancel differential rotation induced by first-order quantities, which is not stratified on cylinders. It is shown that, unlikely the situation in the linearized theory, r-modes do not preserve vorticity of fluid elements at second-order. It is also shown that the physical angular momentum and energy of the perturbation are, in general, different from the corresponding canonical quantities.Comment: 9 pages, revtex4; section III revised, comments added in Introduction and Conclusions, references updated; to appear in Phys. Rev.

The rotational modes of relativistic stars: Numerical results

We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and non-barotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid mixture of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth timescale for these unstable modes and compare the results to previous estimates obtained in Newtonian gravity (i.e. using post-Newtonian radiation formulas). We find that the inertial modes are slightly stabilized by relativistic effects, but that previous conclusions concerning eg. the unstable r-modes remain essentially unaltered when the problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure

Generalized Global Defect Solutions

We investigate the presence of defect structures in generalized models described by real scalar field in $(1,1)$ space-time dimensions. We work with two distinct generalizations, one in the form of a product of functions of the field and its derivative, and the other as a sum. We search for static solutions and study the corresponding linear stability on general grounds. We illustrate the results with several examples, where we find stable defect structures of modified profile. In particular, we show how the new defect solutions may give rise to evolutions not present in the standard scenario in higher spatial dimensions.Comment: RevTex, 10 pages, 2 figures; version to appear in EPJ

Dilatonic global strings

We examine the field equations of a self-gravitating global string in low energy superstring gravity, allowing for an arbitrary coupling of the global string to the dilaton. Massive and massless dilatons are considered. For the massive dilaton the spacetime is similar to the recently discovered non-singular time-dependent Einstein self-gravitating global string, but the massless dilaton generically gives a singular spacetime, even allowing for time-dependence. We also demonstrate a time-dependent non-singular string/anti-string configuration, in which the string pair causes a compactification of two of the spatial dimensions, albeit on a very large scale.Comment: 18 pages RevTeX, 3 figures, references amende

Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot

We introduce a new set of generalized Fokker-Planck equations that conserve energy and mass and increase a generalized entropy until a maximum entropy state is reached. The concept of generalized entropies is rigorously justified for continuous Hamiltonian systems undergoing violent relaxation. Tsallis entropies are just a special case of this generalized thermodynamics. Application of these results to stellar dynamics, vortex dynamics and Jupiter's great red spot are proposed. Our prime result is a novel relaxation equation that should offer an easily implementable parametrization of geophysical turbulence. This relaxation equation depends on a single key parameter related to the skewness of the fine-grained vorticity distribution. Usual parametrizations (including a single turbulent viscosity) correspond to the infinite temperature limit of our model. They forget a fundamental systematic drift that acts against diffusion as in Brownian theory. Our generalized Fokker-Planck equations may have applications in other fields of physics such as chemotaxis for bacterial populations. We propose the idea of a classification of generalized entropies in classes of equivalence and provide an aesthetic connexion between topics (vortices, stars, bacteries,...) which were previously disconnected.Comment: Submitted to Phys. Rev.

Jacobi-like bar mode instability of relativistic rotating bodies

We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy $(T/|W|)_{\rm crit}$ for compaction parameter as high as 0.275 is only 30% higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for $M/R=0.275$ is only 2% larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars

For the analysis of the r-mode oscillation of hot young neutron stars, it is necessary to consider the effect of it differential rotation, because viscosity is not strong enough for differentially rotating young neutron stars to be lead to uniformly rotating configurations on a very short time scale after their birth. In this paper, we have developed a numerical scheme to solve r-mode oscillations of differentially rotating polytropic inviscid stars. This is the extended version of the method which was applied to compute r-mode oscillations of uniformly rotating Newtonian polytropic stars. By using this new method, we have succeeded in obtaining eigenvalues and eigenfunctions of r-mode oscillations of differentially rotating polytropic stars. Our numerical results show that as the degree of differential rotation is increased, it becomes more difficult to solve r-mode oscillations for slightly deformed configurations from sphere compared to solving r-mode oscillations of considerably deformed stars. One reason for it seems that for slightly deformed stars corotation points appear near the surface region if the degree of differential rotation is strong enough. This is similar to the situation that the perturbational approach of r-mode oscillations for it slowly rotating stars in general relativity results in a singular eigenvalue problem.Comment: including 7 figures. submitted to PR

Calculating exclusion limits for Weakly Interacting Massive Particle direct detection experiments without background subtraction

Competitive limits on the weakly interacting massive particle (WIMP) spin-independent scattering cross section are currently being produced by 76Ge detectors originally designed to search for neutrinoless double beta decay, such as the Heidelberg-Moscow and IGEX experiments. In the absence of background subtraction, limits on the WIMP interaction cross section are set by calculating the upper confidence limit on the theoretical event rate, given the observed event rate. The standard analysis technique involves calculating the 90% upper confidence limit on the number of events in each bin, and excluding any set of parameters (WIMP mass and cross-section) which produces a theoretical event rate for any bin which exceeds the 90% upper confidence limit on the event rate for that bin. We show that, if there is more than one energy bin, this produces exclusion limits that are actually at a lower degree of confidence than 90%, and are hence erroneously tight. We formulate criteria which produce true 90% confidence exclusion limits in these circumstances, including calculating the individual bin confidence limit for which the overall probability that no bins exceeds this confidence limit is 90% and calculating the 90% minimum confidence limit on the number of bins which exceed their individual bin 90% confidence limits. We then compare the limits on the WIMP cross-section produced by these criteria with those found using the standard technique, using data from the Heidelberg-Moscow and IGEX experiments.Comment: 6 pages, 3 figures, 3 tables, shortened version to appear in Phys. Rev. D, contents otherwise unchange

On gravitational waves emitted by an ensemble of rotating neutron stars

We study the possibility to detect the gravitational wave background generated by all the neutron stars in the Galaxy with only one gravitational wave interferometric detector. The proposed strategy consists in squaring the detector's output and searching for a sidereal modulation. The shape of the squared signal is computed for a disk and a halo distribution of neutron stars. The required noise stability of the interferometric detector is discussed. We argue that a possible population of old neutron stars, originating from a high stellar formation rate at the birth of the Galaxy and not emitting as radio pulsars, could be detected by the proposed technique in the low frequency range of interferometric experiments.Comment: 14 pages, 2 PostScript figures, RevTeX, accepted for publication in Physical Review

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