Pressure driven long wavelength MHD instabilities in an axisymmetric toroidal resistive plasma

A general set of equations that govern global resistive interchange, resistive internal kink and resistive infernal modes in a toroidal axisymmetric equilibrium are systematically derived in detail. Tractable equations are developed such that resistive effects on the fundamental rational surface can be treated together with resistive effects on the rational surfaces of the sidebands. Resistivity introduces coupling of pressure driven toroidal instabilities with ion acoustic waves, while compression introduces flute-like flows and damping of instabilities, enhanced by toroidal effects. It is shown under which equilibrium conditions global interchange, internal kink modes or infernal modes occur. The m = 1 internal kink is derived for the first time from higher order infernal mode equations, and new resistive infernal modes resonant at the q = 1 surface are reduced analytically. Of particular interest are the competing effects of resistive corrections on the rational surfaces of the fundamental harmonic and on the sidebands, which in this paper is investigated for standard profiles developed for the m = 1 internal kink problem.

Axisymmetric equilibrium models for magnetised neutron stars in scalar-tensor theories

Among the possible extensions of general relativity that have been put forward to address some long-standing issues in our understanding of the Universe, scalar-tensor theories have received a lot of attention for their simplicity. Interestingly, some of these predict a potentially observable non-linear phenomenon, known as spontaneous scalarisation, in the presence of highly compact matter distributions, as in the case of neutron stars. Neutron stars are ideal laboratories for investigating the properties of matter under extreme conditions and, in particular, they are known to harbour the strongest magnetic fields in the Universe. Here, for the first time, we present a detailed study of magnetised neutron stars in scalar-tensor theories. First, we showed that the formalism developed for the study of magnetised neutron stars in general relativity, based on the “extended conformally flat condition”, can easily be extended in the presence of a non-minimally coupled scalar field, retaining many of its numerical advantages. We then carried out a study of the parameter space considering the two extreme geometries of purely toroidal and purely poloidal magnetic fields, varying both the strength of the magnetic field and the intensity of scalarisation. We compared our results with magnetised general-relativistic solutions and un-magnetised scalarised solutions, showing how the mutual interplay between magnetic and scalar fields affect the magnetic and the scalarisation properties of neutron stars. In particular, we focus our discussion on magnetic deformability, maximum mass, and range of scalarisation.

Physical explanation for the galaxy distribution on the (λR, ε) and (V/σ, ε) diagrams or for the limit on orbital anisotropy

ABSTRACT In the (λR, ε) and (V/σ, ε) diagrams for characterizing dynamical states, the fast-rotator galaxies (both early type and spirals) are distributed within a well-defined leaf-shaped envelope. This was explained as due to an upper limit to the orbital anisotropy increasing with galaxy intrinsic flattening. However, a physical explanation for this empirical trend was missing. Here, we construct Jeans Anisotropic Models (JAM), with either cylindrically or spherically aligned velocity ellipsoid (two extreme assumptions), and each with either spatially constant or variable anisotropy. We use JAM to build mock samples of axisymmetric galaxies, assuming on average an oblate shape for the velocity ellipsoid (as required to reproduce the rotation of real galaxies), and limiting the radial anisotropy β to the range allowed by physical solutions. We find that all four mock samples naturally predict the observed galaxy distribution on the (λR, ε) and (V/σ, ε) diagrams, without further assumptions. Given the similarity of the results from quite different models, we conclude that the empirical anisotropy upper limit in real galaxies, and the corresponding observed distributions in the (λR, ε) and (V/σ, ε) diagrams, are due to the lack of physical axisymmetric equilibrium solutions at high β anisotropy when the velocity ellipsoid is close to oblate.

Axisymmetric equilibrium of an isotropic elastic solid circular finite cylinder

Axisymmetric equilibrium of an elastic solid circular finite cylinder is one of the oldest problems in the theory of linear elasticity. Crosswise superposition is a well-known method that is used to solve this boundary value problem (BVP); however, technical realization of its underlying ideas still seems to be vague and the solution obtained by this method suffers from some convergence issues. In this study, we follow two main objectives via analyzing a benchmark problem where an isotropic elastic solid circular cylinder of finite length is subjected to normal lateral loading. The first goal is to add more insight into the method of crosswise superposition by extending the ideas that are used for solving classical BVPs via the superposition principle. For this purpose, a new unified approach that naturally gives rise to the subtle concept of corner conditions (CCs) in the context of crosswise superposition method is introduced. Another goal is to demonstrate the influence of CCs on the convergence of the solution obtained by the method of crosswise superposition. In this avenue, the Love function approach is used to convert the Navier equations for an isotropic elastic material to a single axisymmetric biharmonic equation. Next, a general solution for the axisymmetric biharmonic equation consisting of separable and non-separable solutions is presented in cylindrical coordinates. These two classes of solutions are used to construct the Love function and associated elastic fields through the unified approach. Numerical results reveal that considering the CCs can significantly affect the convergence rate of the solution on the boundaries of the cylinder. Furthermore, it is observed that the solution does not converge to the boundary data at the rims without considering the CCs. Far enough from the boundaries of the cylinder, the solution does not seem to be much different with or without taking the CCs into account.