Neutron Star instabilities in full General Relativity using a Γ=2.75\Gamma=2.75 ideal fluid

We present results about the effect of the use of a stiffer equation of state, namely the ideal-fluid $\Gamma=2.75$ ones, on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change on the critical value of the instability parameter $\beta$ for the emergence of the instability when the adiabatic index $\Gamma$ is changed from 2 to 2.75 in order to mimic the behavior of a realistic equation of state. In particular, we show that the threshold for the onset of the bar-mode instability is reduced by this change in the stiffness and give a precise quantification of the change in value of the critical parameter $\beta_c$. We also extend the analysis to lower values of $\beta$ and show that low-beta shear instabilities are present also in the case of matter described by a simple polytropic equation of state.Comment: 16 pages, 16 figure

Dynamical bar-mode instability in rotating and magnetized relativistic stars

We present three-dimensional simulations of the dynamical bar-mode instability in magnetized and differentially rotating stars in full general relativity. Our focus is on the effects that magnetic fields have on the dynamics and the onset of the instability. In particular, we perform ideal-magnetohydrodynamics simulations of neutron stars that are known to be either stable or unstable against the purely hydrodynamical instability, but to which a poloidal magnetic field in the range of $10^{14}$--$10^{16}$ G is superimposed initially. As expected, the differential rotation is responsible for the shearing of the poloidal field and the consequent linear growth in time of the toroidal magnetic field. The latter rapidly exceeds in strength the original poloidal one, leading to a magnetic-field amplification in the the stars. Weak initial magnetic fields, i.e. $\lesssim 10^{15}$ G, have negligible effects on the development of the dynamical bar-mode instability, simply braking the stellar configuration via magnetic-field shearing, and over a timescale for which we derived a simple algebraic expression. On the other hand, strong magnetic fields, i.e. $\gtrsim 10^{16}$ G, can suppress the instability completely, with the precise threshold being dependent also on the amount of rotation. As a result, it is unlikely that very highly magnetized neutron stars can be considered as sources of gravitational waves via the dynamical bar-mode instability.Comment: 18 pages, 13 figure

Bar-mode instability suppression in magnetized relativistic stars

We show that magnetic fields stronger than about $10^{15}$ G are able to suppress the development of the hydrodynamical bar-mode instability in relativistic stars. The suppression is due to a change in the rest-mass density and angular velocity profiles due to the formation and to the linear growth of a toroidal component that rapidly overcomes the original poloidal one, leading to an amplification of the total magnetic energy. The study is carried out performing three-dimensional ideal-magnetohydrodynamics simulations in full general relativity, superimposing to the initial (matter) equilibrium configurations a purely poloidal magnetic field in the range $10^{14}-10^{16}$ G. When the seed field is a few parts in $10^{15}$ G or above, all the evolved models show the formation of a low-density envelope surrounding the star. For much weaker fields, no effect on the matter evolution is observed, while magnetic fields which are just below the suppression threshold are observed to slow down the growth-rate of the instability.Comment: 6 pages, 4 figures, to appear on the proceedings of the 4th YRM (Trieste 2013

Two-dimensional Hybrid Simulations of Kinetic Plasma Turbulence: Current and Vorticity vs Proton Temperature

Proton temperature anisotropies between the directions parallel and perpendicular to the mean magnetic field are usually observed in the solar wind plasma. Here, we employ a high-resolution hybrid particle-in-cell simulation in order to investigate the relation between spatial properties of the proton temperature and the peaks in the current density and in the flow vorticity. Our results indicate that, although regions where the proton temperature is enhanced and temperature anisotropies are larger correspond approximately to regions where many thin current sheets form, no firm quantitative evidence supports the idea of a direct causality between the two phenomena. On the other hand, quite a clear correlation between the behavior of the proton temperature and the out-of-plane vorticity is obtained.Comment: 4 pages, 2 figures, Proceedings of the Fourteenth International Solar Wind Conferenc

Solar wind turbulence from MHD to sub-ion scales: high-resolution hybrid simulations

We present results from a high-resolution and large-scale hybrid (fluid electrons and particle-in-cell protons) two-dimensional numerical simulation of decaying turbulence. Two distinct spectral regions (separated by a smooth break at proton scales) develop with clear power-law scaling, each one occupying about a decade in wave numbers. The simulation results exhibit simultaneously several properties of the observed solar wind fluctuations: spectral indices of the magnetic, kinetic, and residual energy spectra in the magneto-hydrodynamic (MHD) inertial range along with a flattening of the electric field spectrum, an increase in magnetic compressibility, and a strong coupling of the cascade with the density and the parallel component of the magnetic fluctuations at sub-proton scales. Our findings support the interpretation that in the solar wind large-scale MHD fluctuations naturally evolve beyond proton scales into a turbulent regime that is governed by the generalized Ohm's law.Comment: 5 pages, 5 figures; introduction and conclusions changed, references updated, accepted for publication in ApJ

High-resolution hybrid simulations of kinetic plasma turbulence at proton scales

We investigate properties of plasma turbulence from magneto-hydrodynamic (MHD) to sub-ion scales by means of two-dimensional, high-resolution hybrid particle-in-cell simulations. We impose an initial ambient magnetic field, perpendicular to the simulation box, and we add a spectrum of large-scale magnetic and kinetic fluctuations, with energy equipartition and vanishing correlation. Once the turbulence is fully developed, we observe a MHD inertial range, where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power-law scaling with spectral indices of -5/3 and -3/2, respectively. This behavior is extended over a full decade in wavevectors and is very stable in time. A transition is observed around proton scales. At sub-ion scales, both spectra steepen, with the former still following a power law with a spectral index of ~-3. A -2.8 slope is observed in the density and parallel magnetic fluctuations, highlighting the presence of compressive effects at kinetic scales. The spectrum of the perpendicular electric fluctuations follows that of the proton bulk velocity at MHD scales, and flattens at small scales. All these features, which we carefully tested against variations of many parameters, are in good agreement with solar wind observations. The turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions. While the parallel proton heating is found to be independent on the resistivity, the number of particles per cell and the resolution employed, the perpendicular proton temperature strongly depends on these parameters.Comment: 15 pages, 13 figures, submitted to Ap

Stiffness effects on the dynamics of the bar-mode instability of Neutron Stars in full General Relativity

We present results on the effect of the stiffness of the equation of state on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change in the threshold for the emergence of the instability for a range of the adiabatic $\Gamma$ index from 2.0 to 3.0, including two values chosen to mimic more realistic equations of state at high densities.Comment: 12 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1403.806

Dynamical bar-mode instability in magnetized relativistic stars

We present accurate 3D simulations in full general relativity of magnetized and differentially rotating relativistic star models, focusing on the effects that magnetic fields have on the dynamics of bar-stable models and on the onset of the dynamical bar-mode instability in bar-unstable models. In particular, we evolve initial matter equilibrium configurations that are already known to be stable or unstable against this kind of instability in the unmagnetized case, super-imposing a purely poloidal magnetic field, all confined inside the star, with different strength values in the range $10^{11}$-$10^{16}$ Gauss. Low magnetic fields have negligible effetcs on the dynamics of bar-stable models. On the contrary, for very strong magnetic fields, i.e., above $10^{15}$ Gauss, these models are braked considerably in their rotation and evolve into configurations that have uniformly rotating extended cores with large rest-mass densities models. Regarding the effects on the dynamical bar-mode instability, we find that magnetic fields seem to have very low effects on the $m=2$ deformation for field strengths of order $10^{15}$ Gauss or less, only reducing the growth rate of the instability and the maximum distortion of the bar deformation. Magnetic fields greater than some units in $10^{15}$ or $10^{16}$ Gauss (the treshold being different for the different unstable models) are indeed able to completely suppress the purely hydrodinamical instability, making the distorsion of the stars negligible with consequent negative effect on them as possible gravitational wave sources. For all models we observe a sudden formation and linear growth of a toroidal magnetic field component that rapidly overcomes the original poloidal one as a consequence of the winding of the magnetic field lines dragged by differential rotation, and hence an amplification of the total magnetic energy inside the stars of about two orders of magnitude. Later in the evolution, bar-unstable models exhibit and rapid exponential growth of the toroidal magnetic field component. The nature of this growth has been studied by performing additional simulations at finer resolutions, since a possible explanation for this behavior is the onset of the magnetorotational instability, whose charateristic modes require a very high resolution in order to be fully resolved. Due to computational limitations, we could only observe a few features that seem to support our hypothesis, without providing a firm evidence