14227222
Two-Dimensional Stellar Evolution Code Including Arbitrary Magnetic Fields. II. Precision Improvement and Inclusion of Turbulence and Rotation
In the second paper of this series we pursue two objectives. First, in order to make the code more sensitive to small effects, we remove many approximations made in Paper I. Second, we include turbulence and rotation in the two-dimensional framework. The stellar equilibrium is described by means of a set of five differential equations, with the introduction of a new dependent variable, namely the perturbation to the radial gravity, that is found when the nonradial effects are considered in the solution of the Poisson equation. Following the scheme of the first paper, we write the equations in such a way that the two-dimensional effects can be easily disentangled. The key concept introduced in this series is the equipotential surface. We use the underlying cause-effect relation to develop a recurrence relation to calculate the equipotential surface functions for uniform rotation, differential rotation, rotation-like toroidal magnetic fields, and turbulence. We also develop a more precise code to numerically solve the two-dimensional stellar structure and evolution equations based on the equipotential surface calculations. We have shown that with this formulation we can achieve the precision required by observations by appropriately selecting the convergence criterion. Several examples are presented to show that the method works well. Since we are interested in modeling the effects of a dynamo-type field on the detailed envelope structure and global properties of the Sun, the code has been optimized for short timescales phenomena (down to 1 yr). The time dependence of the code has so far been tested exclusively to address such problems.
10120589
The nonhomologous nature of solar diameter variations
We show in this Letter that the changes of the solar diameter in response to variations of large-scale magnetic fields and turbulence are not homologous. For the best current model, the variation at the photospheric level is over 1000 times larger than the variation at a depth of 5 Mm, which is about the level at which f-mode solar oscillations determine diameter variations. This model is supported by observations that indicate larger diameter changes for high-degree f-modes than for low-degree f-modes, since the energy of the former is concentrated at shallower layers than the latter.
10496964
Asymptotically universal crossover in perturbation theory with a field cutoff
We discuss the crossover between the small and large field cutoff (denoted as x max ) limits of the perturbative coefficients for a simple integral and anharmonic oscillators. We show that in the limit where the order k of the perturbative coefficient a k (x max ) becomes large and for x max in the crossover region, a k (x max ) ∝ ∫ xmax -∞ e -A(x-x 0 (k))2 dx. The order-independent constant A and the function x 0 (k) are determined empirically and compared with exact (for the integral) and approximate (for the anharmonic oscillator) calculations. Numerically, our best estimates are A ≃ 1.5, 1.3 and 1.2 for a λx 4 , λx 6 and λx 8 perturbation respectively.
118706095
Non-relativistic fluid dual to asymptotically AdS gravity at finite cutoff surface
Using the non-relativistic hydrodynamic limit, we solve equations of motion for Einstein gravity and Gauss-Bonnet gravity with a negative cosmological constant within the region between a finite cutoff surface and a black brane horizon, up to second order of the non-relativistic hydrodynamic expansion parameter. Through the Brown-York tensor, we calculate the stress energy tensor of dual fluids living on the cutoff surface. With the black brane solutions, we show that for both Einstein gravity and Gauss-Bonnet gravity, the ratio of shear viscosity to entropy density of dual fluid does not run with the cutoff surface. The incompressible Navier-Stokes equations are also obtained in both cases.
119085474
Evolution of magnetic fields around a Kerr black hole
The evolution of magnetic fields frozen to a perfectly conducting plasma fluid around a Kerr black hole is investigated. We focus on the plunging region between the black hole horizon and the marginally stable circular orbit in the equatorial plane, where the centrifugal force is unable to stably balance the gravitational force. Adopting the kinematic approximation where the dynamical effects of magnetic fields on the fluid motion are ignored, we exactly solve Maxwell's equations with the assumptions that the geodesic motion of the fluid is stationary and axisymmetric, the magnetic field has only radial and azimuthal components and depends only on time and radial coordinates. We show that the stationary state of the magnetic field in the plunging region is uniquely determined by the boundary conditions at the marginally stable circular orbit. If the magnetic field at the marginally stable circular orbit is in a stationary state, the magnetic field in the plunging region will quickly settle into a stationary state if it is not so initially, in a time determined by the dynamical time scale in the plunging region. The radial component of the magnetic field at the marginally stable circular orbit is more important than the toroidal component in determining the structure and evolution of the magnetic field in the plunging region. Even if at the marginally stable circular orbit the toroidal component is zero, in the plunging region a toroidal component is quickly generated from the radial component by the shear motion of the fluid. Finally, we discuss the dynamical effects of magnetic fields on the motion of the fluid in the plunging region. We show that the dynamical effects of magnetic fields are unimportant in the plunging region if they are negligible on the marginally stable circular orbit. This supports the ``no-torque inner boundary condition'' of thin disks, contrary to the claim in the recent literature.
17648096
Non-Axisymmetric g-Mode and p-Mode Instability in a Thin Accretion Disk
It has been suggested that quasi-periodic oscillations of accreting X-ray sources may relate to the modes named in the title. We idealize a thin accretion disk by means of the shearing sheet model and derive a wave equation for nonaxisymmetric perturbations. We show that the equation can be transformed into the Whittaker equation, which enables us to write down analytical solutions. For modes with vertical wave number n > 0, there are four distinct permitted regions for waves, separated by two forbidden regions and a corotation resonance. We show that each forbidden region behaves like a wave amplifier so that any wave incident on it is reflected with a larger amplitude. The corotation resonance, however, behaves like a strong wave absorber. Following Kato (2001b, 2002), we look for internally trapped growing g-modes in which most of the wave action is concentrated in the region between the two forbidden zones. We find that there are no such modes in the shearing sheet. We discuss whether such modes may be present in more general shear flows that deviate from the idealized shearing sheet. We conclude that instability, though not ruled out, is likely to be rare. We also analyse externally trapped p-modes in which the wave action is concentrated in an external cavity between one of the forbidden zones and the inner edge of the disk. Unstable modes are certainly possible in this case. Moreover, the wave amplification can be substantially larger for n = 1 than for the previously studied case of n = 0. Therefore, n = 1 p-modes might have significant growth rates in realistic disks, provided that the disk inner edge reflects waves reasonably well. Subject headings: accretion, accretion disks — instabilities — waves — X-rays: binaries
116928402
Introduction to holographic superconductor models
In the last years it has been shown that some properties of strongly coupled superconductors can be potentially described by classical general relativity living in one higher dimension, which is known as holographic superconductors. This paper gives a quick and introductory overview of some holographic superconductor models with s-wave, p-wave and d-wave orders in the literature from point of view of bottom-up, and summarizes some basic properties of these holographic models in various regimes. The competition and coexistence of these superconductivity orders are also studied in these superconductor models.