Small-Amplitude Disturbances in a Radiating and Scattering Grey MediumIII. Gravitational Effects on the Solutions of Given Real Wave Number k

We study the fundamental modes of radiation hydrodynamic linear waves that arise from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium by taking into account the gravitational effects. The equation of radiative acoustics is derived from three hydrodynamic equations, Poisson’s equation, and two moment equations of radiation, by assuming a spherical symmetry for the matter and radiation and by using the Eddington approximation. We solve the dispersion relation as a quintic function of angular frequency ω, the wave number k being a real parameter. Numerical results reveal that wave patterns of five solutions are distinguished into three types: the radiation-dominated, type 1, and type 2 matter-dominated cases. In the case of no gravitaional effects (Kaneko et al., 2005), the following wave modes appear: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusions, adiabatic sound wave, cooling-damped and drag-force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. Meanwhile, the gravitaional effects being taken into account, the growing gravo-diffusion mode newly arises from the constant-pressure diffusion at the point that k agrees with Jeans’ wave number specified by the isothermal sound speed. This mode changes to the growing radiation-acoustic gravity mode near the point that k becomes Jeans’ wave number specified by the isentropic radiation-acoustic speed. In step with a transition between them, the isentropic radiation-acoustic wave splits into the damping radiation-acoustic gravity mode and constant-volume diffusion. The constant-volume diffusion emerges twice if the gravitational effects are taken into account. Since analytic solutions are derived for all wave modes, we discuss their physical significance. The critical conditions are given which distinguish between radiation-dominated and type 1 matter-dominated cases, and between type 1 and type 2 matter-dominated cases. Waves in a self-gravitating scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.     

Structure and energy transfer of unstable hot star winds

Due to the instability of the radiation line force, the winds of hot, luminous stars should show a pronounced time-dependence resulting from the nonlinear growth of initially small perturbations. Following the method of Owocki, Castor & Rybicki (1988), we describe the time-dependent wind structure obtained with an independently developed code. Under the central assumption ofisothermality, our results are in very good agreement with the ones by Owocki et al. We find that the response of the wind to periodic base perturbations remains largely periodic, at least up tor 2...3R _* , with no clear evidence of stochastic behaviour.In order to test the foregoing assumption of isothermality and to compute the X-ray emission from models of structured winds, we have also incorporated theenergy equation into our simulations. We encountered the numerical problem that all radiative cooling zones collapse because of the oscillatory thermal instability (cf. Langer et al. 1981). We present a method to hinder this collapse by changing the cooling function at low temperatures. The resulting wind showsresolved cooling zones; but, for a supergiant wind relatively close to the star (r 10R _* ), the macroscopic wind structure is very similar to isothermal calculations. Most of the hot material is caused by shell-shell collisions.     

Simulation of the Magnetothermal Instability

In many magnetized, dilute astrophysical plasmas, thermal conduction occurs almost exclusively parallel to magnetic field lines. In this case, the usual stability criterion for convective stability, the Schwarzschild criterion, which depends on entropy gradients, is modified. In the magnetized long mean free path regime, instability occurs for small wavenumbers when (∂ P/∂z) (∂ ln T/∂ z) > 0, which we refer to as the Balbus criterion. We refer to the convective-type instability that results as the magnetothermal instability (MTI). We use the equations of MHD with anisotropic electron heat conduction to numerically simulate the linear growth and nonlinear saturation of the MTI in plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured from the simulations are in excellent agreement with the weak field dispersion relation. The addition of isotropic conduction, e.g. radiation, or strong magnetic fields can damp the growth of the MTI and affect the nonlinear regime. The instability saturates when the atmosphere becomes isothermal as the source of free energy is exhausted. By maintaining a fixed temperature difference between the top and bottom boundaries of the simulation domain, sustained convective turbulence can be driven. MTI-stable layers introduced by isotropic conduction are used to prevent the formation of unresolved, thermal boundary layers. We find that the largest component of the time-averaged heat flux is due to advective motions as opposed to the actual thermal conduction itself. Finally, we explore the implications of this instability for a variety of astrophysical systems, such as neutron stars, the hot intracluster medium of galaxy clusters, and the structure of radiatively inefficient accretion flows. J. M. Stone: Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544     

Evidence for monochromatic unstable Weibel modes in asymmetric counterstreaming pair plasmas

In this article, an asymmetric counterstreaming distribution function is investigated on the basis of three-dimensional relativistic particle-in-cell simulations for wave propagation at an oblique angle with respect to the axis of the counterstream. For such asymmetric distribution functions, any linear Weibel modes must be isolated and therefore restricted to discrete wavenumber values. Using analytical linear Vlasov theory, this result has recently been proven generally, and has been illustrated by the example of an electron beam counterstreaming with a positron beam. By the means of self-consistent particle-in-cell simulations, in this paper a realistic distribution function is investigated that consists of neutral asymmetric Maxwellian counterstreams. For this scenario, the existence of isolated modes can be confirmed, especially when compared to the case of symmetric counterstreams.      

Exploring local N-body simulations of Saturn's rings

The dynamical behavior of low and moderately high optical depth regions of Saturn's ring system of discrete, mutually gravitating, and inelastically colliding particles is studied by simplified local N-body simulations in Hill's linearized equations context. The focus is on a statistical analysis of time-evolution of fine-scale structures seen in the simulations and the comparison between theoretical predictions and computer experiments. Prospects for the Cassini spacecraft mission are briefly summarized.     

Self-consistent theory of white dwarf burning in supernova ia events

A self-consistent model of white dwarf burning in the Supernovae Ia events is proposed which includes the consequent stages of the flame, the spontaneous explosion and the detonation. The flame is ignited locally at several points near the center of the star, but soon it is pushed out of the center due to the Rayleigh-Taylor instability. Most of the hot fuel of the central part of the star remains unburnt by the flame. The unburnt fuel explodes spontaneously after the time delay determined by the average temperature near the star center. Until the time of the explosion the flame consumes more than 0.1 of the white dwarf mass out of the star center, which causes pre-expansion of the unburnt fuel in the outer layers of the star. The spontaneous explosion triggers the detonation which incinerates the rest of the star and produces the intermediate mass elements in the pre-expanded layers. The detonation overcomes gravitational binding and causes mass ejection. The proposed theory provides the physical basis for the explanation of the observed spectrum of Supernovae Ia.     

Shocks and shells in hot star winds

Radiation-driven winds of hot, massive stars showvariability in UV and optical line profiles on time scales of hours to days.Shock heating of wind material is indicated by the observed X-ray emission. We present time-dependent hydrodynamical models of these winds, where flowstructures originate from a strong instability of the radiative driving. Recent calculations (Owocki 1992) of the unstable growth of perturbations were restricted by the assumptions of 1-D spherical symmetry and isothermality of the wind. We drop the latter assumption and include the energy transfer in the wind. This leads to a severe numerical shortcoming, whereby all radiative cooling zones collapse and the shocks become isothermal again. We propose a method to hinder this collapse. Calculations for dense supergiant winds then show: (1) The wind consists of a sequence of narrow and dense shells, which are enclosed by strong reverse shocks (with temperatures of 10⁶ to 10⁷ K) on their starward facing side. (2) Collisions of shells are frequent up to 6 to 7 stellar radii. (3) Radiative cooling is efficient only up to 4 to 6R _*. Beyond these radii, cooling zones behind shocks become broad and alter the wind structure drastically: all reverse shocks disappear, leaving regions ofpreviously heated gas.     

Instabilities in rotating relativistic stars driven by viscosity

We investigate the instability driven by viscosity in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose an m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study these factors on the critical value T/W for the instability. For a rigidly rotating star, the criterion T/W, where T is the rotational kinetic energy and W the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13–0.16, which slightly differ from that of Newtonian incompressible stars (∼0.14). For differentially rotating stars, the critical value of T/W is found to span the range 0.17–0.25. The value is significantly larger than in the rigidly rotating case with the same compactness of the star. Finally we discuss the possibility of detecting gravitational waves from viscosity-driven instabilities using ground-based interferometers.      

Hydrodynamics of Supernova Evolution in the Winds of Massive Stars

Core-Collapse supernovae arise from stars greater than 8 M_⊙. These stars lose a considerable amount of mass during their lifetime, which accumulates around the star forming wind-blown bubbles. Upon the death of the star in a spectacular explosion, the resulting SN shock wave will interact with this modified medium. We study the evolution of the shock wave, and investigate the properties of this interaction. We concentrate on the evolution of the SN shock wave in the medium around a 35 solar mass star. We discuss the hydrodynamics of the resulting interaction, the formation and growth of instabilities, and deviations from sphericity.     

Kelvin–Helmholtz instability in a weakly ionized layer

We study the linear theory of Kelvin–Helmholtz instability in a layer of ions and neutrals with finite thickness. In the short wavelength limit the thickness of the layer has a negligible effect on the growing modes. However, perturbations with wavelength comparable to layer’s thickness are significantly affected by the thickness of the layer. We show that the thickness of the layer has a stabilizing effect on the two dominant growing modes. Transition between the modes not only depends on the magnetic strength, but also on the thickness of the layer.