On the threshold anisotropy for unstable spherical stellar systems

The radial orbit instability generally arises in anisotropic collisionless stellar systems with the dominance of radial motions over transverse ones. Using the simplest anisotropic generalization of polytrope models for spherical clusters as an example, we show that the instability growth rates become exponentially small as the isotropic limit is approached. Given the finite lifetime of real astronomical objects, these systems should be assumed to become stable at some finite radial anisotropy.     

On the spherical symmetry of static stellar models

This paper completes the proof of the necessity of spherical symmetry in the static general-relativistic stellar models that have equations of state satisfying certain inequalities. The technical assumption — that there exists a reference spherical stellar model — that was essential in the previous discussions of this problem is removed. This paper also extends beyond previous discussions the class of equations of state included in the proof. The analysis of the equations for spherical stellar models, used here to demonstrate the existence of a reference spherical model, may also be of independent interest.     

Relativistic stellar models

We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric field intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to specific neutron star models. We find two charged solutions in terms of elementary functions for particular parameter values. The first charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.     

On the effect of longitude-dependent fields on convection in stellar atmospheres

In rotating stellar convective zones, heat transfer is shown to be associated with unbalanced azimuth forces arising in the radially ascending (heated) or descending (cold) matter. The presence of a longitude-dependent magnetic field generates additional azimuth forces, hence, new ways of compensating for the unbalanced forces. Generally speaking, this magnetic field is variable but may be nearly static in layers where convective equilibrium is replaced by radiative equilibrium. The condition for the coexistence of the static and usual fields is derived. To this end, an axisymmetric azimuth magnetic field of energy comparable to the energy of rotation should be introduced into models under consideration. In such configurations, conditions for magnetic field generation, as in the Sun, may appear.     

Newtonian stellar models

We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a three-dimensional regular dynamical system with bounded dependent variables. The low and high central pressure limits correspond to two two-dimensional boundary subsets, described by homology invariant equations for exact polytropes. Thus the formulation naturally places work about polytropes in a more general context. The introduced framework yields a visual aid for obtaining qualitative information about the solution space and is also suitable for numerical investigations. Moreover, it makes a host of mathematical tools from dynamical systems theory available, which allows us to prove several theorems about the relationship between the equation of state and properties concerning total masses and radii.     

Anisotropic relativistic stellar models

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars.     

Proof that static stellar models are spherical

We give a proof that static general-relativistic stellar models, in other words static perfect fluid stars in asymptotically-flat spacetimes, are spherically symmetric for physically reasonable equations of state. The analysis may also be of independent interest for differential geometric rigidity theorems.     

Starspots,stellar cycles and stellar flares: Lessons from solar dynamo models

We theoretically investigate the multistable behavior of a hybrid optomechanical system,in which a charged mechanical resonator is coupled via Coulomb interaction to an optomechanical cavity containing an optical parametric amplifier(OPA).It is shown that the multistable behavior of the mean intracavity photon number can be controlled flexibly by adjusting the nonlinear gain parameter of the OPA,the phase of the field pumping the OPA,the power and frequency of the field driving the cavity,and the Coulomb coupling strength between the two charged mechanical resonators.In particular,the increase of the nonlinear gain parameter can result in a transition from testability to Instability.Moreover,the effect of the Coulomb coupling strength on the bistable behavior of the steady-state positions of the two mechanical resonators is discussed.     

Starspots,stellar cycles and stellar flares: Lessons from solar dynamo models

In this review, we discuss whether the present solar dynamo models can be extrapolated to explain various aspects of stellar activity. We begin with a summary of the following kinds of data for solar-like stars:(i) data pertaining to stellar cycles from Ca H/K emission over many years;(ii) X-ray data indicating hot coronal activity;(iii) starspot data(especially about giant polar spots); and(iv) data pertaining to stellar superflares. Then we describe the current status of solar dynamo modelling—giving an introduction to the flux transport dynamo model, the currently favoured model for the solar cycle. While an extrapolation of this model to solar-like stars can explain some aspects of observational data, some other aspects of the data still remain to be theoretically explained. It is not clear right now whether we need a different kind of dynamo mechanism for stars having giant starspots or producing very strong superflares.     

On the application of a new formulation of nonlinear eddy viscosity based on anisotropy to numerical ocean models

The present paper explores the derivation of an alternative nonlinear eddy viscosity formulation based on Reynolds stress anisotropy and its implementation to numerical ocean models. This formulation takes into account the vorticity in addition to the mean strain rate. The proposed formulation does not include the stability function method which is a common approach in eddy viscosity calculations used in the present state-of-the-art numerical ocean models. Instead, it depends on the second invariant of anisotropy. Initially, the performance of the formulation is checked through a simple channel flow simulation. Consequently for model calibration, an idealised experiment of mixed-layer entrainment into stably stratified flow has been simulated and compared to empirical data. For sensitivity studies related to shear and stable stratification, concept of steady-state Richardson number is applied for homogeneous shear layer. Finally, the performance of the new formulation is tested by implementing it into one-dimensional General Ocean Turbulence Model. Furthermore, a realistic oceanic test case of a storm has been investigated considering different physical processes for the Fladenground Experiment (FLEX’ 76) in the northern North Sea and the results have been compared to the measured data. The main results signify that the overall performance of the nonlinear eddy viscosity model with a different value of steady-state Richardson number is as good as the Mellor–Yamada model in terms of predictability, and the eddy viscosity and diffusivity profiles follow the principle of law of the wall. Additionally, the present formulation does not require computing the stability functions and the ease of implementation into numerical ocean models gives the present formulation an upper hand over the existing formulations in the field of turbulence modelling in oceanography.     

转动效应对恒星热力学结构与演化的影响研究

转动效应对恒星结构与演化的两大方面的影响体现在动力学效应和元素混合上.本文利用国际MESA程序,研究了转动效应对20 M_⊙恒星在主序阶段热力学结构的影响.发现转动的动力学效应能使恒星中心温度变低,减少了恒星表面的不透明度,中心平均分子量和表面熵.由于动力学效应对恒星热结构的调整,降低了恒星的氢燃烧率,恒星向低温和低光度端演化.转动的元素混合效应减小了恒星的中心温度、密度、压强、紧密度、表面不透明度和平均分子量,使恒星表面氦元素、氮元素明显超丰,中心燃烧核区域变大,延长恒星在主序阶段的寿命.     

On the energy in relativistic stellar dynamics

Using the results of the preceding paper we evaluate in the post-Newtonian approximation the energy integral for a system of extended bodies with arbitrary internal structure and internal motions.On leave of absence from the Astronomy Department, University of Thessaloniki, Thessaloniki, Greece.     

On the magnetic anisotropy of chromium

Magnetization and susceptibility measurements have been performed on a single crystal of chromium for field orientations parallel to the symmetry directions [100], [110] and [111] of the cubic unit cell. Particular emphasis is given to the weak temperature-orientation-and field-dependent contributions to the longitudinal (field parallel) susceptibility. For the high-temperature antiferromagnetic phase with transversally polarized spin-density wave (TSDW) the magnetic easy direction is along [100] and the magnetic hard one along [110]. In the low-temperature phase with longitudinal spin density waves (LSDW) the significance of these directions has reversed. The magnetization is not strictly a linear function of the field and shows a weak minimum atB ₀1.8 T in the TSDW phase. This minimum does shift discontinuously at the spin-flip transition (T _sf=132 K) to a value of 4.6 T in the LSDW phase. TheJ/B ₀-minimum is considered as due to the field induced change from the orientationally degenerated multidomain state into a state with only polarization directions perpendicular to the magnetic field.On leave from Academy of Mining and Metallurgy, Department of Solid State Physics, PL-30-059 Krakow, Poland     

On the magnetic anisotropy of CuO

The anisotropy of the magnetic susceptibility of CuO has been measured. In both, the paramagnetic and the antiferromagnetic state the susceptibility can be described to a good approximation by

Calculation of the effect of anisotropy on the ferromagnetic resonance frequency

The accuracy of the calculation of the effect of magnetocrystalline anisotropy and of elastic stress anisotropies on the ferromagnetic resonance frequency is investigated by introducing effective demagnetization factors. Relationships are found to determine the accuracy of Macdonald's formula.     

On the magnetocrystalline anisotropy of nickel-iron ferrites

In order to determine regularities in the temperature dependence of the magnetocrystalline anisotropy of nickel-iron ferrites, studies of single-crystal spheres of these ferrites of various compositions were made by the torque method. It was established that the function K₁ (T) is affected by the presence of ions of bivalent iron (the presence of cobalt ions in the samples or in the charge was not detected by either chemical or x-ray methods). In the absence of ions of bivalent iron, K₁ decreases in absolute value with rise in temperature, always remaining negative. With increased concentrations of Fe² ions, K₁ can have a positive sign at high and low temperatures, and a negative sign in the intermediate temperature range.The function K₁(T) is affected by initial brief high-temperature (900 ° C, 2 hr) and prolonged low-temperature (300–350 ° C, 2 days) heat treatment of the single crystals. It was established that the heat treatments also affect other magnetic and electric properties of the single crystals studied.