The YNEV stellar evolution and oscillation code

We have developed a new stellar evolution and oscillation code YNEV,which calculates the structures and evolutions of stars,taking into account hydrogen and helium burning.A nonlocal turbulent convection theory and an updated overshoot mixing model are optional in this code.The YNEV code can evolve low-and intermediate-mass stars from the pre-main sequence to a thermally pulsing asymptotic branch giant or white dwarf.The YNEV oscillation code calculates the eigenfrequencies and eigenfunctions of the adiabatic oscillations for a given stellar structure.The input physics and numerical scheme adopted in the code are introduced.Examples of solar models,stellar evolutionary tracks of low-and intermediate-mass stars with different convection theories(i.e.mixing-length theory and nonlocal turbulent convection theory),and stellar oscillations are shown.     

A Note on the Supersonic Convection in Stellar Atmospheres

By using a non-local convection theory, both the local and nonlocal convective envelope models of evolutionary series of stars with masses from 1 to 30 solar masses are calculated. The problem of supersonic convection is reviewed. The results show that the convective velocities in the stellar atmosphere are seriously overestimated by the local mixing-length theory. Convection is strongly supersonic in the atmospheres of yellow giant and super-giants, while the local mixing-length theory is used. However, it becomes subsonic for most stars when convection returns to the normal nonlocal treatment. Convection velocities increase with increase of luminosities of stars. There is still weak supersonic convection in few red and yellow giant and super-giants. It is suspected whether this supersonic convection in stellar atmospheres is true.     

On the stability of mean-field models of the solar convection zone

The stability of the solutions of the mean-field theories of turbulent media is questioned. It is done here for the model equations for the solar convection zone which have been used, in particular, to explain the differential rotation. We present an approximation valid for axisymmetric, short-wave disturbances. A critical local Rayleigh number can be defined - involving eddy diffusivities - above which the stratification becomes unstable. For mixing-length models of the solar convection zone we always find sub-critical Rayleigh numbers. One must be careful, however, with other theoretical models. Those we have considered do not reach sufficiently high surface pressure values so that there the associated Rayleigh numbers exceed their critical limits. In the outermost layers in such models, therefore, the solutions could really be unstable.     

关于恒星大气超声对流的注释

1引言尽管有诸多的不满之处,由于其物理上的直观性和应用上的简单性,至今混合长理论仍几乎是唯一一个广泛用于恒星结构、演化和脉动计算的恒星对流理论.混合长理论预言,在红、黄巨星和超巨星大气中,对流是超声速的.我们曾指出,混合长理论隐含了一个假定,对流是亚声速的.对于超声速对流,无论从物理的真实性,还是从混合长公式的数学表述来看,混合长理论都是不正确的.因此超声对流的真实性是存在问题     

8M_■恒星演化过程中湍流应力作用效果的分析

以恒星结构与演化理论中常用的混合程理论为基础,将湍流作用表现出来的宏 观应力引入恒星结构与演化模型中的流体静力学平衡方程．通过计算8M(?)恒星从主序星 到早期AGB星演化过程中湍流应力梯度与引力的比值来研究湍流作用对恒星演化与结构 的影响．结果发现:在核燃烧阶段其比值很小,湍流作用几乎可以忽略;但在RGB和早 期AGB演化阶段,发现在恒星外部存在一个湍流应力梯度为引力的几倍到几十倍的很小 区域,而该小区域以外的对流区内湍流作用力能达到引力的65％,这些对AGB星的中心 温度变化与热脉动发生的时间等恒星结构与演化规律有不同程度的影响．     

On efficiency of convection of Öpik's cellular convection theory

The physical meaning of the convection efficiency parameter of Öpik's theory is clarified by relating it to that of the mixing-length theory. A compact comparison of both theories is presented to explain the earlier findings of Gough and Weiss (1976), that Öpik's theory becomes indistinguishable from the mixing-length theory when the value of Öpik's cell depth is taken as being equal to 2.44 times the local pressure scale height for the solar convective envelope.     

Models of α Centauri A and B with and without seismic constraints: time dependence of the mixing-length parameter

The α Centauri (α Cen) binary system is a well-known stellar system with very accurate observational constraints on the structure of its component stars. In addition to the classical non-seismic constraints, there are also seismic constraints for the interior models of α Cen A and B. These two types of constraint give very different values for the age of the system. While we obtain 8.9 Gyr for the age of the system from the non-seismic constraints, the seismic constraints imply that the age is about 5.6–5.9 Gyr. There may be observational or theoretical reasons for this discrepancy, which can be found by careful consideration of similar stars. The α Cen binary system, with its solar-type components, is also suitable for testing the stellar mass dependence of the mixing-length parameter for convection derived from the binaries of Hyades. The values of the mixing-length parameter for α Cen A and B are 2.10 and 1.90 for the non-seismic constraints. If we prioritize the seismic constraints, we obtain 1.64 and 1.91 for α Cen A and B, respectively. By taking into account these two contrasting cases for stellar mass dependence of the mixing-length parameter, we derive two expressions for its time dependence, which are also compatible with the mass dependence of the mixing-length parameter derived from the Hyades stars. For assessment, these expressions should be tested in other stellar systems and clusters.     

A new look at the relationship between activity, dynamo number and Rossby number in late-type stars

The correlation between stellar activity, as measured by the indicator Δ R _HK, and the Rossby number Ro in late-type stars is revisited in light of recent developments in solar dynamo theory. Different stellar interior models, based on both mixing-length theory and the full spectrum of turbulence, are used in order to see to what extent the correlation of activity with Rossby number is model dependent, or otherwise can be considered universal. Although we find some modest model dependence, we find that the correlation of activity with Rossby number is significantly better than with rotation period alone for all the models we consider. Dynamo theory suggests that activity should scale with the dynamo number. A current model of the solar dynamo, the so-called interface dynamo, proposes that the amplification of the toroidal magnetic field by differential rotation (the ω -effect) and the production of the poloidal magnetic field from toroidal by helical turbulence (the α -effect) take place in different, adjacent layers near the base of the convection zone. A new scale analysis based on the interface dynamo shows that the appropriate dynamo number does not depend on the Rossby number alone, but also depends on an additional dimensionless factor related to the differential rotation. This leads to a new interpretation of the correlation between activity and Rossby number, which in turn leads to some conclusions about the magnitude of differential rotation in the dynamo layers of late-type main-sequence stars.     

Resistive and magnetized accretion flows with convection

We considered the effects of convection on the radiatively inefficient accretion flows (RIAF) in the presence of resistivity and toroidal magnetic field. We discussed the effects of convection on transports of angular momentum and energy. We established two cases for the resistive and magnetized RIAFs with convection: assuming the convection parameter as a free parameter and using mixing-length theory to calculate convection parameter. A self-similar method is used to solve the integrated equations that govern the behavior of the presented model. The solutions show that the accretion and rotational velocities decrease by adding the convection parameter, while the sound speed increases. Moreover, by using mixing-length theory to calculate convection parameter, we found that the convection can be important in RIAFs with magnetic field and resistivity.     

Studying the influence of turbulent mixing on thermonuclear burning regimes during X-ray bursts of neutron stars using the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">ε</Emphasis></Subscript> model

We study the influence of turbulent mixing on the development of thermonuclear flashes in the surface layers of neutron stars. A simple K _ε model that includes various physical processes is used to describe the turbulent processes. In contrast to the widespread mixing-length theory, the K _ε model does not require using additional dimensional parameters, traces the development of turbulence in dynamics, describes the various turbulence development scenarios (gravitational and shear instabilities, convection, semiconvection, etc.) in a unified way, and can be used in multidimensional numerical simulations. Empirical constants of the model are chosen on the basis of experimental data and direct numerical simulations of typical processes. We have used the Era and Tigr-3T software packages to numerically simulate thermonuclear flashes in the accretion-renewable atmospheres of neutron stars. Turbulence is shown to accelerate significantly the transport of released energy to the stellar surface. Mixing equalizes the concentrations of matter components throughout the burning layer and increases the amount of matter involved in the thermonuclear burning during a flash.     

Some properties of the kinetic energy flux and dissipation in turbulent stellar convection zones

We investigate simulated turbulent flow within thermally driven stellar convection zones. Different driving sources are studied, including cooling at the top of the convectively unstable region, as occurs in surface convection zones; and heating at the base by nuclear burning. The transport of enthalpy and kinetic energy, and the distribution of turbulent kinetic energy dissipation are studied. We emphasize the importance of global constraints on shaping the quasi-steady flow characteristics, and present an analysis of turbulent convection which is posed as a boundary value problem that can be easily incorporated into standard stellar evolution codes for deep, efficient convection. Direct comparison is made between the theoretical analysis and the simulated flow and very good agreement is found. Some common assumptions traditionally used to treat quasi-steady turbulent flow in stellar models are briefly discussed. The importance and proper treatment of convective boundaries are indicated.     

On the effect of turbulent anisotropy on pulsation stability of stars

Within the framework of a non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order(radial order n_r 5) p modes.The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most high-order(n r 5) p modes of all low-temperature stars become unstable. Fortunately,within a wide range of the anisotropic parameter c_3, stellar pulsation stability is not sensitive to the specific value of c_3. Therefore it is safe to say that calibration errors of the convective parameter c_3 do not cause any uncertainty in the calculation of stellar pulsation stability.     

Efficient turbulent compressible convection in the deep stellar atmosphere

We report on an application of gas-kinetic BGK scheme to the computation of turbulent compressible convection in the stellar interior. After incorporating the Sub-grid Scale (SGS) turbulence model into the BGK scheme, we tested the effects of numerical parameters on the quantitative relationships among the thermodynamic variables, their fluctuations and correlations in a very deep, initially gravity-stratified stellar atmosphere. Comparison indicates that the thermal properties and dynamic properties are dominated by different aspects of numerical models separately. An adjustable Deardorff constant in the SGS model cμ = 0.25 and an amplitude of artificial viscosity in the gas-kinetic BGK scheme C2 = 0 are appropriate for the current study. We also calculated the density-weighted auto-and cross-correlation functions in Xiong's turbulent stellar convection theory based on which the gradient type of models of the non-local transport and the anisotropy of the turbulence were preliminarily studied. No universal relations or con-stant parameters were found for these models.     

Anisotropy of turbulent transport in a convective layer

An estimate for the anisotropy of the turbulent viscositys is given in a convective layer heated from below and rotating around a vertical axis. In the case of two-dimensional convection, there is a stationary regime withs⊇2 regardless of the rotation. In the case of three-dimensional convection in a slowly rotating layer (with the Taylor number equal to 1600), nonstationary turbulent regimes take place withs⊇1.6 forR=2.5×10⁴ (R is the Rayleigh number) ands⊇1.2 forR=10⁴. The parameters plays an, important role in the theory of differential rotation of the convective solar or stellar envelopes. So far, it has been evaluated empirically or semi-empirically. Some prospects in the development of the theory of differential rotation are discussed here in terms of the moment theory of hydrodynamic fields. The relation between this strict approach and an anisotropic viscosity approximation is considered.     

Seismic Diagnostics on Stellar Convection Treatment from Oscillation Amplitudes of p-modes

The excitation rate P of solar p-modes is computed with a model of stochastic excitation which involves constraints on the averaged properties of the solar turbulence. These constraints are obtained from a 3D simulation. Resulting values for P are found 4.5 times larger than when the calculation assumes properties of turbulent convection which are derived from an 1D solar model based on Gough (1977)'s formulation of the mixing-length theory (GMLT). This difference is mainly due to the assumed values for the mean anisotropy of the velocity field in each case.Calculations based on 3D constraints bring the P maximum closer to the observational one.We also compute P for several models of intermediate mass stars (1 M 2 M).Differences in the values of P _max between models computed with the classical mixing-length theory and GMLT models are found large enough for main sequence stars to suggest that measurements of P in this mass range will be able to discriminate between different models of turbulent convection.     

Solar and stellar activity: The theoretical approach

The unified sight of solar and stellar activity has revealed a worthwhile concept under several aspects, gaming in the last decade the increasing favour of observers and theorists, and the term solar-stellar connection has recently been introduced to point out the complementarity of solar and stellar observations in the background of the basic role played by the magnetic field.The great development of stellar activity observations suggests a much wider scenario than it were possible to imagine even a few years ago and stimulates theoretical work, most of which is in the framework of the - dynamo theory.Although dynamo theory seems to be plausible and successful in capturing the fundamental mechanism of solar and stellar activity, several uncertainties and intrinsic limits do still exist and are discussed together with alternative or complementary suggestions.Further, it is stressed the relevance of nonlinear problems in dynamo theory — as magnetoconvection, growth and stability of flux tubes against magnetic buoyancy, hydromagnetic global dynamos — to improve our understanding of both small and large scale interaction of rotation, turbulent convection and magnetic field, and of the transition from linear to nonlinear regime. Finally, recent dynamo models of stellar activity are critically reviewed, as to the dependence of activity indexes and cycles on rotation rate and spectral type.Open problems to be solved by future work are outlined, pointing out the role of ever increasing stellar data in widening out our comprehension of the dynamo operation modes, which seem to depend on stellar structure, rotation and age.     

Convection zone of white-dwarf stars

The boundary convection zones of hot helium white-dwarf stars (WDSs) in the range 17000 KT _e30000 K are studied. Recently, an anisotropic mixing-length theory (AMLT) which determines the mixing-length parameter locally is applied for the convection zones calculation. Comparing with the calculations by using the (MLT), it is found that maximum velocity decreases appreciably, and the other boundary conditions are affected.     

An analysis of the effect of turbulent stress on the evolution of an 8M⊙ start

On the basis of the mixing-length theory, macroscopic turbulent stress is incorporated into the hydrostatic equilibrium equation in our model of stellar structure and evolution. For an 8M_⊙ star from the main sequence stage to the early AGB stage, the effect of turbulence was followed through calculation of the ratio of turbulence stress gradient to gravity. The results are: during the stages of nuclear burning the ratio is almost negligibly small; however, during the RGB and early AGB stages, there exists a thin layer in the outer convective layer where the ratio amounts to several units, while outside the thin layer the ratio may attain 65%. These facts have obvious effects on the central temperature of the AGB star and on the star's structure and evolutionary features at the onset of thermal pulsation.     

Turbulent viscosity,magnetic diffusivity,and heat conductivity under the influence of rotation and magnetic field

The old problem of turbulent diffusion is addressed to define the influence of rotation and magnetic field - the usual ingredients of astrophysical bodies - on the effective transport coefficients. Either rotation and magnetism produce the anisotropy and quenching. The tensorial structures of the diffusivities and their dependences on the angular velocity and the field strength are explicitly defined. An example of application of the theory to the global stellar circulation model is given and the implications for cosmic dynamos are briefly discussed.