[en] The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (i.e., ∼10⁻¹²). The results of collision integrals and their derivatives for −7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10⁻¹⁰. For very weakly coupled plasma ( ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10⁻¹¹. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’; for an attractive potential, the results in cases of intermediate and strong coupling show significant differences. The resulting resistance coefficients are tested in the solar model. Comparing with the widely used models of Cox et al. and Thoul et al., the resistance coefficients in the screened Coulomb potential lead to a slightly weaker effect in the solar model, which is contrary to the expectation of attempts to solve the solar abundance problem.

[en] Detached eclipsing binary stars with convective cores provide a good tool to investigate convective core overshoot. It has been performed on some binary stars to restrict the classical overshoot model which simply extends the boundary of the fully mixed region. However, the classical overshoot model is physically unreasonable and inconsistent with helioseismic investigations. An updated model of overshoot mixing was established recently. There is a key parameter in the model. In this paper, we use observations of four eclipsing binary stars, i.e., HY Vir, YZ Cas, χ² Hya, and VV Crv, to investigate a suitable value for the parameter. It is found that the value suggested by calibrations on eclipsing binary stars is the same as the value recommended by other methods. In addition, we have studied the effects of the updated overshoot model on the stellar structure. The diffusion coefficient of convective/overshoot mixing is very high in the convection zone, then quickly decreases near the convective boundary, and exponentially decreases in the overshoot region. The low value of the diffusion coefficient in the overshoot region leads to weak mixing and a partially mixed overshoot region. Semi-convection, which appears in the standard stellar models of low-mass stars with convective cores, is removed by partial overshoot mixing.

[en] Helioseismic investigation has suggested applying turbulent convection models (TCMs) to convective overshoot. Using the turbulent velocity in the overshoot region determined by a TCM, one can deal with overshoot mixing as a diffusion process, which leads to incomplete mixing. It has been found that this treatment can improve solar sound speed and Li depletion in open clusters. In order to investigate whether the TCM can be applied to overshoot mixing outside the stellar convective core, new observations of the eclipsing binary star HY Vir are adopted to calibrate the overshoot mixing parameter. The main conclusions are as follows: (1) the solar TCM parameters and overshoot mixing parameter are also suitable for the eclipsing binary system HY Vir, (2) the incomplete mixing results in a continuous profile of hydrogen abundance, and (3) the e-folding length of the region, in which the hydrogen abundance changes due to overshoot mixing, increases during stellar evolution.

[en] A water quenching method is used to produce as-cast Zr₄₈Cu₃₆Al₈Ag₈ rods with diameters from 20 mm to 25 mm. The microstructures of the as-cast samples were investigated by X-ray diffraction, optical microscopy and scanning electron microscopy. Furthermore, the crystallization behavior of the Zr₄₈Cu₃₆Al₈Ag₈ glassy alloy was examined by XRD and transmission electron microscopy. Based on the results obtained one can assume that the simultaneous precipitation of the Zr₂Cu+AlCu₂Zr eutectic phases is the possible reason for the high stabilization of the quaternary Zr₄₈Cu₃₆Al₈Ag₈ supercooled liquid.

[en] The overshooting in the framework of the turbulent convection model is investigated in the solar overshooting region. The overshooting mixing is treated as a diffusive process. It is found that the sound speed profile can be improved to be in good agreement with helioseismic inversions. The bump in the sound speed differences between solar models and the helioseismical inversions below the base of the solar convective envelope is almost eliminated by the overshooting mixing. The overshooting mixing leads to a significant depletion of Li in the main-sequence stage. Li abundance in the solar surface can be reduced to about 1% of its initial abundance in the solar models with the overshooting mixing. The solar model with the overshooting shows a smooth profile of the temperature gradient, which is also favored by the helioseismology.

[en] Turbulent convection models (TCMs) are thought to be good tools to deal with the convective overshooting in the stellar interior. However, they are too complex to be applied to calculations of stellar structure and evolution. In order to understand the physical processes of the convective overshooting and to simplify the application of TCMs, a semi-analytic solution is necessary. We obtain the approximate solution and asymptotic solution of the TCM in the overshooting region, and find some important properties of the convective overshooting. (1) The overshooting region can be partitioned into three parts: a thin region just outside the convective boundary with high efficiency of turbulent heat transfer, a power-law dissipation region of turbulent kinetic energy in the middle, and a thermal dissipation area with rapidly decreasing turbulent kinetic energy. The decaying indices of the turbulent correlations k, u_r'T'-bar, and T'T'-bar are only determined by the parameters of the TCM, and there is an equilibrium value of the anisotropic degree ω. (2) The overshooting length of the turbulent heat flux u_r'T'-bar is about 1H_k (H_k = |dr/dln k|). (3) The value of the turbulent kinetic energy at the convective boundary k_C can be estimated by a method called the maximum of diffusion. Turbulent correlations in the overshooting region can be estimated by using k_C and exponentially decreasing functions with the decaying indices.

[en] Recent three-dimensional (3D) simulations have shown that the turbulent kinetic flux (TKF) is significant. We discuss the effects of TKF on the size of the convection zone and find that the TKF may help solve the solar abundance problem. The solar abundance problem is that, with new abundances, the solar convection zone depth, the sound speed in the radiative interior, the helium abundance, and the density in the convective envelope are not in agreement with helioseismic inversions. We have performed Monte Carlo simulations on solar convective envelope models with different profiles of TKF to test its effects. The solar abundance problem is revealed in the standard solar convective envelope model with AGSS09 composition, which shows significant differences (∼10)) in density from the helioseismic inversions, but the differences in the model with the old composition GN93 is small (∼0.5)). In the testing models with a different TKF imposed, it is found that the density profile is sensitive to the value of TKF at the base of the convective envelope and insensitive to the structure of TKF in the convection zone. The required value of turbulent kinetic luminosity at the base is about –13% to – 19% L _☉. Comparing with the 3D simulations, this value is plausible. This study is for the solar convective envelope only. Evolutionary solar models with TKF are required to investigat the effects of TKF on the solar interior structure below the convection zone and the whole solar abundance problem, but the profile of the TKF in the overshoot region is necessary

[en] Convective overshoot mixing plays an important role in stellar structure and evolution. However, overshoot mixing is also a long-standing problem; it is one of the most uncertain factors in stellar physics. As is well known, convective overshoot mixing is determined by the radial turbulent flux of the chemical component. In this paper, a local model of the radial turbulent flux of the chemical component is established based on hydrodynamic equations and some model assumptions and is tested in stellar models. The main conclusions are as follows. (1) The local model shows that convective overshoot mixing could be regarded as a diffusion process and the diffusion coefficient for different chemical elements is the same. However, if the non-local terms i.e., the gradient of the third-order moments, are taken into account, the diffusion coefficient for each chemical element should in general be different. (2) The diffusion coefficient of convective/overshoot mixing shows different behaviors in the convection zone and in the overshoot region because the characteristic length scale of the mixing is large in the convection zone and small in the overshoot region. Overshoot mixing should be regarded as a weak mixing process. (3) The diffusion coefficient of mixing is tested in stellar models, and it is found that a single choice of our central mixing parameter leads to consistent results for a solar convective envelope model as well as for core convection models of stars with masses from 2 M to 10 M.

[en] Giant flares on soft gamma-ray repeaters that are thought to take place on magnetars release enormous energy in a short time interval. Their power can be explained by catastrophic instabilities occurring in the magnetic field configuration and the subsequent magnetic reconnection. By analogy with the coronal mass ejection events on the Sun, we develop a theoretical model via an analytic approach for magnetar giant flares. In this model, the rotation and/or displacement of the crust causes the field to twist and deform, leading to flux rope formation in the magnetosphere and energy accumulation in the related configuration. When the energy and helicity stored in the configuration reach a threshold, the system loses its equilibrium, the flux rope is ejected outward in a catastrophic way, and magnetic reconnection helps the catastrophe develop to a plausible eruption. By taking SGR 1806–20 as an example, we calculate the free magnetic energy released in such an eruptive process and find that it is more than 10⁴⁷ erg, which is enough to power a giant flare. The released free magnetic energy is converted into radiative energy, kinetic energy, and gravitational energy of the flux rope. We calculated the light curves of the eruptive processes for the giant flares of SGR 1806–20, SGR 0526–66, and SGR 1900+14, and compared them with the observational data. The calculated light curves are in good agreement with the observed light curves of giant flares.