绝热非径向太阳振动的数值计算方法

本采用改进后的平行Ｓｈｏｏｔｉｎｇ方法，即连续正交归一化方法，通过增加系统的秩和把微分方程从线性变成非线性的方法，使得病态方程变成非病态方程，克服了平行Ｓｈｏｏｔｉｎｇ方法（不连续正交归一化方法）的主要困难：一是选择径向网格点数目的问题，如果被检验振动模的径向节点数大或小，所需要的网格点数则多或少；二是在远离阈值的时候，尚未有合适的方法提高计算精度的问题。数值计算出了标准太阳模型的绝热非径向太阳     

非绝热过程对太阳p模振动的影响

本文讨论了与非绝热性有关的辐射损失和对流转移对太阳ｐ模振动的影响．在非绝热情况下，ｐ模的本征频率增加了虚部σ（１）ｉ和σ（２）ｉ．本文试图探讨一种渐进方法研究非绝热效应对太阳ｐ模振动的影响．在渐进近似失效的太阳外大气层，利用表面相移的相关关系给出了非绝热振动方程的严格解．对低、中间频率的振动模，通过渐进解和表面解在外大气层的拟合，得到表面相移只是频率的函数．与绝热振动相比，考虑非绝热效应有可能改善太阳５分钟振动的理论频率和观测频率之间存在的偏差．     

非绝热过程对太阳P模振动的影响

本讨论了与非绝热性有关的辐射损失和对流转移对太阳ｐ模振动的影响。在非绝热情况下，Ｐ模的本征频率增加虚σｉ和σ＾２（）ｉ。本试图探讨一种渐进方法研究非绝热产应对太阳Ｐ模振动的影响。在渐近近拟效的太阳外大气层，利用表面相移的相关关系给出了非绝热振动方程的严格解。     

红巨星∈Ophiuchi的类太阳振动

最近在红巨星∈ Ophiuchi(G9.5Ⅲ)中观测到了类太阳振动.大频率间隔为4.8μHz,并证实了∈ Ophiuchi中存在非径向振动模.依据∈ Ophiuchi红巨星观测到的振动频率数据和它在赫罗图中的位置,采用恒星演化计算与恒星振动计算相结合的方法,对∈ Ophiuchi红巨星的质量、金属丰度、年龄、半径进行了初步的限制.     

太阳p模振动的激发机制

本文估计了激发单个太阳ｐ模振动需要的能量输入率Ｅ≡ＥΓ,其中谱线宽度Γ假设是振动模能量衰减率的观测值．在改进后的对流湍流三维时空分离描述的基础上,利用太阳对流区的混合长模型计算了振动模的激发率．认为太阳ｐ模振动主要是由雷诺应力扰动激发的,即ｐ模激发对应着对流湍流运动引起的声波发射．对于频率ν＜３ｍＨｚ,振动模的激发率为Ｅ∝ν７;频率ν＞３ｍＨｚ,振动模的激发率为Ｅ∝ν－５．理论计算的振动能谱与观测结果基本符合．     

关于数值求解天体运动方程的几个问题

本文讨论三个问题：1.在采用各种非辛（Symplectic）的数值积分器积分天体运动方程时，截断误差将引起人为的能量耗散，这一问题是不能用简单地在相应的力模型中加进一个人为的阻力因子而得以解决的，被歪曲的能量（或数值轨道）必须在积分过程的每一步用能量关系来进行校正，此即能量控制方法．2.当摄动加速度涉及到坐标轴的旋转时，如何在各种积分器中采用能量控制方法．3.对于大偏心率轨道，用数值方法求解相应运动方程时，积分步长必须随运动天体与中心天体之间的距离变化而改变，显然，这对所有积分器都是不方便的，特别是多步积分器．本义给出了一种步长均匀化的处理，可以使上述大偏心率轨道积分问题按定步长计算．     

行星摄动力对太阳活动的调制

本文采用天体力学方法，考虑太阳系九大行星对太阳表面局部区域的摄动力，建立了太阳表面受行星起潮力的数值计算模型．利用此模型，针对历史上发生的100个大太阳耀斑事件，计算各耀斑区耀斑发生前后所受行星起潮力的变化．从耀斑发生的时间分布统计得到：在100个耀斑中，有75个耀斑发生在行星综合起潮力合力极大前后三天内．证明行星摄动对太阳活动有调制作用．最后，本文还对太阳活动起源、活动周期等问题进行了简要的讨论．     

90年代太阳模型和太阳震荡研究进展(II):太阳振荡研究进展(英)

太阳振荡研究现已成为研究太阳内部性质的新手段,也成为检验太阳模型构造时输入物理参量的最重要工具。90年代以来理论与观测日震频率的差别已随输入物理参量及太阳振荡理论的改进而大为减小,可是现有的差别仍远大于观测误差。由日震反演可对太阳内部对流区、表面氦丰度及自转随纬度和径向的分布都有更多了解。太阳振荡的湍动随机激发及激发源的位置都已得到研究,不过现在问题还未完全解决。今后一方面要探测更多的振动方式,另一方面也需要解决不同观测者得到的结果存在系统差的问题,而最外层的非绝热现象及理论与观测存在差别仍是最关键的难题。     

初轨计算中的病态分析

本文对现有初轨计算方法进行病态性分析与误差分析；研究结果表明：病态对现有初轨算法的影响，主要来源于法方程系数中包含观测误差．系数行列式愈大，定轨精度的损失愈多，当■被随机误差项△μ淹盖时，现有初轨算法将失效．此外，仿真结果还显示：■与△μ的大小还极大地依赖观测弧段的空间位置，当观测弧段包含近站点作为中点时，■最大，而■小，此时定轨精度较高；当观测弧段位于近站点的某一侧时，■小，而■大，此时定轨精度较低，观测弧段愈偏离近站点，病态影响愈大；因而在观测时，应尽量使观测弧段与近站点对称（此时μ值较大），这是提高短弧定轨的一种有效途径．     

用光电等高仪Ⅰ型,Ⅱ型测定太阳直径的方案及其精度估计

精确测定太阳直径具有理论和实际应有和上的双重意义，本文分析了现行测定太阳直径的几种方法的不足之处，指出了用中国光电等高仪测定太阳直径具有若干特点，文中提出了用光电等高仪太阳直径的两种实用方案，并进行了模拟计算。计算表明两种方案都能以优于０″．１的精度测定太阳直径，而单像方案具有更高的精度。     

MHD waves in coronal magnetic arcades

We analyze the eigenmodes of the solar coronal magnetic arcade that describes the magnetic field of a bipolar active region using the eikonal method for ideal magnetohydrodynamic equations. We write out the eikonal equations for Alfvèn and magnetoacoustic waves and derive the equations for the amplitudes of the zeroth approximation. We construct the wave fields for Alfvèn and fast magnetoacoustic modes and derive the expressions for the eigenfrequencies. We show that Alfvèn modes of a given frequency are near a number of magnetic surfaces, while fast magnetoacoustic eigenmodes are near nonmagnetic surfaces. A discrete set of eigenfrequencies that continuously change from one surface to another corresponds to each such surface.     

Internal rotation of the Sun as inferred from GONG observations

Helioseismology is a direct and most informative method of studying the structure and dynamics of the Sun. Determining the internal differential rotation of the Sun requires that the frequencies of its eigentones be estimated with a high accuracy, which is possible only on the basis of continuous long-term observations. The longest quasi-continuous series of data have been obtained by the Global Oscillation Network Group (GONG). The parameters of each individual mode of solar acoustic oscillations with low spherical degrees l=0, 1, 2, 3, 4, 5, 6 are determined by using 1260-day-long series of GONG observations. The mean frequency splitting by rotation for the modes of each radial order n is calculated by using all possible combinations between the eigenfrequencies in multiplets. As a result, it has become possible to statistically estimate the splitting and its measurement errors for the modes of each radial order. The mean splitting for each given degree l=1–6 is presented under the assumption of its independence of oscillation frequency, which holds for the achieved accuracy. The frequencies and splittings for the modes with low spherical degrees l, together with the MDI group results for higher degrees l, are used to invert the radial profile of solar angular velocity. Using the SOLA method to solve the inverse problem of restoring the rotation profile has yielded solutions sensitive to the deepest stellar interiors. Our results indicate that the solar core rotates faster than the surface, and there may be a local minimum in angular velocity at its boundary.     

Late phase gradual enhancements in microwaves and hard X-rays of the 6 November 1980 flare

Solar Physics - We have calculated eigenfrequencies of radial and nonradial p-mode oscillations with low harmonic index l (l = 0, 1, 2, 3, and 4) for a standard solar model with normal composition...     

Numerical integration methods for orbital motion

The present report compares Runge-Kutta, multistep and extrapolation methods for the numerical integration of ordinary differential equations and assesses their usefulness for orbit computations of solar system bodies or artificial satellites. The scope of earlier studies is extended by including various methods that have been developed only recently. Several performance tests reveal that modern single- and multistep methods can be similarly efficient over a wide range of eccentricities. Multistep methods are still preferable, however, for ephemeris predictions with a large number of dense output points.     

An Operable Solution Approach to Interplanetary Hydrodynamic Shock Waves

In this paper, an operable solution approach is proposed to solve interplanetary hydrodynamic shock waves propagating in the interplanetary medium of solar wind background derived from Parker's hydrodynamic model. In our case the problem concerned is reduced to a set of ordinary differential equations (ODEs) involving the solar wind background parameters velocity v0(r), density 0(r), and pressure p0(r). The entire information for the shock can be obtained easily by obtaining the numerical solutions to the set of ODEs.     

A convenient method to obtain stellar eigenfrequencies

The differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. We employ the Cowling-approximation, i.e. neglect the Eulerian perturbation of the gravitational potential, and, in order to preserve selfadjointness, require that the Eulerian pressure perturbation vanishes at the outer boundary. For a solar model, comparison of first results with results obtained from a Henyey method shows that the matrix method is convenient, accurate, and fast.     

Nonaxisymmetric Oscillations of Thin Twisted Magnetic Tubes

In this paper we study nonaxisymmetric oscillations of thin twisted magnetic tubes taking the density variation along the tube into account. We use the approximation of the zero-beta plasma. The magnetic field outside the tube is straight and homogeneous; however, it is twisted inside the tube. We assume that the azimuthal component of the magnetic field is proportional to the distance from the tube axis and that the tube is only weakly twisted (i.e., the ratio of the azimuthal and axial components of the magnetic field is small). Using the asymptotic analysis we show that the eigenmodes and eigenfrequencies of the kink and fluting oscillations are described by a classical Sturm – Liouville problem for a second-order ordinary differential equation. The main result is that the twist does not affect the kink mode.     

The continuous spectrum of MHD waves in 2D solar loops and arcades. First results on poloidal mode coupling for poloidal magnetic fields

A first attempt is made to study the continuous spectrum of linear ideal MHD for 2D solar loops and to understand how 2D effects change the continuum eigenfrequencies and continuum eigenfunctions. The continuous spectrum is computed for 2D solar loops with purely poloidal magnetic fields and it is investigated how non-circularity of the cross-sections of the poloidal magnetic surfaces and variations of density along the poloidal magnetic field lines change the continuous spectrum and induce poloidal wave number coupling in the eigenfunctions. Approximate analytical results and numerical results are obtained for the eigenfrequencies and the eigenfunctions and the poloidal wave number coupling is clearly illustrated. It is found that the continuum frequencies are substantially increased, that the ranges of the continuum frequencies are considerably enlarged and that the derivatives of the continuum frequencies normal to the magnetic surfaces are substantially increased. The eigenfunctions are strongly influenced by poloidal wave number coupling. Implications of these findings for the heating mechanisms of resonant absorption and phase mixing are briefly considered.Research Assistant of the Belgian National Fund for Scientific Research.