热海王星系统HD 106315的近$2:1$ 平运动共振捕获与轨道演化

通过结合理论分析和数值模拟方法,可以对热海王星系统HD 106315轨道迁移中的近2:1平运动共振捕获机制以及潮汐作用下的演化过程进行研究.在轨道迁移阶段,初始轨道半长径、初始偏心率以及行星c的偏心率衰减系数K会对系统轨道构型产生影响.数值模拟结果显示当初始轨道半长径分别为ab～0.4 au、ac～0.8 au,偏心率eb和ec均小于0.03时, HD 106315b和HD 106315c在中央恒星的引力作用以及原行星盘粘滞作用下向内迁移, 65000 yr左右两颗行星均可迁移至当前观测位置附近并形成近2:1平运动共振捕获.此外,中央恒星的潮汐效应也可能会对行星系统共振构型产生影响,理论分析表明当行星潮汐耗散系数Q=100时,潮汐效应造成的轨道半长径衰减使系统轨道周期比发生的变化可能是系统脱离共振构型的原因.数值模拟结果显示, HD 106315系统内两颗行星Q103时,来自中央恒星的潮汐效应并不会使行星系统产生明显的偏心率和轨道半长径衰减,不足以使HD 106315行星系统在剩余寿命内脱离2:1平运动共振轨道构型.     

低质量Kepler行星的潮汐演化研究

Kepler空间计划发现了大量半径小于4 R_⊕(R_⊕为地球半径)的近轨道行星,成为Kepler探测的特色之一,它们对当前的行星形成模型提出了新的挑战.行星与其中心恒星之间的潮汐效应对重塑这类行星的轨道构型具有重要影响.基于各种初始的轨道分布数值模拟了近轨道、低质量行星的潮汐演化,定性地给出了行星最后的轨道分布特征,轨道半长轴和峰值均随着初始的半长轴和偏心率增大而变大.对于初始的平均半长轴在0.1au以内,平均偏心率大于0.25时,数值模拟结果与观测比较接近.潮汐耗散系数、恒星和行星的质量等相关参数对潮汐演化后的半长轴分布影响都比较小.基于数值模拟结果,尝试了揭示低质量行星的形成机制:它们很可能形成于原行星盘的较远处,具有中等的轨道偏心率,后来在原行星盘中经历了Ⅰ类迁移到达目前的轨道,但是这不能排除行星的当地形成机制.     

HD 12661行星系统构形的形成与稳定性

最近的多普勒观测表明恒星HD 12661周围存在两颗中等偏心率轨道上运行的行星,内行星的最小质量为2．3木星质量,轨道周期为263．6天;外行星的最小质量为1．57木星质量,轨道周期为1444．5天．该系统的稳定性要求两颗行星处在平运动轨道共振．用数值方法研究了该系统形成初期在恒星气体盘作用下的轨道迁移与稳定性,计算了行星在迁移中被平运动共振俘获的概率．发现这两颗行星目前很可能正处在11:2平运动共振边缘,且运动是混沌的,从而澄清了关于系统目前构形的不同说法,并且很可能在系统形成后行星迁移到目前构形时,气体盘几乎消失了．     

GJ 876行星系统中潜在类地行星研究

用数值积分方法模拟探讨了GJ876行星系统中存在潜在类地行星的可能性．结果表明分别产生于内外两颗巨行星的长期共振v_1和v_2可激发类地行星(其轨道半长轴分布在0．21AU≤a＜0．50AU之间)的偏心率,并使它们在极短时间内被抛射出系统．然而,从动力学角度而言,类地行星潜在存在区域可分布在0．50 AU≤a≤1．00 AU之间,其能在系统中10~5年时间尺度上稳定地存在．     

天体运动的轨道偏心率研究概述---从恒星系统到行星系统

偏心率是描述天体运动轨道的重要参数之一, 能够为揭示天体的动力学演化提供重要线索, 进而帮助理解天体形成与演化的过程及背后的物理机制. 随着天文观测技术的不断发展, 人们对于天体运动轨道的研究已经走出太阳系, 包含的系统也从大质量端的恒星系统延伸到了低质量端的行星系统. 聚焦天体轨道偏心率研究, 回顾了目前在恒星系统(包括主序恒星、褐矮星以及致密星)和行星系统(包括太阳系外巨行星以及``超级地球''、``亚海王星''等小质量系外行星)方面取得的进展, 总结了不同尺度结构下偏心率研究的一些共同之处和待解决的问题. 并结合当下和未来的相关天文观测设备和项目, 对未来天体轨道偏心率方面的研究工作进行了展望.     

M型恒星周围系外行星统计研究

M型恒星(M dwarf)是主序星中质量较小的恒星,也是银河系中数量最多的恒星类型,在其周围形成的行星通常距离主星较近,宜居带也比F、G、K型恒星更靠近主星,更有利于发现系外宜居行星.研究表明, M型恒星周围平均存在2.5颗小质量行星,约为F、 G、 K型恒星的3.5倍,但M型恒星周围巨行星的出现率(occurrence rate)则比F、 G、K型小一个量级.基于M型恒星周围发现的401颗行星的参数开展了统计研究,发现质量越大的行星平均轨道半长径越大.类地行星约占行星总数的74%,且轨道半长径均小于1 au,其中28颗行星具有潜在宜居性.根据行星质量-半径关系,在质量等于4倍地球质量(M⊕)处存在一拐点,除少数几颗行星外,大部分小于该质量的行星可能都是由约65%的硅酸盐和约35%的铁组成,大于该质量的行星半径则随质量增加而迅速增大.约60%的M型恒星周围的行星位于多行星系统且轨道分布紧密,相邻行星轨道在3:2、5:3及2:1等平运动共振位置处存在峰值. M型恒星的多行星系统形成与演化等问题对现今的行星形成理论提出了新挑战.     

基于无量纲的轨道参数开展卫星性质统计研究

目前已发现了285颗围绕太阳系八大行星公转的卫星, 它们的轨道和物理性质呈现了丰富多样性. 目前为止, 几乎所有的卫星研究工作都基于单个卫星系统或者卫星群, 似乎缺少统一的研究. 提出了一个新的与行星性质无关、只与恒星半径有关的轨道参数n, 定义为以太阳半径为单位的轨道半长轴的自然对数. 不同行星的卫星的n值都存在双极分布, 绝大部分卫星在$n\gtrsim2$区间, 其次在$n\lesssim-1$区间, 位于中间区域的行星则很少. 从卫星物理参数和轨道参数与n的关系中发现, 分属六大行星的卫星有明显的共同特征. 首先, 轨道偏心率和轨道倾角偏大的卫星的n值都在3.5左右, 它们都是巨行星的不规则卫星. 其次, n值在-1和1之间的卫星绝大部分体积大、质量大、反照率高、自转速度慢. 从文献中找到11颗系外卫星候选体, 获得了它们轨道n值和卫星质量, 发现后者也是在-1< n< 1区间最大,其他区间偏小.这些统一的 规律暗示,太阳系内不同行星的卫星形成机制以及太阳系外卫星的形成机制可能一样或类似.     

行星形成数值模拟的研究现状与未来需求Ⅱ:行星迁移、核吸积以及大气逃逸

介绍了行星形成涉及到的几个重要阶段,如行星迁移、核吸积和大气逃逸的基本物理过程和数值模拟研究现状。行星迁移会影响行星的轨道偏心率和倾角,并改变原行星盘的结构;核吸积是决定行星演化为类地行星或者类木行星的关键因素;大气逃逸对行星的气候和演化产生重要影响。这些过程均涉及到复杂的辐射磁流体动力学过程,早期的理论研究往往采用很多人为的简化假设。随着超级计算机计算能力的提高和磁流体数值模拟算法的日渐成熟,人们已经可以对这类复杂的非线性动力学问题开展直接的数值模拟研究,克服了早期理论研究中人为假设的局限。但是,目前人们开展的研究主要基于磁流体动力学数值模拟,对辐射转移如何影响磁流体动力学过程的研究还比较欠缺。强调了进行辐射磁流体动力学数值模拟的必要性和紧迫性。针对辐射磁流体数值模拟程序的开发,从辐射转移,磁场的处理,吸积盘的自引力、三维效应、非理想效应和尘埃的效应等方面提出了相应的技术需求。介绍了本研究领域内发展辐射磁流体数值模拟的策略。     

近地小行星(10302) 1989 ML和(4660) Nereus的轨道特征及演化分析

近地小行星(10302) 1989 ML和(4660) Nereus作为下一代深空探测的候选目标一直备受关注. 在考虑太阳系主要天体的动力学背景下, 通过计算最大Lyapunov指数(MLE)及MEGNO (Mean Exponential Growth factor of Nearby Orbits)指数讨论它们的稳定性. 同时, 对每个小行星, 在其观测误差范围内按多元正态分布各选取1000个克隆粒子, 通过统计分析显示这两个小行星在10万年内可能的运动范围, 给出半长径-偏心率空间中的出现次数分布图, 并统计小行星与地球或其他大行星之间的密近交汇及碰撞的概率. 此外还对这两个小行星的标称轨道进行长期共振、Kozai共振及平运动共振的动力学分析. 综上得出结论, 1989 ML处在平运动共振主导的区域, 发生密近交汇的概率较小, 从而其轨道相对较稳定; 而Nereus处在地球的密近交汇区域, 轨道极不稳定.     

太阳系之外的行星(下)

1.脉冲星的计时法室女座脉冲星(PSRB1257+12)离地球1630光年,1992年观测到它的脉冲信号到达时间存在周期性提前和推迟,推断它有三颗行星环绕,最近又推断有小的第4颗行星,它们的质量跟地球质量(ME)相当。还发现另三个脉冲星可能有行星:PSR1829-10离地球3万光年,有一颗行星,其质量、轨道半径、绕转周期分别为10M_E、6个月;PSR1620-26离地球6000光年,有一颗行星,其质量(M_J 为木星质量)、轨道半径、绕转周期分别为5～10M_J、约10天文单位(AU)、100～120年;PSR0329+54有一颗行星,其质量、轨道半径、绕转周期还     

On the theory of the oblateness of the Sun

In this paper we first emphasize why it is important to know the successive zonal harmonics of the Sun's figure with high accuracy: mainly fundamental astrometry, helioseismology, planetary motions and relativistic effects. Then we briefly comment why the Sun appears oblate, going back to primitive definitions in order to underline some discrepancies in theories and to emphasize again the relevant hypotheses. We propose a new theoretical approach entirely based on an expansion in terms of Legendre's functions, including the differential rotation of the Sun at the surface. This permits linking the two first spherical harmonic coefficients (J ₂ and J ₄) with the geometric parameters that can be measured on the Sun (equatorial and polar radii). We emphasize the difficulties in inferring gravitational oblateness from visual measurements of the geometric oblateness, and more generally a dynamical flattening. Results are given for different observed rotational laws. It is shown that the surface oblateness is surely upper bounded by 11 milliarcsecond. As a consequence of the observed surface and sub-surface differential rotation laws, we deduce a measure of the two first gravitational harmonics, the quadrupole and the octopole moment of the Sun: J ₂=−(6.13±2.52)×10⁻⁷ if all observed data are taken into account, and respectively, J ₂=−(6.84±3.75)×10⁻⁷ if only sunspot data are considered, and J ₂=−(3.49±1.86)×10⁻⁷ in the case of helioseismic data alone. The value deduced from all available data for the octopole is: J ₄=(2.8±2.1)×10⁻¹². These values are compared to some others found in the literature. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005238718479     

Accounting for the viscosity of the fluid core in the problem of the physical libration of the moon

A two-component theoretical model of the physical libration of the Moon in longitude is constructed with account taken of the viscosity of the core. In the new version, a hydrodynamic problem of motion of a fluid filling a solid rotating shell is solved. It is found that surfaces of equal angular velocity are spherical, and a velocity field of the fluid core of the Moon is described by elementary functions. A distribution of the internal pressure in the core is found. An angular momentum exchange between the fluid core and solid mantle is described by a third-order differential equation with a right-hand side. The roots of a characteristic equation are studied and the stability of rotation is proved. A libration angle as a function of time is found using the derived solution of the differential equation. Limiting cases of infinitely large and infinitely small viscosity are considered and an effect of lag of a libration phase from a phase of action of an external moment of forces is ascertained. This makes it possible to estimate the viscosity and sizes of the lunar fluid core from data of observations.     

Calculation of the global system of the field-aligned currents on the dayside of the magnetosphere

Using the well-known equation for the normal component of the current which exist near the tangential discontinuity in the plasma in the case of the frozen-in magnetic field, and supposing that the current closes in the ionosphere in the auroral oval in the region 1, one calculates and compares with the data of observations the dependence of the density of the field-aligned current at the level of the ionosphere on the local time.     

On the systematic errors of the determinations of the absolute orientation of the meridian marks

The classical method of determination of the absolute azimuth (or Bessel's parameter n) can secure sufficiently precision for RA from observations of stars at high geographical latitudes during polar night only.     

Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation

We calculate the so-called convective term, which shows up in the expression for the angular velocity of the elastic Earth, within the Andoyer formalism. The term emerges due to the fact that the elasticity-caused perturbation depends not only on the instantaneous orientation of the Earth but also on its instantaneous angular velocity. We demonstrate that this term makes a considerable contribution into the overall angular velocity. At the same time the convective term turns out to be automatically included into the correction to the nutation series due to the elasticity, if the series is defined by the perturbation of the figure axis (and not of the rotational axis) in accordance with the current IAU resolution. Hence it is not necessary to take the effect of the convective term into consideration in the perturbation of the elastic Earth as far as the nutation is related to the motion of the figure axis.     

Impact of the Quadrupole Moment of the Sun on the Dynamics of the Earth-Moon System

Range of values of the Sun's mass quadrupole moment of coefficient J₂ arising both from experimental and theoretical determinations enlarge across literature on two orders of magnitude, from around 10^-7 until to 10^-5. The accurate knowledge of the Moon's physical librations, for which the Lunar Laser Ranging data reach an outstanding precision level, prove to be appropriate to reduce the interval of J₂ values by giving an upper bound of J₂. A solar quadrupole moment as high as 1.1 10^-5 given either from the upper bounds of the error bars of the observations, or from the Roche's theory, is not compatible with the knowledge of the lunar librations accurately modeled and observed with the LLR experiment. The suitable values of J₂ have to be smaller than 3.0 10^-6. As a consequence, this upper bound of 3.0 10^-6 is accepted to study the impact of the Sun's quadrupole moment of mass on the dynamics of the Earth-Moon system. Such as effect (with J₂ = 5.5±1.3 × 10^-6) has been already tested in 1983 by Campbell & Moffat using analytical approximate equations, and thus for the orbits of Mercury, Venus, the Earth and Icarus. The approximate equations are no longer sufficient compared with present observational data and exact equations are required. As if to compute the effect on the lunar librations, we have used our BJV relativistic model of solar system integration including the spin-orbit coupled motion of the Moon. The model is solved by numerical integration. The BJV model stems from general relativity by using the DSX formalism for purposes of celestial mechanics when it is about to deal with a system of n extended, weakly self-gravitating, rotating and deformable bodies in mutual interactions. The resulting effects on the orbital elements of the Earth have been computed and plotted over 160 and 1600 years. The impact of the quadrupole moment of the Sun on the Earth's orbital motion is mainly characterized by variations of , , and . As a consequence, the Sun's quadrupole moment of mass could play a sensible role over long time periods of integration of solar system models. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the role of the motion of the photospheric footpoints of the magnetic field lines

By means of a simple relation between the velocity v of the fluid particle and the velocity v_f of the photospheric footpoint of the magnetic field line v_z and B_z being respectively the components of v and the magnetic field B normal to the photospheric surface, it is shown formally that through the phtospheric surface the transport of all the quantities attributed to the magnetic field, such as the magnetic flux, the magnetic energy and the helicity, is independent of v_z, and v_f is the only kinematical quantity on which the transport depends. In addition, in the neighborhood of the neutral line the velocity v_l of the moving curve of constant B_z is found to be equal approximately to the component of v or v_f in the direction of v_l. Since v_l can be measured or extimated, so can the components of v and v_f near the neutral line.     

Determination of the temperature of the solar corona from the spectrum of the electron-scattering continuum

When the K-corona is formed by the scattering of photospheric radiation from free electrons, the Fraunhofer lines are greatly broadened by the thermal motions of the hot electrons. This paper discusses the possibility of measuring the coronal electron temperature from the residual depressions in the K-coronal spectrum. If the ratio of the intensities at 4100 Å and 3900 Å can be measured to an accuracy of ±1%, the coronal temperature can be inferred to an accuracy of ±0.2 MK. The temperature of a coronal inhomogeneity may also be measured by this method, provided the position angle is known.Now at Fraunhofer Institute, Freiburg, Germany.     

在后牛顿引力理论(PPN形式)中引力常数变化对地球自转产生的效应

介绍和论述了在后牛顿引力理论(PPN形式)中在优越参考系和非优越参考系中经过参数化后引力常数变化对地球自转产生的效应,其中特别重点介绍了年周期变化的效应。此外也将理论结果同观测结果相对比。