3. Solar System Formation and Early Evolution: the First 100 Million Years

The solar system, as we know it today, is about 4.5 billion years old. It is widely believed that it was essentially completed 100 million years after the formation of the Sun, which itself took less than 1 million years, although the exact chronology remains highly uncertain. For instance: which, of the giant planets or the terrestrial planets, formed first, and how? How did they acquire their mass? What was the early evolution of the “primitive solar nebula” (solar nebula for short)? What is its relation with the circumstellar disks that are ubiquitous around young low-mass stars today? Is it possible to define a “time zero” (t ₀), the epoch of the formation of the solar system? Is the solar system exceptional or common? This astronomical chapter focuses on the early stages, which determine in large part the subsequent evolution of the proto-solar system. This evolution is logarithmic, being very fast initially, then gradually slowing down. The chapter is thus divided in three parts: (1) The first million years: the stellar era. The dominant phase is the formation of the Sun in a stellar cluster, via accretion of material from a circumstellar disk, itself fed by a progressively vanishing circumstellar envelope. (2) The first 10 million years: the disk era. The dominant phase is the evolution and progressive disappearance of circumstellar disks around evolved young stars; planets will start to form at this stage. Important constraints on the solar nebula and on planet formation are drawn from the most primitive objects in the solar system, i.e., meteorites. (3) The first 100 million years: the “telluric” era. This phase is dominated by terrestrial (rocky) planet formation and differentiation, and the appearance of oceans and atmospheres.     

On the periodical structures in populations of galaxies and of clusters of galaxies

Analysing the distribution of the redshift of clusters of galaxies, obtained from the catalogue of SCHMIDT (1986), two already known periodical structures were confirmed and both periods were extended by a number of periods — approximately by two times (We elucidated 5 new periods in the first structure and 4 in the second.). The statistical significance of these structures was estimated to 0.01 in the first case and to 0.02 in the second one. Particularly, the second structure may be the largest known object in the Universe (about 900 Mpc at H = 75 km s^-1 Mpc^-1). These results agree with the predictions of the axion-dominated early Universe. In addition, we discovered periodical structures of an another type — in luminosity functions of galaxies, which are members of rich clusters. Bei der Analyse des Katalogs von SCHMIDT (1986) wurden zwei periodische Strukturen in den Verteilungen der Rotverschiebungen von Galaxienhaufen festgestellt. In den beiden Strukturen wurden 5 bzw. 4 neue Perioden beobachtet, weshalb sich die Periodenzahl in jeder der beiden Strukturen etwa verdoppelt hat. Die statistische Signifikanzen dieser Strukturen wurden zu 0.01 und 0.02 abgeschätzt. Möglicherweise entspricht die zweite Struktur dem größten bekannten Objekt des Weltalls (etwa 900 Mpc bei H = 75 km s^-1 Mpc^-1). Diese Resultate stützen die Theorie eines axiondominierten frühen Universums. Außerdem wurden weitere periodische Strukturen in der Leuchtkraftfunktion von Galaxien aus reichen Galaxien-haufen entdeckt.     

在太阳磁场大气中FeIλ 5324.19(?)谱线的形成深度

本文在用Unno-Beckers方程计算光球和黑子本影磁场内FeIλ5324.19谱线形成过程中,计算了该谱线Stokes参数随5000连续谱光学深度分布的贡献函数及形成深度随波长的变化。计算结果表明:磁光效应的存在给该线横向磁场定标参数Q、U的形成深度的确定带来一定的复杂性,对I和V的形成深度的确定没有明显的影响。结合北京天文台太阳磁场望远镜半宽0.15的双折射滤光器,确定所观测磁场信息的形成深度。当对日面中心观测,在滤光器调至线心时,I形成在光球层及黑子高度100公里左右,在偏离线心0.15时V分量形成高度亦如此,Q、U分量的情况较复杂。     

On the variational approach to the periodic n-body problem

This expository paper gathers some of the results obtained by the author in recent works in collaboration with Davide Ferrario and Vivina Barutello, focusing on the periodic n-body problem from the perspective of the calculus of variations and minimax theory. These researches were aimed at developing a systematic variational approach to the equivariant periodic n-body problem in the two and three-dimensional space. The purpose of this paper is to expose the main problems and achievements of this approach. The material here was exposed in the talk that given at the Meeting CELMEC IV promoted by SIMCA (Società italiana di Meccanica Celeste).     

Magnetic draping of merging cores and radio bubbles in clusters of galaxies

Sharp fronts observed by the Chandra satellite between dense cool cluster cores moving with near-sonic velocity through the hotter intergalactic gas, require strong suppression of thermal conductivity across the boundary. This may be due to magnetic fields tangential to the contact surface separating the two plasma components. We point out that a super-Alfvenic motion of a plasma cloud (a core of a merging galaxy) through a weakly magnetized intercluster medium leads to 'magnetic draping', formation of a thin, strongly magnetized boundary layer with a tangential magnetic field. For supersonic cloud motion,   M _s≥ 1  , magnetic field inside the layer reaches near-equipartition values with thermal pressure. Typical thickness of the layer is  ∼ L / M ²_A≪ L   , where L is the size of the obstacle (plasma cloud) moving with Alfvén Mach number   M _A≫ 1  . To a various degree, magnetic draping occurs for both subsonic and supersonic flows, random and ordered magnetic fields and it does not require plasma compressibility. The strongly magnetized layer will thermally isolate the two media and may contribute to the Kelvin–Helmholtz stability of the interface. Similar effects occur for radio bubbles, quasi-spherical expanding cavities blown up by active galactic nucleus jets; in this case, the thickness of the external magnetized layer is smaller,  ∼ L / M ³_A≪ L   .     

Regular and chaotic dynamics in 3D reconnecting current sheets

We consider the possibility of particles being injected at the interior of a reconnecting current sheet (RCS), and study their orbits by dynamical systems methods. As an example we consider orbits in a 3D Harris type RCS. We find that, despite the presence of a strong electric field, a 'mirror' trapping effect persists, to a certain extent, for orbits with appropriate initial conditions within the sheet. The mirror effect is stronger for electrons than for protons. In summary, three types of orbits are distinguished: (i) chaotic orbits leading to escape by stochastic acceleration, (ii) regular orbits leading to escape along the field lines of the reconnecting magnetic component, and (iii) mirror-type regular orbits that are trapped in the sheet, making mirror oscillations. Dynamically, the latter orbits lie on a set of invariant KAM tori that occupy a considerable amount of the phase space of the motion of the particles. We also observe the phenomenon of 'stickiness', namely chaotic orbits that remain trapped in the sheet for a considerable time. A trapping domain, related to the boundary of mirror motions in velocity space, is calculated analytically. Analytical formulae are derived for the kinetic energy gain in regular or chaotic escaping orbits. The analytical results are compared with numerical simulations.     

利用空间测地技术结果估计地球平均下地幔粘性(英)

基于IEC－4G冰期后地壳反弹模型,和地球上Laurentia,Fennoscandia,Antarctica,andGreenland四大冰盖最近21000年以来的冰融参数,计算了对地球最大主转动惯量的影响△I33,并进而由现代空间测地技术观测资料分析得到的地球自转非潮汐加速项为约束,估计了地球平均下地幔（670km以下）粘性vLM为（0．9～2．5）·1022Pas,这个结果表明了vLM应具有1022Pas量级．