A study on the reference frame consistency in recent Earth gravitational models

All gravity field functionals obtained from an Earth gravitational model (EGM) depend on the underlying terrestrial reference frame (TRF), with respect to which the EGM’s spherical harmonic coefficients refer to. In order to maintain a coherent framework for the comparison of current and future EGMs, it is thus important to investigate the consistency of their inherent TRFs, especially when their use is intended for high precision studies. Following the methodology described in an earlier paper by Kleusberg (1980), the similarity transformation parameters between the associated reference frames for several EGMs (including the most recent CHAMP/GRACE models at the time of writing this paper) are estimated in the present study. Specifically, the differences between the spherical harmonic coefficients for various pairs of EGMs are parameterized through a 3D-similarity spatial transformation model that relates their underlying TRFs. From the least-squares adjustment of such a parametric model, the origin, orientation and scale stability between the EGMs’ reference frames can be identified by estimating their corresponding translation, rotation and scale factor parameters. Various aspects of the estimation procedure and its results are highlighted in the paper, including data weighting schemes, the sensitivity of the results with respect to the selected harmonic spectral band, the correlation structure and precision level of the estimated transformation parameters, the effect of the estimated differences of the EGMs’ reference frames on their height anomaly signal, and the overall feasibility of Kleusberg’s formulae for the assessment of TRF inconsistencies among global geopotential models.     

液核地球自转速率变化的带谐潮效应Ⅱ--数值计算与比较

地球自转速率的潮汐变化可由无量纲参数k/cm)(k和cm分别为壳幔的有效Love数和有效极转动惯量)来表征。对于一个具有弹性地幔、平衡海潮和核幔不耦合的地球k/cm=0.944,且与潮波频率无关。海潮的非平衡扰动使k/cm为复数,且与频率有关。大气对自转速率有效勒夫数的贡献约为Δkat=0.0075。同时地幔滞弹性对勒夫数也产生扰动。利用本文得到的理论公式和最新的潮汐数据计算了地球自转速率的潮汐变化,及其有关地球物理机制的影响。     

Solution to the rotation of the elastic earth by method of rigid dynamics

Hamiltonian mechanics is applied to the problem of the rotation of the elastic Earth. We first show the process for the formulation of the Hamiltonian for rotation of a deformable body and the derivation of the equations of motion from it. Then, based on a simple model of deformation, the solution is given for the period of Euler motion, UT1 and the nutation of the elastic Earth. In particular it is shown that the elasticity of the Earth acts on the nutation so as to decrease the Oppolzer terms of the nutation of the rigid Earth by about 30 per cent. The solution is in good agreement with results which have been obtained by other, different approaches.     

利用Lageos 1 SLR资料解算1990-2001年的地球定向参数

利用 12年的Lageos 1卫星激光测距资料 (1990 - 2 0 0 1)解算得到了地球定向参数 (EOP) ,将该序列的结果与同期的EOP(IERS)C0 4进行比较 ,其外符精度为 :极移XP— 0 .4 0mas,YP— 0 .4 2mas ,日长变化Dr— 0 .0 35ms。     

The shape of the rotation curves of edge-on galaxies

We consider the effects of projection, internal absorption, and gas-or stellar-velocity dispersion on the measured rotation curves of galaxies with edge-on disks. Axisymmetric disk models clearly show that the rotational velocity in the inner galaxy is highly underestimated. As a result, an extended portion that imitates nearly rigid rotation appears. At galactocentric distances where the absorption is low (i.e., it does not exceed 0.3–0.5^m kpc^?1), the line profiles can have two peaks, and a rotation curve with minimum distortions can be obtained by estimating the position of the peak that corresponds to a higher rotational velocity. However, the high-velocity peak disappears in high-absorption regions and the actual shape of the rotation curve cannot be reproduced from line-of-sight velocity estimates. In general, the optical rotation curves for edge-on galaxies are of little use in reconstructing the mass distribution in the inner regions, particularly for galaxies with a steep velocity gradient in the central region. In this case, estimating the rotation velocities for outer (transparent) disk regions yields correct results.     

The Latest Research Progress on El Nino

Cold water in the deep Pacific can be drawn up to the surface (or west warm water drifts eastwards ) because strong tide increases the mixing of seawater both in vertical and horizontal. In this way greenhouse effect is decreased or increased by means of absorbing (or releasing) CO2. Therefore, La Nina cold event (or El Nino warm event) may occur,which is caused by wanning - up or cooling - down air above the ocean. Volcanic action at sea bottom is also controlled by strong tide.     

On the r-mode spectrum of relativistic stars: the inclusion of the radiation reaction

We consider both mode calculations and time-evolutions of axial r modes for relativistic uniformly rotating non-barotropic neutron stars, using the slow-rotation formalism, in which rotational corrections are considered up to linear order in the angular velocity Ω. We study various stellar models, such as uniform density models, polytropic models with different polytropic indices n , and some models based on realistic equations of state. For weakly relativistic uniform density models and polytropes with small values of n , we can recover the growth times predicted from Newtonian theory when standard multipole formulae for the gravitational radiation are used. However, for more compact models, we find that relativistic linear perturbation theory predicts a weakening of the instability compared to the Newtonian results. When turning to polytropic equations of state, we find that for certain ranges of the polytropic index n , the r mode disappears, and instead of a growth, the time-evolutions show a rapid decay of the amplitude. This is clearly at variance with the Newtonian predictions. It is, however, fully consistent with our previous results obtained in the low-frequency approximation.     

对月日潮汐摩擦耗散的估计

月日潮汐摩擦和地球惯量矩变化是日长长期变化的主要原因．在本文中，利用最新的地球物理和古生物钟数据，对过去15亿年以来的月日潮汐摩擦、地球惯量矩变化和日长长期变化等作了数值对比研究．由此得到二个重要结论：一是仅利用地球的自转形变不能解释J2的变化，这说明地球的重力分异现象至今仍存在着；其二是在几亿年前的潮汐摩擦比现在大得多，若取潮汐耗散与距离的立方成反比时，理论结果与由古生物钟得到的回归年日数和朔望月日数数据较为符合。     

Some Problems with Slow Rotation of CP Stars

Some difficulties in explaining the slow rotation of CP stars are discussed. The most likely hypotheses are (1) a loss of angular momentum involving a magnetic field during “pre-main sequence” evolution and (2) the slow rotation existed from the very start of the creation of these stars. The braking hypothesis is supported by only one property of CP stars— the lower the mass of the star is, the greater the difference between its average rotation velocity vsini and that of normal stars. On the other hand, there is another property— the lower the rotation speeds of CP stars are, the greater their fraction among normal stars. The latter property supports the hypothesis that the lower the initial rotation speed of a star is when it is created, the greater the probability will become chemically peculiar. This property is inherent in chemically peculiar stars both with and without a magnetic field. It is proposed that the cause of the slow rotation of CP stars must be sought in the very earliest phases of their formation, as should the cause of the separation into chemically peculiar magnetic, chemically peculiar nonmagnetic, and normal stars.__________Translated from Astrofizika, Vol. 48, No. 2, pp. 229–245 (May 2005).