Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales

Atmospheric angular momentum variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. The exchange of angular momentum between the fluid layers and the solid planet is the main cause for the variations of the planetary rotation at seasonal time scales. In the present study, we investigate the angular momentum variations of the Earth, Mars and Venus, using geodetic observations, output of state-of-the-art global circulation models as well as assimilated data. We discuss the similarities and differences in angular momentum variations, planetary rotation and angular momentum exchange for the three terrestrial planets. We show that the atmospheric angular momentum variations for Mars and Earth are mainly annual and semi-annual whereas they are expected to be “diurnal” on Venus. The wind terms have the largest contributions to the LOD changes of the Earth and Venus whereas the matter term is dominant on Mars due to the CO₂ sublimation/condensation. The corresponding LOD variations (ΔLOD) have similar amplitudes on Mars and Earth but are much larger on Venus, though more difficult to observe.     

Rotational dynamics of celestial deformable bodies

In a previous paper of this series (Tokis, 1974b), we have discussed the solution of the Eulerian equation which governs the axial rotation, applied to the effects of viscous friction exhibited in binary systems which consist of a close pair of fluid bodies of arbitrary structure. The aim of the present paper will be to give an application of those results to the Earth-Moon system. It is shown that synchronism between the axial rotation of the Earth and the revolution of the Moon will occur at the value of 650 h, in a time scale which depends strongly on the value of the mean viscosity of the Earth (regarded as spherical or spheroidal). In particular, the variation of rotational angular velocity of the Earth over the next ten centuries commencing from 1900 A.D., depends sensitively on the value of viscosity. On the other hand, the time for synchronism of axial rotation of the Moon is not affected by the viscosity for values between 10²⁴g cm^?1 s^?1 and 10²⁷g cm^?1 s^?1.     

Central cusp caused by a supermassive black hole in axisymmetric models of elliptical galaxies

We use numerical simulations to investigate the cusp at the centre of elliptical galaxies caused by the slow growth of a supermassive black hole. We study this problem for axisymmetric models of galaxies with or without rotation. The numerical simulations are based on the 'perturbation particles' method, and use GRAPEs to compute the force arising from the cusp. We study the way in which the density cusp is affected by the initial flattening of the model, as well as the role played by initial rotation. The logarithmic slope of the density cusp is found to be very much insensitive to flattening; as a consequence, we deduce that tangential velocity anisotropy – which supports the flattening – is also of little influence on the final cusp. We investigate, via two different kinds of rotating models, the efficiency with which a rotation velocity component builds within the cusp. A cusp in rotation develops only for models where a net rotation component is initially present at high energy levels. The eventual observation of a central rotational velocity peak in elliptical galaxies has, therefore, some implications for the galaxy dynamical history.     

关于章动序列计算中的地球动力学扁率的取值

刚体地球章动序列和非刚体地球章动的转换函数都和地球动力学扁率有关。ＩＡＵ１９８０章动理论中采用了一个不一致的地球动力学扁率值,从而影响了章动振幅的计算。本文介绍了章动序列计算中地球动力学扁率的取值。由地球模型１０６６Ａ或ＰＲＥＭ得到的地球动力学扁率值比由岁差观测得到的约小１％,并且不可靠。当考虑体静力学平衡被破坏时新的地球物理模型,可得到与岁差常数相一致的地球动力学扁率值。地球动力学扁率值Ｈ＝０．     

地球动力学扁率及其与岁差章动的关系

由岁差常数求得的日月岁差是天文学的重要参数之一,它和地球动力学扁率相联系。地球动力学扁率在章动理论的计算中也是一个重要的物理量。介绍了由不同的观测方法和模型给出的地球动力扁率值,并讨论了它也岁差的关系和对章动计算的影响。在刚体地球章动振幅的计算中,地球动力学扁率值起着尺度因子的作用,要改善刚体地球章动振幅的计算,需要修改目前的黄经总岁差值。非刚体地球章动的转换函数中所采用的简正模和常数都直接或间接地依赖地球动力学扁率值。在IAU1980章动理论中,计算刚体地球章动振幅所使用的地球动力学扁率值计算转换函数中简正模频率和常数所使用的地球动力学扁率值并不一致。随着观测和计算精度的提高,地球动力学扁率值的不一致将影响章动振幅的计算。在建立刚体地球章地动理论中,如何解释地球动力学扁率值的差异,如何选取地球动力学扁率值,还有待进一步的研究。     

Rayleigh-Taylor instability of a two-fluid layer under a general rotation field and a horizontal magnetic field

In this paper the Rayleigh-Taylor instability (RTI) of a two-fluid layer system under the simultaneous action of a general rotation field and a horizontal magnetic field is presented. An approximate and an exact solution of the eigenvalue equation are calculated. These solutions are important not only to understand more deeply the physical problem but also to determine the correct numerical solutions. Numerical calculations are done for an unstable density stratification in the cases of horizontal magnetic field parallel and perpendicular to the horizontal component of the angular velocity. For an adverse density stratification, it is shown that in comparison to previous works, the horizontal magnetic field creates new angular areas (of the angle of propagation of the perturbation) at which the perturbation is stable and propagates as traveling waves. It is also shown that the vertical component of the angular velocity has a destabilizing effect because it works to eliminate the stable angular areas.     

A primordial feature at the scale of superclusters of galaxies

We investigate a spatially flat cold dark matter model (with the matter density parameter     with a primordial feature in the initial power spectrum. We assume that there is a bump in the power spectrum of density fluctuations at wavelengths     , which corresponds to the scale of superclusters of galaxies . There are indications for such a feature in the power spectra derived from redshift surveys and also in the power spectra derived from peculiar velocities of galaxies. We study the mass function of clusters of galaxies, the power spectrum of the cosmic microwave background (CMB) temperature fluctuations, the rms bulk velocity and the rms peculiar velocity of clusters of galaxies. The baryon density is assumed to be consistent with the big bang nucleosynthesis value. We show that with an appropriately chosen feature in the power spectrum of density fluctuations at the scale of superclusters, the mass function of clusters, the CMB power spectrum, the rms bulk velocity and the rms peculiar velocity of clusters are in good agreement with the observed data.     

The rotation of magnetic loop systems in the solar atmosphere

Eclipse photographs indicate that large regions of the inner solar corona are confined in various types of closed magnetic configurations and, as a result, do not participate in the general solar wind expansion. In this paper, the rotation of initially poloidal loop configurations of this type, as influenced by differential rotation of the footpoints, is investigated. The analysis is restricted to axially symmetric fields and it is assumed that the toroidal magnetic field induced by differential rotation is small as compared to the initial poloidal field. This restricts the validity of the analysis to times less than about one month.The most interesting physical situation is that of flux tubes existing in one solar hemisphere only, one end of the tube being fixed in the photosphere at a higher latitude than the other. As a consequence, the lower end of the tube rotates at a faster rate than the upper end. Solution of the pertinent equations reveals that the angular velocity measured along a field line increases monotonically from its value at the poleward footpoint to that at the lower footpoint. The variation of angular velocity along the field depends upon the field geometry only and is not directly related to the variation of angular velocity along the solar surface between the footpoints. Depending upon the field configuration, both outward radial increases and decreases are possible. Using the Newton and Nunn model for the surface differential rotation rate, the angular velocity distribution on two particularly simple types of closed magnetic loop systems is determined analytically. It is shown that the angular velocity increases outward in the polar regions but decreases outward near the equator - leading to a decrease in differential rotation with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The Sunyaev–Zel'dovich effect and Faraday rotation contributions of galaxy groups to the CMB angular power spectrum

The Sunyaev–Zel'dovich (SZ) effect and the Faraday rotation from haloes are examined over a wide mass range, including gas condensation and magnetic field evolution. Contributions to the cosmic microwave background (CMB) angular power spectrum are evaluated for galaxy clusters, galaxy groups and galaxies. Smaller mass haloes are found to play a more important role than massive haloes for the B -mode polarization associated with the SZ CMB anisotropies. The B modes from the Faraday rotation dominate the secondary B modes caused by gravitational lensing at  ℓ > 3000  . Measurement of B -mode polarization in combination with the SZ power spectrum can potentially provide important constraints on intracluster magnetic field and gas evolution at early epochs.     

Forced nutations of a two-layer Earth model

In this paper we present a theory of the Earth rotation for a model composed of an inelastic mantle and a liquid core, including the dissipation in the core–mantle boundary (CMB). The main features of the theory are: (i) to be Hamiltonian, therefore the computation of some complex inner torques can be avoided; (ii) to be self-consistent and non-dependent on a previous rigid Earth theory, so there is no need to use transfer functions; (iii) to be analytical, the solution being derived by perturbation methods. Numerical nutation series deduced from the theory are compared with the IERS 96 empirical series, an accuracy better than 0.8 mas in providing celestial ephemeris pole (CEP) offsets .     

On the variation of specific angular momentum among Main Sequence stars

The specific angular momentum is found to vary with mass for earlier and later-type Main Sequence stars. Of various plausible causes, the difference in the interior density distribution of earlier and later-type stars is not sufficient enough to explain the difference either in angular momentum or in its gradient between earlier and later-type stars. The non-rigid rotation, however, may account for this difference in specific angular momentum as well as its gradient, if faster angular velocity in the interior for later-type and/or slower angular velocity for earlier-type stars than the surface value is allowed. A few other possibilities have also been briefly considered to understand this difference.     

引力常数变化对地球自转长期变化的影响

探讨和估计了各种引力常数变化理论对地球角速度和日长变化的影响。各种引力常数变化理论包括了引力常数G随时间、空间以及速度变化等几个方面的影响。另外也估计了对地球自转角速度和日长变化产生的效应。其中有些研究对探讨地球自转变化也有启发意义。     

Microwave background anisotropies arising from non-linear structures in open and universes

A new method arising from a gauge-theoretic approach to general relativity is applied to the formation of clusters in an expanding universe. The three cosmological models (₀=1, =0), (₀=0.3, =0.7) and (₀=0.3, =0) are considered, which extends our application in two previous papers. A simple initial velocity and density perturbation of finite extent is imposed at the epoch z =1000, and we investigate the subsequent evolution of the density and velocity fields for clusters observed at redshifts z =1, z =2 and z =3. Photon geodesics and redshifts are also calculated so that the cosmic microwave background (CMB) anisotropies arising from collapsing clusters can be estimated. We find that the central CMB temperature decrement is slightly stronger and extends to larger angular scales in the non-zero case. This effect is strongly enhanced in the open case. Gravitational lensing effects are also considered, and we apply our model to the reported microwave decrement observed towards the quasar pair PC 1643+4631 A&B.     

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally, we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond.     

海洋角动量对地球自转变化的激发

介绍了海洋角动量模型的现状和发展,以及地球自转变化和海洋之间的关系的一些预研究成果．有关的预研究结果表明,海洋可能是地球自转变化的一个激发源,海洋和地球自转变化之间相互影响、相互作用．但两者之间的关系以及作用机制都有待深入研究。     

Towards Earth AntineutRino TomograpHy (EARTH)

The programme Earth AntineutRino TomograpHy (EARTH) proposes to build ten underground facilities each hosting a telescope. Each telescope consists of many detector modules, to map the radiogenic heat sources deep in the interior of the Earth by utilising direction sensitive geoneutrino detection. Recent hypotheses target the core-mantle boundary (CMB) as a major source of natural radionuclides and therefore of radiogenic heat. A typical scale of the processes that take place at the CMB is about 200 km. To observe these processes from the surface requires an angular resolution of about 3°. EARTH aims at creating a high-resolution 3D-map of the radiogenic heat sources in the Earth’s interior. It will thereby contribute to a better understanding of a number of geophysical phenomena observed at the Earth’s surface. This condition requires a completely different approach from the monolithic detector systems as e.g. KamLAND. This paper presents, for such telescopes, the boundary conditions set by physics, the estimated count rates, and the first initial results from Monte-Carlo simulations and laboratory experiments. The Monte-Carlo simulations indicate that the large volume telescope should consist of detector modules each comprising a very large number of detector units, with a cross section of roughly a few square centimetres. The signature of an antineutrino event will be a double pulse event. One pulse arises from the slowing down of the emitted positron, the other from the neutron capture. In laboratory experiments small sized, ¹⁰B-loaded liquid scintillation detectors were investigated as candidates for direction sensitive, low-energy antineutrino detection.     

Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

Relation between solar sidereal and synodic rotation axes

Kinematic picture concerning the solar synodic and sidereal rotation axes has been considered in some detail. Large changes in the synodic angular rotation velocity and the position of the synodic rotation pole have been found for some hypothetical cases of out-of-ecliptic intra-Mercurian orbits. The influence of solar differential rotation and variable planetary velocity along the orbit have been taken into account and a continuous set of co-existing synodic poles oscillating around a mean position has been found. The relevant numerical values for the Earth are given and the possibility of detecting the existence of the two rotation axes has been pointed out.     

50-day Oscillation of Length-of-day Change

Variations of Earth’s rotation rate (length-of-day, LOD) occur over a wide range of time scales from a few hours to the geological age. Studies showed that the 50-day fluctuation exists in LOD change. In the present paper, the authors use wavelet technique to study the 50-day oscillation in LOD series. Temporal variations of the oscillation are presented in this work. After analyzing the axial component of atmospheric angular momentum (AAM) and oceanic angular momentum (OAM), the 50-day periodic signal is also found in atmospheric and oceanic motion with remarkable time-variation. Meanwhile, the 50-day oscillation of the axial AAM is in good consistence with that of LOD change. This suggests that the 50-day oscillation of LOD change is mainly excited by the axial AAM. Possible origin of the oscillation for Earth system is discussed in the end of this paper.     

Numerical simulations of a Mars geodesy network experiment: Effect of orbiter angular momentum desaturation on Mars' rotation estimation

The scientific objectives of a geodetic experiment based on a network of landers, such as NEIGE (NEtlander Ionosphere and Geodesy Experiment) are to improve the current knowledge of Mars' interior and atmosphere dynamics. Such a network science experiment allows monitoring the motions of the Martian rotation axis with a precision of a few centimeters (or milli-arc-seconds (mas)) over annual and sub-annual periods. Thereto, besides radio tracking of a Mars orbiter from the Earth, radio Doppler shifts between this orbiter and several landers at the planet's surface will be performed. From the analysis of these radio Doppler data, it is possible to reconstruct the orbiter motion and Mars' orientation in space. The errors on the orbit determination (position and velocity of the orbiter) have an impact on the geodetic parameters determination from the Doppler shifts and must be removed from the signal in order to achieve a high enough accuracy. In this paper, we perform numerical simulations of the two Doppler signals involved in such an experiment to estimate the impact of the spacecraft angular momentum desaturations on the determination of Mars' orientation variations. The attitude control of the orbiter needs such desaturation maneuvers regularly repeated. They produce velocity variations that must be taken into account when determining the orbit. For our simulations, we use a priori models of the Martian rotation and introduce the spacecraft velocity variations induced by each desaturation event. By a least-squares adjustment of the simulated Doppler signals, we then estimate the orbiter velocity variations and the parameters of the Mars' rotation model. We show that these velocity variations are ill resolved when the spacecraft is not tracked, therefore requiring a near-continuous tracking from the Earth to accurately determine the orbit. In such conditions we show that only 15- of lander-orbiter tracking per week allows recovering Mars' orientation parameters with a precision of a few mas over a period of 1 Martian year.