Binary formation in stellar clusters

We consider how the tidal potential of a stellar cluster or a dense molecular cloud affects the fragmentation of gravitationally unstable molecular cloud cores. We find that molecular cloud cores which would collapse to form a single star in the absence of tidal shear, can be forced to fragment if they are subjected to tides. This may enhance the frequency of binaries in star-forming regions such as Ophiuchus and the frequency of binaries with separations ≲100 au in the Orion Trapezium Cluster. We also find that clouds which collapse to form binary systems in the absence of a tidal potential will form bound binary systems if exposed to weak tidal shear. However, if the tidal shear is sufficiently strong, even though the cloud still collapses to form two fragments, the fragments are pulled apart while they are forming by the tidal shear and two single stars are formed. This sets an upper limit for the separation of binaries that form near dense molecular clouds or in stellar clusters.     

Are Planetary Tides on the Sun and the Birthplace of Sunspots Related?

We study whether the birthplaces of sunspots (defined as the location of first appearance in the photosphere) are related to the planetary tides on the Sun. The heliocentric longitudes of newly emerging sunspots are statistically compared to the longitudes of tidal peaks caused by the tidal planets Mercury, Venus, Earth, and Jupiter. The longitude differences between new sunspots and tidal planets (and their conjugate locations) as well as the magnitudes of the vertical and horizontal tidal forces at the birthplace of new sunspots are calculated. The statistical distributions are compared with simulation results calculated using a random sunspot distribution. The results suggest that the birthplaces of sunspots (in the photosphere) are independent of the positions of tidal planets and the strength of tidal forces caused by them. However, since the sunspots actually originate near the tachocline (well below the photosphere) and it takes considerable time for the disturbances to reach photosphere, we hesitate to conclude that the formation of sunspots are not related to planetary positions.     

中国及邻区地震的天文潮汐触发特征研究——附加潮汐应力对发震断层的作用模式及其应用

本文在潮汐应力、构造应力、地震断层和岩石破裂滑动理论的基础上 ,建立了潮汐应力对地震断层作用的力学模式 ,该模式将潮汐应力与地震应力作用相结合 ,描述了沿地震主压应力和地震主张应力方向的附加潮汐应力对发震断层的力学作用方式 ,从而切入潮汐应力触发地震的物理机制 ,认为潮汐对地震的触发作用在实质上归结为潮汐应力对地震断层的促滑作用 ,这种促滑作用分增压型和减压型。在此模式基础上 ,对中国大陆及邻区的不同类型地震的潮汐触发性进行了研究 ,内容包括 :计算了中国及邻区一千多个地震震源处沿主压应力P轴和主张应力T轴方向的附加潮汐应力分量 ,分析了这些量对发震断层的作用方式 ,按纬度区域统计了受到潮汐应力促滑作用的发震断层类型以及它们与潮汐应力作用方式的关系 ,得到了如下结论 :受到潮汐应力促滑作用的发震断层的比例随区域纬度增加有减小趋势 ,其中 ,走滑型断层的比例在低纬区较大 ,而倾滑斜型断层的比例在中高纬度区较大 ;对整个统计区域而言 ,受增压型潮汐应力促滑作用的发震断层数比例大于受减压型潮汐应力促滑作用的发震断层 ;对不同的纬度区域 ,不同的潮汐应力作用方式与之促滑的发震断层类型也有不同的分布特征。最后 ,本文将中国及邻区受到潮汐触发作用的地震按构造应力     

Tidal Evolution of the Kepler Candidate Two-planet Systems

The tidal evolution of ten Kepler candidate two-planet systems is investigated by using the general secular perturbation theory, and then a general picture of tidal evolution for these systems is described. Taking the KOI 1239 system as an example, the tidal effect of the system is studied in detail, the results indicate that the dissipative term of the tidal effect causes the attenuation of planets’ orbital eccentricities, and it plays a dominant role in the process of orbital evolution, however, the conservative term of the tidal effect and the relativistic effect may damp the excitation of the eccentricity of the inner planet under the secular perturbation of the outer planet. In addition, the process of tidal evolution is also affected by both the initial eccentricity of the outer planet and the planet's tidal dissipation coeffcient. At the same time, the numerical simulation on the tidal evolution of the KOI 1239 system is also made, and the numerical results are consistent with those of general secular perturbation theory.     

The tidal response of Ganymede and Callisto with and without liquid water oceans

Calculations of the tidal responses of Ganymede and Callisto reveal that tidal amplitudes on these bodies may be as large as a few meters if a liquid ocean exists to decouple the surface ice from the interior. Tides on Ganymede's surface can exceed 7 m peak-to-peak variation, while on Callisto the tidal amplitude can exceed 5 m in the presence of a liquid ocean. Without an ocean, tidal amplitudes are less than 0.5 m on Ganymede and less than 0.3 m on Callisto. An orbiting spacecraft using an altimeter for crossover analysis and Doppler tracking from Earth should be able to achieve sufficient accuracy to identify the tidal amplitude to within about a meter over the course of a few months (observing tens of tidal cycles).     

Tidal evolution of close binary asteroid systems

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than 5 times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent. This work has possible implications for the determination of the Roche limit and for spin-state alteration during close flybys.     

The evolution of massive close binaries

The influence of tidal, interaction on the periods of massive X-ray binaries during the postsupernova evolution is investigated. It is assumed that after a certain time the orbit has become circular and synchronous. The tidal effects of subsequent evolutionary changes in the moment of inertia of the massive component are calculated. It is shown that, as is already suggested by Sparks and Stecher (1974), for small mass ratios and short binary periods a tidal instability may occur resulting in an accelerating inward spiral motion. Before the onset of the instability the tidal forces maintain a nearly synchronous orbit. Possibly the orbits of Cen X-3 and 3 U 1700-37 are already unstable at present.     

银河系恒星潮汐流的探测进展

银晕外区存在众多星流,它们或源自银河系的矮伴星系,或源自晕族球状星团,常分别称为矮星系星流和球状星团潮汐尾。星流可以利用各类示踪星,并通过不同的途径加以探测,对若干代表性矮星系星流和球状星团潮汐尾的探测进展做了简要的介绍。     

On the tidal effects in the motion of artificial satellites

The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorinal elements ω and Ω of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal ‘waves’ over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the ‘global’ Love numbers for the Earth.     

Ridges and tidal stress on Io

Sets of ridges of uncertain origin are seen in twenty-nine high-resolution Galileo images, which sample seven locales on Io. These ridges are on the order of a few kilometers in length with a spacing of about a kilometer. Within each locale, the ridges have a consistent orientation, but the orientations vary from place to place. We investigate whether these ridges could be a result of tidal flexing of Io by comparing their orientations with the peak tidal stress orientations at the same locations. We find that ridges grouped near the equator are aligned either north-south or east-west, as are the predicted principal stress orientations there. It is not clear why particular groups run north-south and others east-west. The one set of ridges observed far from the equator (52° S) has an oblique azimuth, as do the tidal stresses at those latitudes. Therefore, all observed ridges have similar orientations to the tidal stress in their region. This correlation is consistent with the hypothesis that tidal flexing of Io plays an important role in ridge formation.     

天文潮汐与地震

从三个方面综述了天文潮汐与地震关纱的研究，内容包括，日、月、地球的相对位置与地震，天文潮汐的周期，相位与地震，天文潮汐应力与地震，日、月、地球的相对位置与地震和天文潮汐周期与地城的研究均属于从体积力的角度考虑问题，主要是从宏观角度揭示地震发生时的日月位置分布有何规律性，揭示地震发生时间丛集在潮汐周期变化过程中的相位或时段以及地城牟潮汐周期，天文潮汐应力与震的研究从引潮力在地震内部地震源处产生的潮汐应力角度出发，着重研究不同类型性质的发震断层与潮汐应力触发的关系，从物理意义上讲，该研究较深 次地切入了问题的实质，分析了采用某些方法和样本研究结果不一致性的原因，并提出了进一步研究的方向。     

A note on the tidal expansion of the orbit of Mercury

Under the assumption that the secular decrease in the sidereal mean motion of Mercury is due to the Sun-Mercury tidal torque, the expansion of the orbit of Mercury and the tidal phase-lag angle of the tidal bulge are estimated.     

Correlations of cosmic tidal fields

We study correlations amongst tidal fields originated by the large-scale distribution of matter in the Universe. The two-point tidal correlation is described as a rank-4 tensor, the elements of which can be written in terms of four fundamental scalar functions ranging, with respect to the spatial separation, from purely transversal to purely longitudinal correlations. Tidal fields, on both galaxy and cluster scales, are revealed to be correlated over distances larger than the mass–density correlation length, although traceless tidal fields show anti-correlation between diagonal terms along orthogonal directions. The cross-correlation between mass and tidal field is also analysed. These results are relevant for galaxy formation and the interpretation of large-scale weak lensing phenomena.     

Tidal tails of star clusters

Based on recent findings of a formation mechanism of substructure in tidal tails by Küpper et al., we investigate a more comprehensive set of N -body models of star clusters on orbits about a Milky Way like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for the overdensities to build up.
The distance of the overdensities along the tidal tail from the cluster centre depends for circular orbits only on the mass of the cluster and the strength of the tidal field, and therefore decreases monotonically with time, while for eccentric orbits the orbital motion influences the distance, causing a periodic compression and stretching of the tails and making the distance oscillate with time. We provide an approximation for estimating the distance of the overdensities in this case.
We describe an additional type of overdensity which arises in extended tidal tails of clusters on eccentric orbits, when the acceleration of the tidal field on the stellar stream is no longer homogeneous. Moreover, we conclude that a pericentre passage or a disc shock is not the direct origin of an overdensity within a tidal tail. Escape due to such tidal perturbations does not take place immediately after the perturbation but is rather delayed and spread over the orbit of the cluster. All observable overdensities are therefore of the mentioned two types. In particular, we note that substructured tidal tails do not imply the existence of dark matter substructures in the haloes of galaxies.     

Inference of dust opacities for the 1977 Martian great dust storms from Viking Lander 1 pressure data

A δ-Eddington radiative transfer algorithm is used to compute the thermal tidal heating of a dusty Martian atmosphere for a given set of dust optical depth, effective single scattering albedo, and phase function asymmetry parameter. The resulting thermal tidal forcing is used in a classical atmospheric tidal model to compute the amplitudes of the surface pressure oscillations at the Viking Lander 1 site for the two 1977 Martian great dust storms. Parametric studies show that the dust opacities and optical parameters derived from the Viking Lander imaging data are roughly representative of the global dust haze needed to reproduce the tidal surface pressure amplitudes also observed at Lander 1, except that the model-inferred asymmetry parameter is smaller during the onset of a great storm. The observed preferential enhancement during dust-storm onset of the semidiurnal tide at Viking Lander 1 relative to its diurnal counterpart is shown to be due primarily to the elevation of the tidal heating source in a very dusty atmosphere, although resonant enhancement of the main semidiurnal tidal mode makes an important secondary contribution.     

Tidal alignments as a contaminant of redshift space distortions

We investigate the effect of orientation-dependent selection effects on galaxy clustering in redshift space. It is found that if galaxies are aligned by large-scale tidal fields, then these selection effects give rise to a dependence of the observed galaxy density on the local tidal field, in addition to the well-known dependences on the matter density and radial velocity gradient. This alters the galaxy power spectrum in a way that is different for Fourier modes parallel to and perpendicular to the line of sight. These tidal galaxy alignments can thus mimic redshift space distortions (RSD), and thus result in a bias in the measurement of the velocity power spectrum. If galaxy orientations are affected only by the local tidal field, then the tidal alignment effect has exactly the same scale and angular dependence as the RSDs in the linear regime, so it cannot be projected out or removed by masking small scales in the analysis. We consider several toy models of tidal alignments and orientation-dependent selection, normalize their free parameter (an amplitude) to recent observations, and find that they could bias the velocity amplitude   f ( z ) G ( z )  by 5–10 per cent in some models, although most models give much smaller contamination. We conclude that tidal alignments may be a significant systematic error in RSD measurements that aim to test general relativity via the growth of large-scale structure. We briefly discuss possible mitigation strategies.     

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin’s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.     

Tidal dissipation at arbitrary eccentricity and obliquity

Expressions for tidal dissipation in a body in synchronous rotation at arbitrary orbital eccentricity and obliquity are derived. The rate of tidal dissipation for a synchronously rotating body is compared to that in a body in asymptotic nonsynchronous rotation.     

Tides in a body librating about a spin–orbit resonance: generalisation of the Darwin–Kaula theory

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.