Statistical Test of the Correlation Between Earthquakes and Solid Tidal Waves: Implication to Hazard Prediction

The statistical correlation between earthquakes and the characteristics of solid Earth tide was investigated. Worldwide data on earthquakes (4018?M?≥?6.0) from January 1, 1973 to December 31, 2003 were analyzed. The distributions (D) of three relationships among earthquakes and solid tidal forces derived by composite force FI_i [D (FI_i)], azimuth A_i [D (A_i)], and elevation E_i [D (E_i)] from 1,200 waves were examined. These relationships indicate the probability of earthquakes. Twelve large-amplitude waves were investigated in detail to determine if earthquakes can be predicted. A test model P(t, λ, φ, d) consisting of three different wave groups was designed using these distributions. The values of tidal force, including the size and direction of tidal waves at any given time and place, were converted to test the probability of an earthquake. The converted values were then applied to trace and ascertain the great M?=?9.0 Northern Sumatra earthquake on December 26, 2004. Although the results selected from both the 12 maximum-amplitude waves or the 50 best correlation waves did not match well, the model can be significantly improved to produce only a day’s difference when all the 1,200 waves are employed. Therefore, further studies should be conducted to test if this method can be adopted in accurately predicting the occurrence of earthquakes, including time, relevant size, and location.     

On the Andromeda to Milky Way mass ratio

We have explored the hypothesis that the total mass ratio of the two main galaxies of the Local Group, the Andromeda galaxy (M31) and the Milky Way (MW), can be constrained by measuring the tidal force induced by the surrounding mass distribution, M31 included, on the MW. We argue that the total mass ratio between the two groups can be approximated, at least qualitatively, by finding the tidal radius where the internal binding force of the MW balances the external tidal force acting on it. Since M31 is the massive tidal 'perturber' of the local environment, we have used a wide range of M31 to MW mass-ratio combinations to compute the corresponding tidal radii. Of these, only a few match the distance of the zero-tidal shell, i.e. the shell identified observationally by the outermost dwarf galaxies which do not show any sign of tidal effects. This is the key to constraining the best mass-ratio interval of the two galaxies. Our results favour a solution where the mass ratio ranges from 2 to 3, implying a massive predominance of M31.     

The effects of the tidal force on shear instabilities in the dust layer of the solar nebula

The linear analysis of the instability due to vertical shear in the dust layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the dust layer is neglected. (2) One fluid model is adopted, where the dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the dust layer and the dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the dust/gas surface density ratio is equal to that for the solar abundance. On the other hand, the shear instability is suppressed and the planetesimal formation through the gravitational instability may occur, if dust/gas surface density ratio is hundreds times as large as that for the solar abundance.     

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。     

Tidal disruption of a disk galaxy

The tidal force effects of a spherical galaxy passing head-on through a disk galaxy have been studied for various orientations of the disk galaxy with respect to the direction of relative motion of the two galaxies. The density distribution of the spherical galaxy is taken to be that of a polytrope of indexn=4 and that of the disk galaxy is taken to be, (r)=_ce^–4r/R, where _c is the central density andR the radius of the disk. It is found that the disruptive effects due to the tidal force are minimum when the plane of the disk lies along the direction of relative motion, but are maximum when the plane of the disk is slightly inclined to this direction (about 15°). The tidal force effects at the median radius have also been computed. The tadal force effects are much higher in the interior region of the disk.     

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     

Newtonian and post-newtonian tidal theory: Variable G and earthquakes

A mathematical analysis of the Newtonian and parametrized Post-Newtonian tidal stresses is applied to tidal triggering mechanism for earthquakes. We investigate a possible correlation.The procedure used for calculating the solid earth tidal stress is described by the Newtonian theory and the parametrized Post-Newtonian metric. We calculate tidal stress histories for earthquakes between 1908 and 1991 in Greek area. Although no significant tidal correlation was found for the entire data set, which contained earthquakes of magnitudeM 6.0, a fairly striking correlation was observed for an earthquake-tide correlation by computing tidal functions at the time and place of the earthquake events. A successful correlation as used in this paper means that: earthquake events occur during a certain part of the tidal cycle.Also, we have studied a variation of the gravitational constant according to the variation of the velocity of the Earth and the uniform velocity of the Solar System with respect to a preferred Universal rest frame.This work has been supported by the Greek General Secretariat of Research and Technology under Grant No. 89e160.     

Characteristics and Frequency of Weak Stellar Impulses of the Oort Cloud

We have developed a model of the response of the outer Oort cloud of comets to simultaneous tidal perturbations of the adiabatic galactic force and a stellar impulse. The six-dimensional phase space of near-parabolic comet orbital elements has been subdivided into cells. A mapping of the evolution of these elements from beyond the loss cylinder boundary into the inner planetary region over the course of a single orbit is possible. This is done by treating each perturbation separately, and in combination, during a time interval of 5 Myr. We then obtain the time dependence of a wide range of observable comet flux characteristics, which provides a fingerprint of the dynamics. These include the flux distributions of energy, perihelion distance, major axis orientation, and angular momentum orientation. Correlations between these variables are also determined. We show that substantive errors occur if one superposes the separately obtained flux results of the galactic tide and the stellar impulse rather than superposing the tidal and impulsive perturbations in a single analysis. Detailed illustrations are given for an example case where the stellar mass and relative velocity have the ratio M∗/V_rel=0.043 M⊙/km s⁻¹ and the solar impact parameter is 45,000 AU. This case has features similar to the impending Gliese 710 impulse with the impact parameter selected to be close to the low end of the predicted range. We find that the peak in the observable comet flux exceeds that due to the galactic tide alone by ≈41%. We also present results for the time dependence of the flux enhancements and for the mean encounter frequency of weak stellar impulse events as functions of M∗/V_rel and solar impact parameter.     

On the relation between the solar activity cycle and the solar tidal force induced by the planets

The cross-correlation coefficient (t) of the solar tidal force induced by the planets f(x + t) with the sunspot number g(x) during a period of 44 years is about -0.7 when t is about -2 years. This fact will be useful for predicting solar activity. The solar tidal force was calculated from 1928 to 1971 for every degree on the equatorial plane and every time every planet moves one degree. As the solar tidal force, we used the moving annual average by months of the square of the vertical tidal force on the sun, and as the sunspot number we used the Zürich mean annual sunspot number.     

Global properties of nearby galaxies in various environments

We analyze a sample of the Local Volume that contains 451 galaxies within 10 Mpc. We compare the various global parameters of these galaxies with their tidal index that characterizes the local density of the environment. The closest correlation is observed between the density of the galaxy’s environment and its morphological type. The abundance of neutral hydrogen in the members of close groups was found to be, on average, a factor of 3 lower than that in isolated galaxies. However, much of this difference is attributable to different morphological composition for the group members and field galaxies. The total mass-to-luminosity ratio is virtually independent of the tidal index of the galaxy, which indirectly indicates a low percentage of tidal systems among dwarf galaxies. All of the galaxies with three or more companions in the Local Volume are shown to have masses above the threshold value of 10¹⁰M_⊙.     

The kinematic effects on the rotation curve of a galaxy

In this paper, it is pointed out that if the spiral galaxy revolves about some common centre as a whole, the rotation curve will be changed by the kinematic effects. The common centre could be the centre of supercluster or the centre of dark matter and luminous matter.The kinematic effects on rotation curve are calculated. The additional velocity caused by revolving about the common centre is obtained. In case the direction of revolution is opposite (or consistent) to the direction of rotation, then in the outer region of nucleus, a flat rotation curve could be changed to a constant negative (or postive) gradient. The 44 rotation curves of Sb and Sc galaxies are expressed by means of linear least-squares fit, from which the period of revolving and the ratio of tidal force to self-gravitating force are calculated for every galaxy in extreme cases. The periods for most galaxies are in the reasonable region about 10⁹ years. The tidal force is always less than gravitating force, so the system could be maintained in such a revolving cases. At last, rotation curves in all directions of disk are suggested to pick out the kinematic effects from pure rotation.Work supported by the National Science Foundation of China, under Grant No. 1860610.     

Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of hot Jupiters

In this paper we extend the theory of close encounters of a giant planet on a parabolic orbit with a central star developed in our previous work (Ivanov and Papaloizou in MNRAS 347:437, 2004; MNRAS 376:682, 2007) to include the effects of tides induced on the central star. Stellar rotation and orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment that incorporates first order corrections to normal mode frequencies arising from stellar rotation and numerical treatments that are in satisfactory agreement over the parameter space of interest. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5?C6 stellar radii with tides in the star being much stronger for retrograde orbits compared to prograde orbits. Assuming that combined action of dynamic and quasi-static tides could lead to the total circularisation of orbits this corresponds to observed periods up to 4?C5 days. We use the simple Skumanich law to characterise the rotational history of the star supposing that the star has its rotational period equal to one month at the age of 5 Gyr. The strength of tidal interactions is characterised by circularisation time scale, t _ev , which is defined as a typical time scale of evolution of the planet??s semi-major axis due to tides. This is considered as a function of orbital period P _obs , which the planet obtains after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits, respectively, is of order 1.5?C2 for a planet of one Jupiter mass having P _obs ~ 4 days. The ratio grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same P _orb . Note, however, this result might change for more realistic stellar rotation histories. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet?Cplanet scattering, which favours systems with retrograde orbits. The results reported in the paper may also be applied to the problem of tidal capture of stars in young stellar clusters.     

Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: Application to fast rotating Asteroid 2000EB14

This note discusses the stability of collinear equilibrium points around a rotating system composed of two masses rigidly connected by a massless rod in the case, where the centripetal force outweighs the gravitational force. It is found that a stable region appears at L₁ when the ratio of gravitational to centripetal acceleration is less than 0.125, and that there is always no stable area at L₂ and L₃; the result is applied to the fast rotating Asteroid 2000EB₁₄.     

Numerical modeling of galaxy evolution

A very significant problem in the modeling of disk-galaxy formation in the cold dark matter (CDM) cosmology is the so-called `angular momentum problem'. This problem arises when we numerically model the collapse of baryons within a dark halo in the CDM model. The formed baryonic disk has much less angular momentum than observed disk galaxies due to the considerable loss of angular momentum during the progressive merger of small clumps. As a result of efficient radiative cooling, the gas component collapses too deeply within the dark halo. When two such systems are merging, the angular momentum of the material near the center is effectively transported outwards by the tidal force. This is a physical reason for this problem, however, there may be a numerical origin due to the nature of the Smoothed Particle Hydrodynamics (SPH) method widely used in galaxy formation models. To address the numerical origin of the `angular momentum problem' with a much higher-resolution SPH model, we are developing our Parallel Tree-SPH code. After evolving four initial models with different mass and force resolution, we compare the angular momentum content of SPH particles. We find that both mass and force resolutions clearly affect the evolution of radiative cosmological SPH models. In most previous radiative cosmological SPH models, a mass ratio between SPH and dark matter particles is .However, we find that this mass ratio is a crucial parameter when we consider the angular momentum content of SPH particles and it is better to make the mass ratio ∼ 1.0 in such models. This revised version was published online in August 2006 with corrections to the Cover Date.     

Study of the Correlations Between Long-Periodic Terrestrial Tides and Occurrence of Earthquakes in the Vrancea Site

Following studies already performed by various authors concerning specific tectonic faults we analyse statistically the possibility that earthquakes in the very active seismological zone of Vrancea (Roumania) may be triggered by the vertical luni-solar tidal oscillations when retaining only the components other than diurnal and semi-diurnal. Our conclusion is that for three of the four leading tides, with periods 18.6 y, 182.62 d, and 13.66 d, the earthquakes occur preferentially during the ascending part of each of the sine oscillation. This property is especially visible for the leading 13.66 d fortnightly wave, and for the 18.6 y wave, for which results are very similar to that of Kilston and Knopoff (1983), who analyzed data related to the San Andreas fault in Southern California. As a complement, we carried out an analysis of earthquake periodicities w.r.t. the variation rate of each of the tides above, given by the half-period sine oscillation, which also leads to interesting possible correlations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Convection driven by tidal and radiogenic heating in medium size icy satellites

Convection is one of the most important processes responsible for the formation of the surface features on many planetary bodies. Observations of some icy satellites indicate that the satellites’ surfaces are modified due to the internally driven tectonic activity. The tidal heating could be an important source of energy responsible for such internal activity. This suggestion is supported by the correlation of the tidal parameter ψ and tectonic features. Consequently, the tidal and the radiogenic heat sources seem to be of primary importance for the medium size icy satellites. Our research deals with convection in a non-differentiated body. The convection is a results of both uniform radiogenic heating and non-uniform and non-spherically symmetric tidal heating. To investigate the problem a 3D model of convection is developed based on the Navier-Stokes equation, the equation of thermal conductivity, the equation of continuity, and the equation of state. The 3D formulae for the tidal heat generation based on the results of Peale and Cassen [1978. Icarus 36, 245-269] and others are used in the model. To measure the relative importance of radiogenic heating versus tidal heating a dimensionless number C_t is introduced. The systematic investigation of a steady-state convection is performed for different values of the Rayleigh number and for the full range of C_t. The results indicate that for low and moderate value of the Rayleigh number, convection pattern driven by the tidal heating and by the radioactivity in the medium size icy satellites consists of one cell or of two cells. For C_t>0 the critical value of Rayleigh number Ra_cr=0. The one-cell pattern is specific for low Rayleigh numbers but it could be observed for the full range of number C_t. It means that the pattern of convection does not fully follow the pattern of heating. This rather unexpected result could be of great importance for the final stage of convection. All patterns of tidally driven convection are oriented with respect to the direction to the planet. For two-cell patterns the regions of downward motion are situated in the centers of the near and far sides of the satellite, respectively.     

Tidal effects of a massive spheroidal halo on an inner spheroidal contracting visible body: Application to an evolutionary disk-galaxy model

The effects of the tidal interactions between two coaxial, homogeneous spheroids, one (the “Brigt Component”: B) completely embedded in the other (the “Dark Halo”: D), along a quasi-static contraction, are considered. The aim is to look how the dynamical properties and the final morphology of the B subsystem may be affected by the presence of the D component. Three initial configurations are considered: the quasi-spherical “Dark Halo” D coincides with the “Visible Component” B (case C); D is flatter than B but the two spheroids have the same semiminor axis (case N); no D component is assumed; the “visible” spheroid is single (case S). The application to an evolutionary disk-galaxy model is considered under some simple assumptions: i) in cases C and N the spheroidal halo is massive (mass ratio “dark”/“bright” about ten) and dissipationless. For a mass ratio like this, the tidal interaction of the B component over D turns to be negligible in the course of the contraction; adding to that the lack of dissipation, it appears plausible to take the D component as frozen along the evolution; ii) the degree of anisotropy and the angular momentum of B, J_B, are conserved. The conservation of J_B provides us the time-independent relationship among the key physical quantities and gives the possibility to draw the evolutionary tracks on the plane (axis ratio σ_B, semimajor axis a_B) without any explicit time-scale; iii) the global “star formation rate” is parametrized according to a simple “Schmidt power law” proportional to the square of gas density. At every step of the quasi-static contraction, the structure is determined by the tensor virial theorem extended to a double configuration. The model is very idealized, particularly because there are no available tidal gravitational terms other than for the case of two homogeneous. Nevertheless, the method based on the tensor virial appears powerful to gain insight into the correlations among the physical quantities involved and into their trend along the evolution. One of the main result is a clear indication of a leading role played by the axis ratio of the “Dark-Halo” component which might be, to the extent that this simple picture can be compared with a real galactic system, a possible new physical parameter to be added to mass and angular momentum for separating spirals from S0 galaxies.     

Wave-photochemistry coupling and its effect on water vapor, ozone and airglow variations in the atmosphere of Mars

A one-dimensional photochemical-transport model for the martian lower atmosphere has been developed to study the diurnal cycles of wave-photochemistry coupling. The model self-consistently calculates water vapor mixing ratio profiles, which exhibit strong vertical and diurnal variations mainly due to the high sensitivity of the saturation vapor pressure to temperature variation. The dynamical coupling of water vapor caused by the temperature variation induced by tidal waves, vertical transport parameterized by eddy diffusion, and linear relaxation introduced in condensation-sublimation processes all have similar timescales of diurnal variation. This leads to a significant asymmetric distribution of water vapor concentration as a function of local time. As a result, the net effect of the temperature variation by tidal waves depletes the water vapor concentration in its diurnal mean. The coupling processes also deplete the diurnally averaged HO_x concentration, which in turn leads to significant enhancements of both ozone concentration and the associated airglow emissions in the martian atmosphere. The model also shows explicitly the importance of photochemical-transport coupling to the airglow emissions and its implications in species retrievals when the photochemical times of the excited states are comparable to the timescale of diurnal variation.     

The hierarchical stability of the seven known large size ratio triple asteroids using the empirical stability parameters

In this study, the hierarchical stability of the seven known large size ratio triple asteroids is investigated. The effect of the solar gravity and primary’s J ₂ are considered. The force function is expanded in terms of mass ratios based on the Hill’s approximation and the large size ratio property. The empirical stability parameters are used to examine the hierarchical stability of the triple asteroids. It is found that the all the known large size ratio triple asteroid systems are hierarchically stable. This study provides useful information for future evolutions of the triple asteroids.