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In general, “tide” refers to both the body tide and ocean tide of the Earth. While ocean tide is more widely recognized in public than body tide, Earth tide refers to body tide in solid Earth geosciences. In fact, body tide is the largest periodic perturbation in the solid Earth. A brief sketch of ocean tide is included in this chapter, however, the main concern here is “body tide.” To predict the displacement, gravity, deflection of vertical associated with Earth’s body tide at any specified time epoch at certain place has been an important task in gravity prospecting and gravimetric geodesy. “Love numbers,” which are the three kinds of ratios between the response of real Earth and that of an ideal Earth under tidal force, and are quite conveniently used in body tidal predictions. Accurate Love numbers can only be determined through a numerical computation with the Earth’s physical property model. Another information required for body tide prediction are the positions of the Moon and the Sun. Because tidal force rapidly decreases with distance (1/r3), other planets, even Jupiter, induce negligible amounts of tide (relatively less than 10−5). Therefore it is of utmost importance to have the accurate ephemerides computation algorithm about the two largest tide raising celestial bodies; the Moon and the Sun. In this chapter the method to predict body tide of the Earth is described with emphasis on the two algorithms; (1) to compute Love numbers, and (2) to predict body tidal perturbation using Love numbers and lunar/solar ephemerides. And these are actually the main stems of K2-Tide; an Earth tide prediction computer program. Brief explanations about ocean tide model and load Love number as well as fluid Love number are attached at the end of this chapter.

Optical and near-infrared observations are compiled for the three gamma-ray binaries hosting Be stars: PSR B1259-63, LSI+61 303, and HESS J0632+057. The emissions from the Be disk are considered to vary according to the changes in its structure, some of which are caused by interactions with the compact object (e.g., tidal forces). Due to the high eccentricity and large orbit of these systems, the interactions -- and, hence the resultant observables -- depend on the orbital phase. To explore such variations, multi-band photometry and linear polarization were monitored for the three considered systems, using two 1.5 m-class telescopes: IRSF at the South African Astronomical Observatory and Kanata at the Higashi-Hiroshima Observatory., Comment: accepted to Universe

We explore the effect of anisotropic wind driving on the properties of accretion onto black holes in close binaries. We specifically focus on line-driven winds, which are common in high-mass X-ray binaries. In close binary systems, the tidal force from the companion star can modify the wind structure in two different ways. One is the reduction of wind terminal velocity due to the weaker effective surface gravity. The other is the reduction in mass flux due to gravity darkening. We incorporate these effects into the so-called CAK theory in a simple way and investigate the wind flow around the accretor on the orbital scale. We find that a focused accretion stream is naturally formed when the Roche lobe filling factor is $\gtrsim0.8$-0.9, analogous to that of wind Roche lobe overflow, but only when the velocity reduction is taken into account. The formation of a stream is necessary to bring in sufficient angular momentum to form an accretion disc around the black hole. Gravity darkening effects reduce the amount of accreted angular momentum, but not enough to prevent the formation of a disc. Based on these results, we expect there to be a discrete step in the observability of high-mass X-ray binaries depending on whether the donor Roche lobe filling factor is below or above $\sim$0.8-0.9., Comment: accepted for publication in the Publications of the Astronomical Society of Australia

I have carried out simulations of the evolution of dwarf galaxies falling into a Fornax-like Cluster using the Moving Box technique.I am interested in following the journey of the galaxies into the cluster and characterizing their size, star formation rate, gas and dark matter content, stellar dynamics, and evolution, depending on the orbit and the initial mass at the time of orbital injection.Some of the galaxies are effectively transformed into Ultra Diffuse Galaxies (UDG) while some others are allowed to be briefly identified as “jellyfish".Serendipitously, I realized that these simulations produce galaxies whose morphology is similar to a particular galaxy in the Fornax Cluster: NGC1427A. I identified that gaseous and stellar tails of this galaxy may be explainable given that they are subject to different environmental effects (ram-pressure stripping and tidal forces). I was also able to provide some falsifiable predictions on the position of the galaxy with respect to the center of the Cluster and its projected orbital direction. Finally, I have contributed to the development of a technique to study low dimensional-manifolds in the simulations. In particular, I concentrated on the analysis of gaseous tails of simulated jellyfish galaxies with the aim to investigate regions of recent star formation and mixing between the galactic gaseous material and the hot gas of the cluster.

Both classical and relativistic weak-field and slow-motion perturbations to planetary orbits can be treated as perturbative corrections to the Keplerian model. In particular, tidal forces and General Relativity (GR) induce small precession rates of the apsidal line. Accurate measurements of these effects in transiting exoplanets could be used to test GR and to gain information about the planetary interiors. Unfortunately, models for transiting planets have a high degree of degeneracy in the orbital parameters that, combined to the uncertainties of photometric transit observations, results in large errors on the determinations of the argument of periastron and precludes a direct evaluation of the apsidal line precession. Moreover, tidal and GR precession time-scales are many order of magnitudes larger than orbital periods, so that on the observational time-spans required to cumulate a precession signal enough strong to be detected, even small systematic errors in transit ephemerides add up to cancel out the tiny variations due to precession. Here we present a more feasible solution to detect tidal and GR precession rates through the observation of variations of the time interval ($\Delta \tau$) between primary and secondary transits of hot Jupiters and propose the most promising target for such detection, WASP-14 b. For this planet we expect a cumulated $\Delta \tau$ $\approx$ -250 s, due to tidal and relativistic precession, since its first photometric observations., Comment: This paper has been accepted for publication by MNRAS

We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl type $f(Q,T)$ gravity, in which the nonmetricity $Q$ is represented in the standard Weyl form, fully determined by the Weyl vector, while $T$ represents the trace of the matter energy-momentum tensor. The effects of the Weyl geometry and of the extra force induced by the nonmetricity-matter coupling are explicitly taken into account. The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived. As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the nonmetricity-matter coupling, are obtained in the weak field approximation. The tidal motion of test particles is directly influenced by the gradients of the extra force, and of the Weyl vector. As a concrete astrophysical example we obtain the expression of the Roche limit (the orbital distance at which a satellite begins to be tidally torn apart by the body it orbits) in the Weyl type $f(Q,T)$ gravity., Comment: 18 pages, no figures, accepted for publication in EPJC; minor corrections; references added

We have investigated tidal forces and geodesic deviation motion in the 4D-Einstein-Gauss-Bonnet spacetime. Our results show that tidal force and geodesic deviation motion depend sharply on the sign of Gauss-Bonnet coupling constant. Comparing with Schwarzschild spacetime, the strength of tidal force becomes stronger for the negative Gauss-Bonnet coupling constant, but is weaker for the positive one. Moreover, tidal force behaves like those in the Schwarzschild spacetime as the coupling constant is negative, and like those in Reissner-Nordstr\"{o}m black hole as the constant is positive. We also present the change of geodesic deviation vector with Gauss-Bonnet coupling constant under two kinds of initial conditions., Comment: 13 Pages, 4 figures. Accepted for publication in Eur.Phys. J. C

We present a series of chemodynamical simulations of Magellanic-like systems consisting of two interacting, equal-mass dwarf galaxies orbiting a massive host galaxy, including feedback and star formation, tides, and ram pressure. We study the star formation and chemical enrichment history of the dwarfs, and the production of a Magellanic Stream analogue. The dwarfs interact with each other through tidal forces, distorting their morphologies and triggering star formation. A stream is naturally produced as outflows, induced by feedback and interactions, are stretched by tidal forces. Counter to some recent simulations, we find that the leading arm persists even in the presence of ram pressure from the host galaxy. Interactions between the dwarfs and the host galaxies produce multiple kinematic components in the stream, as observed. A combination of ongoing star-formation and entrained low-metallicity gas causes the stream to have a complex chemical structure, with an average metallicity that is generally lower than that of the dwarfs., Accepted to ApJ

The origin of the two small prograde natural satellites of Mars may, or may not, be important in deciphering the early history of planet Mars. There have been many proposals for the origin of Phobos and Deimos but there is no generally accepted model for their origin. There is, however, substantial evidence for oblique impact of large bodies onto the surface of Mars in the retrograde (clock-wise) direction. These features suggest that a sizeable body, probably an asteroid, broke up in the vicinity of Mars and the disrupted debris, large and small, impacted along a great circle pattern on the martian surface. The proponents of this model also suggest that this orbiting retrograde satellite, before breaking apart, could have powered a martian core dynamo via tidal forces. I show the results of numerical simulations in which portions of asteroids could be gravitationally extracted from parent bodies in hyperbolic orbits passing through the weightlessness limit of Mars. The extracted bodies are then inserted into unstable orbits around Mars. These bodies eventually would impact onto the martian surface. Again, there is no consensus model for the origin of Phobos and Deimos.

Stellar components in binaries are subject to tidal forces which influence asteroseismic properties. Tidally pertubed pulsations have been reported for different objects but none of these are in their pre-main sequence phase of evolution. This makes RS Cha, consisting of two $\delta$ Scuti stars and with pulsational characteristics influenced by tidal effects , the first such object observed. We aim to investigate the pulsational properties of the eclipsing binary RS Cha in terms of the theory of tidally perturbed pulsations. Based on photometric time series obtained from the TESS satellite, we performed binary modelling using PHOEBE to interpret the binary light curve and to allow the investigation of the pulsations of both components in RS Cha. We modelled the detrended light curve with the superposition of linear modes. The frequencies were then interpreted as self excited modes perturbed by tidal forces. We find evidence for tidally perturbed modes, which enables the identification of pulsation modes. RS Cha mainly exhibits dipole modes, while one prominent $l=2$ or $l=3$ mode is also inferred. The latter verifies previous results from spectroscopic time series. This work shows that RS Cha is an ideal candidate to test the theory of tidally perturbed pulsations within the framework of asteroseismic modelling. The identification of multiple pulsation modes using this theory is unprecedented and will be a keystone in the future of pre-main sequence asteroseismology. However, amplitude modulation caused by the changing light ratio during the orbital phase in an eclipsing binary also plays a significant role, which can complicate mode identification., Comment: 11 pages plus 7 for the appendix, 8 pages plus 8 for the appendix, accepted for publication in Astronomy & Astrophysics

Neutron star (NS) binaries formed dynamically may have significant eccentricities while emitting gravitational waves (GWs) in the LIGO/VIRGO band. We study tidal effects in such eccentric inspiralling NS binaries using a set of hybrid equations. The NS is modelled as a compressible ellipsoid, which can deform nonlinearly due to tidal forces, while the orbit evolution is treated with the post-Newtonian (PN) theory up to 2.5-PN order. We find that in general, the tidal interaction can accelerate the inspiral, and cause orbital frequency and phase shifts. For circular inspirals, our calculations reproduce previous linear result at large binary separations, but incorporate the dynamical response of the NS at small separations. For eccentric inspirals, the frequency and phase shifts oscillate considerably near pericenter passages, and the oscillating amplitudes increase with eccentricities. As a result, the GW phase is also significantly influenced by the tidal effect. At merger, the cumulative GW phase shift can reach more than 10 radians (for typical NS mass $1.4M_\odot$ and radius 11.6 km), much larger than the circular inspiral case. Although the event rate of eccentric NS mergers is likely low, the detection of such mergers could provide a useful constraint on the NS equation of state., Comment: 9 pages, 8 figures, accepted to Phys. Rev. D

Aims. Planets with large moon(s) or those in the habitable zone of low-mass stars may experience much stronger tidal force and tide-induced ocean mixing than that on Earth. Thus, the vertical diffusivity (or, more precisely, diapycnal diffusivity) on such planets, which represents the strength of vertical mixing in the ocean, would be greater than that on Earth. In this study, we explore the effects of extremely high diffusivity on the ocean circulation and surface climate of Earth-like planets in one asynchronous rotation orbit. Methods. The response of planetary climate to 10 and 100 times greater vertical diffusivity than that found on Earth is investigated using a fully coupled atmosphere–ocean general circulation model. In order to perform a clear comparison with the climate of modern Earth, Earth’s orbit, land–sea configuration, and present levels of greenhouse gases are included in the simulations. Results. We find that a larger vertical diffusivity intensifies the meridional overturning circulation (MOC) in the ocean, which transports more heat to polar regions and melts sea ice there. Feedback associated with sea ice, clouds, and water vapor act to further amplify surface warming. When the vertical diffusivity is 10 (100) times the present-day value, the magnitude of MOC increases by ≈3 (18) times, and the global-mean surface temperature increases by ≈4 °C (10 °C). This study quantifies the climatic effect of an extremely strong vertical diffusivity and confirms an indirect link between planetary orbit, tidal mixing, ocean circulation, and surface climate. Our results suggest a moderate effect of varying vertical ocean mixing on planetary climate.

Phobos is one of the two moons of Mars, the only other terrestrial planet to have companions. In spite of certain common orbital characteristics between Earth’s Moon and Phobos, such as almost circular, low-inclination, and synchronous orbits, the origin of the Martian moons remains to be understood. This unsettled state of affairs reflects a scarcity of data pertinent to its interior structure and bulk composition, both of which hold the key to solving the question of the provenance of the satellites. Drawing on the importance of interior structure as a means of providing further constraints on this problem, we construct a series of models of the interior of Phobos in accordance with current observations and determine their tidal deformation. The models include a homogeneous body, ice-rock mixtures, models with positive and negative density gradients, and layered models. To compute the deformation of Phobos precisely, we solve the three-dimensional elastostatic problem to obtain the full displacement field. For this, we rely on a higher-order spectral-element method and to account for a correct representation of shape and resulting displacement field, we accurately mesh the figure of Phobos by employing the digital terrain model of Willner et al. (2014). To enable us to further distinguish between models, we also rely on currently available geophysical data (e.g., magnitude of libration in longitude, mean density, gravity field, and moments of inertia). Our results show that the homogeneous, ice-rock mixture, and negative density gradient models are largely degenerate and therefore difficult to separate, but that models with a density increase with depth can be differentiated from the former model families. From a purely deformational point of view, we find that for positive gradient and layered models, the largest deformation occurs on the rim of the Stickney crater, rather than immediately at the sub-Mars point on Phobos, as in the case of the other models, where tidal forces are largest. These observations will be of considerable interest and should provide important anchoring points for the future exploration of Phobos as envisaged with the Martian Moons Exploration mission.

We consider the fate of a massless (or ultra-relativistic massive) string probe propagating down the BTZ-like throat of a microstate geometry in the D1-D5 system. Far down the throat, the probe encounters large tidal forces that stretch and excite the string. The excitations are limited by the very short transit time through the region of large tidal force, leading to a controlled approximation to tidal stretching. We show that the amount of stretching is proportional to the incident energy, and that it robs the probe of the kinetic energy it would need to travel back up the throat. As a consequence, the probe is effectively trapped far down the throat and, through repeated return passes, scrambles into the ensemble of nearby microstates. We propose that this tidal trapping may lead to weak gravitational echoes., 39 pages, 3 figures; v2: references and acknowledgment added

We used statistical approach by coupling redundancy analysis with linear regression analysis, which is useful to understand potential sources of antibiotics in the tide rising and ebbing of surface water in the Yongjiang Estuary, China. This study aimed to investigate the relationship between 29 antibiotics at five sites over four seasons and 13 environmental parameters during the tide rising and ebbing durations. The results found that dissolved organic carbon (DOC), salinity, temperature and chlorophyll a (Chla) were the main factors to impact antibiotics. The concentrations of macrolides were increasing with DOC, suggesting DOC may influence the adsorption capacity of antibiotics. The concentrations of tetracyclines had significant correlation with temperature and Chla during the tide rising period. This study demonstrated a method of exploring the relationship between the concentrations of antibiotics and environmental parameters, which is beneficial to future antibiotics research in estuaries.

The North Water (NOW), situated between Ellesmere Island and Greenland in northern Baffin Bay, is the largest recurring polynya in the Canadian Arctic. Historically, the northern border of the NOW is defined by an ice arch that forms annually in Kane Basin, which is part of the Nares Strait system. In 2007 the NOW ice arch failed to consolidate for the first time since observations began in the 1950s. The non-formation of the NOW ice arch occurred again in 2009, 2010, 2017 and 2019. Satellite Advanced Very High Resolution Radiometry data shows that large floes broke off from the normally stable landfast ice in Kane Basin for each of these years, impeding ice arch formation. A closer analysis of a 2019 event, in which 2500 km2 of ice sheared away from Kane Basin, indicates that significant tidal forces played a role. The evidence suggests that thinning ice from a warming climate combined with large amplitude tides is a key factor in the changing ice dynamics of the NOW region. The non-formation of the NOW ice arch results in an increased loss of multiyear ice through Nares Strait.

There is compelling evidence for subsurface water oceans among the three outer Galilean satellites, and evidence for an internal magma ocean in the innermost moon, Io. Tidal forces from Jupiter periodically deform these bodies, causing heating and deformation that, if measured, can probe their interior structures. In addition to Jupiter-raised tides, each moon also raises tides on the others. We investigate moon-moon tides for the first time in the Galilean moons, and show that they can cause significant heating through the excitation of high-frequency resonant tidal waves in their subsurface oceans. The heating occurs both in the crust and ocean, and can exceed that of other tidal sources and radiogenic decay if the ocean is inviscid enough. The resulting tidal deformation can be used to constrain subsurface ocean thickness. Our understanding of the thermal-orbital evolution and habitability of the Jovian system may be fundamentally altered as a result.

In order to improve the accuracy of tide prediction, a modularized tide real-time prediction model based on wavelet neural network is proposed. The tides are divided into astronomical tides affected by the tidal force of celestial bodies and non-astronomical tides affected by environmental factors. The harmonic analysis method and WNN (wavelet neural network) are used to forecast the astronomical tide and non-astronomical tide respectively. The final tidal forecast data is composed of the output results of the two methods. In the prediction of non-astronomical tides, the parameters of wavelet neural network based on GA (genetic algorithm) are optimized to improve the prediction accuracy. The tide prediction simulation is carried out by using the measured tide data of old port Tampa tide station. The simulation results show that the method has high prediction accuracy.

In order to make tide prediction more efficient and accurate, this paper proposes a method based on adding momentum term to optimize wavelet neural network for modular tide prediction. In the study, the tides are divided into astronomical tides which are affected by the tidal force of celestial bodies and non astronomical tides which are affected by environmental factors and other factors. The harmonic analysis method and wavelet neural network are used to predict the tides respectively. When using wavelet neural network to predict non astronomical tide, the method of adding momentum term is used to optimize the weight and parameters of wavelet neural network to improve the prediction accuracy. The simulation experiment is carried out by using the data measured at Tampa tide station in western Florida. The results show that the tide prediction model can improve the prediction accuracy and is efficient and feasible.

During close approaches to planets or stars, the morphological and dynamical properties of rubble-pile small bodies can be modified, and some may catastrophically break up. This phenomenon is of particular interest for understanding the evolution and population of small bodies, and for making predictions for future encounters. Previous numerical explorations typically used methods that do not adequately represent the nature of rubble piles. The encounter outcomes and influence factors are still poorly constrained. Based on recent advances in modeling rubble piles, we aim to provide a better understanding of the tidal encounter processes through soft-sphere discrete element modeling (SSDEM) and to establish a database of encounter outcomes and the dependencies on encounter conditions and rubble-pile properties. We performed thousands of numerical simulations using the SSDEM implemented in the N-body code pkdgrav to study the dynamical evolution of rubble piles during close encounters with the Earth. The effects of encounter conditions, material strength, arrangement, and resolution of constituent particles are explored. Three typical tidal encounter outcomes are classified, i.e., deformation, mass shedding, and disruption, ranging from mild modifications to severe damages of the progenitor. The encounter speed and distance required for causing disruption events are much smaller than those predicted by previous studies, indicating a smaller creation rate of tidally disrupted small body populations. Extremely elongated fragments with axis ratios ~1:6 can be formed by moderate encounters. Our analyses of the spin-shape evolution of the largest remnants reveal reshaping mechanisms of rubble piles in response to tidal forces, consistent with stable rubble-pile configurations derived by continuum theory. A case study for SL9 suggests a low bulk density (0.2-0.3 g/cc) for its progenitor., 15 pages, 15 figures, Accepted for publication in A&A, author version

We examine the inertial modes of vibration of a Maclaurin spheroid and determine how they are driven by an external tidal field, either Newtonian (gravitoelectric) or post-Newtonian (gravitomagnetic). The context and motivation for this work come from the realization that inertial modes of rotating neutron stars can be resonantly excited in binary inspirals, with a measurable effect on the phasing of the emitted gravitational waves. We aim to provide additional insights into this phenomenon. We calculate how the frequencies of the relevant inertial modes, and their overlap integrals with the tidal forces, vary as the star's rotation rate increases, spanning almost the full range between zero rotation and the mass-shedding limit. We prove that a single inertial mode couples to a Newtonian tidal field; overlap integrals with all other modes vanish. We prove also that four inertial modes couple to a post-Newtonian, gravitomagnetic tidal field; overlap integrals with all other modes vanish. Finally, we determine the rather extreme conditions under which the gravitoelectric driving of inertial modes dominates over the gravitomagnetic driving., 28 pages, 7 figures, revised after referee comments, new Appendix, matches published version

Context. The strong tidal dissipation in the couple Jupiter-Io is spread to all the moons involved in the Laplace resonance (Io, Europa, and Ganymede), leading to a migration of their orbits. Aims. We aim to characterize the future behavior of the Galilean satellites over the Solar System lifetime and to quantify the stability of the Laplace resonance. Since tidal dissipation makes possible the exit from the current resonances or capture into new ones, we investigate the capture of Callisto into resonance. Methods. We perform hundreds of propagations using an improved version of a recent semi-analytical model. As Ganymede moves outwards, it approaches the 2:1 resonance with Callisto, inducing a temporary chaotic motion in the system. For this reason, we draw a statistical picture of the outcome of the resonant encounter. Results. The system can settle into two distinct outcomes: A) a chain of three 2:1 two-body resonances (Io-Europa, Europa-Ganymede and Ganymede-Callisto), or B) a resonant chain involving the 2:1 two-body resonance Io-Europa plus at least one pure 4:2:1 three-body resonance, most frequently between Europa, Ganymede and Callisto. In case A (56\% of the simulations), the Laplace resonance is always preserved and the eccentricities remain confined to small values below 0.01. In case B (44\% of the simulations), the Laplace resonance is generally disrupted and the eccentricities of Ganymede and Callisto can increase up to about 0.1, making this configuration unstable and driving the system into new resonances. Conclusion. From our results, the capture of Callisto into resonance appears to be extremely likely (100\% of our simulations). Assuming the most recent estimate of the dissipation between Io and Jupiter, the resonant encounter happens at about 1.5 Gyrs from now. Therefore, the stability of the Laplace resonance is guaranteed at least up to about 1.5 Gyrs., Comment: 22 pages, 13 figures, 6 sections. Accepted for publication in Astronomy & Astrophysics

We developed a 3-D elastic Boundary Element Method (BEM) computer code, called AstroSeis, to model seismic wavefields in a body with an arbitrary shape, such as an asteroid. Besides the AstroSeis can handle arbitrary surface topography, it can deal with a liquid core in an asteroid model. Both the solid and liquid domains are homogenous in our current code. For seismic sources, we can use single forces or moment tensors. The AstroSeis is implemented in the frequency domain and the frequency-dependent Q can be readily incorporated. The code is in MATLAB and it is straightforward to set up the model to run our code. The frequency-domain calculation is advantageous to study the long-term elastic response of a celestial body due to a cyclic force such as the tidal force with no numerical dispersion issue suffered by many other methods requiring volume meshing. Our AstroSeis has been benchmarked with other methods such as normal modes summation and the direct solution method (DSM). This open-source AstroSeis will be a useful tool to study the interior and surface processes of asteroids., 27 pages, 10 figures

Large‐scale flooding causing widespread devastation is expected to increase in the low‐lying river basin of developing countries. Flood inundation occurring in deltaic environments are caused by both river runoff and tides. Furthermore, flood risk in deltas can be exacerbated by composite driving forces, such as future climate change, land‐use change, and sea‐level rise. Flood hazard maps have provided one way to visualize flood risk, and are generally created with future projection. However, existing hazard maps have not incorporated the tidal effect and have not assessed the impact of these three future driving factors simultaneously. Here we presented a method to quantify and visualize the tidal effect on flood inundation under current and future scenarios by coupling rainfall‐runoff and inundation models, and tide level data. We found simulations of the composite future scenario indicate a 1.27‐fold increase in the inundation area, with a two‐fold increase in the extent of the tidal effect for the case of a with any return period rainfall event. These achievements can be used to provide flood hazard maps that also visualize the tidal effect. This new information will enhance our understanding of flood risk in low‐lying areas and contribute further to disaster risk reduction.

Tidal forces are an important feature of General Relativity, which are related to the curvature tensor. We analyze the tidal tensor in Kerr spacetime, with emphasis on the case along the symmetry axis of the Kerr black hole, noting that tidal forces may vanish at a certain point, unlike in the Schwarzschild spacetime, using Boyer-Lindquist coordinates. We study in detail the effects of vanishing tidal forces in a body constituted of dust infalling along the symmetry axis. We find the geodesic deviation equations and solve them, numerically and analytically, for motion along the symmetry axis of the Kerr geometry. We also point out that the intrinsic Gaussian curvature of the event horizon at the symmetry axis is equal to the component along this axis of the tidal tensor there., Comment: 13 pages, 15 figures, accepted for publication in The European Physical Journal Plus

White dwarf stars that enter the tidal radius of black holes with masses $\lesssim$ $10^5$ M$_{\odot}$ are doomed to be ripped apart by tidal forces. Black holes in this mass range between stellar black holes and supermassive black holes have not been conclusively identified so the detection of a tidal disruption of a white dwarf would provide clear evidence for the existence of intermediate-mass black holes. In this review, we present a theoretical and observational overview of the transient events that result from the tidal disruptions of white dwarfs by intermediate-mass black holes. This includes discussion of the latest simulations and predicted properties, the results of observational searches, as well as a summary of the potential for gravitational wave emission to be detected with upcoming missions., Accepted for publication in Springer Space Science Reviews. Chapter in review, 'The Tidal Disruption of Stars by Massive Black Holes', editors: P. G. Jonker, S. Phinney, E. M. Rossi, S. v. Velzen, I. Arcavi & M. Falanga

The long-wavelength coherent overdensity and tidal force, which are not direct observables for a finite-volume survey, affect time evolution of cosmic structure formation and therefore clustering observables through the mode coupling. In this paper we develop an "anisotropic" separate universe (SU) simulation technique to simulate large-scale structure formation taking into account the effect of large-scale tidal force into the anisotropic expansion of local background. We modify the TreePM N-body simulation code to implement the anisotropic SU simulations, and then study the "response" function of matter power spectrum that describes how the matter power spectrum responds to the large-scale tidal effect as a function of wavenumber and redshift for a given global cosmology. We test and validate the SU simulation results from the comparison with the perturbation theory predictions and the results from high-resolution PM simulations. We find that the response function displays characteristic scale dependences over the range of scales down to nonlinear scales, up to k ~ 6 h/Mpc., 15 pages, 10 figures, 1 table, accepted for publication in MNRAS, added a figure and a subsection, changed to double column

The authors realize a flexible optical experiment system to simulate a wormhole by applying a two dimensional embedded curved waveguide. By observing the beam propagation in the waveguide, they demonstrate a strong gravitational effect on wavepackets around a wormhole and study the onset of a tidal force effect

In this chapter we first deduce Newton’s law of gravitation in its local form as a preparation for comparing Newton’s and Einstein’s theories, including a discussion of tidal forces. Then we give a presentation of the main conceptual foundation of the general theory of relativity, emphasizing the principle of equivalence and the principle of relativity.

We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of singularities emerges since two boundary points can be connected by a nontrivial null geodesic in the bulk, encircling the photon sphere of the black hole. We show that these new singularities are resolved by tidal effects due to the black hole curvature, by solving the string worldsheet theory in the Penrose limit. Singularities in the asymptotically flat black hole geometry are also discussed., Comment: 26 pages; minor corrections, references added

Since 2007, in the context of the SOMLIT network, we installed a CTD (SeaBird SBE19+) below the ASTAN buoy located in the Western English Channel (WEC) off Roscoff (48° 46′ 40 N 3° 56′ 15 W; depth 5 m) between the SOMLIT-Coast and SOMLIT-Offshore sampling sites. These sensors provided high-frequency (HF) measurements (hourly) of sea surface salinity (SSS), sea surface temperature (SST), fluorescence and dissolved oxygen (DO) all year. Since 2014, we added a SAMI-CO2 sensor, which measured the sea surface partial pressure of CO2 (pCO2) to investigate the seasonal dynamic of the pCO2 and associated air-sea CO2 exchange at the ASTAN site. From this high-frequency database, we were able to separate the signal according to the tide to determine the physicochemical and biological characteristics of two water masses: the coastal water mass (CWM) and the offshore water mass (OWM). These two water masses were strongly influenced by the biological productivity of the environment, more importantly in the CWM, and limited by the available light. Surface waters at the ASTAN site were near equilibrium with the atmosphere with an annual air-sea flux of 0.12 mmol C m−2 d−1 during 2016. The year can be divided into three distinct regimes: at the beginning of the year (winter period), the ASTAN site was a source of CO2, controlled by thermodynamic at 1.23 mmol C m−2 d−1, from April to September (spring–summer), it became a sink of CO2 with an important impact of biological activity (−0.64 mmol C m−2 d−1), and at the end of the year (fall), it reversed to a weaker source of CO2 at 0.26 mmol C m−2 d−1. In order to further assess the signal, we used signal processing tools such as wavelet analysis. From the frequency/time representation, it was possible to follow how the signal varied over time, and thus deduce the presence of the two water masses due to the tidal effect, but also observes a significant impact of the day/night cycle on the biological parameters.

Paper on the creep tide theory and its applications to satellites and planets with emphasis on a new set of differential equations allowing easier numerical studies. The creep tide theory is a new paradigm that does not fix a priori the tidal deformation of the body, but considers the deformation as a low-Reynolds-number flow. The evolution under tidal forces is ruled by an approximate solution of the Navier-Stokes equation depending on the body's viscosity with no ad hoc assumptions on its shape and orientation. It reproduces closely the results of Darwinian theories in the case of gaseous planets and stars, but the results are completely different in the case of stiff satellites and planets. It explains the tidal dissipations of Enceladus and Mimas. The extension of the theory to nonhomogeneous icy satellites with a subsurface ocean allows the amplitude of the forced oscillations around synchronization (librations) to be better determined., Comment: 27 pages, 8 figures

When a star passes close to a supermassive black hole (BH), the BH's tidal forces rip it apart into a thin stream, leading to a tidal disruption event (TDE). In this work, we study the post-disruption phase of TDEs in general relativistic hydrodynamics (GRHD) using our GPU-accelerated code H-AMR. We carry out the first grid-based simulation of a deep-penetration TDE ($\beta$=7) with realistic system parameters: a black-hole-to-star mass ratio of $10^6$, a parabolic stellar trajectory, and a nonzero BH spin. We also carry out a simulation of a tilted TDE whose stellar orbit is inclined relative to the BH midplane. We show that for our aligned TDE, an accretion disk forms due to the dissipation of orbital energy with $\sim$20 percent of the infalling material reaching the BH. The dissipation is initially dominated by violent self-intersections and later by stream-disk interactions near the pericenter. The self-intersections completely disrupt the incoming stream, resulting in five distinct self-intersection events separated by approximately 12 hours and a flaring in the accretion rate. We also find that the disk is eccentric with mean eccentricity e$\approx$0.88. For our tilted TDE, we find only partial self-intersections due to nodal precession near pericenter. Although these partial intersections eject gas out of the orbital plane, an accretion disk still forms with a similar accreted fraction of the material to the aligned case. These results have important implications for disk formation in realistic tidal disruptions. For instance, the periodicity in accretion rate induced by the complete stream disruption may explain the flaring events from Swift J1644+57., Comment: Accepted to MNRAS on November 23rd, 2021, 23 pages, 25 figures, uses mnras.cls. Comments welcome. Movies available at https://www.youtube.com/playlist?list=PL7YbfRC6zxzAqIPXWbJgXpr4Wq_nwHiDu

Tidal straits are characteristic narrow marine passageways constricted between emerged or shallowly submerged landmasses, where tidal flows undergo phenomena of hydraulic amplification if repeatedly and cyclically moving through the narrowest strait centre. Modern systems share general hydrodynamic and sedimentological aspects if governed by tidal forces. Tidal currents reproduce characteristic bottom features and sediment accumulations that generate predictable facies tracts and stratigraphies that can be used as proxy to decipher ancient strait deposits preserved in outcrop or subsurface. Straits are here regarded as individual depositional systems, including definite environments or sedimentary zones. We describe the stratigraphic and sedimentological features here suggested to be diagnostic for identifying the strait centre, the dune-bedded zones, the strait-end zones, as well as the strait margins, based on the observation of some tide-influenced or tide-dominated reference ancient system.

This chapter presents the optical photometry of superoutbursts in the three WZ Sge-type dwarf novae ASASSN-15jd, ASASSN-16dt, and ASASSN-16hg. They commonly showed a luminosity dip in the middle of the plateau stage in their main superoutbursts. Also, it was confirmed that they have some observational features characteristic to the candidates for the period bouncer which has an extremely low-mass secondary star. We succeeded to estimate the binary mass ratio of ASASSN-16dt to be 0.036(2) by using stage A superhumps, which is much smaller than that of the systems at the period minimum. Summarizing these results, all of the three systems are possible candidates for the period-bouncer. The expected weak tidal effect by very low mass secondaries in these systems would be responsible for the slow growth of the tidal instability in the disk. We proposed that the luminosity dip in the plateau stage is attributed to the slow development of the eccentricity in the disk.

When a star comes too close to a supermassive black hole, it gets torn apart by strong tidal forces in a tidal disruption event, or TDE. Half of the elongated stream of debris comes back to the stellar pericenter where relativistic apsidal precession induces a self-crossing shock. As a result, the gas gets launched into an outflow that can experience additional interactions, leading to the formation of an accretion disc. We carry out the first radiation-hydrodynamics simulations of this process, making use of the same injection procedure to treat the self-crossing shock as in our previous adiabatic study (Bonnerot & Lu 2020). Two sets of realistic parameters of the problem are considered that correspond to different strengths of this initial interaction. In both cases, we find that the injected matter has its trajectories promptly circularized by secondary shocks taking place near the black hole. However, the generated internal energy efficiently diffuses away in the form of radiation, which results in a thin vertical profile of the formed disc. The diffusing photons promptly irradiate the surrounding debris until they emerge with a bolometric luminosity of $L\approx 10^{44} \, \rm erg\, s^{-1}$. Towards the self-crossing shock, diffusion is however slowed that results in a shallower luminosity increase, with a potentially significant component in the optical band. Matter launched to large distances continuously gains energy through radiation pressure, which can cause a significant fraction to become unbound. This work provides direct insight into the origin of the early emission from TDEs, which is accessed by a rapidly increasing number of observations., 23 pages, 19 figures, accepted by MNRAS. Movies of the simulation are available at http://www.tapir.caltech.edu/~bonnerot/first-light.html

A tidal disruption event (TDE) occurs when a star passes too close to a supermassive black hole and gets torn apart by its gravitational tidal field. After the disruption, the stellar debris form an expanding gaseous stream. The morphology and evolution of this stream is particularly interesting as it ultimately determines the observational properties of the event itself. In this work we perform 3D hydrodynamical simulations of the TDE of a star modelled as a polytropic sphere of index {\gamma} = 5/3, and study the gravitational stability of the resulting gas stream. We provide an analytical solution for the evolution of the stream in the bound, unbound and marginally bound case, that allows us to describe the stream properties and analyse the time-scales of the physical processes involved, applying a formalism developed in star formation context. Our results are that, when fragmentation occurs, it is fueled by the failure of pressure in supporting the gas against its self-gravity. We also show that a stability criterion that includes also the stream gas pressure proves to be far more accurate than one that only considers the black hole tidal forces, giving analytical predictions of the time evolution of the various forces associated to the stream. Our results point out that fragmentation occurs on timescales longer compared with the observational windows of these events and is thus not expected to give rise to significant observational features., Comment: 12 pages,15 figures, accepted for publication in MNRAS

The gravitomagnetic tidal Love number of a slowly rotating body was calculated previously under the assumption that the velocity perturbation created by the tidal field consists of an induction piece proportional to the vector potential, and a rotational piece that scales with $\Omega$, the body's angular velocity. The second part of this assumption is wrong: the rotational piece of the velocity perturbation scales in fact like $\Omega^0 = 1$. The previous calculations are therefore incorrect, and the purpose of this paper is to repair the mistake. To keep the technical difficulties to a minimum, the treatment here is restricted to a post-Newtonian expansion carried out to leading order -- previous calculations of the gravitomagnetic Love number were performed in full general relativity. On the other hand, the computation presented here is not restricted to a stationary tidal field. I show that the correct scaling of the velocity perturbation with $\Omega$ leads to the promotion of the Love number to a Love tensor $k_{jk}^{\ \ pq}$, a four-index object that relates the body's current quadrupole moment $S_{jk}$ to the gravitomagnetic tidal moment ${\cal B}_{pq}$. The tensorial nature of this quantity has to do with the fact that each $e^{im\phi}$ piece of the tidal force gives rise to an $m$-specific velocity perturbation, and therefore to a Love number that depends on $m$. The collection of these $m$-specific Love numbers makes up the Love tensor $k_{jk}^{\ \ pq}$., Comment: 20 pages, 3 figures, new appendix, matches published version

An origin of the Optical/UV radiation from tidal disruption events (TDEs) has recently been discussed for different scenarios, but observational support is generally missing. In this Letter, we test applicability of the `Wind-Driven model' (Uno & Maeda 2020) to a sample of UV/Optical TDEs. With the model, we aim to derive the physical properties of the Optical/UV TDEs, such as mass-loss rates and characteristic radii. The model assumes optically thick continuous outflows like stellar winds, and one key question is how the wind-launched radius is connected to physical processes in TDEs. As one possibility, through a comparison between the escape velocities estimated from their black-hole masses and the wind velocities estimated from observed line widths, we propose that the outflow is launched from the self-interaction radius ($R_{\rm SI}$) where the stellar debris stretched by the tidal force intersects; we show that the escape velocities at $R_{\rm SI}$ are roughly consistent with the wind velocities. By applying the model to a sample of Optical/UV TDE candidates, we find that explosive mass ejections ($\gtrsim 10 ~M_{\odot}{\rm yr^{-1}}$) from $R_{\rm SI}$ ($\sim 10^{14}{\rm ~cm}$) can explain the observed properties of TDEs around peak luminosity. We also apply the same framework to a peculiar transient, AT2018cow. The model suggests that AT2018cow is likely a TDE induced by an intermediate-mass black hole ($M_{\rm BH} \sim 10^{4}~M_{\odot}$)., 8 pages, 1 table, 4 figures, accepted for publication in the ApJL

As a first step in the computation of the orbital phase evolution of spinless compact binaries including tidal effects up to the next-to-next-to-leading (NNL) order, we obtain the equations of motion of those systems and the associated conserved integrals in harmonic coordinates. The internal structure and finite size effects of the compact objects are described by means of an effective Fokker-type action. Our results, complete to the NNL order, correspond to the second-post-Newtonian (2PN) approximation beyond the leading tidal effect itself, already occurring at the 5PN order. They are parametrized by three polarizability (or deformability) coefficients describing the mass quadrupolar, mass octupolar and current quadrupolar deformations of the objects through tidal interactions. Up to the next-to-leading (NL) order, we recover previous results in the literature; up to the NNL order for quasi-circular orbits, we confirm the known tidal effects in the (PN re-expansion of the) effective-one-body (EOB) Hamiltonian. In a future work, we shall derive the tidal contributions to the gravitational-wave flux up to the NNL order, which is the second step required to find the orbital phase evolution., 21 pages

As evidenced by the coincident detections of GW170817 and GRB 170817A, short gamma-ray bursts are likely associated with neutron star-neutron star merger events. Although rare, some bursts display episodes of early emission, with precursor flares being observed up to $\sim 10$ seconds prior to the main burst. As the stars inspiral due to gravitational wave emission, the exertion of mutual tidal forces leads to the excitation of stellar oscillation modes, which may come into resonance with the orbital motion. Mode amplitudes increase substantially during a period of resonance as tidal energy is deposited into the star. The neutron star crust experiences shear stress due to the oscillations and, if the resonant amplitudes are large enough, may become over-strained. This over-straining can lead to fractures or quakes which release energy, thereby fueling precursor activity prior to the merger. Using some simple Maclaurin spheroid models, we investigate the influence of magnetic fields and rapid rotation on tidally-forced $f$- and $r$- modes, and connect the associated eigenfrequencies with the orbital frequencies corresponding to precursor events seen in, for example, GRB 090510., Comment: 16 pages, 8 figures, 1 table. Added a few references. Accepted for publication in Phys. Rev. D

During a tidal disruption event, a star is torn apart by the tidal forces of a supermassive black hole, with about 50% of the star's mass eventually accreted by the black hole. The resulting flare can, in extreme cases of super-Eddington mass accretion, result in a relativistic jet. While tidal disruption events have been theoretically proposed as sources of high-energy cosmic rays and neutrinos, stacking searches indicate that their contribution to the diffuse extragalactic neutrino flux is very low. However, a recent association of a track-like astrophysical neutrino with a tidal disruption event (AT2019dsg) indicates that some tidal disruption events can accelerate cosmic rays to PeV energies. Here we introduce a phenomenological concordance scenario with a relativistic jet to explain this association: an expanding cocoon progressively obscures the X-rays emitted by the accretion disk, while at the same time providing a sufficiently intense external target of back-scattered X-rays for the production of neutrinos via proton-photon interactions. We also reproduce the delay (relative to the peak) of the neutrino emission by scaling the production radius with the black body radius. Our energetics and assumptions for the jet and the cocoon are compatible with expectations from numerical simulations of tidal disruption events., Comment: LaTeX, 25 pages, 3 figures. One figure and various clarifications added. Title and text modified to meet journal requirements. Results unchanged. Version accepted for publication in Nature Astronomy; available at https://www.nature.com/articles/s41550-021-01305-3 . Free read-only access at https://rdcu.be/cfDWF

The frequent detection of binary mergers of ∼30 M ⊙ black holes (BHs) by the Laser Interferometer Gravitational-Wave Observatory (LIGO) rekindled researchers’ interest in primordial BHs (PBHs) being dark matter (DM). In this work, we investigated PBHs distributed as DM with a monochromatic mass of 30 M ⊙ and examined the encounter-capture scenario of binary formation, where the densest central region of DM halo dominates. Thus, we paid special attention to the tidal effect by the supermassive black hole (SMBH) present. In doing so, we discovered a necessary tool called loss zone that complements the usage of loss cone. We found that the tidal effect is not prominent in affecting binary formation, which also turned out to be insufficient in explaining the totality of LIGO’s event rate estimation, especially due to a microlensing event constraining the DM fraction in PBH at the mass of interest from near unity to an order smaller. Meanwhile, an early-universe binary formation scenario proves so prevailing that the LIGO signal in turn constrains the PBH fraction below one percent. Thus, people should put more faith in alternative PBH windows and other DM candidates.

An extended gravitational object embedded in a parent system comprised of gas and collisionless particles may undergo both dynamical friction (DF) and mass loss by tidal forces. If the object is compact enough, it can increase its mass through accretion of material from the surrounding medium. We extend the classical linear analysis of DF on a constant-mass body in a gaseous medium to the case where its mass changes with time. We show that the structure of the wake may differ significantly from the constant-mass case. For instance, the front-back symmetry of density about subsonic constant-mass perturbers is broken down for variable-mass perturbers. The density wake keeps a memory of the past mass history of the perturber. For dissolving perturbers, the density field is more dense than expected using the instantaneous mass of the perturber in the classical formula. As a consequence, the instantaneous-mass approximation underestimates the drag force for mass-losing perturbers and overestimates it for mass-gaining perturbers. We present cases in which the percentage error in the drag force using the instantaneous-mass approximation is greater than 50%., Comment: 16 pages, 15 figures, accepted for publication in MNRAS

In hierarchical triple systems, the inner binary is perturbed by a distant companion. For large mutual inclinations, the Lidov-Kozai mechanism secularly excites large eccentricity and inclination oscillations of the inner binary. The maximal eccentricity attained, $e_{\rm max}$ is simply derived and widely used. However, for mildly hierarchical systems (i.e. the companion is relatively close and massive), non-secular perturbations affect the evolution. Here we account for fast non-secular variations and find new analytic formula for $e_{{\rm max}}$, in terms of the system's hierarchy level, correcting previous work and reproducing the orbital flip criteria. We find that $e_{{\rm max}}$ is generally enhanced, allowing closer encounters between the inner binary components, thus significantly changing their interaction and its final outcome. We then extend our approach to include additional relativistic and tidal forces. Using our results, we show that the merger time of gravitational-wave (GW) sources orbiting massive black-holes in galactic nuclei is enhanced compared with previous analysis accounting only for the secular regime. Consequently, this affects the distribution and rates of such GW sources in the relevant mild-hierarchy regime. We test and confirm our predictions with direct N-body and 2.5-level Post-Newtonian codes. Finally, we calculate the formation and disruption rates of hot-Jupiters (HJ) in planetary systems using a statistical approach, which incorporates our novel results for $e_{{\rm max}}$. We find that more HJ migrate from further out, but they are also tidally disrupted more frequently. Remarkably, the overall formation rate of HJs remains similar to that found in previous studies. Nevertheless, the different rates could manifest in different underlying distribution of observed warm-Jupiters., Comment: Accepted to MNRAS

The low mass star ASASSN-13db experienced an EXor outburst in 2013, which identified it as a Young Stellar Object (YSO). Then, from 2014 to 2017 it had another outburst, longer and more luminous than the earlier. We analyze the observations of the second outburst, and compare it to eruptions of Intermediate Luminosity Optical Transients (ILOTs). We show that the decline of the light curve is almost identical to that of the V838 Mon, a prototype of a type of ILOT known as Luminous Red Nova (LRN). This similarity becomes conspicuous when oscillations that are associated with rotation are filtered out from the light curve of ASASSN-13db. We suggest that the eruption was the result of accretion of a proto-planet of a few Earth masses. The proto-planet was shredded by tidal forces before it was accreted onto the YSO, releasing gravitational energy that powered the outburst for &asymp, 800 days , and ended in a &asymp, 55 days decline phase. When the accretion material started depleting the accretion rate lowered and the eruption light curve declined for almost two months. Then it exhausted completely, creating a sharp break in the light curve. Another possibility is that the mass was a result of an instability in the proto-planetary disk that lead to a large episode of accretion from an inner viscous disk. We find that the variation of the temperature of the outburst is consistent with the surface temperature expected from a depleted viscous accretion disk. The 2014&ndash, 2017 outburst of ASASSN-13db may be the least energetic ILOT to have been discovered to date, with an energy budget of only &asymp, 10 42 erg .

We present a sample of 446 galaxy pairs constructed using the cosmological simulation IllustrisTNG-100 at z = 0, with M$_{FoF, dm}$ = 10$^{11}$-10$^{13.5}$ M$_{\odot}$. We produce ideal mock SDSS g-band images of all pairs to test the reliability of visual classification schema employed to produce samples of interacting galaxies. We visually classify each image as interacting or not based on the presence of a close neighbour, the presence of stellar debris fields, disturbed discs, and/or tidal features. By inspecting the trajectories of the pairs, we determine that these indicators correctly identify interacting galaxies $\sim45\%$ of the time. We subsequently split the sample into the visually identified interacting pairs (VIP; 38 pairs) and those which are interacting but are not visually identified (nonVIP; 47 pairs). We find that VIP have undergone a close passage nearly twice as recently as the nonVIP, and typically have higher stellar masses. Further, the VIP sit in dark matter haloes that are approximately 2.5 times as massive, in environments nearly 2 times as dense, and are almost a factor of 10 more affected by the tidal forces of their surroundings than the nonVIP. These factors conspire to increase the observability of tidal features and disturbed morphologies, making the VIP more likely to be identified. Thus, merger rate calculations which rely on stellar morphologies are likely to be significantly biased toward massive galaxy pairs which have recently undergone a close passage., 20 pages, 11 figures, thumbnail catalog of interacting pairs sample