Tidal Deformation Research Articles

О влиянии деформаций астероида при тесном сближении с Землей на его вращательную и орбитальную динамику

During close approach to the Earth, the asteroid’s figure may experience noticeable deformations. Numerical experiments were used to examine the effect of changes in the asteroid’s figure on the magnitudes of disturbances arising in its rotational motion during approach and on the orbital dynamics by changing the magnitude of the Yarkovsky effect. It was found that due to tidal deformation of the asteroid’s figure during approach, accompanied by a change in the moments of inertia, the magnitudes of disturbances in rotation are significantly higher than in the case of an unchanged figure. It was shown that a change of 10–25% in the inertial parameters of the asteroid (99942) Apophis during its approach to the Earth in 2029 leads to a 2–4-fold increase in the sizes of the regions in which the rotational period and the magnitude of the angle characterizing the inclination of the rotation axis to the orbital plane may change. Perturbations in the rotation of the asteroid lead to a change in the parameter A2, which characterizes the Yarkovsky effect, for the size of the region of change of which a similar conclusion is made.

Unequivocal detection of the tidal deformation of a red giant in a binary system via interferometry

While mass transfer in binary systems is a crucial aspect of binary evolution models, it remains far from understood. HD 352 is a spectroscopic binary exhibiting ellipsoidal variability, likely due to a tidally deformed giant donor filling its Roche lobe and transferring matter to a faint companion. Here, we analyze VLTI/PIONIER interferometric observations of the system, obtained between 2010 to 2020. We demonstrate that observations near the system's quadrature cannot be explained by simple symmetric disk models, but they are consistent with the shape of a Roche-lobe-filling star. We think that this is the first case of tidal deformation of a red giant being observed directly, thanks to the interferometric technique. By combining our interferometric modeling results with the analysis of the optical spectrum, multifrequency spectral energy distribution, and published radial velocities and light curves, we constrained the system parameters and show that HD 352 will likely soon enter the common envelope phase, although we cannot reject the hypothesis that it is undergoing stable mass transfer against theoretical predictions. This has important consequences for modeling a large class of binary systems. Additionally, our observations confirm that Roche-lobe-filling giants can be resolved with interferometry under favorable conditions. Such observations may help resolve the mass transfer dichotomy in systems such as symbiotic binaries, where the predominant mass transfer mode remains unclear.

Librations and obliquity of the largest moons of Uranus

Following the discovery of several ocean worlds in the solar system, and the selection of Uranus as the highest priority objective by the Planetary Science and Astrobiology Decadal Survey 2023-2032, the five largest moons of Uranus (Miranda, Ariel, Umbriel, Titania and Oberon) have been receiving renewed attention as they may also harbor a subsurface ocean. We assess how rotation measurements could help confirm the internal differentiation of the bodies and detect internal oceans if any. Because of the time-varying gravitational torque of Uranus on the flattened shape of its synchronous satellites, the latter librate with respect to their mean rotation and precess with a non zero obliquity. For a range of interior models with a rocky core surrounded by a hydrosphere, either solid or divided into an outer ice shell with a liquid ocean underneath, we compute their diurnal libration amplitude and obliquity. We find that if the Uranian satellites were two-layer solid bodies, libration measurement accuracies from around 0.25 m for Oberon to around 6 m for Miranda would rule out the possibility of homogeneous interiors. In combination with independent estimates of the mean moment of inertia (MOI), libration measurements could also be used to detect the presence of an ocean, the measurement precision required for this depending on the actual value of the libration amplitude. To compute the obliquity, we first build series for the orbital precession of all five satellites with a secular perturbations model. With the exception of Miranda, we show that due to the mutual gravitational interactions between the satellites, the obliquity of the large Uranian moons exhibits relatively large periodic variations around the mean value. We find that an obliquity measurement accuracy from around 1 m for Ariel to around 400 m for Oberon can rule out the homogeneous case. The presence of an internal global ocean could allow a resonant amplification of the obliquity, facilitating its detection. If no such resonance occurs, the obliquity would be almost indistinguishable from that expected for a solid body. The effect of tidal deformations on the rotation of the small to medium-sized Uranian moons is showed to be limited. Librations would be reduced by up to 10% and obliquity increased by up to 15% for Titania and Oberon, the effects being negligible for Miranda.

Instability and warping in vertically oscillating accretion discs

Abstract Many accretion discs have been found to be distorted: either warped due a misalignment in the system, or non-circular as a result of orbital eccentricity or tidal deformation by a binary companion. Warped, eccentric, and tidally distorted discs are not in vertical hydrostatic equilibrium, and thus exhibit vertical oscillations in the direction perpendicular to the disc, a phenomenon that is absent in circular and flat discs. In extreme cases, this vertical motion is manifested as a vertical ‘bouncing’ of the gas, potentially leading to shocks and heating, as observed in recent global numerical simulations. In this paper we isolate the mechanics of vertical disc oscillations by means of quasi-2D and fully 3D hydrodynamic local (shearing-box) models. To determine the numerical and physical dissipation mechanisms at work during an oscillation we start by investigating unforced oscillations, examining the effect of initial oscillation amplitude, as well as resolution, boundary conditions, and vertical box size on the dissipation and energetics of the oscillations. We then drive the oscillations by introducing a time-dependent gravitational potential. A key result is that even a purely vertically oscillating disc is (parametrically) unstable to developing inertial waves, as we confirm through a linear stability analysis. The most important of these has the character of a bending wave, whose radial wavelength depends on the frequency of the vertical oscillation. The nonlinear phase of the instability exhibits shocks, which dampen the oscillations, although energy can also flow from the bending wave back to the vertical oscillation.

Electron and muon dynamics in neutron stars beyond chemical equilibrium

A neutron star harbors 𝒪(1056) electrons in its core, and almost the same number of muons, with muon decay prohibited by Pauli blocking. However, as macroscopic properties of the star such as its mass, rotational velocity, or magnetic field evolve over time, the equilibrium lepton abundances (dictated by the weak interactions) change as well. Scenarios where this can happen include spin-down, accretion, magnetic field decay, and tidal deformation. We discuss the mechanisms by which a star disrupted in one of these ways re-establishes lepton chemical equilibrium. In most cases, the dominant processes are out-of-equilibrium Urca reactions, the rates of which we compute for the first time. If, however, the equilibrium muon abundance decreases, while the equilibrium electron abundance increases (or decreases less than the equilibrium muon abundance), outward diffusion of muons plays a crucial role as well. This is true in particular for stars older than about 104 yrs whose core has cooled to ≲ 20 keV. The muons decay in a region where Pauli blocking is lifted, and we argue that these decays lead to a flux of 𝒪(10 MeV) neutrinos. Realistically, however, this flux will remain undetectable for the foreseeable future.

Constraining the Thickness of the Conductive Portion of Europa's Ice Shell Using Sparse Radar Echoes

AbstractIce penetrating radar sounding is the primary geophysical technique for imaging the subsurface of planetary ice shells and has the potential to directly detect the ice–ocean interface. However, many sounding measurements may lack laterally extensive features that would aid their physical interpretation. In this scenario, the detection of sparse echoes can also provide rich information on ice shell properties. To explore and demonstrate this possibility, we consider three cases of isolated radar signatures: pore‐curing, eutectic melt, and unattributed echoes. We show that through detection of unattributed sparse echoes, the thickness of the conductive portion of Europa's ice shell can be constrained. These constraints can be improved by attributing sparse echoes to thermally diagnostic signatures such as pore‐curing and eutectic melt. Notably, this approach to radar sounding echo analysis is particularly compatible with joint inversions with other planetary geophysical observations such as tidal deformation, magnetic induction, and rotation state.

Black hole—neutron star binary mergers: the impact of stellar compactness

Abstract Recent gravitational wave (GW) observations include possible detections of black hole—neutron star binary mergers. As with binary black hole mergers, numerical simulations help characterize the sources. For binary systems with neutron star components, the simulations help to predict the imprint of tidal deformations and disruptions on the GW signals. In a previous study, we investigated how the mass of the black hole has an impact on the disruption of the neutron star and, as a consequence, on the shape of the GWs emitted. We extend these results to study the effects of varying the compactness of the neutron star. We consider neutron star compactness in the 0.113–0.2 range for binaries with mass ratios of 3 and 5. As the compactness and the mass ratio increase, the binary system behaves during the late inspiral and merger more like a black hole binary. For the cases with the least compact neutron star, the GWs emitted, in terms of mismatches, are the most distinguishable from those by a binary black hole. The disruption of the star significantly suppresses the kicks on the final black hole. The disruption also affects, although not dramatically, the spin of the final black hole. Lastly, for neutron stars with low compactness, the quasi-normal ringing of the black hole after the merger does not show a clean quasi-normal ringing because of the late accretion of debris from the neutron star.

Extracting parity-violating gravitational waves from projected tidal force tensor in three dimensions

Gravitational waves (GWs) may be produced by various mechanisms in the early universe. In particular, if parity is violated, it may lead to the production of parity-violating GWs. In this paper, we focus on GWs on the scale of the large-scale structure. Since GWs induce tidal deformations of the shape of galaxies, one can extract such GW signals by observing images of galaxies in galaxy surveys. Conventionally the detection of such signals is discussed by considering the three-dimensional power spectra of the E/B-modes. Here, we develop a complementary new technique to estimate the contribution of GWs to the tidal force tensor field projected on the celestial sphere, which is a directly observable quantity. We introduce two two-dimensional vector fields constructed by taking the divergence and curl of the projected tidal field in three dimensions. Their auto-correlation functions naturally contain contributions of the scalar-type tidal field. However, we find that the divergence of the curl of the projected tidal field, which is a pseudo-scalar quantity, is free from the scalar contribution and thus enables us to extract GW signals. We also find that we can detect parity-violating signals in the GWs by observing the nonzero cross-correlation between the divergence of the projected tidal field and the curl of it. It roughly corresponds to measuring the cross-power spectrum of E and B-modes, but these are complementary to each other in the sense that our estimator can be naturally defined locally in position space. Finally we present expressions of the correlation functions in the form of Fourier integrals, and discuss the properties of the kernels specific to the GW case, which we call the overlap reduction function, borrowing the terminology used in the pulsar timing array experiments.

Lifetime of starspots on detached eclipsing binaries: Detecting the effects of tides on stellar activity

Context. Tidal deformation breaks the axisymmetric structure of stars, and this may affect stellar activity. This effect has been demonstrated in theoretical analyses and simulations, but it lacks observational support. In this paper, we use spot-modulated detached binaries to study the effect of tides on stellar activity. We show this effect by analyzing the properties of the spot lifetime, the harmonic decay timescale, and the orbital parameters. Aims. We aim to explore the differences in spot lifetimes between binaries and single stars, the main mechanisms of spot decay in binaries, and the correlation between orbital parameters and spot lifetimes. These differences will provide clues to the effect of tides on stellar activity. Methods. We collected data of 311 spot-modulated detached binaries and 3272 single stars. The relative orbital parameters of the binaries were derived by combining Kepler photometry, stellar atmospheric parameters from LAMOST DR9 and Gaia DR3, and 2MASS photometry. We then used the ACF method to obtain the rotational periods, lifetimes, and harmonic decay timescales. Finally, we analyzed the correlation between the lifetime of spots and orbital parameters, explored the dominant decay mechanism of spots, and examined the differences in spots for binaries and single stars. Results. The relative lifetime of a starspot is correlated with the sum of the fractional radii, the orbital eccentricity, and the synchronization ratio. Longer lifetimes are observed in close, circular, and synchronous binaries than in the other binaries. The main mechanism for the decay of star spots in binaries is large-scale convective motion. However, on close, cool, and fast-rotating binaries, horizontal diffusion or subphotospheric diffusion are dominant. Compared to single stars, the median lifetime of a starspot on binaries was found to be longer. Moreover, this difference decreases with rotation period. Additionally, it should be noted that spots on binaries experience increased horizontal or subphotospheric diffusion at the same rotation period and effective temperature. Conclusions. According to the observation results, we conclude that the lifetime of starspots on detached close binaries is affected by tidal interactions.

Tidal Disruption of a Star on a Nearly Circular Orbit

We consider Roche lobe overflow (RLO) from a low-mass star on a nearly circular orbit, onto a supermassive black hole (SMBH). If mass transfer is unstable, its rate accelerates in a runaway process, resulting in highly super-Eddington mass accretion rates, accompanied by an optically thick outflow emanating from the SMBH vicinity. This produces a 1–4 week long, bright optical/ultraviolet flare, accompanied by a 1–10 year long X-ray precursor and post-cursor emitted from the accretion flow onto the SMBH. Such “Circular Tidal Disruption Events” (TDEs) represent a new class of nuclear transients, occurring at up to 1%–10% of the canonical parabolic tidal disruption event rate. Near-breakup rotation and strong tidal deformation of the star prior to disruption could lead to strong magnetic fields, making circular TDEs possible progenitors of jetted TDEs. Outflows prior to the final stellar disruption produce a circumnuclear environment (CNM) with ∼10−2 M⊙ at distances of ∼0.01–0.1 pc, likely leading to bright radio emission, and also similar to the CNM inferred for jetted TDEs. We discuss broader connections between circular TDEs and other recently identified classes of transients associated with galactic nuclei, such as repeating TDEs and quasi-periodic X-ray eruptions, as well as possible connections to luminous fast blue optical transients such as AT2018cow. We also discuss observational signatures of the analogous RLO of a white dwarf around an intermediate-mass BH, which may be a multimessenger source in the LISA era.

Tidal dissipation with 3-D finite element deformation code CitcomSVE v2.1: comparisons with the semi-analytical approach, in the context of the Lunar tidal deformations

Tidal dissipation with 3-D finite element deformation code CitcomSVE v2.1: comparisons with the semi-analytical approach, in the context of the Lunar tidal deformations

Coupled tidal tomography and thermal constraints for probing Mars viscosity profile

Computing the tidal deformations of Mars, we explored various Mars spherically symmetric internal structures with different types of interface between the mantle and the liquid core. By assessing their compatibility with a diverse set of geophysical observations we show that despite the very short periods of excitation, tidal deformation is very efficient to constrain Mars interior. We calculated densities and thicknesses for Martian lithosphere, mantle, core–mantle boundary layers and core and found them consistent with preexisting results from other methods. We also estimated new viscosities for these layers. We demonstrated that the geodetic records associated with thermal constraints are very sensitive to the presence of a 2-layered interface on the top of the liquid core in deep Martian mantle. This interface is composed by 2 layers of similar densities but very different viscosity and rheology: the layer on the top of the core is liquid (Newtonian, NBL) and the one at the base of the mantle, overlaying the liquid one, is an Andrade layer (ABL) with a viscosity in average 10 orders of magnitude greater than the Newtonian layer. Our results also indicate that the existence of this 2-layered interface significantly impacts the viscosity profiles of the mantle and the lithosphere. More precisely, models including the 2-layered interface do not display significant viscosity contrast between the mantle and the lithosphere, preventing mechanical decoupling between a lithosphere and the mantle immediately below. Such models are in favor of a stagnant lid regime that can be supported by the current absence of an Earth-like plate tectonics on Mars. Finally, in our results, the presence of liquid Newtonian layer at the top of the liquid core is incompatible with the existence of a solid inner core.

Variations in plume activity reveal the dynamics of water-filled faults on Enceladus

After discovering a jet activity near the south pole of Saturn’s moon Enceladus, the Cassini mission demonstrated the existence of a subsurface water ocean with a unique sampling opportunity through flybys. Diurnal variations in the observed brightness of the plume suggest a tidal control, although the existence and timing of two activity maxima seem to contradict stress analysis predictions. Here, we re-interpret the observed plume variability by combining a 3D global model of tidal deformation of the fractured ice shell with a 1D local model of transport processes within south-polar faults. Our model successfully predicts the observed plume’s temporal variability by combining two independent vapour transport mechanisms: slip-controlled jet flow and normal-stress-controlled ambient flow. Moreover, it provides a possible explanation for the differences between the vapour and solid emission rates during the diurnal cycle and the observed fractionation of the various icy particle families. Our model prediction could be tested by future JWST observations targeted when Enceladus is at different positions on its orbit and could be used to determine the optimal strategy for plume material sampling by future space missions.

Tidal deformations of slowly spinning isolated horizons

Tidal deformations of slowly spinning isolated horizons

Discovering Love numbers through resonance excitation during extreme mass ratio inspirals

General Relativity predicts that black holes (BHs) do not possess an internal structure and consequently cannot be excited. This leads to a specific prediction about the waveform of gravitational waves (GWs) which they emit during a binary BH inspiral and to the vanishing of their Love numbers. However, if astrophysical BHs do possess an internal structure, their Love numbers would no longer vanish, and they could be excited during an inspiral by the transfer of orbital energy. This would affect the orbital period and lead to an observable imprint on the emitted GWs waveform. The effect is enhanced if one of the binary companions is resonantly excited. We discuss the conditions for resonant excitation of a hypothetical internal structure of BHs and calculate the phase change of the GWs waveform that is induced due to such resonant excitation during intermediate- and extreme-mass-ratio inspirals. We then relate the phase change to the electric quadrupolar Love number of the larger companion, which is resonantly excited by its smaller companion. We discuss the statistical error on measuring the Love number by LISA and show that, because of this phase change, the statistical error is small even for values of the Love number as small as 10−4 for moderate values of the spin parameter. Our results indicate that, for extreme-mass-ratio inspirals with moderate spin parameter, the Love number could be detected by LISA with an accuracy which is higher by up to two orders of magnitude than what can be achieved via tidal deformation effects. Thus, our results indicate that resonant excitation of the central BH during an extreme- or intermediate-mass-ratio inspirals is the most promising effect for putting bounds on, or detecting, non-vanishing tidal Love numbers of BHs.

Ringdown Gravitational Waves from Close Scattering of Two Black Holes.

We have numerically investigated close scattering processes of two black holes (BHs). Our careful analysis shows for the first time a nonmerging ringdown gravitational wave induced by dynamical tidal deformations of individual BHs during their close encounter. The ringdown wave frequencies turn out to agree well with the quasinormal ones of a single BH in perturbation theory, despite its distinctive physical context from the merging case. Our study shows a new type of gravitational waveform and opens up a new exploration of strong gravitational interactions using BH encounters.

Application of the Korla volumetric strain to explore the triggering effects of tidal stress on tidal deformation before earthquakes

When the fault in a focal area enters the critical state, nonlinear accelerated deformation and disturbance changes may occur during tide-induced loading and unloading. In this study, the anomalies in the Korla volumetric strain caused by earth tide were investigated using a theoretical model of tidal force. Results show that the step changes in the Korla volumetric strain may be triggered by tidal force within a short time frame, ranging from a few to tens of days, prior to a moderate earthquake. The azimuthal angles at the time of step changes are mainly distributed in the ranges of 124–158° and 185–228°, and the azimuth angle at the time of many nearby medium-to-strong earthquakes occurring in this step concentration area, suggesting that the step anomalies in the Korla volumetric strain are closely related to the horizontal tide-induced force in a specific direction. Using the Schuster method, it was found that the tide-induced azimuth angle of the step changes occurred mostly at the minimum value of the solid tide, providing evidences of the modulation of the solid tide. These results may present new ideas for using crustal deformation observations for short-term earthquake predictions.

Exploring the tidal responses of ocean worlds with PyALMA3

Observations of the tidal response of celestial bodies quantified by the Love numbers are highly relevant in planetary geophysical investigations because they provide unique insight into the interior structures. For example, the high sensitivity of tidal deformations to the properties of the oceans detected beneath the icy surfaces of some moons is of paramount importance for investigations of their habitability. We present here PyALMA3, a software framework developed in Python devoted to the computation of planetary Love numbers. PyALMA3 is based on ALMA3, a previous version developed in Fortran. Conversion to Python significantly improves the accessibility and portability of the software. We tested PyALMA3 by applying it to the exploration of the tidal responses of Europa and the other Galilean moons. We show that accurate modeling of effects such as the viscoelastic deformations of ice and the water density gradient in the ocean (variations of 2–3% on the real part of k2) will be important in the context of geophysical investigations that will be conducted by future missions targeting icy moons, such as Europa Clipper and JUICE.

The tidal deformation and atmosphere of WASP-12 b from its phase curve

Context. Ultra-hot Jupiters present a unique opportunity to understand the physics and chemistry of planets, their atmospheres, and interiors at extreme conditions. WASP-12 b stands out as an archetype of this class of exoplanets, with a close-in orbit around its star that results in intense stellar irradiation and tidal effects. Aims. The goals are to measure the planet’s tidal deformation, atmospheric properties, and also to refine its orbital decay rate. Methods. We performed comprehensive analyses of the transits, occultations, and phase curves of WASP-12b by combining new CHEOPS observations with previous TESS and Spitzer data. The planet was modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number of the planet, h2, which quantifies its radial deformation and provides insight into the interior structure. Results. We measured the tidal deformation of WASP-12b and estimated a Love number of h2 = 1.55−0.49+0.45 (at 3.2σ) from its phase curve. We measured occultation depths of 333 ± 24 ppm and 493 ± 29 ppm in the CHEOPS and TESS bands, respectively, while the nightside fluxes are consistent with zero, and also marginal eastward phase offsets. Our modeling of the dayside emission spectrum indicates that CHEOPS and TESS probe similar pressure levels in the atmosphere at a temperature of ~2900 K. We also estimated low geometric albedos of Ag = 0.086 ± 0.017 and Ag = 0.01 ± 0.023 in the CHEOPS and TESS passbands, respectively, suggesting the absence of reflective clouds in the high-temperature dayside of the planet. The CHEOPS occultations do not show strong evidence for variability in the dayside atmosphere of the planet at the median occultation depth precision of 120 ppm attained. Finally, combining the new CHEOPS timings with previous measurements refines the precision of the orbital decay rate by 12% to a value of −30.23 ± 0.82 ms yr−1, resulting in a modified stellar tidal quality factor of Q′★ = 1.70 ± 0.14 × 105. Conclusions. WASP-12 b becomes the second exoplanet, after WASP-103b, for which the Love number has been measured from the effect of tidal deformation in the light curve. However, constraining the core mass fraction of the planet requires measuring h2 with a higher precision. This can be achieved with high signal-to-noise observations with JWST since the phase curve amplitude, and consequently the induced tidal deformation effect, is higher in the infrared.

Uranus Orbiter and Probe: A Radio Science Investigation to Determine the Planet’s Gravity Field, Depth of the Winds, and Tidal Deformations

The most recent Planetary Science and Astrobiology Decadal Survey has proposed Uranus as the target for NASA’s next large-scale mission. The interior structure and atmosphere of the planet are currently poorly understood, and objectives for investigating Uranus’s deeper regions and composition are highly ranked. Traditionally, gravity science has served as one of the primary means for probing the depths of planetary bodies and inferring their internal density distributions. In this work, we present precise numerical simulations of an onboard radio science experiment designed to determine Uranus’s gravity field and tidal deformations, which would offer a rare view into the planet’s interior. We focus on the mission’s orbital planning, discussing crucial parameters such as the number of pericenter passes, orbital inclination, and periapsis altitude necessary to meet the gravity measurement requirements for a Uranus orbiter. Our findings suggest that eight close encounters may be sufficient to determine the zonal gravity field up to J 8 with a relative accuracy of 10%, if the trajectory is optimized. This would allow for the decoupling of the gravity field components due to interior structure and zonal winds. Additionally, we find that the expected end-of-mission uncertainty on Uranus’s Love number k 22 is of order ∼0.01 (3σ). This level of accuracy may offer crucial information about Uranus’s inner state and allow for discriminating between a liquid and solid core, thus shedding light on crucial aspects of the planet’s formation and evolution.