arXiv subjects

Michael Efroimsky

Publications and source records attributed to Michael Efroimsky.

At least 19 recordsLinked to original sources

arXiv2026

Synchronisation of a tidal binary by inward orbital migration. The case of Pluto and Charon

It is usually taken for granted that mutual synchronisation of a tidal two-body system is attained through tidal recession, assuming the reduced Hill sphere is not reached. However, synchronisation can be achieved also via tidal approach, provided the Roche limit is not crossed. For each of the two scenarios, we derive the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit. We consider the two scenarios for the Pluto-Charon system and examine the impact-origin hypothesis of Charon's formation against capture. Based on geophysical evidence, we propose that capture appears more likely. Motivated by this conclusion, we investigate the capture scenario, wherein the orbital evolution of Charon starts at a larger distance than present and undergoes tidal descent, both analytically and numerically. We also consider the possibility that Pluto's initial prograde spin underwent a reversal by a tidally approaching retrograde Charon. Depending on the initial conditions, we observe temporary locking of Charon into higher spin-orbit resonances (3:2 to 7:2) during the first 0.5 Myr of the system's evolution. Owing to a greater initial separation between the partners, the power dissipated in each of them turns out to be much lower than in the case of tidal recession of bodies of the same internal structure. The greater initial separation also results in lower tidal stress, which may explain the absence of tidally generated fracture patterns.

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arXiv2026

Evolution of a synchronous planet-moon pair due to solar tides. Demise of the synchronous moon that initiated Mars' triaxiality. A possible link to tidalites in Vastitas Borealis and Gale Crater

Mars' asymmetric figure with two opposing equatorial elevations stems from a frozen tidal bulge raised by a synchronous palaeo-moon Nerio. Nerio's emergence, via in situ accretion or by capture in the disk's remnants, and its synchronisation with Mars' rotation preceded or was coeval with crust formation. The submoon and antimoon regions hypothetically developed thinner crusts, intensifying the tectonics that further amplified Mars' triaxiality. We study Nerio's orbit stability and demise and its impact on Mars' rotation. Nerio may also have been the cause of the tidalites found in sediments. Stellar tides in the planet shrink the orbit of a planet-moon pair, so their synchronism is stable transiently. At some critical distance from the planet, the moon desynchronises and spirals down, spinning the planet up. Application to Mars and Nerio shows that Mars' spin rate at the desynchronisation moment matches the present rate to the first decimal. The coincidence should not be overinterpreted, as post-desynchronisation evolution included Mars' continued spin-up during Nerio's descent (till its destruction amid the LHB), followed by Mars' despinning by solar tides. Nerio's reaching the Roche limit intact is questionable. Beyond LHB hazards, it would imply Mars' larger spin-up, necessitating up to k2/Q ~ 18 to allow subsequent despinning to the present rate. This value may be high even for shallow oceans. Absent future evidence supporting such elevated k2/Q values, Nerio likely perished during the LHB. This verdict may be reconsidered should new data on Mars' ocean show up. The existence and subsequent demise of Nerio are indirectly confirmed by the presence of tidalites in Vastitas Borealis and Gale Crater. During its post-desynchronisation descent, Nerio was capable of producing tidalites in the ocean. After Nerio's demise, this work may have been continued by its massive remnant

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arXiv2025

Initial conditions for tidal synchronisation of a planet by its moon

Moons tidally interact with their host planets and stars. A close moon is quickly synchronised by the planet, or becomes captured in a higher spin-orbit resonance. However, the planet requires much more time to significantly alter its rotation rate under the influence of moon-generated tides. The situation becomes more complex for close-in planets, as star-generated tides come into play and compete with the moon-generated tides. Synchronisation of the planet by its moon changes the tidal dynamics of the entire star-planet-moon system and can lead to long-term stable configurations. In this paper, we demonstrate that a certain initial condition must be met for this to occur. Based on the angular-momentum conservation, the derived condition is universal and bears no dependence upon the planet's internal structure or tidal dissipation model. It is applicable to dwindling systems as well as tidally expanding orbits, and to the cases of initially retrograde motion. We present calculations for specific planet-moon systems (Earth and the Moon; Neptune and Triton; Venus and its hypothetical presently-extinct moon Neith; Mars, Phobos, and Deimos; Pluto and Charon), to constrain the dynamically plausible formation and evolution scenarios. Among other things, our analysis prompts the question of whether Pluto and Charon evolved into their current state from an initially more compact configuration (as is commonly assumed) or from a wider orbit -- a topic to be discussed at length elsewhere. Our results are equally applicable to exoplanets. For example, if asynchronous close-in exoplanets are detected, the possibility of tidal synchronisation by an exomoon should be considered.

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arXiv2024

A synchronous moon as a possible cause of Mars' initial triaxiality

The paper addresses the possibility of a young Mars having had a massive moon, which synchronised the rotation of Mars, and gave Mars an initial asymmetric triaxiality to be later boosted by geological processes. It turns out that a moon of less than a third of the lunar mass was capable of producing a sufficient initial triaxiality. The asymmetry of the initial tidal shape of the equator depends on timing: the initial asymmetry is much stronger if the synchronous moon shows up already at the magma-ocean stage. From the moment of synchronisation of Mars' rotation with the moon's orbital motion, and until the moon was eliminated (as one possibility, by an impact in the beginning of the LHB), the moon was sustaining an early value of Mars' rotation rate.

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arXiv2023

On the orbital decay of the gas giant Kepler-1658b

The gas giant Kepler-1658b has been inferred to be spiralling into its sub-giant F-type host star Kepler-1658a (KOI-4). The measured rate of change of its orbital period is $\dot{P}_{\rm orb}=-131^{+20}_{-22}\mathrm{ms/yr}$, which can be explained by tidal dissipation in the star if its modified tidal quality factor is as low as $Q^{\,\prime}\approx 2.50\times {10}^{4}$. We explore whether this could plausibly be consistent with theoretical predictions based on applying up-to-date tidal theory in stellar models (varying stellar mass, age, and metallicity) consistent with our newly-derived observational constraints. In most of our models matching the combined constraints on the stellar effective temperature and radius, the dissipation in the star is far too weak, capable of providing $Q^{\,\prime}\gtrsim 10^9$, hence contributing negligibly to orbital evolution. Using only constraints on the stellar radius, efficient tidal dissipation sufficient to explain observations is possible due to inertial waves in the convective envelope during the sub-giant phase, providing $Q^{\,\prime}\sim 10^4$, but this period in the evolution is very short-lived (shorter than $10^2$ yrs in our models). We show that dissipation in the planet is capable of explaining the observed $\dot{P}_\mathrm{orb}$ only if the planet rotates non-synchronously. Tidally-induced pericentre precession is a viable explanation if the periastron argument is near $3π/2$ and the quadrupolar Love number is above 0.26. Further observations constraining the stellar and planetary properties in this system have the exciting potential to test tidal theories in stars and planets.

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arXiv2023

Is there a semi-molten layer at the base of the lunar mantle?

Parameterised by the Love number $k_2$ and the tidal quality factor $Q$, and inferred from lunar laser ranging (LLR), tidal dissipation in the Moon follows an unexpected frequency dependence often interpreted as evidence for a highly dissipative, melt-bearing layer encompassing the core-mantle boundary. Within this, more or less standard interpretation, the basal layer's viscosity is required to be of order $10^{15}$ to $10^{16}$ Pa s, and its outer radius is predicted to extend to the zone of deep moonquakes. While the reconciliation of those predictions with the mechanical properties of rocks might be challenging, alternative lunar interior models without the basal layer are said to be unable to fit the frequency dependence of tidal $Q$. The purpose of our paper is to illustrate under what conditions the frequency-dependence of lunar tidal $Q$ can be interpreted without the need for deep-seated partial melt. Devising a simplified lunar model, in which the mantle is described by the Sundberg-Cooper rheology, we predict the relaxation strength and characteristic timescale of elastically-accommodated grain boundary sliding in the mantle that would give rise to the desired frequency dependence. Along with developing this alternative model, we test the traditional model with a basal partial melt; and we show that the two models cannot be distinguished from each other by the available selenodetic measurements. Additional insight into the nature of lunar tidal dissipation can be gained either by measurements of higher-degree Love numbers and quality factors or by farside lunar seismology.

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arXiv2023

Pathways of Survival of Exomoons and Inner Exoplanets

It is conceivable that a few thousand confirmed exoplanets initially harboured satellites similar to the moons of the Solar system or larger. Could some of them have survived over the aeons of dynamical evolution to the present day? The dynamical conditions are harsh for exomoons in such systems because of the greater influence of the host star and of the tidal torque it exerts on the planet. We investigate the stability niches of exomoons around hundreds innermost exoplanets for which the needed parameters are known today, and determine the conditions of these moons' long-term survival. General lower and upper bounds on the exomoon survival niches are derived for orbital separations, periods, and masses. The fate of an exomoon residing in a stability niche depends on the initial relative rate of the planet's rotation and on the ability of the moon to synchronise the planet by overpowering the tidal action from the star. State of the art models of tidal dissipation and secular orbital evolution are applied to a large sample of known exoplanet systems with their estimated physical parameters. We show that in some plausible scenarios, exomoons can prevent close exoplanets from spiraling into their host stars, thus extending these planets' lifetimes. This is achieved when exomoons synchronise the rotation of their parent planets, overpowering the tidal action from the stars. Massive moons are more likely to survive and to maintain a high rotation rate of their host planets (higher than these planets' mean motion).

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arXiv2022

Tidal insights into rocky and icy bodies: An introduction and overview

Solid body tides provide key information on the interior structure, evolution, and origin of the planetary bodies. Our Solar system harbours a very diverse population of planetary bodies, including those composed of rock, ice, gas, or a mixture of all. While a rich arsenal of geophysical methods has been developed over several years to infer knowledge about the interior of the Earth, the inventory of tools to investigate the interiors of other Solar-system bodies remains limited. With seismic data only available for the Earth, the Moon, and Mars, geodetic measurements, including the observation of the tidal response, have become especially valuable and therefore, has played an important role in understanding the interior and history of several Solar system bodies. To use tidal response measurements as a means to obtain constraints on the interior structure of planetary bodies, appropriate understanding of the viscoelastic reaction of the materials from which the planets are formed is needed. Here, we review the fundamental aspects of the tidal modeling and the information on the present-day interior properties and evolution of several planets and moons based on studying their tidal response. We begin with an outline of the theory of viscoelasticity and tidal response. Next, we proceed by discussing the information on the tidal response and the inferred structure of Mercury, Venus, Mars and its moons, the Moon, and the largest satellites of giant planets, obtained from the analysis of the data that has been provided by space missions. We also summarise the upcoming possibilities offered by the currently planned missions.

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arXiv2022

The tidal quality of the hot Jupiter WASP-12b

WASP-12b stands out among the planets of its class of hot Jupiters because of the observed fast orbital decay attributed to tidal dissipation. The measured rate of the orbital period is $\stackrel{\bf\centerdot}{\textstyle{P}}_{\rm orb}\,=\,-\,29\pm3\;\mbox{ms/yr}\;$=$\;(9.2\pm1.0)\times10^{-10}\;\mbox{s/s}$. In the literature heretofore, all attempts to explain this high rate were based on the assumption that the orbital evolution is dominated by the tides in the star. Since the modified tidal quality factor in yellow dwarfs is insufficient to warrant such a decay rate, a hypothesis was put forward that the star may actually be a subgiant. Using the latest data from the Gaia mission, we deduce that WASP-12a at $1.36\,{M_{Sun}}$ is an evolving dwarf at an early stage of post-turn-off evolution that has not yet depleted hydrogen in its core. Its unremarkable position in the color-magnitude diagram and the existence of close planets orbiting red giants of similar mass contradict the hypothesis of an abrupt boost of tidal quality due to structural internal changes. On the other hand, the previous research neglected the tidal dissipation in the planet assuming it to be negligible due to the likely synchronisation of its rotation and a presumed high quality factor. We critically reassess this assumption in the light of recent astrometric results for Jupiter and Saturn. Assuming that the structure of WASP-12b is similar to that of our Jupiter and Saturn, we find that the observed orbital decay is well explained by the tides in the planet. The estimated value of the planet's modified quality factor coincides almost precisely with that of our Jupiter.

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arXiv2021

Analysis of the PPN Two-Body Problem Using Non-Osculating Orbital Elements

The parameterised post-Newtonian (PPN) formalism is a weak-field slow-motion approximation for both GR and some of its generalisations. It permits various parameterisations of the motion, among which are the Lagrange-type and Gauss-type orbital equations. Often, these equations are developed under the Lagrange constraint, which makes the evolving orbital elements parameterise instantaneous conics tangent to the orbit. Arbitrary mathematically, this choice of a constraint is convenient under perturbations dependent only on positions. Under perturbations dependent also on velocities (like relativistic corrections) the Lagrange constraint unnecessarily complicates solutions that can be simplified by introducing a freedom in the orbit parameterisation, which is analogous to the gauge freedom in electrodynamics and gauge theories. Geometrically, this freedom is the freedom of nonosculation, i.e. of the degree to which the instantaneous conics are permitted to be non-tangent to the actual orbit. Under the same perturbation, all solutions with different degree of nonosculation look mathematically different, though describe the same physical orbit. While non-intuitive, the modeling of an orbit with a sequence of nontangent instantaneous conics can at times simplify calculations. The appropriately generalised ("gauge-generalised") Lagrange-type equations, and their applications, appeared in the literature hitherto. We in this paper derive the gauge-generalised Gauss-type equations and apply them to the PPN two-body problem. Fixing the gauge freedom in three different ways (i.e. modeling an orbit with non-osculating elements of three different types) we find three parameterisations of the PPN two-body dynamics. These parameterisations render orbits with either a fixed non-osculating semimajor axis, or a fixed non-osculating eccentricity, or a fixed non-osculating argument of periastron.

gr-qc↗

arXiv2019

Tidal evolution of the Keplerian elements

We address the expressions for the rates of the Keplerian orbital elements within a two-body problem perturbed by the tides in both partners. The formulae for these rates have appeared in the literature in various forms, at times with errors. We reconsider, from scratch, the derivation of these rates and arrive at the Lagrange-type equations which, in some details, differ from the corresponding equations obtained previously by Kaula (1964). We also write down detailed expressions for $da/dt$, $de/dt$ and $di/dt$, to order $e^4$. They differ from Kaula's expressions which contain a redundant factor of $M/(M+M^{\prime}),$ with $M$ and $M^{\prime}$ being the masses of the primary and the secondary. As Kaula was interested in the Earth-Moon system, this redundant factor was close to unity and was unimportant in his developments. This factor, however, must be reinstated when Kaula's theory is applied to a binary composed of partners of comparable masses. We have found that, while it is legitimate to simply sum the primary's and secondary's inputs in $da/dt$ or $de/dt$, this is not the case for $di/dt$. So our expression for $di/dt$ differs from that of Kaula in two regards. First, the contribution due to the dissipation in the secondary averages out when the apsidal precession is uniform. Second, we have obtained an additional term which emerges owing to the conservation of the angular momentum: a change in the inclination of the orbit causes a change of the primary's plane of equator.

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arXiv2019

Orbital relaxation and excitation of planets tidally interacting with white dwarfs

Observational evidence of white dwarf planetary systems is dominated by the remains of exo-asteroids through accreted metals, debris discs, and orbiting planetesimals. However, exo-planets in these systems play crucial roles as perturbing agents, and can themselves be perturbed close to the white dwarf Roche radius. Here, we illustrate a procedure for computing the tidal interaction between a white dwarf and a near-spherical solid planet. This method determines the planet's inward and/or outward drift, and whether the planet will reach the Roche radius and be destroyed. We avoid constant tidal lag formulations and instead employ the self-consistent secular Darwin-Kaula expansions from Boué & Efroimsky (2019), which feature an arbitrary frequency dependence on the quality functions. We adopt wide ranges of dynamic viscosities and spin rates for the planet in order to straddle many possible outcomes, and provide a foundation for the future study of individual systems with known or assumed rheologies. We find that: (i) massive Super-Earths are destroyed more readily than minor planets (such as the ones orbiting WD 1145+017 and SDSS J1228+1040), (ii) low-viscosity planets are destroyed more easily than high-viscosity planets, and (iii) the boundary between survival and destruction is likely to be fractal and chaotic.

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arXiv2018

Spin-orbital tidal dynamics and tidal heating in the TRAPPIST-1 multi-planet system

We perform numerical simulations of the TRAPPIST-1 system of seven exoplanets orbiting a nearby M dwarf, starting with a previously suggested stable configuration. The long-term stability of this configuration is confirmed, but the motion of planets is found to be chaotic. The eccentricity values are found to vary within finite ranges. The rates of tidal dissipation and tidal evolution of orbits are estimated, assuming an Earth-like rheology for the planets. We find that under this assumption the planets b, d, e were captured in the 3:2 or higher spin-orbit resonances during the initial spin-down but slipped further down into the 1:1 resonance. Dependent on its rheology, the innermost planet b may be captured in a stable pseudosynchronous rotation. Non-synchronous rotation ensures higher levels of tidal dissipation and internal heating. The positive feedback between the viscosity and the dissipation rate -- and the ensuing runaway heating -- are terminated by a few self-regulation processes. When the temperature is high and the viscosity is low enough, the planet spontaneously leaves the 3:2 resonance. Further heating is stopped either by passing the peak dissipation or by the emergence of partial melt in the mantle. In the post-solidus state, the tidal dissipation is limited to the levels supported by the heat transfer efficiency. The tides on the host star are unlikely to have had a significant dynamical impact. The tides on the synchronized inner planets tend to reduce these planets' orbital eccentricity, possibly contributing thereby to the system's stability.

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arXiv2018

Exoplanet Science Priorities from the Perspective of Internal and Surface Processes for Silicate and Ice Dominated Worlds

The geophysics of extrasolar planets is a scientific topic often regarded as standing largely beyond the reach of near-term observations. This reality in no way diminishes the central role of geophysical phenomena in shaping planetary outcomes, from formation, to thermal and chemical evolution, to numerous issues of surface and near-surface habitability. We emphasize that for a balanced understanding of extrasolar planets, it is important to look beyond the natural biases of current observing tools, and actively seek unique pathways to understand exoplanet interiors as best as possible during the long interim prior to a time when internal components are more directly accessible. Such pathways include but are not limited to: (a) enhanced theoretical and numerical modeling, (b) laboratory research on critical material properties, (c) measurement of geophysical properties by indirect inference from imprints left on atmospheric and orbital properties, and (d) the purpose-driven use of Solar System object exploration expressly for its value in comparative planetology toward exoplanet-analogs. Breaking down barriers that envision local Solar System exploration, including the study of Earth's own deep interior, as separate from and in financial competition with extrasolar planet research, may greatly improve the rate of needed scientific progress for exoplanet geophysics. As the number of known rocky and icy exoplanets grows in the years ahead, we expect demand for expertise in 'exogeoscience' will expand at a commensurately intense pace. We highlight key topics, including: how water oceans below ice shells may dominate the total habitability of our galaxy by volume, how free-floating nomad planets may often attain habitable subsurface oceans supported by radionuclide decay, and how deep interiors may critically interact with atmospheric mass loss via dynamo-driven magnetic fields.

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arXiv2018

Highly Volcanic Exoplanets, Lava Worlds, and Magma Ocean Worlds: An Emerging Class of Dynamic Exoplanets of Significant Scientific Priority

Highly volcanic exoplanets, which can be variously characterized as 'lava worlds', 'magma ocean worlds', or 'super-Ios' are high priority targets for investigation. The term 'lava world' may refer to any planet with extensive surface lava lakes, while the term 'magma ocean world' refers to planets with global or hemispherical magma oceans at their surface. 'Highly volcanic planets', including super-Ios, may simply have large, or large numbers of, active explosive or extrusive volcanoes of any form. They are plausibly highly diverse, with magmatic processes across a wide range of compositions, temperatures, activity rates, volcanic eruption styles, and background gravitational force magnitudes. Worlds in all these classes are likely to be the most characterizable rocky exoplanets in the near future due to observational advantages that stem from their preferential occurrence in short orbital periods and their bright day-side flux in the infrared. Transit techniques should enable a level of characterization of these worlds analogous to hot Jupiters. Understanding processes on highly volcanic worlds is critical to interpret imminent observations. The physical states of these worlds are likely to inform not just geodynamic processes, but also planet formation, and phenomena crucial to habitability. Volcanic and magmatic activity uniquely allows chemical investigation of otherwise spectroscopically inaccessible interior compositions. These worlds will be vital to assess the degree to which planetary interior element abundances compare to their stellar hosts, and may also offer pathways to study both the very young Earth, and the very early form of many silicate planets where magma oceans and surface lava lakes are expected to be more prevalent. We suggest that highly volcanic worlds may become second only to habitable worlds in terms of both scientific and public long-term interest.

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arXiv2018

Tidal viscosity of Enceladus

In the preceding paper (Efroimsky 2017), we derived an expression for the tidal dissipation rate in a homogeneous near-spherical Maxwell body librating in longitude. Now, by equating this expression to the outgoing energy flux due to the vapour plumes, we estimate the mean tidal viscosity of Enceladus, under the assumption that the Enceladean mantle behaviour is Maxwell. This method yields a value of $\,0.24\times 10^{14}\;\mbox{Pa~s}\,$ for the mean tidal viscosity, which is very close to the viscosity of ice near the melting point.

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arXiv2018

Dissipation in a tidally perturbed body librating in longitude

Internal dissipation in a tidally perturbed librating body differs from the tidal dissipation in a steadily spinning rotator. First, libration changes the spectral distribution of tidal damping across the tidal modes, as compared to the case of steady spin. This changes both the tidal heating rate and the tidal torque. Second, while a non-librating rotator experiences alternating deformation only due to the potential force exerted on it by the perturber, a librating body is also subject to a toroidal force proportional to the angular acceleration. Third, while the centrifugal force in a steadily spinning body renders only a permanent deformation, in a librating body this force contains two alternating components $-$ one radial, another a degree-2 potential force. Both contribute to heating, as well as to the tidal torque and potential. We build a formalism to describe dissipation in a homogeneous terrestrial body performing small-amplitude libration in longitude. This formalism incorporates a linear rheological law defining the response of the material to forcing. While the formalism can work with an arbitrary linear rheology, we consider a simple example of a Maxwell material. We show that, independent of rheology, the forced libration in longitude can provide a considerable and even leading input in the tidal heating. Based on the observed parameters, this input amounts to 52% in Phobos, 33% in Mimas, 23% in Enceladus, and 96% in Epimetheus. This supports the hypothesis by Makarov & Efroimsky (2014) that the additional damping due to forced libration may have participated in the early heating up of some moons. As one possibility, a moon could have been chipped by collisions $-$ whereby it acquired a higher triaxiality and a higher forced-libration magnitude and, consequently, a higher heating rate. After the moon warms up, its triaxiality reduces, and so does the tidal heating.

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arXiv2017

Precession Relaxation of Viscoelastic Oblate Rotators

Perturbations of all sorts destabilise the rotation of a small body and leave it in a non-principal spin state. In such a state, the body experiences alternating stresses generated by the inertial forces. This yields nutation relaxation, i.e., evolution of the spin towards the principal rotation about the maximal-inertia axis. Knowledge of the timescales needed to damp the nutation is crucial in studies of small bodies' dynamics. In the literature hitherto, nutation relaxation has always been described with aid of an empirical quality factor $\,Q\,$ introduced to parameterise the energy dissipation rate. Among the drawbacks of this approach was its inability to describe the dependence of the relaxation rate upon the current nutation angle. This inability stemmed from our lack of knowledge of the quality factor's dependence on the forcing frequency. In this article, we derive our description of nutation damping directly from the rheological law obeyed by the material. This renders us the nutation damping rate as a function of the current nutation angle, as well as of the shape and the rheological parameters of the body. In contradistinction from the approach based on an empirical $\,Q\,$-factor, our development gives a zero damping rate in the spherical-shape limit. Our method is generic and applicable to any shape and to any linear rheological law. However, to simplify the developments, here we consider a dynamically oblate rotator with a Maxwell rheology.

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