arXiv subjects

Sylvio Ferraz-Mello

Publications and source records attributed to Sylvio Ferraz-Mello.

At least 19 recordsLinked to original sources

arXiv2026

Exoplanets synchronization in the habitable zone: Learning from Venus' retrograde rotation

The rotation of a planet located in the habitable zone of a solar-type star can be reversed by a smooth process associated with the formation of its atmosphere and the increase of stronger torques, opposite to normal tidal torques. Our understanding of the rotational dynamics of Venus is revisited to analyze what might happen to exoplanets in the habitable zone of a solar-type star. The creep tide theory is used to calculate the gravitational tidal torque. Mathematical analysis is used to study the differential equation resulting from the combined effects of tidal torque and atmospheric torque. It shows that no collision with other bodies or critical planetary perturbations is necessary to convert the rotation of an Earth or super-Earth with a significant atmosphere formed during its evolution into a retrograde rotation. The reversal of a planet's rotation is not an exceptional event and may have occurred many times among known exoplanets in the habitable zone. It is sufficient for the planet to be at a sufficiently short distance from its host star to allow tidal torques to nearly synchronize the planet's rotation before most of its atmosphere forms (but not so close that stellar radiation destroys the formed atmosphere). When atmospheric torques become more important than tidal torques, a pitchfork bifurcation occurs: the synchronous attractor bifurcates into two asynchronous attractors, and the system evolves toward one of the asynchronous attractors. If it evolves toward the subsynchronous branch, the rotation may subsequently become retrograde. Venus's rotation is an example. None of these processes is catastrophic. Planetary atmosphere formation is a continuous and smooth process, which may be more or less efficient, but it is not a low-probability event.

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arXiv2025

The tidal heating of the exoplanet 55 Cnc e. The role of the orbital eccentricity

Context. Observations with warm Spitzer and JWST revealed high and variable brightness in the planet 55 Cnc e. Aims. Inventory of the tidal effects on the rotational and orbital evolution of the planet 55 Cnc e enhanced by the nonzero orbital eccentricity. Methods. The creep-tide theory is used in simulations and dynamical analyses that explore the difficult trapping of the planet rotation in a 3:2 spin-orbit resonance and the most probable synchronization of the rotation. Results. The strong tidal dissipation of energy, enhanced by the non-zero orbital eccentricity, may explain the observed brightness anomalies. However, the strong dissipation should also circularize the orbit. The observed non-zero eccentricity, if true, would indicate that an unknown planet in a close orbital resonance with 55 Cnc e perturbing the motion of this planet should exist.

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arXiv2025

Tidal dissipation and synchronization of the temperate exo-Earth LP 791-18d

The creep tide theory is used to explore several aspects of the tidal evolution of the planetary system of the M-star LP 791-18 . We discuss the early synchronization of the exo-Earth LP 791-18d and show that the trapping of its rotation in a 3:2 spin-orbit resonance would only have been possible if its eccentricity were approximately 0.04 or larger. The planet is likely in synchronous rotation. The perturbations of the other planets in the system do not allow the complete damping of the orbital eccentricity, and the resulting mechanical energy balance indicates that the tidal energy dissipated inside the planet may flow through the planetary surface at approximately 1 watt per square meter.

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arXiv2025

Extension of the creep tide theory to exoplanet systems with high stellar obliquity. The dynamic tide of CoRoT-3b

This paper extends the creep tide theory to exoplanetary systems with significant obliquities. The extended theory allows us to obtain the stellar and planetary hydrodynamic equilibrium tides and the evolution of the rotational state of the bodies. The dynamic ellipsoidal figure of equilibrium of the body is calculated taking into account that its reaction to external forces is delayed by its viscosity. The derived equations are used to determine the motion of the tidal bulge of the planetary companion CoRoT-3b (a brown dwarf) and its host star. We show how the tides deform the figure of the companion and how its tidal bulge moves close to the substellar meridian from one hemisphere to another. The stellar lag is mostly positive and is braking the star's rotation.

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arXiv2022

Creep tide theory. Equations for differentiated bodies with aligned layers

The creep tide theory is used to establish the basic equations of the tidal evolution of differentiated bodies formed by aligned homogeneous layers in co-rotation. The mass concentration of the body is given by the fluid Love number $k_f$. The formulas are given by series expansions valid for high eccentricity systems. They are equivalent to Darwin's equations, but formally more compact. An application to the case of Enceladus, with $k_f=0.942$, is discussed.

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arXiv2021

On Tides and Exoplanets

This paper reviews the basic equations used in the study of the tidal variations of the rotational and orbital elements of a system formed by one star and one close-in planet as given by the creep tide theory and Darwin's constant time lag (CTL) theory. At the end, it reviews and discusses the determinations of the relaxation factors (and time lags) in the case of host stars and hot Jupiters based on actual observations of orbital decay, stellar rotation and age, etc. It also includes a recollection of the basic facts concerning the variations of the rotation of host stars due to the leakage of angular momentum associated with stellar winds.

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arXiv2021

Ellipsoidal equilibrium figure and Cassini states of rotating planets and satellites deformed by a tidal potential in the spatial case

The equilibrium figure of an inviscid tidally deformed body is the starting point for the construction of many tidal theories such as Darwinian tidal theories or the hydrodynamical Creep tide theory. This paper presents the ellipsoidal equilibrium figure when the spin rate vector of the deformed body is not perpendicular to the plane of motion of the companion. We obtain the equatorial and the polar flattenings as functions of the Jeans and the Maclaurin flattenings, and of the angle $θ$ between the spin rate vector and the radius vector. The equatorial vertex of the equilibrium ellipsoid does not point toward the companion, which produces a torque perpendicular to the rotation vector, which introduces terms of precession and nutation. We find that the direction of spin may differ significantly from the direction of the principal axis of inertia $C$, so the classical approximation $\mathsf{I}\vecω\approx C\vecω$ only makes sense in the neighborhood of the planar problem. We also study the so-called Cassini states. Neglecting the short-period terms in the differential equation for the spin direction and assuming a uniform precession of the line of the orbital ascending node, we obtain the same differential equation as that found by Colombo (1966). That is, a tidally deformed inviscid body has exactly the same Cassini states as a rotating axisymmetric rigid body, the tidal bulge having no secular effect at first order.

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arXiv2020

Tidal evolution of exoplanetary systems hosting Potentially Habitable Exoplanets. The cases of LHS-1140 b-c and K2-18 b-c

We present a model to study secularly and tidally evolving three-body systems composed by two low-mass planets orbiting a star, in the case where the bodies rotation axes are always perpendicular to the orbital plane. The tidal theory allows us to study the spin and orbit evolution of both stiff Earth-like planets and predominantly gaseous Neptune-like planets. The model is applied to study two recently-discovered exoplanetary systems containing potentially habitable exoplanets (PHE): LHS-1140 b-c and K2-18 b-c. For the former system, we show that both LHS-1140 b and c must be in nearly-circular orbits. For K2-18 b-c, the combined analysis of orbital evolution timescales with the current eccentricity estimation of K2-18 b allows us to conclude that the inner planet (K2-18 c) must be a Neptune-like gaseous body. Only this would allow for the eccentricity of K2-18 b to be in the range of values estimated in recent works ($e=0.20 \pm 0.08$), provided that the uniform viscosity coefficient of K2-18 b is greater than $2.4 \times 10^{19} \ \textrm{Pa s}$ (which is a value characteristic of stiff bodies) and supposing that such system has an age of some Gyr.

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arXiv2020

Tidal friction in satellites and planets. The new version of the creep tide theory

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.

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arXiv2019

Rotation and figure evolution in the creep tide theory. A new approach and application to Mercury

This paper deals with the rotation and figure evolution of a planet near the 3/2 spin-orbit resonance and the exploration of a new formulation of the creep tide theory (Folonier et al. 2018). This new formulation is composed by a system of differential equations for the figure and the rotation of the body simultaneously (which is the same system of equations used in Folonier et al. 2018), different from the original one (Ferraz-Mello, 2013, 2015a) in which rotation and figure were considered separately. The time evolution of the figure of the body is studied for both the 3/2 and 2/1 spin-orbit resonances. Moreover, we provide a method to determine the relaxation factor gamma of non-rigid homogeneous bodies whose endpoint of rotational evolution from tidal interactions is the 3/2 spin-orbit resonance, provided that (i) an initially faster rotation is assumed and (ii) no permanent components of the flattenings of the body existed at the time of the capture in the 3/2 spin-orbit resonance. The method is applied to Mercury, since it is currently trapped in a 3/2 spin-orbit resonance with its orbital motion and we obtain 4.8 times 10 -8 s -1 lower than gamma lower than 4.8 times 10 -9 s -1 . The equatorial prolateness and polar oblateness coefficients obtained for Mercury's figure with such range of values of gamma are the same as the ones given by the Darwin-Kaula model (Matsuyama and Nimmo 2009). However, comparing the values of the flattenings obtained for such range of gamma with those obtained from MESSENGER's measurements (Perry et al. 2015), we see that the current values for Mercury's equatorial prolateness and polar oblateness are 2-3 orders of magnitude larger than the values given by the tidal theories.

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arXiv2019

Tidal synchronization of close-in satellites and exoplanets. III. Tidal dissipation revisited and application to Enceladus

This paper deals with a new formulation of the creep tide theory (Ferraz-Mello, Cel. Mech. Dyn. Astron. {\bf 116}, 109, 2013 $-$ Paper I) and with the tidal dissipation predicted by the theory in the case of stiff bodies whose rotation is not synchronous but is oscillating around the synchronous state with a period equal to the orbital period. We show that the tidally forced libration influences the amount of energy dissipated in the body and the average perturbation of the orbital elements. This influence depends on the libration amplitude and is generally neglected in the study of planetary satellites. However, they may be responsible for a 27 percent increase in the dissipation of Enceladus. The relaxation factor necessary to explain the observed dissipation of Enceladus ($γ=1.2-3.8\times 10^{-7}\ {\rm s}^{-1}$) has the expected order of magnitude for planetary satellites and corresponds to the viscosity $0.6-1.9 \times 10^{14}$ Pa s, which is in reasonable agreement with the value recently estimated by Efroimsky (2018) ($0.24 \times 10^{14}$ Pa s) and with the value adopted by Roberts and Nimmo (2008) for the viscosity of the ice shell ($10^{13}-10^{14}$ Pa s). For comparison purposes, the results are extended also to the case of Mimas and are consistent with the negligible dissipation and the absence of observed tectonic activity. The corrections of some mistakes and typos of paper II (Ferraz-Mello, Cel. Mech. Dyn. Astron. {\bf 122}, 359, 2015) are included at the end of the paper.

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arXiv2017

A modified CoRoT detrend algorithm and the discovery of a new planetary companion

We present MCDA, a modification of the CoRoT detrend algorithm (CDA) suitable to detrend chromatic light curves. By means of robust statistics and better handling of short term variability, the implementation decreases the systematic light curve variations and improves the detection of exoplanets when compared with the original algorithm. All CoRoT chromatic light curves (a total of 65,655) were analysed with our algorithm. Dozens of new transit candidates and all previously known CoRoT exoplanets were rediscovered in those light curves using a box-fitting algorithm. For three of the new cases spectroscopic measurements of the candidates' host stars were retrieved from the ESO Science Archive Facility and used to calculate stellar parameters and, in the best cases, radial velocities. In addition to our improved detrend technique we announce the discovery of a planet that orbits a $0.79_{-0.09}^{+0.08}\,R_\odot$ star with a period of $6.71837\pm0.00001$ days and has $0.57_{-0.05}^{+0.06}\,R_{\rm J}$ and $0.15\pm0.10\,M_{\rm J}$. We also present the analysis of two cases in which parameters found suggest the existence of possible planetary companions.

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arXiv2017

Tidal synchronization of an anelastic multi-layered body: Titan's synchronous rotation

This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the spin rates increase if the orbital eccentricity increases. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies n/2,n,3n/2,... . We apply the theory to Titan. The main results are: i) the rotational constraint does not allow us confirm or reject the existence of a subsurface ocean in Titan; and ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini's observation, we limit the possible value of the shell relaxation factor, when a subsurface ocean is assumed, to 10^-9 Hz, which correspond to a shell's viscosity 10^18 Pa s, depending on the ocean's thickness and viscosity values. In the case in which the ocean does not exist, the maximum shell relaxation factor is one order of magnitude smaller and the corresponding minimum shell's viscosity is one order higher.

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arXiv2017

Tidal synchronization of close-in satellites and exoplanets. II. Spin dynamics and extension to Mercury and exoplanets host stars

This paper deals with the application of the creep tide theory (Ferraz-Mello, CeMDA 116, 109, 2013) to the rotation of close-in satellites, Mercury, close-in exoplanets and their host stars. The solutions show two extreme cases: close-in giant gaseous planets, with fast relaxation (low viscosity) and satellites and Earth-like planets, with slow relaxation (high viscosity). The rotation of close-in gaseous planets follows the classical Darwinian pattern: it is tidally driven towards a stationary solution which is synchronized, but, if the orbit is elliptical, with a frequency larger than the orbital mean-motion. The rotation of rocky bodies, however, may be driven to several attractors whose frequencies are 1/2,1,3/2,2,5/2 ... times the mean-motion. The number of attractors increases with the viscosity of the body and with the orbital eccentricity. The classical example is Mercury, whose rotational period is 2/3 of the orbital period (3/2 attractor). The planet behaves as a molten body with a relaxation that allowed it to cross the 2/1 attractor without being trapped, but not to escape being trapped in the 3/2 one. In that case, the relaxation is estimated to lie in the interval 4.6 -- 27 x 10^{-9} s^{-1} (equivalent to a quality factor roughly constrained to the interval 5<Q<50). The stars have relaxation similar to the hot Jupiters and their rotation is also driven to the only stationary solution existing in these cases. However, solar-type stars may lose angular momentum due to stellar wind, braking the rotation and displacing the attractor towards larger periods. Old active host stars with big close-in companions generally have rotational periods larger than the orbital periods of the companions. The paper also includes the study of the energy dissipation and the evolution of the orbital eccentricity.

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arXiv2016

The Solar Twin Planet Search. V. Close-in, low-mass planet candidates and evidence of planet accretion in the solar twin HIP 68468

[Methods]. We obtained high-precision radial velocities with HARPS on the ESO 3.6 m telescope and determined precise stellar elemental abundances (~0.01 dex) using MIKE spectra on the Magellan 6.5m telescope. [Results]. Our data indicate the presence of a planet with a minimum mass of 26 Earth masses around the solar twin HIP 68468. The planet is a super-Neptune, but unlike the distant Neptune in our solar system (30 AU), HIP 68468c is close-in, with a semi-major axis of 0.66 AU, similar to that of Venus. The data also suggest the presence of a super-Earth with a minimum mass of 2.9 Earth masses at 0.03 AU; if the planet is confirmed, it will be the fifth least massive radial velocity planet discovery to date and the first super-Earth around a solar twin. Both isochrones (5.9 Gyr) and the abundance ratio [Y/Mg] (6.4 Gyr) indicate an age of about 6 billion years. The star is enhanced in refractory elements when compared to the Sun, and the refractory enrichment is even stronger after corrections for Galactic chemical evolution. We determined a NLTE Li abundance of 1.52 dex, which is four times higher than what would be expected for the age of HIP 68468. The older age is also supported by the low log(R'HK) (-5.05) and low jitter. Engulfment of a rocky planet of 6 Earth masses can explain the enhancement in both lithium and the refractory elements. [Conclusions]. The super-Neptune planet candidate is too massive for in situ formation, and therefore its current location is most likely the result of planet migration that could also have driven other planets towards its host star, enhancing thus the abundance of lithium and refractory elements in HIP 68468. The intriguing evidence of planet accretion warrants further observations to verify the existence of the planets that are indicated by our data and to better constrain the nature of the planetary system around this unique star.

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arXiv2016

Tidal evolution of CoRoT massive planets and brown dwarfs and of their host stars

Aims: Revisit and improvement of the main results obtained in the study of the tidal evolution of several massive CoRoT planets and brown dwarfs and of the rotation of their host stars. Methods: Simulations of the past and future evolution of the orbital and rotational elements of the systems under the joint action of the tidal torques and the braking due to the stellar wind. Results: Presentation of several paradigms and significant examples of tidal evolution in extrasolar planetary systems. It is shown that the high quality of the photometric and spectrographic observations of the CoRoT objects allow for a precise study of their past and future evolution and to estimate the tidal parameters ruling the dissipation in the systems.

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arXiv2015

The small and large lags of the elastic and anelastic tides. The virtual identity of two rheophysical theories

The aim of this letter is to discuss the virtual identity of two recent tidal theories: the creep tide theory of Ferraz-Mello (Cel. Mech. Dyn. Astron. 116, 109, 2013) and the Maxwell model developed by Correia et al. (Astron. Astrophys. 571, A50, 2014). It includes the discussion of the basic equations of the theories, which, in both cases, include an elastic and an anelastic component, and shows that the basic equations of the two theories are equivalent and differ by only a numerical factor in the anelastic tide. It also includes a discussion of the lags: the lag of the full tide (geodetic), dominated by the elastic component, and the phase of the anelastic tide. In rotating rocky bodies not trapped in a spin-orbit resonance (e.g., the Earth) the geodetic lag is close to zero and the phase of the semi-diurnal argument in the anelastic tide is close to 90 degrees. The results obtained from combining tidal solutions from satellite tracking data and from Topex/Poseidon satellite altimeter data, by Ray et al., are extended to determine the phase of the semi-diurnal argument in the Earth's anelastic tide as sigma_0=89.80 \pm 0.05 degrees.

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arXiv2015

The flattenings of the layers of rotating planets and satellites deformed by a tidal potential

We consider the Clairaut theory of the equilibrium ellipsoidal figures for differentiated non-homogeneous bodies in non-synchronous rotation adding to it a tidal deformation due to the presence of an external gravitational force. We assume that the body is a fluid formed by $n$ homogeneous layers of ellipsoidal shape and we calculate the external polar flattenings and the mean radius of each layer, or, equivalently, their semiaxes. To first order in the flattenings, the general solution can be written as $ε_k={\cal H}_k*ε_h$ and $μ_k={\cal H}_k*μ_h$, where $\cal{H}_k$ is a characteristic coefficient for each layer which only depends on the internal structure of the body and $ε_h, μ_h$ are the flattenings of the equivalent homogeneous problem. For the continuous case, we study the Clairaut differential equation for the flattening profile, using the Radau transformation to find the boundary conditions when the tidal potential is added. Finally, the theory is applied to several examples: i) a body composed of two homogeneous layers; ii) bodies with simple polynomial density distribution laws and iii) bodies following a polytropic pressure-density law.

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